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THE MODULATION OF OUTDOOR RUNNING SPEED:
THE INFLUENCE OF GRADIENT
A thesis submitted for the degree
Doctor of Philosophy
2010
Andrew D Townshend
B. App Sc (QUT)
School of Human Movement Studies
Queensland University of Technology
Brisbane, Australia
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KEY WORDS
Downhill
Field study
Gait
Global Positioning System
Gradient
Locomotion
Overground
Pacing strategy
Performance
Running
Speed regulation
Speed measurement
Uphill
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ABSTRACT
This thesis aimed to investigate the way in which distance runners modulate their
speed in an effort to understand the key processes and determinants of speed selection
when encountering hills in natural outdoor environments. One factor which has limited
the expansion of knowledge in this area has been a reliance on the motorized treadmill
which constrains runners to constant speeds and gradients and only linear paths.
Conversely, limits in the portability or storage capacity of available technology have
restricted field research to brief durations and level courses. Therefore another aim of
this thesis was to evaluate the capacity of lightweight, portable technology to measure
running speed in outdoor undulating terrain.
The first study of this thesis assessed the validity of a non-differential GPS to measure
speed, displacement and position during human locomotion. Three healthy participants
walked and ran over straight and curved courses for 59 and 34 trials respectively. A
non-differential GPS receiver provided speed data by Doppler Shift and change in GPS
position over time, which were compared with actual speeds determined by
chronometry. Displacement data from the GPS were compared with a surveyed 100m
section, while static positions were collected for 1 hour and compared with the known
geodetic point. GPS speed values on the straight course were found to be closely
correlated with actual speeds (Doppler shift: r = 0.9994, p < 0.001, Δ GPS position/time:
r = 0.9984, p < 0.001). Actual speed errors were lowest using the Doppler shift method
(90.8% of values within ± 0.1 m.sec -1). Speed was slightly underestimated on a curved
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path, though still highly correlated with actual speed (Doppler shift: r = 0.9985, p <
0.001, Δ GPS distance/time: r = 0.9973, p < 0.001). Distance measured by GPS was
100.46 ± 0.49m, while 86.5% of static points were within 1.5m of the actual geodetic
point (mean error: 1.08 ± 0.34m, range 0.69-2.10m). Non-differential GPS
demonstrated a highly accurate estimation of speed across a wide range of human
locomotion velocities using only the raw signal data with a minimal decrease in
accuracy around bends. This high level of resolution was matched by accurate
displacement and position data. Coupled with reduced size, cost and ease of use, the
use of a non-differential receiver offers a valid alternative to differential GPS in the
study of overground locomotion.
The second study of this dissertation examined speed regulation during overground
running on a hilly course. Following an initial laboratory session to calculate
physiological thresholds (VO2 max and ventilatory thresholds), eight experienced long
distance runners completed a self- paced time trial over three laps of an outdoor
course involving uphill, downhill and level sections. A portable gas analyser, GPS
receiver and activity monitor were used to collect physiological, speed and stride
frequency data. Participants ran 23% slower on uphills and 13.8% faster on downhills
compared with level sections. Speeds on level sections were significantly different for
78.4 ± 7.0 seconds following an uphill and 23.6 ± 2.2 seconds following a downhill.
Speed changes were primarily regulated by stride length which was 20.5% shorter
uphill and 16.2% longer downhill, while stride frequency was relatively stable. Oxygen
consumption averaged 100.4% of runner’s individual ventilatory thresholds on uphills,
78.9% on downhills and 89.3% on level sections. Group level speed was highly
predicted using a modified gradient factor (r2 = 0.89). Individuals adopted distinct
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pacing strategies, both across laps and as a function of gradient. Speed was best
predicted using a weighted factor to account for prior and current gradients. Oxygen
consumption (VO2) limited runner’s speeds only on uphill sections, and was maintained
in line with individual ventilatory thresholds. Running speed showed larger individual
variation on downhill sections, while speed on the level was systematically influenced
by the preceding gradient. Runners who varied their pace more as a function of
gradient showed a more consistent level of oxygen consumption. These results suggest
that optimising time on the level sections after hills offers the greatest potential to
minimise overall time when running over undulating terrain.
The third study of this thesis investigated the effect of implementing an individualised
pacing strategy on running performance over an undulating course. Six trained distance
runners completed three trials involving four laps (9968m) of an outdoor course
involving uphill, downhill and level sections. The initial trial was self-paced in the
absence of any temporal feedback. For the second and third field trials, runners were
paced for the first three laps (7476m) according to two different regimes (Intervention
or Control) by matching desired goal times for subsections within each gradient. The
fourth lap (2492m) was completed without pacing. Goals for the Intervention trial were
based on findings from study two using a modified gradient factor and elapsed distance
to predict the time for each section. To maintain the same overall time across all paced
conditions, times were proportionately adjusted according to split times from the self-
paced trial. The alternative pacing strategy (Control) used the original split times from
this initial trial. Five of the six runners increased their range of uphill to downhill speeds
on the Intervention trial by more than 30%, but this was unsuccessful in achieving a
more consistent level of oxygen consumption with only one runner showing a change
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of more than 10%. Group level adherence to the Intervention strategy was lowest on
downhill sections. Three runners successfully adhered to the Intervention pacing
strategy which was gauged by a low Root Mean Square error across subsections and
gradients. Of these three, the two who had the largest change in uphill-downhill speeds
ran their fastest overall time. This suggests that for some runners the strategy of
varying speeds systematically to account for gradients and transitions may benefit race
performances on courses involving hills.
In summary, a non – differential receiver was found to offer highly accurate measures
of speed, distance and position across the range of human locomotion speeds. Self-
selected speed was found to be best predicted using a weighted factor to account for
prior and current gradients. Oxygen consumption limited runner’s speeds only on
uphills, speed on the level was systematically influenced by preceding gradients, while
there was a much larger individual variation on downhill sections. Individuals were
found to adopt distinct but unrelated pacing strategies as a function of durations and
gradients, while runners who varied pace more as a function of gradient showed a
more consistent level of oxygen consumption. Finally, the implementation of an
individualised pacing strategy to account for gradients and transitions greatly increased
runners’ range of uphill-downhill speeds and was able to improve performance in some
runners. The efficiency of various gradient-speed trade- offs and the factors limiting
faster downhill speeds will however require further investigation to further improve the
effectiveness of the suggested strategy.
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TABLE OF CONTENTS
ABSTRACT ................................................................................................................................. 3
TABLE OF CONTENTS ................................................................................................................ 7
LIST OF FIGURES ....................................................................................................................... 9
LIST OF TABLES ....................................................................................................................... 10
ABBREVIATIONS ..................................................................................................................... 11
STATEMENT OF ORIGINAL AUTHORSHIP ............................................................................... 12
ACKNOWLEDGEMENTS .......................................................................................................... 13
1 GENERAL INTRODUCTION ................................................................................................... 14
2 LITERATURE REVIEW ........................................................................................................... 17
2.1 Introduction ................................................................................................................. 17
2.2 Regulation of speed ..................................................................................................... 17
2.3 Regulation of gait parameters ..................................................................................... 26
2.4 Pacing strategies .......................................................................................................... 32
2.5 Conclusion .................................................................................................................... 43
3 ASSESSMENT OF SPEED AND POSITION DURING HUMAN LOCOMOTION USING NON-DIFFERENTIAL GPS ................................................................................................................. 44
3.1 Introduction ................................................................................................................. 44
3.2 Methods ....................................................................................................................... 47
3.3 Results .......................................................................................................................... 53
3.4 Discussion ..................................................................................................................... 59
4 SPONTANEOUS PACING DURING OVERGROUND HILL RUNNING ....................................... 65
4.1 Introduction ................................................................................................................. 65
4.2 Methods ....................................................................................................................... 67
4.3 Results .......................................................................................................................... 74
4.4 Discussion ..................................................................................................................... 84
5 THE EFFECT OF AN INDIVIDUALISED PACING STRATEGY ON RUNNING PERFORMANCE OVER AN UNDULATING COURSE ........................................................................................... 94
5.1 Introduction ................................................................................................................. 94
5.2 Methods ....................................................................................................................... 95
5.3 Results ........................................................................................................................ 104
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5.4 Discussion ................................................................................................................... 114
6 GENERAL DISCUSSION ....................................................................................................... 120
6.1 Introduction ............................................................................................................... 120
6.2 Contribution to the literature .................................................................................... 120
6.3 Limitations and suggested improvements ................................................................. 128
6.4 Recommended areas of further research .................................................................. 129
6.5 Summary .................................................................................................................... 132
References ........................................................................................................................... 133
APPENDIX ONE- Adherence to an imposed pacing strategy................................................ 144
APPENDIX TWO - Differences in displacement of the GPS receiver at three different locomotion speeds. .............................................................................................................. 159
APPENDIX THREE - Spatial distribution of GPS positions relative to known geodetic point 160
APPENDIX FOUR –Validation studies of GPS and DGPS for speed (A) and distance/position (B) ......................................................................................................................................... 161
APPENDIX FIVE - Summary of regression weightings for group and individual subjects .... 163
APPENDIX SIX - Circle Earth Formula ................................................................................... 164
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LIST OF FIGURES
Figure Page
2.1 Theoretical representation of time v energy cost 19
3.1 Plot of errors in speed determination using GPS (Doppler shift-top figure) or GPS (∆ distance/time-bottom figure) over a straight course 57
3.2 Plot of errors in speed determination using GPS (Doppler shift-top figure) or GPS (∆ distance/time-bottom figure) over a curved path 58
4.1 Overhead picture and schematic showing section length, average gradients and subsection divisions for one lap of course 73
4.2 Changes in speed, kinematics and physiological variables across three laps of an undulating course 81
4.3 Speed changes on level sections following uphill or downhill running 82
4.4 Individual pacing strategies showing relative differences in speeds across (top) gradients and (bottom) laps 83
5.1 Experimental Design (A) and Schematic (B) of self-paced and researcher-paced field trials 102
5.2 Overhead picture and schematic showing section length, average gradients and subsection divisions for one lap of course 103
5.3 Speed on uphill/downhill sections expressed as the difference from the mean level speed 112
5.4 Oxygen consumption (VO2) on uphill/downhill sections expressed as the difference from the mean VO2 on the level 112
5.5 Total time to complete course across different conditions 113
5.6 Time to complete lap four following the paced conditions expressed as the difference from the self-paced trial 113
A2 Differences in displacement of the GPS receiver at three different locomotion speeds 159
A3 Spatial distribution of GPS positions relative to known geodetic point 160
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LIST OF TABLES
Table Page
2.1 Studies of self-paced strategies in distance running 35
2.2 Experimental pacing interventions in distance running 36
3.1 Comparison of two different GPS methods of speed determination with actual speeds using the mean of all one second values across the entire 20-60m straight section 56
3.2 Comparison of GPS speed determination with actual speeds before and after corrections for reductions in GPS displacement due to leaning 56
4.1 Demographic and physiological data for participants 79
4.2 Kinematic and physiological variables across sections and laps 80
5.1 Demographic and physiological data for participants 109
5.2 Comparison of speed on laps/gradients between conditions 110
5.3 Comparison of VO2 on laps/gradients between conditions 112
A1.1 Pacing adherence on intervention trial using different criteria 149
A1.2 Pacing adherence on control trial using different criteria 150
A1.3 Individual pacing adherence across different gradients 151
A1.4 Group pacing adherence as a function of gradients 152
A1.5 Wet Bulb Globe Temperature for each trial 153
A1.6 Assessment of adherence to pacing by different criteria: INT trial 154
A1.7 Assessment of adherence to pacing by different criteria: CON trial 154
A4 Validation studies of GPS and DGPS during human locomotion 161
A5 Summary of regression weightings for group and individual subjects 163
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ABBREVIATIONS
GPS Global Positioning System
HR Heart rate (beats per minute, bpm)
VO2 Volume of oxygen consumed (L/min)
VO2 max Maximal Oxygen Consumption (mls.kg.min -1)
VT Ventilatory Threshold (L/min, % of VO2 max)
vVO2 max Speed at point of Maximal Oxygen Consumption (m.s -1, km/hr)
vVT Speed at Ventilatory Threshold (m.s -1, km/hr)
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STATEMENT OF ORIGINAL AUTHORSHIP
The work contained in this thesis has not been previously submitted to meet the
requirements for an award at this or any other higher education institution. To the best
of my knowledge and belief, the thesis contains no material previously published or
written by another person except where due reference is made.
Andrew D Townshend Date
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ACKNOWLEDGEMENTS First and foremost I thank my principal supervisor Charles Worringham for providing the
initial encouragement to embark upon this journey. Throughout this process I have
benefitted from your diversity of knowledge, sense of humour and calm manner. You
always knew when to assist and when to encourage independence to aid me in my learning
process as a researcher.
I also wish to thank my associate supervisor Ian Stewart, for your honest appraisals and
pragmatic approach which always kept me on track as well as the patience and
understanding you displayed when I needed it the most and the self-belief you always tried
to engender in me.
QUT (APA) and the Australian Research Council (APAI) are gratefully acknowledged for
providing much needed financial support. Sincere appreciation is also extended to Alive
Technologies for financial and technical support provided in the early stages of my PhD.
I am deeply indebted to all my participants. Your enthusiasm and good humour when asked
to run up hills early in the morning made the trials possible and enjoyable.
Thanks also to all the postgraduate students for their empathy, assistance, encouragement
and welcome distractions, especially Mandy, Corey, Emily and Sandi.
Sincere thanks to my parents for their support and encouragement. Thank you Dad for
enabling me to have the types of opportunities you never had and Mum for continually
inspiring me to do my best and realise my potential in every way.
And last but not least, thankyou to Adam and Brandon for providing an unwavering source
of motivation and inspiration. You always provided me with a sense of perspective and a
reason to smile at the end of the most demanding or tiring of days. I couldn’t have
completed this without you.
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1 GENERAL INTRODUCTION
A long-term goal of research in locomotion is to understand the physiology and
biomechanics of the organism when it is moving freely in a natural environment. A
particular challenge in this scenario is to understand the determinants and constraints
which affect the self selection of locomotion speeds. In early man, the need to select these
speeds effectively may have been essential for survival, either to hunt or scavenge
successfully (21) or to escape from prey or changing weather conditions. In modern day
humans, the need to optimize speed selection is particularly important in endurance sports
such as distance running, where it is crucial in order to minimize the time taken to complete
the given distance.
While the duration of the event will play a major role in the selection of the overall average
speed, running outdoors also requires the runner to vary speeds continually in response to
changing conditions. This may include alterations in temperature, head or tailwinds, varying
surfaces, and positive and negative gradients of varying degree and length. Of these factors,
gradients pose a particular challenge as they may lead to large changes in speed which have
a significant effect on energy expenditure.
While many aspects of distance running have been extensively researched (12, 13, 22, 89,
90, 101, 116), there are few studies on the self selection of speed (93, 141). A particular
problem is that speeds selected in the majority of studies are determined by the researcher
and paced by the use of the motorized treadmill. Conversely, outdoor studies which allow
spontaneous speed selection have generally been restricted to level courses, thus excluding
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analysis of speed changes as a function of gradient (14, 52, 141). Therefore the available
literature on self-selected speed is very limited.
Only two studies of distance running have investigated self-selected speeds over hills and
both had methodological limitations considered later in the review of literature (Chapter
Two). Staab et al (123) measured the energy cost of preferred speeds over positive and
negative gradients during trials on the motorized treadmill. Although runners adjusted their
speeds inversely with gradient, this was insufficient to achieve a consistent level of energy
expenditure. In contrast, Mastroianni et al (84) examined natural speed changes on an
overground course but found a surprisingly small proportion of speed could be explained by
gradient.
This paucity of studies leaves many questions unanswered regarding the way in which
runners manage trade-offs to spontaneously modulate their speed in hilly terrain. For
example, one key trade-off is the way in which runners balance the minimization of time
with the need to select an optimal level of energy expenditure, while another is the
selection of an appropriate combination of stride length and stride frequency to produce
these speeds. Accordingly, this thesis aimed to investigate the way in which runners
modulate their speeds in an effort to understand the key processes and determinants of
speed selection when encountering hills in natural outdoor environments.
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Overall Research Aims
The overall aims of this research were twofold:
1. Characterize the way in which runners spontaneously change speeds as a function
of gradient on an undulating course while simultaneously investigating the
concomitant changes in oxygen consumption and aspects of the gait cycle.
2. Determine whether an individually prescribed pacing strategy which varied speeds
at frequent intervals to account for hills and transitions between gradients could
improve performance compared with a self- paced run.
More specific aims for each study are presented in the relevant chapters.
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2 LITERATURE REVIEW
2.1 Introduction This review of the literature will examine current knowledge on the way in which runners’
self-select speed. The initial section will examine the role that potential regulatory
mechanisms play in the continuous self-selection of speeds. Next, the characteristics and
determinants of gait parameters which produce these speeds will be examined. Finally
empirical evidence will be presented on spontaneous speed selection from treadmill and
field studies as well as studies which have manipulated runners’ speeds and examined the
consequent effects on physiological responses and performance.
2.2 Regulation of speed It is generally acknowledged that no single factor governs the regulation of sub-maximal
endurance running speed (134). While a range of factors have been shown to be involved in
the process of modulating one’s effort (and therefore speed), the influence of some are
only prominent under certain conditions. For example, humans have been shown to
routinely decrease exercise intensity in order to prevent core temperature reaching
excessive levels, with a proposed critical ceiling of approximately 40 degrees Celsius (99,
103). A similar decrease in intensity is shown when the availability of energy substrates,
such as glycogen, is limited (110). These factors, however, may play a limited role in speed
regulation for brief exercise durations or in cool environments. Related to these internal
factors are external variables such as the terrain or the presence of hills which may also
play a role in regulating speed. A decreased perception of stability (32) as may be
experienced on uneven terrain (84) or increased eccentric loading (9) experienced when
running downhill (87, 88) have both been shown to decrease running speeds in these
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specific conditions. While factors such as these may be more influential under specific
conditions, one regulator that is prominent under all conditions is the selection and
appropriate management of energy expenditure (measured indirectly by oxygen
consumption). The role of energy expenditure in speed selection will thus be the focus of
the following section.
Energy Cost
Optimal performance requires a continuous trade off between speed and the resultant
energy cost, which in turn involves appropriate contributions of aerobic and anaerobic
metabolism. Thus optimal performance is constrained by a range of variables. While
external factors such as gradient and task duration will be considered later in the review,
the primary internal factor which governs selection of a suitable speed is the individual’s
current physiological capacity. When attempting to minimise time, runners thus need to
select a running speed that corresponds to the highest level of oxygen consumption they
can sustain for the required duration (35). This relationship between performance time and
energy cost can be represented by a parabolic shaped function (Figure 2.1). When speed is
too low (shown at ‘A’ on the descending portion of the curve), the time cost exceeds any
time saving due to the lower energy expenditure. Conversely, if the speed selected is too
fast (‘B’ on the ascending part of the curve), the rate of energy expenditure will exceed the
individual’s current aerobic capacity, ultimately causing them to slow excessively, thus
incurring a time cost that more than offsets the gains of the preceding period at a higher
speed. To minimise time, an energetically optimal speed (EOS) must be selected.
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Time
Energy Cost
Figure 2.1: Theoretical representation of time v energy cost
Optimal energy cost - running v walking
Though energy expenditure during walking has been extensively studied , the dynamics of
walking and running differ in several important respects which make it difficult to apply
optimization principles to running that have been identified for walking. Mechanically,
walking can be likened to the motion of an inverted pendulum where the work to move the
body segments in sequence is produced by the exchange of potential and kinetic energy
(114). As a result, the relationship between metabolic cost (as measured by VO2) and
walking speed has been found to fit a quadratic expression when VO2 is expressed as an
energetic cost per unit of distance walked (68). Accordingly, walking has an optimal speed
of approximately 1.1- 1.2 m.s-1 (corresponding to 2j.kg-1.m-1), which is close to the speed
that is self-selected by humans (114). Conversely, running has been described as a bouncing
spring where work is produced by the exchange of elastic energy (114). Although
mechanical power increases monotonically with increasing running speed, (28) the energy
cost of running a unit distance relative to mass is approximately the same across a wide
range of sub-maximal speeds (about 4 j.kg-1.m-1) (27, 74, 114) Thus the relationship
A B
EOS
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between energy cost and speed is linear with almost zero slope, although this linkage may
cease to be linear at extremely low and high running speeds (24).
It has been proposed that humans have evolved to select gait patterns (and thus speeds)
that minimize energy cost and that individually people learn energy saving behaviours
through trial and error and adapt their patterns of movement accordingly (86). It is likely
that the speed-energy cost trade-off is regulated continuously throughout exercise in
response to a range of feedback signals (132). Analysis of world record performance in
distance running events shows that runners routinely increase speeds in the final stages
(133). This suggests that runners must be conserving energy resources sufficiently to allow
this brief acceleration towards the end of their event (acknowledging that part of this
increase is obviously met by an unsustainable use of anaerobic energy stores). This implies
that runners are modulating efforts based on a perceived end-point. It is has been
suggested that when exercise duration is known, humans often subconsciously pre-set their
exercise intensity (termed teleo-anticipation) based on prior experience of what is required
to complete the exercise duration within the biomechanical and metabolic limitations of
the body (60). Thus optimal speed control likely commences with a ‘feed-forward’
selection of pace based on event duration, current fitness levels and prior experience, and
is subsequently regulated in response to afferent feedback from internal and external
sources.
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Effect of gradient on VO2
While knowledge of the exercise duration and experience may contribute to the selection
of an energy efficient pace on level ground, running overground frequently entails changes
of gradient and non-linear paths, which may play an increased role in the trade-off between
energy cost and speed. When free to vary their speed in treadmill studies, runners have
been shown to vary speeds inversely with gradient as expected but are unable to balance
speed changes sufficiently to achieve a consistent level of energy expenditure (123). Staab
(123) reported that although runners decreased speeds on uphills this was not enough to
affect increased anaerobic metabolic demands as evidenced by higher levels of blood
lactate compared with level sections. Conversely, though they increased speeds on
downhills this did not prevent a fall in oxygen consumption. This confirmed findings from
other treadmill studies that downhill speed is not limited by energy cost (83, 94). This study,
however, was not without limitation as speeds were adjusted manually by verbal direction
to a tester which does not accurately represent the spontaneous fluctuations experienced
during normal outdoor running. Conversely, Mastroianni (84) reported that runners’
relative effort (measured as % of VO2 max) was not related to gradient, suggesting that
runners attempted to achieve a constant level of energy expenditure. This conclusion was
weakened, however, by its method of calculation which used heart rate data and a heart
rate to oxygen consumption regression developed from earlier laboratory trials. In addition,
the short length of hills and sudden transitions between changing gradients limited
conclusions drawn on the speed-gradient relationship.
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With energy cost thus affected by a range of factors, variations in the relative contribution
of aerobic and anaerobic energy systems to meet the demands of the exercise task can be
expected. Accordingly, various physiological measures can be used as indicators of the
potential running speed which may be achieved or maintained for varying durations. One of
these is the anaerobic threshold.
Anaerobic threshold
When running continuously for longer than three to five minutes, aerobic metabolism
contributes the largest proportion of an individual’s energy supply (66). If an individual
attempts to run too fast in events of this duration, the rate of energy supply will be unable
to be met purely through these means and there will be an increased reliance on anaerobic
metabolism. This can be maintained only briefly, as the body’s mechanisms for lactate
removal will be inadequate to accommodate the rate of lactate produced. As a result, the
accompanying accumulation of lactate will cause the runner to slow down in order to
continue. The point at which this accumulation commences is generally referred to as the
“anaerobic threshold”(124). Among the multitude of studies of anaerobic threshold, many
provide indirect evidence that the selection of energetically optimal speeds (EOS) for
distance running are related to this marker (126). Runners who exceed this speed are
represented by the ascending portion of the curve in Figure 2.1.
The concept of anaerobic threshold and its determination is the subject of considerable
debate (23). The two most commonly used determinants of this proposed threshold are
derived from changes in either levels of blood lactate or respiratory variables.
Unfortunately, efforts to relate an individual’s anaerobic threshold with self-selected
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running speed have been problematic. For example, during a road relay, Zamparo et al
(141) found that variation in overall running speed was lower than variation in speed at the
lactate threshold, concluding that factors other than avoiding lactate accumulation must
dictate the speeds selected. The lack of a clear finding may also be a reflection of the
validity of the marker chosen for comparison. In this study, the anaerobic threshold was
defined by the onset of blood lactate accumulation (OBLA) at a measure of 4mM. This use
of an absolute lactate marker to represent an the anaerobic threshold can result in
inaccurate conclusions however, as it is insensitive to individual differences (124).
A major obstacle to the assessment of anaerobic contribution to energy expenditure
includes the practical difficulties of measuring all the relevant variables (23). For example, it
is dependent upon knowledge of the concentrations of ATP, CP, muscle glycogen and
lactate, the total water pool in the body available for lactate uptake, the distribution
between extra and intracellular water and the amount of exercising muscle mass (7). There
is also a lack of consensus surrounding the definition of an exact speed-energy cost
relationship at higher running speeds, although it is likely that this may be non-linear as
individuals are not in a “steady state” (107).
Fractional utilization of VO2 max
A less problematic approach to characterizing the relationship between running speed and
energy cost is by assessing the relative quantity of VO2 max used at sub-maximal speeds.
The highest proportion that is sustainable for a given distance was coined “fractional
utilization of VO2 max” by Costill et al (35) and is expressed as a percentage of a VO2 max
calculated for an individual during a progressive incremental test.
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Fractional utilization of VO2 max varies with the duration of the event and the capacity of
the individual and has been proposed as a primary determinant of running speed, especially
between runners with a similar VO2 max. This relative VO2 cost can be used as a predictor
of running speed in two ways. Firstly, faster runners have been found capable of
maintaining a higher percentage of VO2 max than slower runners for the same distance
(138) . Secondly, the economy or efficiency of runners can be compared by analyzing their
relative oxygen uptake per unit of mass and distance at relevant sub-maximal speeds.
Running economy has been shown to play a key role in the variance in speeds between
runners with similar VO2 max values. For example Scrimgeour et al (120) found that
variation in running economy between runners readily explained differences in their speeds
at each of several distances between 10 and 90 kms. Other research has detailed a
continuum of fractional proportions sustainable for different durations. This ranges from
85% of VO2 max during a 10km race (37), 75% during a marathon (34) , and approximately
65-75% for continuous runs of up to 4 hours (43). It is acknowledged, however, that a
comparison of absolute maintainable oxygen consumption requires that athletes have a
similar VO2 max as a significantly lower value will influence the relative intensity that can be
achieved. While providing a broad description of the relationship between relative oxygen
consumption and exercise duration, there is no information presently available as to how
this varies as a function of gradient when speeds are self-selected. The self reports of
competitive runners, however, suggest that even relatively modest gradients encountered
during long-distance events, (e.g. “heartbreak hill” in the Boston Marathon), can greatly
perturb attempts to maintain a constant energy expenditure.
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Heart rate
As an indirect measure of oxygen consumption (and thus energy cost), heart rate is often
used as a measure of physiological effort. Zamparo (141) has reported that runners self-
select speeds during level road running which minimize heart rate variation. This was
further supported by Mastroianni (84) on a hilly course who reported no relationship
between relative effort (estimated by heart rates) and hill grade. Both studies have
proposed that this reflects an attempt to maintain a constant level of energy cost. Esteve-
Lanao et al (48) has further shown that the relative heart rate (% maximum HR) profile was
similar between faster and slower runners, varied systematically with race distance and was
regulated by variations in running pace. There are, however, a number of factors to
consider when examining the heart rate-running speed relationship. It is widely known that
various physiological, environmental and psychological factors can affect heart rates. For
example, in constant exercise where intensities exceed the lactate threshold, a slow
component is evident and heart rates gradually increase (cardiac drift). Proposed causes
include an increase in catecholamines via stimulation of the sympathetic nervous system
resulting from increases in body temperature or dehydration (19). As a result, the heart
rate – running speed relationship changes with the duration of effort during high intensity
continuous exercise; if running speed is constant, heart rate increases over time, if heart
rate remains constant, running speed decreases over time (19). Variation has also been
noted between heart rates in competition and training at the same speeds which cannot be
explained by differences in terrain or psychological stress (121), while endurance training
can result in a decrease in sub-maximal heart rates at similar speeds due to increases in
stroke volume. As heart rate is subject to variation due to these and other factors, it is clear
that running speed and heart rate are not perfectly related (19). Despite these limitations,
heart rate may also play a role in effort regulation regardless of its association with energy
26
expenditure. Billat et al (15) reported maintenance in the similarity of heart rate variability
between trials and suggested that this may be indicative of its role as a feedback signal
which is used to minimize cardiovascular strain during exercise.
Summary
Despite the lack of agreement about the exact nature of the speed-energy cost
relationship, and the continued debate about the best measures, it is widely accepted that
runners select speeds for distance events in a way that reflects this relationship in a
predictable and individual manner. Whatever principles of energy expenditure are finally
determined as appropriate predictors of running speed, there are other aspects of speed
regulation that are not well understood. One of these is the question of how, at any given
speed, a runner will select the key biomechanical determinants of running speed, i.e. stride
length and stride frequency. In the following section of the review a series of factors will be
outlined which influence the selection of these fundamental gait parameters.
2.3 Regulation of gait parameters In the biomechanical analysis of gait, speed is commonly expressed as the simple product of
the number of gait cycles and the distance covered in each cycle, i.e. stride frequency
multiplied by stride length. Accordingly, running speed can be altered by changing either
one or both of these parameters. The factors that regulate which combination is selected is
however, not completely known (107). The following section reviews findings on the
characteristics of these gait parameters and their suggested regulators before discussing
some of the limitations in this field of research.
27
Stride frequency
Stride frequency can be increased in two ways: either (i) decreasing ground contact time
and/or (ii) decreasing the time to reposition the limb for the next step (139) . Of these two,
the primary component is swing time as it represents the majority of total stride time (139).
Stride frequency has been found to be a stable and relatively invariant property with less
than 5% difference within individual distance runners across different days, speeds,
gradients or due to aging (detailed below). Brisswalter et al (23) reported stride frequency
to be the most stable of various physiological and kinematic parameters assessed during
sub-maximal treadmill running with a day to day variance of only 0.2-2.6 strides/min in
trained middle distance runners. Conoboy et al (33) also found that although running
speeds decrease with age, there is minimal variation in stride frequency, with less than 2%
difference between the stride frequency of older (60+) and younger (< 40) runners during a
marathon. The range of stride frequencies used by runners across different speeds has also
been shown to be narrow, with a study by Cavanagh and Kram (29) reporting only a 4%
increase as speeds increased from 3.15 – 4.12 m .s -1. Minetti et al (93) extended these
findings to gradient locomotion using a novel feedback-controlled treadmill, and reported
less than 5% variation in self-selected stride frequency from 0-10% gradients while speed
and stride length steadily decreased. It is suggested that this near independence of stride
frequency observed with speed and gradient is a reflection of the specific biomechanical
characteristics which differentiate running from walking (92).
Despite the finding of these low levels of individual variance across a range of conditions,
the determinants of self-selected stride frequencies are less clear and a range of factors has
28
been suggested, including various physical characteristics as well as the minimization of
energy cost and mechanical power.
Determinants of stride frequencies
Higher stride frequencies have been found in runners with a higher proportion of fast
twitch muscle fibres (6, 36) . Though this may suggest a genetic influence on the ability to
achieve a higher cadence, repositioning the limb during running is mainly achieved through
passive means by elastic recoil and inter-segment energy transfers (74), rather than power
generated actively by the muscles (135). Accordingly, muscle fibre types are unlikely to
greatly affect the minimum swing time (139). Cavanagh and Kram (29) compared the
relationship between various anthropometric characteristics and gait parameters of male
recreational distance runners during treadmill running at 3.15-4.12 m.s-1. No significant
interaction was found between stride frequency or stride length and leg length, height or
leg segment mass. These results suggest that anthropometric characteristics cannot be
used to predict stride frequency or stride length on an individual basis (29).
In contrast, analysis of constant speed running between 9-16 km.hr-1 has found that oxygen
consumption is minimized near the freely chosen step frequency (28). Cavagna (28) has also
showed that at speeds of less than 13km.hr-1, energy is saved by selecting a stride
frequency in line with the apparent natural frequency of the body’s ‘bouncing system’ (2.6-
2.8 Hz) even if this requires a mechanical power larger than necessary. Thus, for constant
speeds, it is suggested that people choose the stride frequency that minimizes energy
consumption.
29
Stride length
As stride frequencies have been found to be relatively invariant across a range of speeds
and gradients (64, 93), it is unsurprising that most studies point to regulation of stride
length as the main determinant of running speed (33). The primary determinants of the
specific stride lengths selected have been attributed to different factors, which are outlined
below.
Determinants of stride lengths
Links between physical characteristics and stride lengths are conflicting. As noted earlier,
Cavanagh and Kram (29) found no link between stride length and either leg length or leg
mass. Conversely, longer limbs have been shown to increase stride length by resulting in a
greater forward propulsion (71, 135), suggesting that physical characteristics may play
some role. Despite this sprinters have been found to take longer strides than non-sprinters
without having longer legs (6) so anthropometric characteristics are unlikely to be the only
determinant of variations in runner’s stride lengths.
As with stride frequency, it is suggested that runners freely select the stride length which
minimizes energy cost at any given speed (86). This claim has been supported by studies
which have shown that the aerobic demand of running increases when stride lengths are
shorter or longer than preferred (30), Kaneko, 1987. Conversely, Morgan (96) showed that
a number of runners exhibit uneconomical stride lengths. Consequently, their study
successfully used audiovisual feedback to adjust these runners’ strides to more economical
lengths thus reducing the aerobic demand of their running at any given speed. It is been
30
suggested that this deviation from optimal stride lengths may be an individual characteristic
reflecting differential responses to other factors, such as the attenuation of shock.
Research by Mercer (87) has shown that shock attenuation was only altered with changes
in stride length rather than frequency. Hamill et al (59) has suggested that this would be
most relevant to individuals with injuries or other pathologies as they may choose to
forsake maximising oxygen consumption and choose gait parameters which maximise shock
attenuation and protect injured structures. This may also apply to healthy individuals when
running on downhill gradients. In support of this, research by Minetti (94) showed that on
extreme downhill slopes, runners choose speeds approximately 30% lower than
energetically optimal. As stride length is known to provide the largest contribution to
alterations in running speed, this suggests that during sufficiently steep downhill gradients,
shock attenuation may be a stronger determinant of preferred stride lengths than energy
cost even within healthy individuals.
These variations in stride length due to gradients and possible shock attenuation contrast
sharply with the relatively invariant reports for stride frequencies across a range of
conditions. Fatigue and aging have also been reported to contribute to short and long-term
variation in stride lengths respectively within individual distance runners, though reports on
the latter are conflicting. Conoboy (33) noted that decreases in speed between older (60+)
and younger (40-49) runners during a marathon race could only be attributed to changes in
stride length rather than frequency. Differences in reported changes of stride length
because of fatigue may be due to variations in the duration, intensity and protocol used in
the analyses. Elliott (46) found stride length to decrease due to fatigue during track
31
running. Conversely, Gazeau et al (54) found increases in stride length over time during a
run to exhaustion at VO2 max pace on the treadmill. A recent study by Hayes (63) however,
further highlights the extent of individual factors as their results showed considerable intra-
individual variability with some runners increasing stride length due to fatigue, others
decreasing and others remaining the same.
Summary
In summary it appears that stride frequency is relatively invariant across a range of
conditions and its selection may be determined by both physiological and biomechanical
factors. Research suggests that frequencies selected may be based on minimizing both the
external mechanical power per step as well as the metabolic energy cost (28). In contrast,
changes in speed have been shown to be regulated primarily through alterations to stride
lengths. The most likely candidate for the selection of stride lengths during running appears
to be the minimization of energy cost, as preferred stride lengths are usually the most
economical, however the determinants of this parameter may change based on conditions
such as gradient or vary between or within individuals due to fatigue, aging or the need to
attenuate shock.
The literature on stride length and stride frequency is still incomplete. In particular, the
effects of gradient rely on treadmill studies using imposed speeds. Conversely, studies
allowing speeds to be self-selected generally occur on flat courses. It remains unclear
whether these principles apply in the same way when runners are free to self-select speed
and encounter changing gradients.
32
In addition to understanding the regulators that determine the selection of gait parameters
(and speed) a thorough understanding of speed selection also requires knowledge of the
way in which people distribute their speed across an exercise bout. This distribution is
termed a “pacing strategy” (50) and has been studied in a range of time based events such
as cycling (51, 65), running (14, 55) , swimming (128) and rowing (53) Findings from studies
such as these are reviewed in the following section.
2.4 Pacing strategies Pacing strategies can be broadly categorized into either positive (speed declines throughout
the event), negative (speed increases towards the end of the event) or even pacing. When
technology allows analysis of smaller time segments, pace variations can be identified
which may reflect a range of variable strategies; i.e. starting and finishing faster while
slowing in the middle stages of the event (a parabolic shaped speed curve) or more subtle
variations from an even strategy (2). Such pacing strategies may reflect both a conscious
and unconscious regulation of speed in response to internal (physiological, biomechanical)
and external (distance, gradient, competition) factors. Investigations of pacing have
generally used one of two approaches. Firstly, observations of self-paced events have been
conducted to understand the systematic variations self-selected during races or simulated
time trials. Alternatively, other researchers have conducted experimental trials where
athletes are constrained to different strategies to compare the effects on performance
and/or the accompanying physiological responses. A summary of these two types of pacing
studies are presented in Table 2.1 and Table 2.2 respectively. Findings from both of these
models will be explored to illustrate current knowledge in pacing.
33
Self pacing in short duration events (approximately < 10 minutes)
Mathematical modeling has provided evidence that athletes may benefit from a positive
pacing strategy in short duration events (135). Observations from swimming (127) cycling
(50) and speed skating (50) have further confirmed that elite athletes naturally adopt these
strategies in competition. It has been suggested that the prime reason that athletes adopt
a fast start strategy in events of this duration is to minimise the time spent in the
acceleration phase (2). While the role of aerodynamics or the effects of frictional or drag
forces play a decreased role in running when compared with these other sports, analysis of
elite runners in an event of similar duration (800m) has also shown the dominance of a
positive pacing strategy in 24 of the last 26 world records (133). While the need to minimise
acceleration time may influence the selection of a fast start in these events, it has been
shown that such strategies result in an increased oxygen consumption (115) and
accumulation of fatigue related metabolites (128) which may result in the latter stage
decrease in speed and a positive split race profile.
Conversely, in events which take longer than approximately four minutes to complete,
there appears to be a transition in the adopted strategies. Analysis of running events from
1500m to 2413m has shown that speed changes fitted a parabolic shaped curve, with a fast
start, a slower middle section before increasing speed again towards the end. This pattern
has been consistently shown in solo track trials (41, 61, 69) or in the presence of
competition (100). This pattern is also seen in other events, as shown, for example by
analysis of race profiles in the 2000m rowing event at the 2000 Olympics although the
increase in speed in the latter stages was not as large (53). Such ‘parabolic’ pacing
strategies are likely to combine elements of positive and negative pacing. While the former
34
is in keeping with a minimisation of acceleration time as for shorter events, the increase in
speed at the finish is likely to reflect a conscious harbouring of resources that if judged
optimally, enables the athlete to exhaust their anaerobic capacity upon (but not before) the
termination of the event (16).
Experimental manipulations of pacing-short duration events
In an effort to gauge whether the strategies adopted by athletes are optimal, a number of
studies have manipulated starting speed with mixed results on overall performance. The
most frequently cited study focused on performance of a brief duration (2-3 minutes) and
was conducted with cyclists during a 2000m ergometer time trial (51). Foster et al (51)
reported that an even paced strategy in which the first half of exercise was completed in
51% of the total time was more effective than a fast, very fast or very slow start. In
contrast, other studies have reported that a faster start is more effective. Ariyoshi et al (5)
compared trials in which runners covered 1400m in four minutes under fast-slow, even
pacing, and slow-fast conditions, followed by a time-trial to exhaustion (TTE) at a constant
speed. Six of the eight runners were found to run further during the TTE following the fast-
slow pacing condition, although this outcome measure has been shown to exhibit a much
higher level of within-individual variability compared with time trials in distance runners
(80). Support for a faster start has also been shown by Bowles et al (20) in a field study over
one mile where runners who ran the first quarter five seconds faster had better
performances compared with a comparatively slower start or even pacing. Though these
two studies offer persuasive evidence of the benefit of a faster start, both findings are
limited by the fact that mean speeds for the even paced trials were based on arbitrarily
Table 2.1: Studies of self-paced strategies in distance running
Author (year) Distance (m) or
Duration (mins)
Surface/terrain Subjects Observed strategy
Tucker et al (2006) 800m Track (level) 26 world record holders Positive
Hanon et al (2008) 1500m Track (level) 11 elite middle distance Fast start & finish
Noakes et al (2009) 1609m Track (level) 32 world record holders Fast start & finish
Crouter et al (2001) 1609m Track (level) 15 trained cross country Fast start & finish
Jackson et al (1981) 2413m Track (level) 67 college aged males Fast start & finish
Nummela et al (2008) 5000m Track (level) 18 trained distance Fast start & finish
Tucker et al (2006) 5000m Track (level) 32 world record holders Even with “endspurt”
Staab et al (1992) 30 minutes Treadmill (hills) 11 trained N/A-times constrained
Mastroianni et al (2000) 8250m Trail (hills) 10 recreational Positive
Tucker et al (2006) 10000m Track (level) 34 world record holders Even with “endspurt”
Ely et al (2008) 42200m Road (level) 219 elite marathoners Even: winners
Positive: others
Lambert et al (2004) 100000m Road (level) 67 elite ultra marathoners Positive
Table 2.2: Experimental pacing interventions in distance running
F: Fast, S: Slow, V.S: Very slow, M: Medium, E: Even, Free: Freely paced, Race: 25m acceleration then constant, Acc: Acceleration
La: Blood lactate, RPE: Rate of perceived exertion, vVO2 max: velocity at VO2 max, dlim: distance run at selected intensity, HR: heart rate
Author (year) Distance (m) or Duration (mins)
Surface/terrain Pacing strategies Subjects Findings
Sandals et al (2006) 800m Treadmill (level) E v Acc v Race 8 sub-elite VO2 highest with race
Leger et al (1974) 1207m Treadmill (level) F/M/VS v S/M/S 8 trained No difference in VO2 or peak lactate
Robinson et al (1958) 1264m Treadmill (level) F/S, S/F, E 2 trained VO2 /La lowest with S/F, highest with F/S
Ariyoshi et al (1979a) 1400m Treadmill (level) F/S, S/F, E 10 trained La/ RPE lowest after F/S
Ariyoshi et al (1979b) 1400m (4 mins)
Treadmill (level) F/S, S/F, E 8 collegiate 6 of 8 had best performance with F/S
Bowles et al (1968) 1609m Track (level) F/S, S/F, E 16 collegiate Overall time was fastest with F/S
Adams et al (1968) 1609m Treadmill (level) F/S, S/F, E 9 trained Total oxygen debt lower in E trial
Billat et al (2001) ≈ 3-11 mins Track (level) E v Free 11 trained Free improved dlim 105% v VO2 max
Garcin et al (2008) ≈ 10-11 mins Track (level) E v Free 10 trained No difference in RPE/VO2
Cottin et al (2002) ≈ 10-11 mins Track (level) E v Free 10 trained Free did not improve performance
Gosztyla et al (2006) 5000m Treadmill (level) E v F (+3, +6%) 11 trained Fastest with F (+6%). Slowest with E
Billat et al (2006) 10000m Track (level) E v Free 3 endurance trained Higher VO2, La/HR with E trial
37
chosen speeds rather than a self-paced trial, so intensities were not assigned according to
any objective measure of each runner’s current condition. Aisbett et al (4) and Bishop et al
(17) have provided more rigorous support for the benefits of a faster start in short duration
activities. Aisbett et al (3) reported that a fast start resulted in a better performance than
an even or slow start and that a six second sprint start gradually decreasing to a constant
pace was even more effective (4). During a kayak ergometer trial, Bishop et al (17) has also
demonstrated the superiority of a brief sprint start with a ten second all-out start followed
by a constant power output producing a higher total work in a two minute bout than even
pacing. It has been suggested that this improvement in performance may be due to an
accelerated oxygen delivery (as evidenced by a higher VO2) which may have spared
anaerobic energy utilisation until later in the event (4).
Self pacing in long duration events (approximately >10 minutes)
As the duration of events increase, a more even pattern of pacing emerges. In a maximal
30 minute trial, Chaffin et al (31) showed that cyclists had minimal variation in speed
throughout with only a brief increase in the last 30 seconds. Similarly, Padilla et al (105)
showed that a successful attempt at the one hour cycling world record was achieved with
very minimal deviations from the overall mean speed. An analysis of distance running
world records for 5000-10000m has also demonstrated consistently even split times for the
majority of the event. Though generally run with an even pacing strategy, competitors sped
up in the last kilometre as this was the fastest split in 66% of 5000m world records and 74%
of 10000m records (133). It is suggested that this ability to speed up towards the end of
long distance races (termed the “endspurt”) is evidence that pacing strategies are regulated
in anticipation of the event’s known duration and are not purely the result of peripheral
38
fatigue (100, 133). In events of even longer duration, pacing strategies may vary depending
on the ability of the athlete. While the lead runners in marathons (47) and ultra marathons
(76) have been shown to maintain an even pace for longer durations, less successful
athletes have shown a large positive pacing strategy. Unlike shorter events where this
strategy is consciously chosen and effected through a faster start, the decreases in speed in
the second half of events of longer durations (81, 98) are more likely to be an unintentional
slowing as a result of glycogen depletion (39) or neuromuscular fatigue (62).
Experimental manipulations of pacing - long duration events
Only one pacing manipulation study has shown a benefit to a faster start in an event of a
longer duration. Gostzyla et al (55) paced runners for the first 1.63kms of a 5km treadmill
trial before allowing them to pace freely for the remainder of the trial with the aim of
minimising their overall time. Three strategies were compared: completing the first
1.63kms equal to the best baseline pace, 3% faster and 6% faster. Eight of the 11 runners
were subsequently found to run their fastest time when starting 6% faster and the
remaining three during the 3% faster trial (55). All runners ran the slowest trial using the
even paced strategy. It is important to note that this study only compared faster starts with
even pacing. Accordingly, it is impossible to gauge whether a slower starting strategy may
also have been more effective than an even start, or significantly different from the faster
start strategy.
Unlike studies which consider the merits of slower or faster starts for portions of the total
distance, the only outdoor pacing interventions in distance running have compared freely
paced runs with a constant pace at the same average speed or power output (14, 15, 38,
39
52). All of these studies individualized the intensities for the constant pace runs as a
percentage of the velocity that the subject was able to sustain at their maximal oxygen
uptake in initial testing (vVO2 max). In the studies by Cottin et al (38) and Garcin et al (52)
the chosen intensity was 90% vVO2 max while in the study by Billat et al (14) four intensities
were tested (90%, 95%, 100% and 105% vVO2 max). In each study, runners ran their
maximal distance while following a cyclist at the prescribed pace (termed “dlim”). This
constant pace run was then compared with a later run covering the same distance but
freely paced. Cottin et al (38) reported that a variable (self selected) pace did not enhance
performance compared with a constant pace while Garcin et al (52) showed that the free
pace only increased performance by allowing athletes to finish the run with a sprint. Billat
et al (14) reported that a performance improvement only at the highest intensity (the
distance run at 105% vVO2 max was run faster with a variable rather than constant pace).
While the evidence from their findings seems to strongly advocate no advantage of self-
pacing over a constant paced run, only a limited range of intensities were tested. No tests
were performed at velocities below 90% vVO2 max, nor were any tested above 105%,
although this was the first point at which a performance advantage became apparent. By
constraining the imposed pacing regimes to only constant speeds, these studies did not
allow a field assessment of findings from treadmill interventions, to further assess whether
starting at a significantly slower or faster pace for a portion of the trial would result in an
advantage over either a constant pace or a freely paced run.
An additional study by Billat et al (15) over 10000m differed from the three mentioned
above in that the speed of the constant pace run was determined by the freely paced trial
rather than assigned to an arbitrarily decided intensity, which ensured that the paces
tested were in line with the self-selected speed of the runners involved. It also compared
40
physiological response rather than performance as the outcome measure and found that a
freely paced run resulted in a lower mean VO2, HR and blood lactate concentration than
one constrained to a constant pace at the same average speed. This finding of a lower
overall physiological stress from a freely paced run is the first conclusive evidence of a
benefit to variable pacing over a constant pace in a field based pacing trial. Although it is
noted that no apparent systemization in running speed changes was reported, no data is
presented as to the strategies self selected by the runners in their freely paced runs.
Accordingly, no conclusions can be drawn on whether the athletes chose to employ a
consistent strategy in their freely paced runs (fast/slow, slow fast etc) and which was more
effective in lowering the physiological load as was reported overall.
Although the studies reviewed in the preceding section appear to show a predictable
pattern of changes in pacing as a function of event duration, speeds selected in overground
events such as cycling and running are also dependent on environmental conditions, such
as temperature, wind, terrain or the presence of hills. Of particular interest is the effect of
hills, as this factor is more consistently present in daily training and racing and has the
largest and most immediate effects on speed and energy expenditure. Despite its
importance, the reliance on ergometers for cycling studies and treadmills and level tracks
for examinations of running has limited investigations of how pacing strategies are selected
in the presence of either uphills or downhills (84, 123).
Pacing over hills-Self paced
Kyle (75) has demonstrated mathematically that time added to a cyclist’s performance
when going uphill is greater than time saved when going downhill despite there being no
41
net elevation change. This has been confirmed with distance runners in treadmill studies.
Staab et al (123) reported that although runners increased speeds on downhill sections, it
was not enough to offset the increased time spent on uphill sections. As a result, overall
times were slower on the courses involving hills compared with a level course (though
there was no net change in elevation). In this study, speeds were adjusted via hand signals
to a tester operating the treadmill, which does not reflect the continuous natural
fluctuations in speed that are self-selected during unconstrained running. A further
limitation of this modality is that it confines analysis to linear gaits, while normal outdoor
locomotion often involves movement along undulating or curvilinear paths. The only other
study to consider pacing over hills, and the only one to use an outdoor setting was a
comparison of off road running and cycling by Mastroianni et al (84) on a gravel course.
Runners and cyclists in this study completed three laps of a 2.75km course and were shown
to complete the first lap faster than the remaining two (positive lap strategy). The short
distances of many of the hills and frequent gradient transitions made it difficult to
categorise the effectiveness of the pacing strategy as a function of gradient as participants
were unable to attain a steady state. As a result, only 40% of speed variation was explained
by gradient for runners and 19% for cyclists, with the balance being attributed to the nature
of the soil and the trail. Despite these shortcomings, these two studies represent the only
two studies to characterise how athletes self pace in the presence of hills.
Pacing over hills- experimental manipulations
Swain (125) has shown through mathematical modeling that cyclists could improve
performance on an undulating course by slightly increasing power on uphills and
decreasing power on downhills without any change in mean overall power. This
theoretical finding was supported by a study by Atkinson et al (8) who reported that
42
five out of seven cyclists performed better in a one hour ergometer trial over hills by
varying power by 5% in the recommended direction. It is important to emphasise here
that the goal was a constant speed through a variation in power rather than a variation
in speed itself. This represents the only known study to this author’s knowledge which
has attempted to manipulate effort as a function of gradient in an endurance event and
there has been no comparative study in distance running.
Summary of pacing research
In summary, data from observational studies have shown that athletes routinely adopt fast
starts in events of brief durations (133), middle distance events are characterized by fast
starts and finishes separated by slower middle sections (41, 61, 69, 100) while even pacing
has been noted to be more common in events of longer durations (133). As a number of
these observation studies have drawn conclusions from the results of races (47, 53, 100,
133), however, it is impossible to rule out the effect of other competitors and the ensuing
tactical decisions on the strategies chosen. In running events, there is also the added
difficulty in confirming that the intermediate times recorded were indeed that of the
winner (100, 133). It is likely (especially when sourcing older data) that split times have only
been accurately recorded for the leader at that interval, hence the actual pacing of the
overall winner (and thus record breaker) may have differed depending upon their position
in the field at each interval. In contrast, while solo trials are free from competitive
influences, the provision of pacing feedback (in the form of split times) during the course of
the event may mean that regulation of speeds was influenced by this external feedback,
rather than simply in response to afferent input (41, 61, 102).
43
Experimental manipulations of pacing have supplied evidence that performance (55) or
physiological responses (15) can be improved through imposed (55) or self selected (15)
variations from a constant pace. Although changing pace to account for hills has been
recognised and recently studied in cycling (8, 125), this aspect is a notable omission from
pacing interventions in distance running. A further limitation has been the use of only
infrequent changes in pacing interventions across all sports, where changes are routinely
implemented for a quarter (20), a third (55) or even larger proportions (5) of the total
distance, which does not allow for any transitions between changing conditions such as
gradients. It is thus clear that research into “optimal pacing” strategies must address these
two key limitations to further understand speed selection in the natural conditions which
predominate in training and racing for the majority of runners.
2.5 Conclusion Despite a wealth of literature on running performance and physiology, it is clear that many
questions remain unanswered about the way in which runners regulate speeds in natural
outdoor settings. Although runners frequently encounter undulating terrain in training and
racing, there is a particular shortage of research into the self-selection of speeds, gait
parameters and pacing strategies over hills.
44
___________________________________________________________________
The following chapter is based on a paper which was accepted and published in the
January 2008 edition of Medicine and Science in Sports and Exercise.
____________________________________________________________________
3 ASSESSMENT OF SPEED AND POSITION DURING HUMAN LOCOMOTION USING NON-DIFFERENTIAL GPS
3.1 Introduction The ability to accurately determine speed, position and displacement is fundamental to the
study of human locomotion. Measurement of speed and position during field studies is
often limited by the characteristics of study locations, including the complexity of the
terrain and other conditions which influence the accuracy, cost or volume of information
that can be captured. Techniques to directly measure distance have ranged from the
standard tape, rule or measuring wheel through to optical systems involving laser
measurements. The determination of speed during field studies has often been based on
chronometry using stopwatches or light gates, yet this requires highly controlled conditions
and gives only average speed, rather than continuous speed information throughout the
trial. Video analysis has also been used but this is time consuming, expensive and is limited
by frame rate, viewing angle, range and the suitability of the location. The introduction of
the Global Positioning System in the 1990s offered an alternative method for the
measurement of speed and position during locomotion studies in the field, with the
potential to circumvent some of the limitations and minimise others.
45
The Global Positioning System (GPS), originally developed as a military tool and funded by
the U.S Department of Defense, consists of a network of 24 operational satellites. These
satellites orbit the earth twice daily on one of six paths, emitting radio signals with a unique
code sequence and an encrypted navigation message containing the satellite ephemeris.
This message is decoded by a GPS receiver to give information about exact time and
position, allowing the calculation of the distance to each satellite by multiplying the signal
travel time by the speed of light. By calculating the distances to at least four satellites, a
single three-dimensional position can then be determined trigonometrically.
In most commercially available GPS systems, speed of displacement is determined by
measuring the rate of change in the satellites’ signal frequency due to movement of the
receiver (Doppler shift)(13). Speed can also be calculated from changes in the given GPS
distance divided by the time between each logged position. GPS accuracy is influenced by
atmospheric conditions as well as deflection of the signal off local obstructions, but the
largest source of error in early GPS measurements was caused by an intentional
degradation of the civilian signal by the U.S Department of Defense known as “Selective
Availability”.
To overcome this limitation, various methods were developed in order to “correct” for
these errors in the standard signal. One method involves placing a stationary receiver at a
known location which compares its position with that given by the satellites and sends
correctional information to the roving receiver. Known as differential GPS (DGPS), this
method has been shown to substantially improve the accuracy of both GPS position and
speed data (13). Recently, research groups have utilised DGPS to study the biomechanics of
46
overground walking (14-17), while others have used it in conjunction with a portable
metabolic analyser to enable the examination of physiological responses at specific
positions during orienteering (7) and cross-country skiing (8).
In contrast to differential receivers, the use of non-differential GPS offers several distinct
advantages to researchers: far lower cost, lighter and smaller unit, and substantially less
complex data collection procedures as no stationary receiver is needed. As selective
availability was switched off in May 2000, this promised an immediate increase in the
precision of measurements for standard GPS receivers. Adequate validation of non-
differential GPS therefore offers the prospect of far wider adoption of this technique in
studies of human performance in the field.
Unfortunately, despite some very useful validation studies on differential GPS, there are
several shortcomings in the available reports using non differential receivers. While
reductions in positional errors have been demonstrated (1), improvements in the
determination of speed have been less clear. The most complete validation of a non-
differential GPS since the removal of Selective Availability was conducted by Witte & Wilson
(140). Their study found that GPS can provide accurate velocity data for relatively constant
speeds along straight trajectories with accuracy decreasing on curved paths. However, even
on straight paths, 43% of values were reported to have errors exceeding 0.2 m.sec -1. This
would appear to indicate minimal improvement in accuracy over a validation conducted by
Schutz & Chambaz prior to the removal of Selective Availability, who reported errors of
0.19, 0.31 and 0.22 m.sec -1 for running, walking and cycling, respectively (118) .
47
Witte & Wilson (140) assessed speed measurement over a wide range of velocities (2-10.8
m.sec -1); yet no specific information was provided as to the unit’s performance below 10
km.h-1 with only a median value and an inter-quartile range reported. Moreover, no values
were recorded below 2m.sec -1. As this range covers all comfortable walking speeds for
healthy humans (18), it is important to validate non-differential GPS within this range of
velocities. In addition, as the alternative method of speed calculation involves
differentiating changes in position over time, the precision of distance measurements by
non-differential GPS also needs to be determined.
The accuracy of the non-differential GPS receiver used in this study was thus assessed in
numerous ways. The specific aims of this study were:
1. To assess the ability of a non-differential GPS receiver to accurately measure speed
across the full range of human locomotion speeds.
2. To investigate whether the accuracy of speed measurements was maintained
around circular paths.
3. To evaluate the validity of measurements of distance and static positions.
3.2 Methods
Subjects
Three healthy participants took part in this study. Two participants (male, age: 38, body
mass 67 kg, height 176 cm and female, age: 22, body mass 52 kg, height 162 cm) were
currently involved in regular physical activities of an aerobic nature, while a third (male,
age: 29, body mass 70kg, height 178 cm) was an international level sprinter in current
48
training. While a larger sample of participants is a necessity in most studies of exercise
science to achieve a suitable level of statistical power, the physical and physiological
characteristics of the subject(s) selected (gender, height, body weight, fitness level, etc.)
have no effect on the accuracy of GPS measurements (78). As a result, past validation
studies of GPS in human locomotion have used a single subject for multiple trials rather
than the reverse (78, 118, 119, 140). In the current study three participants were chosen to
enable the completion of a large number of trials, with the third participant specifically
selected for his ability to attain a velocity at the extreme end of the range of human
locomotion. Written informed consent was obtained from all participants and the study
was approved by the Human Research Ethics Committee of the Queensland University of
Technology.
Apparatus
This study used a commercially available GPS receiver (GPS-BT55, Wonde Proud
Technology Co., Ltd, cost approximately $80 US) which operated in non-differential mode.
The BT-55 is one of a range of current receivers which are Bluetooth TM enabled allowing
wireless connectivity, lower power consumption and a reduction in size and weight. The
model used in the current study (50g, 61.5 x 43.8 x 21.5 mm) was worn within a cap on the
head to provide a consistent unobstructed view of the sky at all times while a phone was
attached to the person’s arm with a Velcro® strap. No participants complained of any
discomfort or impediment to their normal gait from wearing the equipment. The GPS
receiver collected and streamed NMEA0183 data to the phone at 1 Hz. NMEA is the
National Marine Electronics Association standard protocol for the transmission of GPS data
(140). Information provided included time (Universal Time Constant; UTC), position
49
(latitude, longitude, altitude), distance travelled, speed via Doppler shift and satellite
information such as the number of satellites used for the fix and the dilution of precision.
All data were logged using GPS evaluation software GPSBabelGUI-2 (BETA).
Reference locations and distances
This study involved four separate experiments. The first three were conducted on a grass
sporting oval within the grounds of the Queensland University of Technology, while the
remaining experiment utilised a location in the surrounding area (Kelvin Grove,
Queensland, Australia). For the validation of distance and speed measurements over a
straight course a distance of 100m was surveyed to an accuracy of ± 10mm using an
electronic distance measurement device and theodolite (Total Station EDM 520, Sokkia Co.
Ltd, Japan). Points were also marked at distances of 20, 30, 40, 50 and 60m to enable the
collection of a number of intermediate measurements. For brevity, reference distances will
subsequently be denoted to the nearest whole metre.
Experiment 1- Validation of GPS Distance measurements
Distance measurements were validated by walking the 100m section 40 times and logging
the position and distance travelled every second. The same participant performed all trials
and a string line along the marked points was used as a guide to minimise lateral deviations.
Before the first trial the participant moved into position so that the GPS receiver was
directly over the starting point as viewed from a lateral position by the tester. An offset
mark was placed at the end of the person’s feet to enable consistent positioning for all
subsequent trials. The same procedure was used at the finish position. The start and finish
50
of each trial was also clearly delineated by recording a few seconds of stationary data. The
specific algorithm used to generate distance measurements by the GPS receiver is
proprietary and therefore unavailable. Accordingly, the coordinates determined by the
receiver for the start and end positions of each trial were also used to calculate changes in
displacement using the Great Circle Earth Formula (Appendix 6).
Experiment 2- Validation of GPS Speed measurements- straight course
GPS speed measurements were assessed while participants walked or ran along a straight
60m section of the course used in Experiment One. Timing gates (Speed Light Sports Timing
System, Swift Performance Equipment, Australia) were placed at 20, 30, 40, 50 and 60m
and provided times accurate to one hundredth of a second. Each set of gates were
mounted on tripods which were adjusted such that the higher and lower infra red beams
passed to their opposing reflector at heights of 1m and 0.67m respectively, which
corresponded approximately to the level of the pelvis. Values generated by the gates were
used to determine average speeds (referred to subsequently as ‘actual speed’) for all speed
validation calculations. This enabled comparison of GPS speeds with ‘actual speed’ values
for four 10m sections: 20-30, 30-40, 40-50, and 50-60m. Participants were instructed to
attempt to maintain a constant pace between the 20 and 60m gates and feedback on their
split times was provided at the end of each trial to assist in achieving this aim. The session
commenced with a slow walk of approximately 1m.sec -1 and increased in pace until the
maximal consistent speed was obtained. 59 trials were conducted in total.
Two different methods of GPS speed determination were compared with actual speed data:
(i) speed determined by Doppler shift, (ii) speed calculated by differences in GPS position
51
over time. Raw GPS values were compared with reference speeds for those sections in
which subjects were deemed to be at constant velocity. The criterion for constant velocity
was that speed changes between adjacent 10m sections, using the reference (timing gate)
values, was less than 2%. Speeds were also compared over the entire 20-60m section using
the mean of all 1 second GPS values for both methods of speed determination.
Experiment 3- Validation of GPS Speed measurements-circular path.
This experiment evaluated the accuracy of GPS speed measurements around a circular
path. Participants walked and ran so that their feet directly followed a marked line which
defined the circumference of a circle of exactly 10m radius. 34 trials were conducted in
total. As in Experiment two, actual speed values were provided by timing gates which were
placed at 15, 25, 35 and 45 m from the start position and feedback was provided to
participants on split times at the end of each trial to assist in the achievement of a
consistent pace. As the participant leant into the bend at higher speeds, this should lead to
a measurable reduction in the distance travelled as derived from the GPS receiver
compared to that travelled by the participant’s body. Actual speeds were determined by
the person’s legs (rather than their head) breaking the infra-red beam between opposing
light gates, and running on bends causes a velocity dependent inward lean, which becomes
significant at higher speeds. To quantify this effect, a pole was placed vertically at a tangent
to the curve next to the 15m timing gate and within the field of view of a video camera
which recorded each trial. This allowed subsequent viewing and measurement of the lean
angle to allow a comparison of head and ground displacements at different velocities. From
these measurements the following regression equation was generated: lean angle
(degrees) = (speed- 2.1264) / 0.3324. Once the lean angle was calculated, actual speed data
52
were adjusted using the following trigonometric formulae as presented by Witte & Wilson
(140). Adjusted speed (m.sec -1) = actual speed [62.83- (2 π 1.6 cos α)]/ 62.83, where actual
speed is average speed determined by the timing gates, 1.6 = the height of the GPS receiver
above the ground, 62.83 is the circumference of the circle (radius 10m) and α = the lean
angle calculated from the regression equation. This speed reduction was used to adjust all
actual speed data during trials which exceeded velocities of 2 m.sec -1 (as lean angles were
observed to be insignificant at lower velocities). It should be noted that lean angles may
depend on the specific height of the subject. All three subjects used in this study were of
average heights for their gender. While a taller person might be expected to exhibit an
increased body lean on a circle of similar radii and a shorter person may hold a more
vertical body position, the procedures for calculation of angles and subsequent adjustments
of speeds would be unchanged.
Experiment 4- Validation of GPS position measurements.
Validity of positional measurements was assessed by placing the unit for 1 hour on a
geodetic point (latitude 27 ° 26΄ 47.5588˝ and longitude 153° 1΄13.7314˝ GDA 94)
maintained by the Queensland Department of Natural Resources. The unit recorded 3600
data points and static validity was assessed by comparing the spatial distribution of co-
ordinates provided by the GPS unit relative to the known co-ordinates of the geodetic
point. Simultaneous altitude measurements logged by the GPS were also compared with
the known altitude (16.49m).
53
Statistics
Differences between the actual surveyed distance and the distance measured by the GPS
are reported as the mean and standard deviation as well as the 95% confidence intervals.
GPS speed measurements by (i) Doppler shift and (ii) changes in GPS position per unit time
were compared with actual speed using Pearson product moment correlations as well as
tabulating the proportion of values within the manufacturer’s reported specifications of
0.1-0.2 m.sec -1 Bias, precision and confidence intervals are also displayed using Bland and
Altman plots. Positional validity is illustrated on a map with the frequency of points
displayed relative to the true geodetic point. Differences between the actual altitude and
that given by the GPS were compared using descriptive statistics with the mean, standard
deviation and range of measurements reported.
3.3 Results
Experiment 1- GPS Distance
Compared with the surveyed distance of 100m, the mean measured GPS distance was
100.46m (SD 0.49m, range 99.48-101.77m, 95% confidence interval -0.52 to 1.44 m). The
mean distance calculated using the Great Circle Earth Formula was 100.31m (SD 0.47m,
range 99.41- 101.44m, 95% confidence interval -0.63 to 1.26m).
Experiment 2- GPS Speed-straight course
Raw GPS data were compared with actual speed for those sections in which subjects met
the criterion for constant velocity. 89 of a possible 177 ten metre sections from the overall
54
data set met this criterion. From these sections, 337 total speed values were obtained with
velocities assessed from 1.06-9.62 m.sec -1. The reason for presenting these data is that this
is the most demanding test of the raw speed output from the system.
Speed determined by GPS (Doppler shift) was highly correlated with actual speed (r =
0.9994). The regression equation was: actual speed (m.sec -1) = 0.0124 + 1.0006 (GPS
speed). Mean error was 0.01 m.sec -1 (SD: 0.07) with 90.8% of GPS speed values within 0.1
m.sec -1 of speed by chronometry and 97.9% within 0.2 m.sec -1. These findings are in line
with the dynamic accuracy specifications for the unit provided by the manufacturer of 0.1
m.sec -1 .GPS speed calculated from changes in position over time was also compared with
actual speeds. The correlation coefficient using this method was 0.9984. Mean error was
0.01 m.sec -1 (SD: 0.11), with 66.5% of GPS speed values within 0.1 m.sec -1 of actual speeds
and 94.4% within 0.2 m.sec -1. Absolute speed errors for both GPS methods are shown in
Figure 3.1. Summary validation data is also provided for speeds averaged over longer
distances (Table 3.1), as many potential users will not require the highest level of
resolution.
Experiment 3- GPS Speed- curved path
An acceptable consistency of speed (<2% difference in speed from the preceding section as
determined by the timing gates) was achieved in 31 of a possible 68 ten metre sections. 128
speed values were obtained within these sections at velocities ranging from 1.23-5.81 m.sec
-1. Speed determined by GPS (Doppler shift) was closely correlated with actual speed (r =
0.9985). The regression equation produced was: actual speed (m.sec -1) = -0.1114 + 1.0748
(GPS speed). Mean error was 0.06 m.sec -1 (SD: 0.12). 71.1% of GPS speed values were
55
within 0.1 m.sec -1 of speed by chronometry, with 86.7% within 0.2 m.sec -1. GPS speed
calculated from changes in position over time was also compared with actual speeds. The
correlation coefficient using this method was 0.9973, mean error 0.07 m.sec -1 (SD: 0.13).
53.1 % of GPS speed values were within 0.1 m.sec -1 of actual speeds with 88.3 % within 0.2
m.sec -1. Absolute speed errors for both GPS methods are shown in Figure 3.2.
These results were based on the raw data which did not include adjustments in
displacements of the GPS receiver due to any lateral lean by the participant. A visual
representation of these reduced displacements is shown in Appendix 2 that compares the
path travelled by the GPS receiver for three selected velocities. Data were adjusted using
the methods described previously on trials where velocities exceeded 2m/sec. This data is
compared with raw values and summarised in Table 3.2.
Experiment 4- GPS- Static position
The figure in Appendix 3 shows the spatial distribution of the 3600 recorded GPS points
relative to the known geodetic point. The average distance recorded from the unit to the
geodetic point was 1.08 ± 0.34m with a range of 0.69-2.10m. 86.5 % of observations were
within 1.5 m and 99.89 % of observations within 2m of the known point. These results are
better than the static accuracy claimed by the manufacturer (7 metres circular error
probable for 90% of horizontal position values). Mean altitude was 14.75m (SD: 1.24m)
compared with the actual altitude of 16.49m with a range of 11.90-17.60m.
56
Table 3.1: Comparison of two different GPS methods of speed determination with actual
speeds using the mean of all 1 second values across the entire 20-60m straight section
GPS method Doppler shift ∆ GPS position/time
Correlation coefficient 0.9998 0.9997
Mean error (m.s -1 ) 0.01 ± 0.04 0.01 ± 0.06
Values ± 0.1 m.s -1 of reference value (%) 96.6 89.8
Values ± 0.2 m.s -1 of reference value (%) 100 96.6
Table 3.2- Comparison of GPS speed determination around a circular path with actual
speeds before and after corrections for reductions in GPS displacement due to leaning.
Comparison measure Doppler shift ∆ GPS position/time
Raw data Adjusted Raw data Adjusted
Correlation coefficient 0.9985 0.9986 0.9973 0.9973
Mean error (m.s -1 ) 0.06 ± 0.12 0.04 ± 0.08 0.07 ± 0.13 0.04 ± 0.10
Values ± 0.1 m.s -1 of
reference value (%)
71.1 77.3 53.1 64.1
Values ± 0.2 m.s -1 of
reference value (%)
86.7 95.3 88.3 93.7
57
Figure 3.1- Plot of errors in speed determination using GPS (Doppler shift- top figure) or GPS (∆ distance/time -bottom figure) over a straight course. Mean error of the measurement and the 95% confidence limits are indicated by the central and outer broken lines respectively.
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Figure 3.2- Plot of errors in speed determination using GPS (Doppler shift- top figure) or GPS (∆ distance/time-bottom figure) over a curved path. Mean error of the measurement and the 95% confidence limits are indicated by the central and outer broken lines respectively.
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3.4 Discussion
The current study showed that non-differential GPS offers an accurate estimation of speed
and displacement in addition to static position during human overground locomotion.
Speed measured by Doppler Shift was found to be more accurate than differentiating the
unit’s distance output as a function of time, while errors were slightly increased around
bends.
Non exercise science fields such as engineering and studies of vehicular motion require
higher levels of static and dynamic accuracy from GPS receivers. Using high precision
geodetic receivers, sub-centimetre static positional accuracy has been reported in research
to detect deflections in long bridges (111), while dynamic measurements in the study of
vehicle states have reported velocity measurements with errors as low as 0.05m/s (11).
Locomotion research does not usually require this high level of accuracy; however a
comparison of the measurement precision achieved requires consideration of a range of
factors that can vary between human validation studies. This can include variations in the
type of receiver employed (differential, non-differential, WAAS enabled), the sampling
frequency utilised and the measurements assessed (speed by Doppler change, speed by
positional change, displacement, static position etc). Accordingly, a summary of the various
characteristics of previous GPS validation studies is included in Appendix 4.
When assessing speed using GPS, an important consideration is the time interval over
which to average measurements as this will often vary based on the requirements of the
60
investigator. While measuring variation of speed within the gait cycle requires high
frequency receivers such as those used in Geomatics (50-60 Hz), comparison of speed
variations across long periods of data collection such as endurance activities (78, 79), can
involve averaging over intervals of seconds or even minutes. Similarly, comparison of speed
changes with relatively slowly changing physiological processes does not require data to be
collected at especially high frequencies. The current study was wholly concerned with
validation of the unit’s determination of speed. Accordingly, the raw, individual GPS values
were compared as this offered the most challenging test of the system’s performance. The
sampling frequency of 1Hz meant that the number of actual values collected within each
10m section ranged from a single value during the highest speeds to as many as nine data
samples during slow walking.
As the determination of actual speeds (using timing gates) still relied on average speed, a
number of steps were taken to minimise comparison errors. Firstly, the gates were placed
10m apart as this was the smallest distance which would ensure at least one sample would
be recorded within each interval at the highest speeds. To be confident in the validity of the
reference value, it was also imperative that there was minimal variation in speed, thus
sections were only compared where speeds varied by less than 2% from the preceding
section. Using the median speed values of 5 m.s -1, this represents a difference of less than
0.1 m.s -1 which is comparable to the proposed error of the system. Using these methods,
the highest level of precision was found using speed determined by Doppler shift with over
90% of values within 0.1 m.s -1 of actual speed. This represents an improved performance
relative to the study of Witte and Wilson (140) who reported errors in excess of 0.2 m.s -1
for 43% of values during straight trials, despite their study using reference values obtained
over shorter intervals
61
Changes in satellite geometry are related to the accuracy of the position fix in terms of
latitude and longitude. Accordingly, it has been suggested that that this may also be
reflected in the accuracy of speed measurements(140) . These changes in satellite
availability are expressed by the Horizontal Dilution of Precision (HDOP) which is dependent
on the number of satellites used and their position, with a spread of satellites about the
horizon producing higher positional accuracy than many at the zenith (78). Higher
positional accuracy is reflected by a lower HDOP value, with values approaching 1 most
accurate, while a value of 50 would be considered unreliable). Despite this, HDOP values
were extremely low throughout this study (range 0.8-1.3) and showed no relationship with
speed errors. This finding agrees with Witte & Wilson (140) who also found no significant
relationship between HDOP and the accuracy of speed measurements.
Real human locomotion often involves walking and running around winding paths, hence it
was necessary to examine the systems performance over a course involving bends. As
found in previous studies (140), this study found GPS to slightly underestimate speed on a
curved path, with error increasing at higher velocities. Correcting data to account for lean
angles reduced the magnitude of these errors (see Table 3.2). Adjustments due to lean
were based on observations at only one location (the first timing gate). As this may over or
underestimate the average lean throughout the trial, the raw data is also presented (Table
3.2). Errors increased marginally when calculating speed by changes in GPS position over
time when compared with Doppler shift (Figure 3.2-bottom figure). This can be attributed
to the determination of the route as a series of chords inside the curves which would tend
to underestimate speeds (especially at higher velocities) as has been previously noted
(140). The bends involved in the curvilinear course used in the current study (radius 10m)
are in excess of those that are likely to be consistently experienced during outdoor running,
62
yet the performance by this method still offered greater than 90% of adjusted values with
errors less than 0.2 m.s -1.
This study extends the only other validation study of GPS speed measurements using a non-
differential GPS since the removal of Selective Availability (140) in two ways. Firstly, by
assessing performance during human locomotion, where the braking and propulsive
characteristics within the gait cycle differ from the more continuous motion of cycling, and
additionally, by characterising specific performances at velocities more representative of
locomotion. Future validation studies using locomotion should look at further
improvements in the precision of the reference method, as more comprehensive
biomechanical studies may be able to employ non-differential GPS. As GPS chips are now
becoming commercially available with higher sampling frequencies, further validation may
also be needed to assess their impact upon speed determination with non-differential
receivers.
This study confined its analysis to the performance of only one model of GPS receiver.
Potential users of GPS for locomotion research would, in theory, have to repeat validation
procedures similar to those used here if alternative receivers are used. Clearly this is not
always practical. The following steps may, however, give the user some assurance of valid
data. A) Depending on the user’s accuracy requirements, the manufacturer’s specifications
for position and velocity error should meet or exceed those for the unit studied here if
comparable accuracy is required. B) Measurement of a stationary receiver over a period of
hours gives important basic information about error variance and drift, even if no geodetic
reference point is available. C) In many locations, accurately surveyed geodetic reference
63
points are available and marked in public locations. This allows absolute position error to
be assessed. D) Velocity error is harder to assess, but a starting point would be to compute
average velocity over an accurate straight line course, such as the 100m straight of a
running track. This provides a straight reference line, a known distance, the possibility of
electronic timing accurate to 0.01 s, and in general, very good satellite availability.
Systematic average velocity errors should be apparent, even if assessing instantaneous
velocity errors is not feasible. This procedure has the additional advantage of providing
high precision evaluation of displacement.
The high level of measurement accuracy and portability of GPS offers the potential for a
broad range of applications across many scientific disciplines. The accurate measurement
of speed and displacement in the field enables an opportunity to conduct sports-specific
testing in the natural environment of the athlete, rather than the controlled environment
of the laboratory (77). Within the field of exercise science, the use of GPS in conjunction
with technology such as heart rate monitors, gas analysers and accelerometers can assist
field research into exercise physiology, metabolism and biomechanics (119). In addition to
the many exercise science and sports applications, this technique has many other potential
applications across clinical, rehabilitative or even occupational settings.
The positional validity found in this study would allow the researcher to relate changes in
position within a specific route to other variables of interest which can be simultaneously
measured. This could allow comparison of changes which take place when a person was
locomoting on different surfaces or within different “micro-climates”, while the accurate
64
displacement data would enable examination of any aspect of data per unit distance, for
example, changes in kinematics in conjunction with step detection.
The high level of resolution in the raw speed measurements reported here would enable
even relatively subtle and short-term velocity differences to be detected. This could be
within an individual as a result of factors such as fatigue, weather conditions, gradients and
medications; or between groups, such as age cohorts, clinical intervention and control
subjects, or other groups defined by the research. For example, a change in gait speed of
the magnitude of 0.15-0.25 m/s has been established as representative of a clinical
difference in patients following traumatic brain injury (136). Similarly, a difference of
0.1m.s- 1 has been reported as significant in people with chronic obstructive pulmonary
disease or older patients with heart failure (1) while as little as 0.2 m.s - 1 differentiates
normal gait speed between healthy men in their forties and healthy women in their
seventies (18). A further advantage is the availability of continuous velocity data, which
could be of value even when average speeds over longer distances may not be reliable,
such as oscillations in speed due to environmental conditions or from different pacing
strategies in athletic events
In summary, non differential GPS receivers can provide highly accurate speed, displacement
and position data for human locomotion at varying speeds and on bends as well as
straights, while offering researchers advantages in size, weight and cost over differential
GPS.
65
____________________________________________________________________
The following chapter is based on a paper which has been accepted and published in the
January 2010 edition of Medicine and Science in Sports and Exercise.
____________________________________________________________________
4 SPONTANEOUS PACING DURING OVERGROUND HILL RUNNING
4.1 Introduction The capacity to manage energy resources optimally by matching locomotion speed to
terrain and distance may have its origins in the early history of hominids. Recently,
biologists have proposed that the ability of humans to run long distances has played an
important role in our evolution, enabling successful hunting and scavenging (21).
Minimizing the time to cover distances on foot would also have allowed early humans to
locate and transport food and water, and aided them in escaping from predators, adverse
weather conditions, and other threats to survival.
Given this long-standing evolutionary advantage for optimal speed regulation, it could be
assumed that humans retain the ability to select locomotion speeds in a near-optimal
manner without external pacing, provided that they have adequate fitness levels and
experience of running in varying conditions and for a range of distances. Indeed, the
optimal management of resources is essential if an endurance event is to be completed in
the least possible time. For this reason numerous studies of athletic performance have
focused on pacing and the factors which affect it. One common issue arising from these
studies, which have been well reviewed by Abbiss and Laursen (2), is the need for runners
66
to select an optimal speed and vary it to meet environmental conditions, including changes
in surface, direction and gradient. Of these factors, changes in gradient pose a special
challenge as they involve the largest changes in energy expenditure, and any
misjudgements of pace carry high performance costs. While the self-selected speed of
walking in natural environments has been investigated extensively (25, 42, 58, 67) a
number of factors, including limitations of the available measurement technology, have
hindered a comparable analysis of running.
The use of laboratory treadmills to simulate running over hills poses significant technical
challenges, in particular by limiting the runner’s ability to regulate speed freely and
continuously. These problems notwithstanding, treadmill studies have been used to
confirm that selected running speeds were inversely associated with gradient (93, 123), and
have demonstrated that runners were unable to maintain a constant energy expenditure
due to an inability to increase speed sufficiently on downhill gradients (123).
In contrast to the relatively constant rate of energy expenditure achievable on straight and
level courses (141), the only study so far to investigate speed regulation over an undulating
off-road course found that gradient accounted for only 40% of the variation in speed (84).
In contrast to the findings of Staab et al (123) subjects appeared to maintain a steady rate
of energy expenditure across different grades, while relative effort, determined indirectly
from a heart rate (HR) oxygen consumption regression, was found not to be related to
gradient.
67
To better understand the determinants of and constraints on the selection of speeds during
distance running on undulating terrain, the physiological profiles of subjects from the
laboratory should be combined with a field study in which runners are completely free to
regulate speed. The course should include a range of gradients and level sections, with each
of sufficient length that the time course of speed changes can be observed. Ideally, the
continuous measurement of physiological, kinematic and trajectory variables would be
included so that a more comprehensive account of factors affecting speed regulation can
be achieved. The current study was designed to accomplish this, using experienced
runners on a three-lap course, and employing a portable gas analyser, heart monitoring,
accelerometry to measure stride length and frequency, and a Global Positioning System
(GPS) receiver to provide continuous velocity and location data. Specifically, the aims of
this study were:
1. To characterize the effect of gradient on self-selected running speed and the
concomitant changes in oxygen consumption, stride frequency and stride length
2. To develop prediction equations for self-selected speed based on key variables
4.2 Methods
Participants
Eight healthy male distance runners (age 28.1 ± 9 years, height 178.9 ± 7.3 cm, weight 70.2
± 7.6 kg) were recruited for this study from local running clubs. All runners had completed a
10000m race in less than 40 mins in the previous 12 months (or a longer distance at an
equivalent pace) and were free from any musculo-skeletal injuries of the lower limbs.
Individual data is detailed in Table 4.1. Written informed consent was obtained from all
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participants and the study was approved by the Human Research Ethics Committee of the
Queensland University of Technology.
Laboratory test
All participants completed both a laboratory and a field trial. At the initial session,
participants completed an incremental exercise test to exhaustion on a motorized
treadmill. After a brief warm up at a speed of their choice, runners commenced the
incremental test at a speed between 12 and 14km/hr. The treadmill speed was increased by
0.3km/hr each minute while the grade was held constant at 1% to simulate the oxygen
consumption of outdoor running (70). Respiratory gas-exchange data was collected breath
by breath and averaged for every 15 second period using a portable gas analyser (details in
apparatus section) which was calibrated beforehand according to the manufacturer’s
instructions. Heart rate was measured continuously using a single-lead ECG monitor (Alive
Technologies, Australia). Achievement of at least two of the following variables was taken
to indicate that a participant had performed a maximal test: heart rate ± 10 beats per
minute of age-predicted maximum, respiratory exchange ratio > 1.10, and an increase in
oxygen consumption of less than 150mls.min-1 with an increase in workload. Maximum
oxygen consumption (VO2 max) was determined by averaging the four highest successive
15 second values. If a plateau in oxygen uptake was not clearly evident, a supra-maximal
test was performed after an adequate rest period to confirm that the participant’s highest
VO2 had been attained. Maximal oxygen consumption (VO2 max) was defined as the highest
value achieved in either the laboratory or field test. Ventilatory threshold was determined
using the ventilatory equivalent method (10) and velocities at this threshold (vVT) recorded
from the treadmill speed.
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Field test
Within 14 days of their laboratory trial participants completed a field time-trial consisting of
three laps of a 3175m circuit. This was divided into four sections completed in the following
order: level section (765m), uphill (820m), level (770m), downhill (820m). (NB: The
uphill/downhill portion of the course used the same section of road completed in opposite
directions). The initial level section utilised a compacted dirt road which was free of loose
gravel while the other sections consisted of bitumen roads and concrete footpaths. Each
section was further divided into 8 sub-sections of equal distance for subsequent analysis. A
picture and schematic of the course design is provided in Figure 4.1. Gradients for each
subsection for the uphill (in order) were as follows: 6.3%, 9.3%, 11.2%, 6.8%, 11.7%, 10.7%,
1.5%, and 7.8%. Gradients and distances were calculated by reference to topographic
survey data, following the route measured using the GPS receiver.
At the end of the third lap, participants completed an additional level section of 380m. This
section reduced risks to the participant by finishing on a level section rather than a downhill
and minimised the effects of any finishing sprint - as this was likely to include a high
anaerobic component and not be representative of the pacing throughout the remainder of
the trial. Despite small differences in finishing speeds, this section had only a negligible
effect on overall mean speeds (average change: 0.02m/sec or 0.55%), and did not alter the
finishing order of the participants. This section was not included in subsequent analyses.
On laps 2 and 3 participants were provided with a drink stop at the midpoint of the 2nd level
section (following the downhill). As the gas analyser had to be partly unclipped from the
headgear to enable drinking, participants were held stationary for a set 30 second period
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while this took place. Accordingly, data for that sub-section (all variables) and the following
sub-section (HR and VO2 only) have been replaced with estimates through subject-by-
subject linear interpolation from values for the adjacent sections. This correction applied to
either one or two of the 96 sub-sections only and allowed a fully balanced statistical
analysis to be performed.
Participants were asked to adhere to their normal training and dietary schedules between
sessions but to abstain from vigorous exercise, caffeine and alcohol in the preceding 24
hours. All trials were held between 6-7 am to avoid large variations in temperature. To
familiarize each participant with the nature and length of the course, they were driven over
it by car before each trial. Sessions were run as individual trials and runners were given the
explicit goal of trying to minimise their overall time, but were free to select their own
pacing strategy. No watches were worn by participants and no feedback was given so as to
prevent any form of external pacing.
Apparatus
For the field trials, runners were equipped with a GPS receiver, activity monitor and
portable metabolic analyser (described below) to provide physiological, speed and stride
frequency data. Information from the GPS and activity monitor were wirelessly streamed
(Bluetooth TM) to a smart phone (i-mate SP3, i-mate, Dubai) which was attached to the arm
with a Velcro strap while the metabolic analyzer transmitted and logged information to its
own internal memory for subsequent analysis.
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GPS. Each runner wore a cap containing a lightweight, non-differential GPS receiver (GPS-
BT55, Wonde Proud, Taiwan). The GPS receiver was used to provide speed, position and
displacement values once each second and has been previously validated (130).
Activity Monitor. An activity monitor (Alive Technologies, Australia), containing a single lead
ECG recorder and a tri-axial accelerometer, was attached to the participant’s dorsal lumbar
spine with double sided tape. ECG data was collected at 300Hz and R-R intervals used to
determine heart rate. Electrodes were placed as for a standard limb lead II position. The tri-
axial piezo-electric accelerometer (rated to ± 2.4g) concurrently logged body accelerations
in the sagittal, frontal and transverse planes. Acceleration data were sampled at 75Hz and
converted to earth acceleration units (g) based on a prior calibration. Peaks in the vertical
acceleration data were used to detect steps in a manner similar to previous reports for
walking (72, 142) and stride frequencies were subsequently calculated using a custom
program (C++, Microsoft, Redmond, Washington). Direct interpolation from GPS speed data
was then used to derive average stride lengths based on speed and stride frequency.
Metabolic Analyzer
Participants were fitted with a portable metabolic analyzer (K4b2, Cosmed, Italy) which
provided information on oxygen consumption, carbon dioxide production and ventilation.
Values were collected breath by breath and averaged over 15 second intervals.
Data reduction and analysis
Data from the different systems (smart phone and gas analyser) were synchronised using a
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custom program (C++, Microsoft, Redmond, Washington) and converted to a common file
format (Excel 2003, Microsoft, Redmond, Washington). For each of the five dependent
variables (speed, oxygen uptake, heart rate, stride frequency and stride length), mean
values were calculated for each of the 96 sub-sections separately for each runner. These
values were then used for subsequent statistical analyses.
Statistics
A three way repeated measures analysis of variance was used to characterize performance
and determine the effects of the independent variables of gradient, lap and section
(portion of each gradient- divided into 8 equal parts by distance).Tukey’s post-hoc tests and
planned comparisons were used to further examine the dependent variables where
appropriate.
Multiple regression was used to develop prediction equations for self-selected running
speed based on gradient and lap, first at the Group level (i.e. for each of the 96 sub-sections
by averaging across subjects), and then at the individual level (i.e. by predicting speeds of
the whole data-set (96 sub-sections x 8 runners). The Group level analyses facilitated
comparison with the report by Mastroianni et al (84) and removed variance attributable to
individual pacing strategies, while the individual analyses include alternative measures of
physiological capacity obtained in the earlier laboratory testing as predictor variables.
73
Figure 4.1: Overhead picture and schematic showing section length, average gradients
and subsection divisions for one lap of course.
Colours in picture refer to similarly coloured sections in diagram with uphill/downhill
sharing same path completed in opposite directions. NB: Each of the four gradients was
subdivided into eight equal sections. Only one is shown here for illustrative purposes.
74
4.3 Results
Laboratory test
Maximal oxygen consumption (VO2 max) was defined as the highest value achieved in
either the laboratory or field test. These tests yielded the following physiological measures:
VO2 max, 69.8 ± 5.4 mls. kg. min -1; velocity at VO2 max (vVO2 max), 4.87 ± 0.40 m.s -1 (17.5 ±
1.4 km/hr) ; ventilatory threshold (VT), 88.2 ± 6.4 % VO2 max; speed at ventilatory threshold
(vVT), 4.40 ± 0.21 m.s -1 (15.8 ± 0.8 km/hr).
Field test
The results are divided into three parts. First the effect of lap, gradient and section on
group level performance is outlined for each dependent variable. Secondly, the regulation
of speed as a function of gradient is explored through multiple regression analysis, and
finally, individual pacing strategies are outlined. All dependent variables are depicted in
Figure 4.2, together with a profile of the course.
Speed
Speeds varied significantly between both laps and gradients. The lap effect was confined to
lap 1 (820 ± 76 secs), which was run 56 seconds and 60 seconds faster, p < 0.05,
respectively, than laps 2 (876± 74 secs) or 3 (880± 65 secs). Laps 2 and 3 did not differ from
one another (p = 1.0). Runners varied their speed significantly between different gradients,
running 13.8% faster on the downhill and 23.0% slower on the uphill when compared with
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the level sections (p< 0.001). Table 4.2 illustrates mean values as a function of lap and
gradient.
While speed varied across the 8 sub-sections as a main effect (p < 0.001), this can only be
interpreted in light of its significant interaction with gradient (p < 0.001). A strong effect
was a persistence of speed from the preceding gradient. This is most clearly evident on the
two level sections which showed a deceleration following a downhill gradient and an
acceleration following an uphill. This is shown in Figure 4.3. One difference between the
two level sections was that speed stabilised rapidly after a downhill, reaching an asymptote
after just one sub-section, whereas this did not occur until the fourth sub-section after an
uphill. This was confirmed by planned comparisons within each series. Following a
downhill, the first and second subsections were the only two adjacent sections which
differed significantly (p < 0.05). Following an uphill, each of the first three sub-sections
were significantly slower than the last four (p < 0.05). Therefore runners took some time to
adjust their speeds to a new gradient, and this adjustment took much longer after an uphill.
Stride Frequency
Stride frequency was remarkably stable across all sections of the course (Table 4.2). None
of the three independent variables (lap, gradient, sub-section) reached significance as main
effects (p = 0.52, p= 0.08, p= 0.08, respectively). There was, however, a significant
interaction between gradient and sub-section (p<0.001). Runners decreased their cadence
from level to uphill, an effect that became significant only after the first two uphill sub-
sections (uphill sub-sections 1&2 = 86.9 strides/min, subsections 3-8 = 84.7 strides/min,
p<0.001, planned comparison). They maintained this lower cadence throughout the first
half of the following level section, after which it slightly but significantly increased again
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(level after uphill subsections 1-4 = 85.1 strides/min, subsections 5-8 = 85.7 strides/min,
p <.05).
Stride length
In contrast to the relatively stable stride frequency values, it was clear that speed was
predominantly regulated by stride length. Accordingly, changes across laps and gradients
closely mirrored changes in speed. Stride length on lap 1 was longer than lap 2 or lap 3
(p<0.05), while laps 2 and 3 did not differ from one another (p = 1.0). While there were no
difference in stride lengths between the two level sections (p = 0.79), stride lengths were
20.5 % shorter uphill and 16.2% longer downhill when compared with the level (p< 0.05).
Oxygen uptake (VO2)
As with speed, VO2 varied across laps and gradients (Table 4.2). Variation across laps was
primarily due to lap 1 which was higher than either lap 2 or lap 3 (p<0.05) while there was
no difference between oxygen consumption on laps 2 and 3 (p = 0.93). VO2 was significantly
higher uphill and lower downhill compared with level sections (p< 0.05). Relative to
individual thresholds, these values were below VT for both downhill and level sections. On
the uphill sections, runners slightly exceeded VT on lap 1(105.2 ± 13.1%), but reduced
speeds on subsequent laps such that VO2 was in line with individual thresholds on
subsequent uphill sections (97.7 ± 11.5% - Lap 2, 98 ± 9.6%- Lap 3).
Heart rate
All three independent variables (lap, gradient, section) and their interactions had a
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significant effect on heart rate (HR). Values were significantly lower on lap 1 (170 ± 17
bpm), than lap 2 (180 ± 12 bpm) and lap 3 (184 ± 11 bpm; p < 0. 05) as the subject started
from rest. As HR increases only relatively slowly on starting to run, the effects of gradient
can be better appreciated in Lap 2. Analyzed separately, this shows HR averaging 186.1 ±
1.9 bpm uphill, 179.5 ± 2.1 bpm on the level, and 175.5 ± 2.4 bpm downhill.
Prediction of speed
The study in Chapter Four sought to characterise how well running speed can be predicted
from gradient data and lap, using multiple regression analyses. The outcomes of these
regressions are presented in Appendix 5. Group level analyses showed a high adjusted R2
of 0.825 in which gradient was by far the more important term. This value increased to
0.891 when a modified gradient factor was substituted for the gradient of each section.
This took into account the influence of the immediately preceding sub-section gradients on
speed, using a geometric decay function to weight gradients of the current and seven
preceding sub-sections as follows: Modified gradient = (0.5 x g n + 0.25 x gn-1 + 0.125 x gn-2
…+ 0.003906 x g n-7 ) where g = gradient and n = current sub-section. As this modified
gradient improved prediction and can be readily calculated for any course, it was used in
the subsequent individual level regressions. As individual regressions could not account for
differences in pacing strategies, R2 values were slightly lower than Group level predictions
(Appendix 5).
Individual pacing strategies
As stated above; mean speeds were fastest for lap 1, while there was no significant
78
difference between laps 2 and 3 for the group (Table 4.2). Within the group however, there
were large inter-individual differences in pacing strategies adopted across the three laps.
Runners fell into two distinct groups. As seen in Figure 4.4 (top panel), four of the runners
slowed monotonically across the three laps (lap one: 4.10 ± 0.34 m/s, lap two: 3.77 ± 0.33
m/s, lap three: 3.64 ± 0.28 m/s; p< 0.0001). Conversely, the other four runners significantly
increased speeds from lap 2 to lap 3 (3.57 ± 0.36 v 3.72 ± 0.34 m/s; p< 0.05). These
apparently distinct strategies are discussed later. Figure 4.4 (bottom panel) also shows that
individual runners differed considerably in their modulation of pace as a function of
gradient. In general, those who decreased speed more uphill (relative to level speed) ran
faster downhill, and vice versa, and differences in downhill running speed were notably
larger than those for the uphill sections. To gauge the degree to which these differences
may have stemmed from more or less effective energy consumption optimisation, the
range of running speed (downhill – uphill) was correlated with the range of oxygen
consumption (downhill – uphill), expressing all values relative to level. The r of -0.775
suggests that those runners who minimised fluctuations in their oxygen consumption
across the gradients achieved this by varying their speed more (i.e., by running slower on
uphills and faster on downhills).
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Table 4.1 –Demographic and physiological data for participants
Runner Age (yrs) Height (cm) Weight (kg) VO2 Max
(mls.kg-1.min -1)
Best 10000m run in last 12 months (mins)
A 46 182 61.6
65.6 37.0
B 22 185
75.2
66.1
37.0
C 25
174
72.0
75.4
32.9
D 24 192 79.0 64.2 36.1
E 33 177 80.0 68.0 39.2
F 19 177 65.0 76.2 32.8
G 34 168 68.2 66.2 37.7
H 22 176.5 60.4 76.8 37.0
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Table 4.2 – Speed, gait parameters and oxygen consumption across sections
Section/Lap Speed (m/s) Stride frequency (strides/min)
Stride length (m) VO2 (L/min) VO2 (% of VT)
Level 3.83 ± 0.43 86.1 ± 3.0 2.76 ± 0.29
3.81 ± 0.64 89.3 ± 13.8
Uphill 2.95 ± 0.40* 85.2 ± 3.5
2.19 ± 0.28*
4.28 ± 0.51*
100.4 ± 11.9*
Downhill 4.36 ± 0.62*
86.0 ± 3.8
3.20 ± 0.36*
3.38 ± 0.59*
78.9 ± 11.3*
Lap 1 3.88 ± 0.67 85.6 ± 3.5 2.79 ± 0.45 3.98 ± 0.75 92.5 ± 17.4
Lap 2 3.67 ± 0.63** 86.1 ± 3.3 2.68 ± 0.45** 3.75 ± 0.61** 87.2 ± 13.2**
Lap 3 3.68 ± 0.76** 86.0 ± 3.3 2.68 ± 0.51** 3.72 ± 0.63** 88.6 ± 12.8**
Values are means ± SD. VO2, oxygen consumption; VT, ventilatory threshold.
* significantly different compared with level, p < 0.05.
** significantly different compared with Lap 1, p < 0.05.
81
Figure 4.2: Means and standard deviations for speed, kinematics and physiological
variables across three laps of an undulating course. Individual graphs represent (top to
bottom): Speed, stride length, cadence, oxygen consumption, heart rate and course profile.
82
Figure 4.3- Means and standard deviations for speed on level sections following uphill or downhill running.
3
3.2
3.4
3.6
3.8
4
4.2
4.4
4.6
1 2 3 4 5 6 7 8Sub sections
Spee
d (m
.s -1
)
Level after uphillLevel after downhill
* Significantly greater than all other level subsections after downhill, p< 0.05
** Subsections 1-3 after uphill significantly less than subsections 5-8, p< 0.05
*
**
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Figure 4.4- Individual pacing strategies showing relative differences in speeds across
gradients (top panel) and laps (bottom panel). Columns and identifier letters represent
individual runners. In the bottom panel, values for all laps are read from 0.
-8
-4
0
4
8
1 2 3 4 5 6 7 8
Diff
eren
ce fr
om a
vera
ge s
peed
(%
)
Lap 3Lap 2Lap 1
A
B
CD
E
F
G
H
-8
-4
0
4
8
3 5 6 8
Diff
eren
ce fr
om a
vera
ge s
peed
(%
)
Lap 3Lap 2Lap 1
A
B
C
D E
F
G
H
84
4.4 Discussion Walking or running speed has long been considered a key variable to either measure or to
control when studying the physiology of human locomotion, in part because of its strong
association with energy expenditure. Generally, investigators conducting treadmill studies
have been restricted to controlling speed, or both speed and gradient, so that the
corresponding physiological processes are the dependent variables. While this procedure
has been highly informative, it prevents the subject from spontaneously changing speed in
response to changes in gradient (a very small number of studies in which the treadmill’s
speed is changed to match the subject’s preferred speed are exceptions (93, 123)).
Similarly, the overwhelming majority of studies that have specifically examined self-pacing
have used data from track events or experimental trials on flat and level courses, thus
excluding one of the most crucial determinants of speed in undulating terrain, namely
changing gradient. It is largely for these reasons that spontaneous speed regulation in hilly
terrain remains a poorly understood process, as does the concomitant regulation in the gait
cycle, oxygen consumption and other physiological variables.
The current study extends this knowledge in several ways, firstly by characterising the
gradient/speed relationship in more detail than previous studies, secondly by showing how
speed regulation on hills co-varies with physiological measures and aspects of the gait
cycle, and finally, by allowing some new insights into optimal pacing strategies in hilly
terrain.
85
Effects of gradient on running speed
In the only previous study that examined the speed/gradient relationship on an undulating
overground course, running speed was reported to change by 0.034 m.s-1 for every one
percent change in gradient(84) , while in the current study; this figure was substantially
higher at 0.082 m.s-1. This substantially greater influence of gradient was true even when
the raw (not modified) gradient values were used. The reason for the better predictions
obtained by substituting the modified gradient values are addressed in a following section-
a number of possible reasons for the differences between these studies are outlined here:
The runners in the current study were fitter (69.8 ± 5.4 vs. 61.2 ± 6.9 mls. kg. min -1), and
could therefore run about 18% faster on the level than this earlier study (84), but the most
likely reason for this nearly two-and-a-half-fold greater degree of speed change is the
length and order of the various uphill, level and downhill sections in each study. While the
runners in the study by Mastrioanni et al (84) changed between uphill and downhill running
23 times in just under 9 km, runners in the current study made only 11 transitions in 9.5
km, and half of these were between level and uphill or level and downhill rather than
downhill to uphill or vice versa. While runners in the present study were able to attain a
steady state on each gradient, runners in Mastrioanni et al’s (84) study had some more
abrupt transitions (including one steep ascent of 90m in between two downhill sections),
which will have attenuated some of the speed changes.
A similar explanation may underlie the fact that, while Mastrioanni et al (84) reported that
gradient accounted for 40% of the variation in running speed, higher values were found in
the current study, ranging from 65% to 89%, depending on whether individual or group
data is examined. Because gradient transitions represented a smaller proportion of the
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course in our study, running speed was more closely associated with gradient magnitude.
Thus Mastroianni et al’s (84) conclusion that terrain characteristics other than gradient
(such as the nature of the soil and the trail) may be of similar significance to gradient in
determining speed may apply only if gradients change frequently or if the surface
conditions impede gait. However, there are also very clear - though relatively short-lived –
lags in speed changes at these transitions.
Modified gradient, transition effects and lags
A novel finding in the current study was that by substituting for raw gradient values a
modified gradient index that included a diminishing influence of the gradients prior to the
current one, the prediction of speed was further improved. It is likely that this superior
prediction reflects a set of transition and lag effects as runners encounter a change in
gradient. For example, although runners immediately accelerated following an uphill and
slowed after a downhill, the effect of the preceding section persisted and only gradually
diminished across the next section (Figure 4.3). While Staab et al (123) has previously
reported that runners slowed on a 0% treadmill gradient following an uphill of 5% grade,
their use of mean speeds for the two gradients prevented any analysis of the time-course of
this effect. Following the uphill section of 820m (gradient 6.3-11.7%) speeds were
significantly different for each of the first three subsections on the level which
corresponded to a time delay of 78.4 ± 7.0 seconds. As suggested by Staab et al (123), this
lag in returning to the prior level speed is likely to be a result of runners being forced to
recover from the high anaerobic cost of uphill running.
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In addition to finding diminished speeds on level sections after an uphill, the current study
found that speed also remained elevated following a downhill. This decrease in speed
however, was noticeably shorter and was complete by the end of the first subsection (23.6
± 2.2 seconds or approximately 95 metres) for these runners. While a small component of
this higher initial speed may be a simple momentum effect, this is likely to be confined to
only a few seconds. The second phase of slowing probably reflects the gradual return of
oxygen consumption as a limiting factor.
Downhill speeds limited by factors other than oxygen consumption
The ventilatory threshold (VT) has previously been reported to be the strongest
physiological predictor of endurance performance during running on level ground (108).
Accordingly, it seems likely that runners on a hilly course may also adjust their efforts in
response to intrinsic cues in order to prevent exceeding this threshold. Runners in this
study appeared to regulate their efforts in line with their threshold on uphill sections. After
a faster uphill on lap 1 where VO2 averaged ≈ 105% of VT, runners subsequently reduced
speeds such that VO2 was just under VT on the uphill sections of laps 2 and 3.
While this tendency is consistent with a physiological limitation on uphill running speed,
this was not the case on the downhills. Firstly, overall downhill speed was increased
substantially less than uphill speed was reduced– a 13.8% increase compared to a 23%
reduction uphill. Despite this increase, downhill speeds were not limited by physiological
cost as, as oxygen consumption was substantially less than VT (Table 4.2). This suggests that
other factors limited runners’ downhill speeds, confirming findings from earlier laboratory
studies. Minetti et al (94) has previously shown that speed estimates based on energy cost
88
compare favourably with actual performances in uphill races, but overestimate
performance in downhill only competitions. Similarly, Staab et al (123) reported that
runners were unable to run fast enough downhill to completely compensate for their
slower pace uphill. These findings are in contrast to studies on level courses which have
reported that runners spontaneously vary their pace to maintain a relatively constant level
of effort as evidenced by a low variance in heart rates (48, 141). In this study, it was evident
that speeds on downhill sections were not limited by the capacity to use oxygen.
Relative to the individual’s ventilatory threshold, it was also apparent that there was a large
range in the energy expended on the downhill section (equivalent to 64.5- 93.7 % of VT)
showing that while some runners took full advantage of the downhills, others may have
used this section for recovery from preceding sections. A recent study by Baron et al (9) has
proposed that the degree of eccentric muscle loading may also influence pacing strategy.
This may suggest that runners who did not increase speed as much downhill may have
attempted to attenuate the shock of running downhill as an injury prevention mechanism.
As the limiting factors on downhills are thus likely to be biomechanical rather than
physiological, changes in variables such as stride length and stride frequency may represent
some of these constraints on downhill speed.
Effects of gradient on stride length and cadence
While historically, analysis of stride parameters in distance running has often been confined
to the treadmill or restricted to brief durations when conducted outdoors, the recent use of
accelerometry to detect steps now allows the collection and analysis of data over longer
periods and in more natural settings (82). Using this method the mean stride frequency was
89
not found to be significantly different between level, uphill and downhill sections (Table
4.2) with changes in speed primarily regulated by changes in stride length. This confirms
previous studies which have reported a near independence of stride frequency with speed
(29) and gradient (93). Although this finding was generally supported on a broad
comparison between the overall mean for each gradient, analysis at the section level
showed that after the first two sections of the uphill had been completed there was a small
but statistically significant decrease in stride frequency which carried over to the first half
of the subsequent level section.
Despite this small contribution from stride frequency to speed changes in these sections,
speed was still primarily regulated by stride length. While improving speed on downhill
sections offers a potential opportunity for improving performance in hilly races, other
factors may limit the full utilisation of these strategies. It has previously been suggested
that individuals with musculoskeletal injuries may choose to forsake minimising energy cost
in order to select gait parameters which maximize shock attenuation and protect the
injured structures (59). This could also be expected in healthy individuals when running on
downhill gradients, and both normal and shear forces have been shown to rise substantially
(54% and 73% respectively), when running at 3 m/s on a -9% grade compared to the level,
substantially increasing the likelihood of overuse injury (56). Shock attenuation has been
shown to be altered primarily by changes in stride length rather than frequency (87, 88).
The current study, where downhill speeds were not limited by physiological cost, suggests
that on sufficiently steep downhill grades shock attenuation may be a stronger determinant
of preferred stride length (and thus speed) than energy cost even within healthy
individuals.
90
Pacing strategies - lap effects
As shown in Figure 4.4 (bottom panel), runners fell into two clear groups, with half slowing
continuously across the three laps while the other half were able to accelerate from lap 2 to
lap 3. A “positive split” pacing strategy (first half faster than second half) has been shown to
be effective in events lasting less than 2 mins where the accompanying anaerobiosis can be
tolerated for the duration of the event, however, there is no clear consensus as to the
optimal strategy for more prolonged durations (2).
Despite a wealth of literature on pacing in athletic events, studies involving distance
running are scarce with the majority of research dominated by studies of cycling or running
events of less than 2 mins duration (2). Based on studies of swimming and cycling as well as
mathematical modeling, it has been suggested that endurance athletes may benefit most
from a more even distribution of their energy expenditure (44, 128).
Conversely, from the few studies of running, there is evidence that variable pacing may be
more optimal. Billat et al (15) has demonstrated that runners constrained to a constant
pace (on the level) incur a higher physiological cost (↑ VO 2, HR and blood lactate), when
compared with a freely paced run at the same mean speed. Comparison of different pacing
strategies has also shown that running the first 1/3 of a 5km race 3-5% faster than the
mean speed resulted in faster times during a treadmill trial when compared with even
pacing (55). While all of these studies took place on level ground, many athletes engage in
road races which involve positive and negative gradients. As such, speed is likely to vary
naturally in response to changes in terrain, so it is less clear as to how this variation should
be managed so as to optimise performance.
91
Pacing strategies - gradient effects
Our results show large individual variations in pacing with respect to gradient (Figure 4.4
top panel). In general, those runners who varied their pace more over gradients showed
smaller changes in oxygen consumption, and this was proposed to be indicative of a more
effective pacing strategy. Downhill running speed showed particularly wide individual
variation. It is noteworthy that distinct strategies have been observed in downhill running
kinematics (32), attributed to the conflict between the need to attenuate shock and the
requirements of controlling the stability of the head, arms and trunk. Resolving this conflict
in different ways may in part determine why some runners are capable of much faster
downhill running than others.
A final note concerning pacing strategies is that there was little if any relationship between
pacing over the three laps and pacing over the varying gradients, that is, those who
adopted a conservative strategy with respect to laps (minimising lap-to-lap energy
expenditure fluctuations by keeping average speed consistent) did not necessarily do so
over hills (minimising uphill vs. downhill energy expenditure fluctuations by increasing
speed differences on these sections) (Figure 4.4 bottom and top panels). If confirmed in
larger studies this would suggest that different factors can influence pacing at the macro
(whole distance) and micro (component section) levels.
Optimal pacing over a hilly course may thus require a more detailed analysis with strategies
varying throughout to take account of the length, type and gradient of any hills. This study
has shown that runners tended to limit uphill running to a speed which resulted in oxygen
consumption values in line with their ventilatory threshold. Conversely, there was a large
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potential to improve time on downhill sections as runners were not limited by physiological
cost. Despite this, runners may be unable or unwilling to greatly increase speeds on these
sections due to biomechanical or psychological factors already discussed. As reported
earlier, speeds on level sections have been shown to be affected by a preceding uphill or
downhill. In this study speeds on level sections following an uphill were lower than mean
level speeds for almost 80 seconds.
Conversely, while speeds were elevated for a short time on levels after a downhill, the VO2
on these sections was still well below their ventilatory threshold. One possible suggestion
for minimising time on hilly courses may be to balance the time cost of running slightly
slower uphills, with the potential time saving if runners can return to a faster speed on the
level in a shorter time frame. Similarly, runners should take full advantage of running faster
on level sections following a downhill but limit increases to keep VO2 just below their
ventilatory threshold.
Summary
This study is the first to characterise how runners regulate their speeds during a time trial
on a hilly course through the recording of continuous metabolic, kinematic and speed data.
Speed was shown to be strongly predicted using a weighted gradient factor which
accounted for the influence of prior and current gradients. This was supported by findings
on the effect of hills on subsequent level sections where a lag effect on speed persisted for
almost 80 seconds. This research has suggested that these level sections following hills
represent the most likely source of potential improvements for runners wishing to minimise
their overall time in distance races on hilly courses. Future studies should test the feasibility
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of athletes adopting these strategies. The limits on downhill running speed and the
efficiency of various gradient-speed trade-offs on hills also warrant further investigation,
not only to enhance performance, but, more broadly, to understand the optimisation
principles that account for the self-selected choice of running speed in humans.
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5 THE EFFECT OF AN INDIVIDUALISED PACING STRATEGY ON RUNNING PERFORMANCE OVER AN UNDULATING COURSE
5.1 Introduction
As athletes approach the limits of human endurance, scientists and coaches alike seek out
new ways to improve performance. One recent focus of attention has been the selection of
an appropriate pacing strategy (2, 134). As this is only relevant when performance
outcomes are time-based, research has primarily centred on a small group of sports,
including cycling (4, 51, 65), swimming (128, 129), rowing (53, 73) and running (14, 55).
Studies of pacing during running have generally taken one of two different methodological
approaches. The first has utilised a retrospective analysis of pacing from historical data of
noteworthy athletic events (47) or during successful world record attempts (100, 133). The
alternative approach, using experimental interventions to modify pacing, has been scarcer
and generally limited to events of short durations (< 5 minutes) (5, 20, 115). Of the few
studies which have investigated the application of different pacing regimes on events of
longer durations, all have been restricted to level courses such as athletic tracks (15) or
treadmills (55). Although positive and negative gradients are a key feature of courses used
for cycling and road running, the influence of this variable on pacing has only rarely been
investigated in cycling (8, 125) and not at all in distance running.
Manipulations of pacing in running have been further limited by the use of strategies which
only alter speeds at infrequent intervals. These have generally been confined to comparing
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faster (55) and/or slower starts (5) with even paced runs. The runner is then generally
allowed to run freely towards the end of the trial to assess the effectiveness of the prior
strategies, with a successful outcome defined by a faster overall time. Alternatively,
runners have been constrained to a constant pace throughout the trial and the associated
physiological responses compared with a freely paced run (14, 15, 38, 52).
Accordingly, to more closely align pacing to the demands frequently encountered in
outdoor running, a strategy must not only account for the presence of hills, but also use a
micro-level approach, where speeds are adjusted more frequently to account for the length
and grade of hills and transitions between gradients. Accordingly, this study had the
following aims:
1. To test the feasibility of athletes adhering to an imposed strategy such as this.
2. To assess whether this imposed strategy could improve running performance
compared with a self-paced run.
3. To examine the effects of the pacing strategy on the speed-VO2 trade off over hills.
4. To investigate whether the equation developed in Chapter Four could predict speed
as effectively using a different course and group of runners.
5.2 Methods
Participants.
Six healthy, well trained, male distance runners (age 31.2 ± 8.6 years, height 182.5 ± 7.7 cm,
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weight 71.4 ± 8.4 kg) were recruited for this study from local running clubs. All runners had
completed a 10 km race in less than 40 minutes in the previous 12 months (best time: 34.6
± 2.5 minutes). Individual participant data is listed in Table 5.1. Written informed consent
was obtained from all participants and the study was approved by the Human Research
Ethics Committee of the Queensland University of Technology.
Laboratory Trial.
All participants completed one laboratory and three field trials (Figure 5.1-A). The
laboratory session involved an incremental test on a motorised treadmill (Nautilus T718,
Nautilus, U.S.A) to determine the participants VO2 max and ventilatory threshold. Following
a brief warm up at a speed of their choice, participants commenced the test at a speed
between 13.5 and 15.5 km/hr. The treadmill speed was increased by 0.3 km/hr each
minute, while the grade was held constant at 1% as this has been shown to more accurately
reflect the energy cost of outdoor running (70). Pulmonary gas-exchange data was
collected using a breath by breath portable gas analyser (Cosmed K4b2, Cosmed, Rome,
Italy) which was calibrated before each test according to the manufacturer’s instructions.
Heart rate data from the accompanying chest strap was logged into the analyser’s memory
via an attached sensor. Achievement of at least two of the following variables was taken to
indicate that a participant had performed a maximal test: heart rate ± 10 beats per minute
of age-predicted maximum, respiratory exchange ratio > 1.10, and an increase in oxygen
consumption of less than 150 mls.min-1 with an increase in workload. Maximum oxygen
consumption (VO2 max) was determined by averaging the four highest successive 15
second values and was defined as the highest value achieved in either the laboratory or
field test, while ventilatory threshold was determined using the ventilatory equivalent
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method (10).
Field tests.
Each participant completed three field trials within a 3-6 week period. All trials were held in
the early morning hours (0600-0800) to attempt to minimise variations in environmental
conditions. Participants were asked to adhere to their normal training and dietary
schedules between sessions but to abstain from vigorous exercise, caffeine and alcohol in
the preceding 24 hours. Throughout each test, respiratory data was collected using the
same analyser worn in the laboratory, while continuous speed, position and displacement
data was provided by a lightweight, non-differential receiver (GPS-BT55, Wonde Proud,
Taiwan) which was worn within a specially designed pouch fitted to the rear of a cap.
Information from the GPS was wirelessly streamed (Bluetooth TM) to a smart phone (i-
mate SP3, i-mate, Dubai) which was attached to the arm with a Velcro strap.
Participants were driven over the course by car before their initial trial to familiarize them
with the nature and length of the course. The course consisted of four laps of a 2492m m
circuit which was conducted on bitumen roads. Each circuit was divided into four sections
completed in the following order: level section (650 m), uphill (557 m), level (750 m),
downhill (535 m). (NB: The uphill/downhill portion of the course used the same section of
road completed in opposite directions but the downhill section was slightly shorter due to
an earlier entry point following completion of the level section). These four sections were
further subdivided to allow a more frequent delivery of pacing information. The initial level
section consisted of two out and back stretches along a flat, level residential street. In order
to provide convenient locations for delivering pacing feedback, this was divided into four
equal parts with each turnaround point marking the end of a section. For each of the other
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sections (uphill, level after uphill and downhill), the roads were divided into six equal parts
by distance and marked with chalk to enable visual assessment of each sections completion
and the subsequent collection of split times. Gradients for each section for the uphill (in
order) were as follows: 5.1, 7.4, 7.8, 8.0, 11.0 and 9.3 %. Gradients were calculated using
trigonometry based on elevation changes measured with a surveyor’s level and staff and
distances measured by tape and measuring wheel following the route whose overall length
was measured using the GPS receiver.
Pacing Conditions
During the initial trial, runners were given the explicit goal of trying to minimise overall time
but were free to select their own pacing strategy. Trials were run as individual time trials,
no watches were worn by participants and no feedback was given so as to prevent any form
of external pacing. While it is acknowledged that pacing under these conditions is not
purely spontaneous as some degree of regulating intensity must be pre-selected even
before exercise has begun, the term ‘spontaneously paced’ is used to describe this
condition throughout this chapter.
For the second and third field trials, runners were paced for the first three laps according to
two different pacing regimes (Intervention and Control) while maintaining the same overall
time as that for the first three laps in the initial spontaneously paced trial. Runners
completed the fourth lap with no pacing (Figure 5.1-B).
The experimental pacing strategy (Intervention, INT) was based on an earlier study by the
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authors (131) (Chapter Four), which used a modified gradient factor to account for the
effect of the current and prior gradients. This predicted 89% of the variation in speed on an
undulating overground course. As the current study utilised both a different course and a
different group of runners, the authors adjusted the equation in two ways in an effort to
improve its predictive power. Firstly, as a second smaller predictor variable in the original
equation was the number of laps completed, this was recalculated and expressed as
elapsed distance in metres, a measure applicable to any course. Secondly, to better
determine what speeds would be optimal, the authors also recalculated the initial equation
using only those runners who had the lowest variation in energy expenditure as measured
by VO2. The rationale for this adjustment was that an optimal pacing regime would
minimise variations in energy expenditure. By selecting those runners from the preceding
study who had the lowest uphill-downhill oxygen consumption differences (and greatest
uphill-downhill speed differences), it was theorized that a pacing regime would be
instigated that more closely approached an optimal formula. For the two paced conditions,
section times predicted by this model were then proportionately adjusted according to the
split times from the initial spontaneously paced trial. This ensured that compliance with
the pacing strategies would result in the same overall time as in the spontaneous condition.
The alternative pacing strategy (Control, CON) used the original split times recorded by the
runner during the initial spontaneous trial. This condition allowed the effects of providing
pacing feedback to be determined when no actual change from spontaneous pacing for
each runner was required.
To deliver this pacing feedback at regular intervals, runners were provided with their split
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time when each subsection for the paced laps was completed (90-165 m) and instructed to
vary their pace upon receiving this feedback (speed up, slow down or maintain pace) in
order to achieve the desired goal time for the next subsection. Collection of splits and
provision of feedback was managed by a researcher who rode a moped ahead of the
runner. The order of trials was counterbalanced to rule out any learning effects.
Post trial questioning
Following each trial, each runner was questioned as to how easily they found it to adhere to
the pacing strategy. This question was asked specifically for each of the four gradients in
the order in which they were completed. Where runners expressed difficulty in adhering
during a particular gradient, they were further questioned as to their perceptions of
possible contributing factors. Although this information was subjective and anecdotal, all
runners were highly trained and experienced so their comments add potentially useful
insights about adherence to the imposed pacing strategy.
Data reduction and analysis
Data from the GPS and metabolic analyser were synchronised and converted to a common
file format using spreadsheets (Excel 2003, Microsoft, U. S.A). Mean speed and VO2 values
were calculated for each of the 16 gradients for each runner and these values were then
used for subsequent statistical analyses. Breath by breath VO2 data were removed from the
analysis if deemed to be higher or lower than physiologically possible according to the
following criteria: data were deemed too high if more than 10% above the highest 15
second average obtained during the laboratory trial, too low if equivalent to the VO2 of
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running at 7km/hr according to the ACSM metabolic equations (this was 2km slower than
the lowest average speed on any section). In two runners there was also some erroneous
ventilation data (1.2% of total data) due to secreted saliva temporarily impeding the
oscillation of the turbine. This led to a characteristic step-change in readings followed by a
steady return to expected values over a few seconds. These values were identified and
removed with remaining data averaged for the respective sections.
Statistical analysis
The effects of the independent variables of condition (spontaneous (SPON), intervention
(INT) or control (CON)), lap and gradient on speed and VO2 was assessed using a three way
repeated measures analysis of variance. Although the two level sections did not differ in
grade, they were treated as separate gradients for the purpose of analysis as this reflected
the differing effects of the preceding downhill or uphill sections. Tukey post hoc tests and
planned comparisons were further used to examine dependent variables where relevant.
Descriptive statistics were used to report performance differences across conditions and to
explore the effect that pacing regimes had on altering changes in speed and VO2 with
respect to gradient. To categorize and rank overall individual adherence to the pacing
regime, the root mean square error was calculated using the percentage deviation from the
intended goal time at both the gradient and subsection level (refer to Appendix 1 for full
details on assessment of adherence). Finally, multiple regression was used to determine
whether the prediction equation developed in Chapter Four remained valid when applied
to a different course. For all analyses, Statistica Software (Version 7, Statsoft, U.S.A.) was
used and the level of significance was set at p < 0.05.
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Figure 5.1 Experimental Design
A.
LAB SPONT PACED PACED
At least 7 days
B. Schematic of spontaneous and paced field trials
LAP ONE LAP TWO LAP THREE LAP FOUR
UNPACED (SPONTANEOUS)
PACED (CONTROL)
PACED (INTERVENTION)
Paced lap
Unpaced lap
NB. Control pacing matched split times from spontaneous, intervention used times based on prediction equation.
Three lap goal time was equal across trials. Order of paced trials was randomised and counterbalanced
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Figure 5.2: Overhead picture and schematic showing section length, average gradients and subsection divisions for one lap of course
Colours in picture refer to similarly coloured sections in diagram with uphill/downhill sharing same path completed in opposite directions. The downhill is slightly shorter than the uphill due to an earlier exit point following the level section circuit marked in blue.
NB: Each of the four gradients was subdivided into eight equal sections. Only one is shown here for illustrative purposes.
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5.3 Results
Laboratory test
These tests resulted in the following measures of physiological capacity: VO2 max, 69 ± 8.3
mls.kg -1. min -1; ventilatory threshold (VT), 92 ± 3.3 % VO2 max.
Field test
The field results are divided into several sections. Firstly, the effect of condition, lap and
gradient is noted for each dependent variable. Secondly, speed and oxygen consumption
across gradients are compared across conditions. Next, performance outcomes are
presented across the three conditions, while finally individual adherence to the pacing
regime is examined.
Speed
The individual effects of each condition on speeds are outlined in Table 5.2 across both laps
and gradients. Speed was not significantly different between the conditions (p = 0.71) but
did vary significantly across laps (p < 0.001) and gradients (p< 0.001). Averaged across all
conditions, Lap 1 (4.30 ± 0.60 m.s -1) and Lap 2 (4.22 ± 0.58 m.s -1) were both significantly
faster than Lap 3 (4.10 ± 0.60 m.s -1), p< 0.001 and p = 0.04 respectively. Lap 1 was also
significantly faster than Lap 4 (4.17 ± 0.64 m.s -1, p = 0.02), while Laps 1 and 2 did not
significantly differ from one another (p= 0.14).
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As expected, runners ran significantly slower on the uphill (3.48 ± 0.36 m.s -1) and faster on
the downhill (4.80 ± 0.51 m.s -1) than either of the two level sections (p<0.001). The level
after the downhill (4.36 ± 0.30 m.s -1) was faster than the level after the uphill (4.16 ± 0.29
m.s -1), but the difference was not significant (p = 0.12). There was also a significant
interaction between Condition and Gradient (p < 0.001). Speed on the downhill section was
significantly faster on the INT trial (4.95 ± 0.46 m.s -1) compared with either the SPON or
CON trials (4.69 ± 0.48 m.s -1, p = 0.002, 4.75 ± 0.57 m.s -1, p = 0.03 respectively). There was
no significant difference between any of the remaining gradients across the different
conditions.
Oxygen consumption (VO2)
In three of the eighteen trials (one intervention trial and two control trials) oxygen
consumption could not be analyzed due to equipment problems. Accordingly, to extract
more power from the analysis three two way analyses were performed using only those
runners who had complete data in both conditions: SPON with INT (N=5), SPON with CON
(N = 4) and CON with INT (N=3). Table 5.3 shows VO2 data across laps and gradients for
each of the three conditions, while the effect of each dependent variable is summarized
below.
Condition
There was no significant effect of condition on VO2 or any interaction effects involving
condition across any of the analyses (SPON v INT, p = 0.22; SPON v CON, p = 0.95; CON v
INT, p = 0.31).
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Lap
As with condition, there was no main effect of lap on VO2 (SPON v INT, p = 0.10; SPON v
CON, p = 0.87; CON v INT, p = 0.23). There was, however, an interaction between Lap and
Gradient (p < 0.001). Tukey’s post hoc tests showed that this was confined to the VO2 on
the uphill and the following level section (level after uphill) which was higher on lap 1 than
either Lap 3 or Lap 4 (p< 0.01).
Gradient
There was a significant effect of gradient which was apparent in all three two-way analyses
(p< 0.001). While the VO2 did not differ between the downhill and the level after the
downhill, it was significantly higher on the uphill than the level after the uphill, and the VO2
on both these sections was higher than that on the other two gradients (p < 0.05).
Prediction of speed
A secondary result was the confirmation of the use of a modified gradient factor to predict
group level speed. Although gradients and section lengths varied from the earlier course
(131) (Chapter Four), the modified gradient factor coupled with a small weighting to
account for elapsed distance exhibited a consistently high prediction of speed at a group
level: speed = 4.36 - 8.76 (modified gradient) - 0.04 (distance) (r2 = 0.92). (NB: speed
measured in m.s-1, distance in kilometers).
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Speed and VO2 as a function of gradient
Figure 5.3 shows the speed on the uphill and downhill sections expressed as the difference
from the mean level speed for all conditions. The range of uphill to downhill speeds was
significantly larger in the INT condition compared with the SPON trial (p = 0.05). At an
individual level five of the 6 runners increased their range of uphill to downhill speeds on
the INT trial compared with the SPON trial (54 ± 48%, range 33-131%). There was no
difference in this range of speeds between the SPON and CON trials (p = 0.93).
Figure 5.4 illustrates changes in mean VO2 across gradients compared with the level
sections. Unlike speed, the VO2 range was not significantly different between the SPON trial
and either the CON or INT trials (p = 0.41, p = 0.43 respectively).
Performance
Though there was an overall condition by gradient effect on speed, there was no significant
difference in performance between the three conditions at a group level. Performances
were compared in two ways, across the entire course (Figure 5.5) and just the un-paced
component of the two paced trials (lap 4, Figure 5.6). No difference was found between
conditions by either measure; Overall time: SPON: 2401 ± 192 sec, CON: 2381 ± 192 sec,
INT: 2389 ± 180 sec, (p = 0.57), Lap 4 only: SPON: 613 ± 42 sec, CON: 590 ± 43 sec, INT: 606
± 42 sec, (p = 0.22). On an individual basis, the fastest overall times were evenly distributed
across the three conditions (Figure 5.5). Runners B and F ran fastest on the INT trial (3.7%
and 2.0% faster than SPON respectively), A and C ran fastest on CON (2.1% and 1.7% faster
than SPON) while D and E ran fastest on their initial trial (SPON, 1.0% faster than INT (both),
0.2% and 2.5% faster than CON respectively.
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Adherence to the pacing regime
Each runner’s adherence to the prescribed pacing regime was assessed and ranked during
the INT and CON trials using a range of criteria (Appendix 1-table A1.6 and A1.7). Runners B,
C, and F met all the criteria for adherence during the INT trial, while the other runners had
significant departures from the prescribed pacing when assessed at a gradient (Runners D
and E) or section level (Runner A). Conversely during the CON trial, only Runners B, D and F
met all criteria for adherence. For a full description of the selection of assessment criteria,
the reader is referred to Appendix One.
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Table 5.1 –Demographic and physiological data for participants
Runner ID Age (yrs) Height (cm)
Weight (kg)
VO2 Max
(mls.kg-1.min -1)
Best 10000m in last 12 months (mins)
A 44 179 63.0 70.9 35.7
B 32 178 69.7 68.8 33.7
C 20 177 65.8 77.2 31.8
D 22 180 69.4 78.5 32.3
E 34 182 75.9 64.3 35.5
F 35 198 87.9 56.2 38.5
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Table 5.2-Comparison of speed on laps/gradients between conditions
Speed (m.s-1) Spontaneous Control Intervention
Level after Downhill 4.35 ± 0.29 4.35 ± 0.29 4.37 ± 0.33
Uphill 3.53 ± 0.38* 3.53 ± 0.38* 3.38 ± 0.31*
Level after Uphill 4.16 ± 0.28 4.19 ± 0.28 4.12 ± 0.31*
Downhill 4.69 ± 0.48* 4.75 ± 0.57* 4.95 ± 0.46*
Lap 1 4.34 ± 0.59 4.25 ± 0.57 4.32 ± 0.66
Lap 2 4.20 ± 0.52** 4.20 ± 0.57 4.24 ± 0.67
Lap 3 4.09 ± 0.54** 4.11 ± 0.57 4.11 ± 0.69
Lap 4 4.10 ± 0.58** 4.27 ± 0.67 4.15 ± 0.68
Values are means ± SD.
* significantly different compared with level after downhill, p < 0.05.
** significantly different compared with Lap 1, p < 0.05.
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Table 5.3- Comparison of VO2 on laps/gradients between conditions
VO2 (L.min -1) Spontaneous (n=6) Control (n=4) Intervention (n=5)
Level after Downhill 3.62 ± 0.34 3.50 ± 0.26 3.59 ± 0.24
Uphill 4.20 ± 0.41* 4.26 ± 0.28* 4.03 ± 0.32*
Level after Uphill 3.97 ± 0.44* 3.96 ± 0.28* 3.76 ± 0.26
Downhill 3.34 ± 0.35* 3.32 ± 0.25 3.34 ± 0.30
Lap 1 3.82 ± 0.59 3.78 ± 0.52 3.77 ± 0.43
Lap 2 3.77 ± 0.50 3.84 ± 0.47 3.70 ± 0.36
Lap 3 3.77 ± 0.48 3.67 ± 0.45 3.61 ± 0.36
Lap 4 3.77 ± 0.47 3.74 ± 0.40 3.64 ± 0.36
Values are means ± SD. VO2, oxygen consumption.
* significantly different compared with level after downhill, p < 0.05.
NB: VO2 not significantly different compared with Lap 1 on laps 2, 3 or 4 across all conditions.
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Figure 5.3- Speed on uphill/downhill sections expressed as the difference from the mean level speed. Labels refer to individuals ordered from largest to smallest difference between Spontaneous and Intervention
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-25
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35D
iffer
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%)
B F D E C A
DOWNHILL
UPHILL - Spontaneous Trial -Control Trial -Intervention Trial
Figure 5.4-VO2 on uphill/downhill sections expressed as the difference from the mean VO2 on the level. Labels refer to individual runners.
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-10
0
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Diff
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B F D E C A
- Spontaneous Trial -Control Trial -Intervention Trial
DOWNHILL
UPHILL
NB: some individuals only have VO2 data for 2 trials
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Figure 5.5-Total time to complete course across different conditions
Figure 5.6-Time to complete lap 4 as the difference from the spontaneous
trial
-30
-20
-10
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20
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40
50
60
70
Diff
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5.4 Discussion This research represents the first study of overground running to apply an experimental
pacing intervention on a course involving positive and negative gradients. The current
study produced several key findings:
(i) Two of the three runners who adhered to the prescribed pacing intervention (INT)
improved their overall time.
(ii) The pacing intervention (INT) produced a significant condition by gradient effect on
speed in the expected direction, but this was unsuccessful in achieving a more consistent
level of VO2.
(iii) The two runners who exhibited the largest change in the range of uphill to downhill
speeds on the INT trial had the greatest improvements in overall performance.
Effect of the prescribed pacing strategy on speed and performance
The intervention strategy was largely successful in increasing runner’s range of speeds on
hills relative to their mean level speed (Figure 5.3). Five of the six runners increased their
range of speeds by more than 30% while one runner (A) had minimal change (- 4.2 %). To
consider the effectiveness of the prescribed pacing strategy on performance, it is necessary
to consider only those runners who adhered to this prescribed pattern (Appendix One).
Three runners showed a significantly higher level of adherence to the intervention strategy
at both the gradient and subsection level (B, C and F). Two of these three runners (B and F)
consequently achieved their fastest overall time for the four lap course during the
intervention trial (Figure 5.5). A separate analysis of the unpaced fourth lap (Figure 5.6)
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shows that runner B also ran this final lap fastest during the intervention trial (10 % faster
than spontaneous). Runner F ran a faster fourth lap on both paced trials although the
control trial was the faster of the two (4.1 and 6.3 % faster than the spontaneous trial
respectively). Conversely, Atkinson et al (8) has shown during cycling that increasing power
on uphills and decreasing power on downhills improved performance compared with a
constant paced strategy. This can be explained by differences between the two modalities.
Unlike runners, cyclists can increase speeds on downhills even when power is decreased by
using momentum. As a result, cyclists can optimize performance by increasing power on
uphills to minimise lost time in the knowledge that they can achieve a more complete
recovery from these efforts than runners on subsequent downhill sections with no loss in
time.
The other runner who adhered successfully to the prescribed strategy on the INT trial
(Runner C) was unable to improve his performance and recorded a very similar overall time
to his SPON trial (INT trial 0.55 % slower). The reason why this runner was unable to
improve his performance is unclear. While runners B and F experienced the largest changes
in their range of speeds across hills relative to their level speed (131 and 91 % respectively),
runner C improved by a more modest 32%. It is possible that this change was not enough to
have the energy sparing effect required for a performance enhancement.
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Effect of pacing on oxygen consumption
Results of the study in Chapter Four of the spontaneous regulation of speed and oxygen
consumption over hills showed that runners who varied their pace the most as a function of
gradient showed the smallest changes in oxygen consumption. As it was proposed that this
was indicative of a more effective pacing strategy this was used as the basis for the current
study’s pacing regime. The aim of the current study was to see whether runners’ pacing
could be manipulated at frequent intervals to achieve this trade off (i.e. larger speed
changes resulting in a more even distribution of energy expenditure). It was expected that
a successful pacing regime would enable runners to run faster on the final lap when their
speed was unconstrained.
As mentioned earlier, the INT trial was largely successful in increasing the range of speeds
on hills relative to their mean level speed. Conversely, of the five runners who had
complete oxygen consumption data for the SPON and INT trials, only one showed a
substantial change in energy expenditure as a result of the pacing intervention. During the
SPON trial, the VO2 for runner F was + 8.2% on uphills and -14.2% on downhills relative to
the VO2 on the level (5.4). During the INT trial, this variation was halved to + 4.4% on uphills
and -8.2% on downhills respectively. This change in the range of VO2 between uphills and
downhills (-44%) was considerably more than the other four runners who all had less than -
10% variation between the two conditions.
This unexpected finding of an increased range of speeds across uphills and downhills,
without a consistent corresponding decreased range of VO2, could have several
explanations. One aspect of the pacing regime involved increasing the runners’ speeds on
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downhills. However, two runners (D and E) showed significant departures from the
intended paces with relative errors more than double that of the next lowest adherer on
these sections (Appendix A1.3). One commented in post-trial questioning of running
cautiously on downhills due to earlier experiences of “shin splints” from over striding, while
the other mentioned feeling “a decreased feeling of stability and balance” when attempting
to match the faster downhill paces prescribed in this trial. This suggests that for these
runners, conscious strategies, other than optimization of energy expenditure, played a part
in limiting speeds on downhill sections.
For the other two runners, however, it is possible that the speeds prescribed for the
downhill sections were not fast enough or maintained for long enough and therefore could
not minimize the difference between uphill and downhill VO2. This limitation may have
been contributed to by the selected course which used the same section of road (in reverse
order) for the uphill/downhill section. As noted by Swain for cycling (125), this results in
less time spent on downhills than the equivalent uphill section. Though differences are
more marked in cycling, the runners in this study still spent 49% less time on downhill
sections during the intervention trial (158 ± 18 sec uphill, 106 ± 9 sec downhill).
Consequently, any increase in VO2 would need to be larger to account for the decreased
time spent on these sections.
A further reason for the failure to minimise VO2 variance may be the very nature of the
induced pacing regime. A variable pace has been shown to result in a lower physiological
cost than a constant one at the same average speed (15). The reasons for these
spontaneous variations are however, unknown and may be in response to transient
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changes in a range of afferent feedback. While the INT trial attempted to induce a variable
pace, this variation was determined and constrained by the tester rather than allowing the
runner to respond naturally to internal and external stimuli. It has been previously
suggested that accelerations and decelerations, resulting from speed changes, can be
expected to increase the energy cost of running as the extra kinetic energy due to the
acceleration is not recovered in the subsequent deceleration (38). Although pacing
feedback was delivered at relatively small intervals (range: 90-165 m), it is possible that the
additional accelerating and braking needed to make the necessary changes in pace for each
new section of the INT trial was less efficient than the natural spontaneous changes of pace
in the CON trial and may have contributed to unexpected changes in oxygen consumption.
This study initially suggested that a more even distribution of oxygen consumption across
gradients was the potential mechanism by which improvements in performance would be
achieved. The minimal change in oxygen consumption in some runners despite changes in
performance may suggest however that pacing and thus performance is also mediated by
other means. It has been recently suggested that glycogen may play a signaling role where
pace is regulated in response to afferent feedback as to the current level of substrate
availability (110). Palmer et al (106) has previously shown that the use of a variable rather
than a constant intensity, during a cycling study, resulted in a reduction in the utilisation of
total muscle glycogen as well as the number of glycogen depleted type I muscle fibres.
While not measured in this study, a similar mechanism may have operated in this study.
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Conclusion
This study aimed to improve running performance on an undulating course through the
provision of a pacing strategy which accounted for the current and previous gradients and
adjusted pacing at small, frequent intervals. Two of the three runners who adhered to this
pacing regime, and exhibited the largest increase in speeds across gradients, subsequently
ran their fastest overall time in this trial. While acknowledging that the small number of
trials precludes broadly applicable conclusions, this nevertheless suggests that for runners
able to adhere to this strategy improvements in race performances are possible.
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6 GENERAL DISCUSSION
6.1 Introduction This chapter will review the major findings from each of the studies in this thesis and the
implications of these findings will be discussed with relevance to their contribution to the
literature. The methodological processes involved in these studies will then be assessed
together with possible limitations and suggested improvements for future studies. Finally,
recommendations will be given for potential further research in this area.
6.2 Contribution to the literature An examination of the available literature shows that scientific knowledge of the way in
which runners self-regulate speeds and the concomitant changes in gait parameters and
energy cost has been limited by the use of treadmills (93, 123), flat outdoor courses (15, 38,
52) or limited experimental designs and procedures (84) - see Chapter Two. While treadmill
studies have incorporated the use of gradients, they are limited by their artificial
simulations of self-selected speeds, resolution of speed and gradient changes and linear
paths (93, 123). Accordingly, many findings using these methods have not been validated in
field studies. This is essential if conclusions are to be extrapolated to all forms of running.
Conversely, most outdoor studies have excluded gradient, which has precluded any
investigation of the effects of this key variable (15, 38, 141). By contrast, the findings of the
only outdoor study which did examine speed selection over hills had its findings weakened
by the inclusion of numerous abrupt gradient transitions (see 4.4.1 Effects of gradient on
running speed) and the absence of key data such as oxygen consumption, stride frequency
and stride length (84). The experimental design employed in the current studies was
developed in order to overcome many of these limitations. Firstly, the use of recently
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developed portable technology (GPS receiver, portable metabolic analyser, accelerometer),
allowed the collection of continuous speed, metabolic and stride frequency data at a high
sampling rate in an unconstrained natural environment. Secondly, the long, consistent
gradients of the courses employed in the current studies, were chosen to allow a more
accurate characterization of changes in variables as a function of gradient, as well as the
effects of transitions between new gradients. This enabled the extension of previous
research and permitted several new findings. Several of these findings are detailed in the
following section.
GPS - measurement of speed, distance and position
As the studies in Chapters Four and Five focused on the modulation of speed outdoors, the
initial methodological study (Chapter Three) assessed the validity of a non-differential GPS
receiver to provide accurate measurements of speed, distance and position. A high
precision of speed measurement was found using the data based on Doppler shift with 91%
of values within 0.1 m.sec-1 of actual speed on straight paths and 71% on a curved path of
10m radius. In addition, this study provided the first comparison of the alternative method
of speed measurement from differentiated changes in position over time, which proved to
be slightly less accurate. Distance and positional accuracy were also high with only 0.5%
error in linear distance measurements and 99% of values within 2m of a known static
position. While the results of this study allowed a confident utilization of this technology in
the subsequent studies in Chapters Four and Five they also represented the first validation
of a non-differential GPS to measure speeds across the range of human locomotion speeds
since the removal of Selective Availability (see Chapter Three for explanation). As such,
these findings may contribute to the prospect of far wider adoption of this technique in
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studies of human performance in the field as these types of receivers also have clear
advantages to researchers in size, weight and cost over differential GPS receivers.
Uphills and following level sections
Staab et al (123) has previously shown, using a time trial on the treadmill, that speeds on
level sections were slower when preceded by an uphill but only compared mean speeds for
each section. While confirming this also applies outdoors, the study in Chapter Four
extended this finding by characterising the time course of this change, where runners were
found to take approximately 80 seconds to return to their previous speeds on the level. As
suggested by Staab et al (123), a slower speed on the following level section is undoubtedly
due to the need to recover from the high anaerobic cost of running uphill. The consistent
time course found in the study in Chapter Four suggests that runners may be consciously
regulating the magnitude of this anaerobic contribution. Billat et al (16) has suggested that
in middle distance races on level tracks, running speed is controlled by the remaining
anaerobic energy store and that the time to exhaustion at the instantaneous anaerobic
power is held constant by variations in speed. It is possible that runners may also regulate
the intensity of increased efforts on uphill sections against the remaining anaerobic
reserve. Accordingly, too large an incursion on the anaerobic energy stores will result in an
increased delay in returning to prior speeds on the following level while too small an
incursion will result in a loss of time on the uphill section. Runners in this study all
encountered the highest anaerobic cost during the uphill of lap 1 (105 ± 13% VT), but
adjusted efforts on subsequent laps to be more in line with their individual ventilatory
threshold. Understanding the trade-off between anaerobic involvement and the
subsequent time cost in recovery offers some initial insights into the way in which runners
attempt to optimise performance in these conditions.
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Downhills and following level sections
Several treadmill studies have confirmed that downhill speeds do not appear to be limited
by oxygen cost (83, 94, 123). In addition, Staab et al (123) has previously reported that
runners’ self-selected speeds on downhills did not offset the decreased speeds of uphill
sections. These two key findings have not been validated in outdoor studies, with much of
the work in this area focusing on shock attenuation and markers of muscle damage (26, 49,
85, 95). The studies in Chapters Four and Five confirmed that both of these findings were
valid when running freely outdoors but also contributed additional information to the
effects of downhill gradients. For example, there were much greater inter-individual
differences in the amount of effort expended on these sections (range of oxygen
consumption 65-94% of VO2) suggesting that conscious strategies play a role in the
selection of speed on these sections. This finding was confirmed during the pacing
intervention in Chapter Five where the largest deviations from the imposed pacing strategy
were on downhill sections, where some runners were unable or unwilling to increase
speeds to match the intended pace. Feedback from runners in Chapter pointed to
maintenance of stability and the need to attenuate shock as key determinants of
constraining pace on downhill sections. In addition to the decreased speeds following an
uphill, level speeds were also increased on level sections following a downhill, albeit for a
shorter timeframe (≈ 20 seconds). This is the first time that this finding has been measured
and quantified in an outdoor running study. Despite speeds increasing on the preceding
downhill section, oxygen consumption decreased. It is suggested that runners were able to
take advantage of this in the following level section by maintaining this higher speed until
the gradual resumption of oxygen consumption as a limiting factor.
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Prediction of speed
A key finding from the study in Chapter Four which was confirmed in the study from
Chapter Five was an improvement in the prediction of speed as a function of gradient.
Mastroianni et al (84) had previously reported that less than half of speed changes (40%)
were predicted by the current gradient. As noted in Chapter Four, differences in runners’
fitness levels, but more importantly, course design, enabled a substantial improvement in
predictive power. An important novel finding of study two was the use of a modified
gradient factor. As this accounted for transitions between gradients and lags in speed, this
further improved predictions such that the equation developed in Chapter Four explained
89% of the variation in speed on a hilly course. The applicability of this equation was
confirmed in the subsequent study in Chapter Five which found an equally high correlation
(R2 = 0.92) despite using a different group of runners and a course with hills of different
lengths and gradients. This represents an important advancement in increasing the
applicability of such a prediction equation as it recognizes the limits of a simple
mathematical calculation to relate gradient and speed. For example, previous studies which
have developed correlations between gradient and speed (84) have ignored the fact that
the speed on any one gradient is influenced by the effects of the previous section. This
includes the lags in speed that we have noted and quantified following both uphills and
downhills (Chapter Four). Through the use of a modified gradient which took into account
the (diminishing) influence of the immediately preceding sub-section gradients on speed,
this index better represented the actual changes in self-selected speeds noted in the
studies from Chapters Four and Five.
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Stride frequency and Stride length
One aspect that was absent in previous studies of self paced running over hills was an
analysis of the contribution of stride frequency and stride length to variations in speed (84,
123). The study in Chapter Four thus incorporated an analysis of these variables showing
that stride length was the predominantly changed variable of the two, with stride
frequency relatively stable. Although these findings largely confirm previous findings, the
study in Chapter Four was able to make a small but significant contribution to the literature
in this area due to two key improvements in methodology. Firstly, conclusions on changes
as a function of gradient have been derived almost entirely from treadmill studies (91, 92),
thus parameters have been studied at constant speeds set by the researcher rather than
freely selected. Secondly, outdoor studies have been limited to level courses and/or brief
durations thus excluding analysis of any changes which are manifested after extended time
periods, such as those due to fatigue (40, 45, 97, 107, 137). By examining changes in self
selected speeds in an outdoor undulating setting, the findings from Chapter Four confirmed
that stride frequency is consistent and invariant, but also revealed a small but systematic
decrease in the latter parts of uphills and on the following level sections. Sloniger et al (122)
found that muscle activation alters during exhaustive uphill running with an increased use
of lower extremity muscles. It is possible that this small decrease in stride frequency may
thus represent an additional limitation in speed imposed by the neuromuscular system.
Self- pacing
An additional aspect of speed regulation is the selection of different pacing strategies as
this may reflect both conscious and unconscious regulation of speed. While this topic has
been extensively researched in cycling, an examination of the pacing literature in running
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has revealed two key limitations. Firstly, observations of self-pacing have been on
predominantly level courses, thus variation has been largely attributed to differences in
event durations (133). By comparing strategies as a function of both lap (duration) and
gradient, Chapter Four thus allowed some new insights into pacing strategies freely
adopted in hilly terrain. For example, two distinct but different strategies were found with
the runners exhibiting either positive (decreasing speed each lap) or parabolic
(fast/slow/fast) strategies across the three laps. There was also no relationship found
between pacing over laps and pacing over the varying gradients, which suggests that
different factors can influence pacing at the macro (distance) and micro (component
section) levels. In addition, runners who minimized fluctuations in VO2 across gradients
achieved this by varying their speed more as evidenced by the high correlation between
uphill-downhill speed and uphill-downhill oxygen consumption (r = -0.775). This relatively
consistent rate of energy expenditure was suggested to be indicative of a more optimal
pacing strategy and was used as the basis for the intervention strategy tested in Chapter
Five.
Implementation and effectiveness of pacing strategies
The other key limitation noted from the pacing literature was that manipulations of pacing
strategies have only adjusted speeds at infrequent intervals to compare large differences in
time distributions, for example – the effects of altering speeds for the first quarter (20) or
third (55) of the total distance. Combined with the earlier absence of gradient information,
this has failed to account for the effect of transitions between gradients or the subtle
changes due to extended durations. By incorporating both gradients and more frequent
pacing feedback, the study in Chapter Five was the first to include these factors. An
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additional finding presented was the ability of runners to adhere to the imposed strategies
(Appendix One), as the use of treadmills (55, 123), ergometers (3, 51, 65) and level courses
(14, 15) has not required an analysis of this aspect of pacing.
Adherence to a pacing schedule was achieved by half of the involved runners with lack of
adherence predominantly explained by larger errors on downhill sections. Even with
incomplete adherence, the majority of runners (five out of six) showed substantial
increases in the range of uphill-downhill speeds following the intervention trial compared
with the spontaneous trial, but this did not lead to equivalent changes in the variation of
VO2 ,with only one runner decreasing the range across gradients by a significant amount.
While the incomplete adherence restricted analysis of the interventions’ effects, two of
three adherers showed some performance improvements on the INT trial. As these two had
by far the largest changes in their range of uphill-downhill speeds this offers some
preliminary evidence that some runners may improve performance by adopting this
strategy.
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6.3 Limitations and suggested improvements
Familiarisation trials
As suggested by Hampson et al (60), multiple trials are needed to evaluate day to day
variability when attempting to distinguish meaningful differences from pacing
interventions. Using experienced runners and three trials, a low co-efficient of variation in
performance has been shown during treadmill trials on level courses (113, 117).
Accordingly, this research used a homogenous group of runners and included a control trial
which used split times from the spontaneous trial.
The way in which pacing would be accomplished was explained thoroughly to the runners
before each trial. As they had completed the spontaneous trial before the pacing
intervention was imposed they were also familiar with the course. However, it is possible
that the degree of adherence to the imposed pacing strategy may have been improved by
giving runners a practice trial at sub-maximal paces. This would serve two purposes. Firstly
it would familiarize them with the pacing method and secondly, it would allow us to
exclude runners who were unable to make accurate adjustments in pace when not
restricted by physiological or biomechanical limitations.
Control of inter-trial recovery
When evaluating repeatability in performance over hills however, it is possible that inter-
individual and intra-individual differences may exist in recuperation rates from muscle
soreness due to the eccentric loading experienced in downhill running. The effects on
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subsequent trial performance may need to be assessed using measurement of markers of
muscle damage and inflammatory responses (e.g. creatine kinase, interleukin 6). Duration
between trials may thus need to be defined by a return to pre-trial levels of these markers
to ensure inadequate recovery does not overly contribute to differences in performance.
Assessment of psychological factors
Post trial questioning in the current study revealed that conscious regulation may limit
some runners from unduly increasing downhill speeds. Mastroianni et al (84) has noted
that differences in downhill speeds for cyclists may reflect individual differences in risk
tolerance. Thus, it is possible that psychological assessments and pre trial surveys which
detail runners injury histories, degree and amount of training and racing over hills and
normal approaches to running on downhills may provide further understanding of reasons
for inter-individual differences.
6.4 Recommended areas of further research
Explore reasons for differences in individual performance over hills
Staab et al (123) has previously found that the inclusion of an uphill and downhill of equal
gradient and duration resulted in approx 2-3% decrease in overall time compared with a
level course even if net elevation changes were equal. Though a comparison trial was not
conducted over a level course, recent performance times over level courses of equal
distance were recorded for each of the runners in Chapters Four and Five. It was noticeable
that each runner ran between four and seven minutes slower than recent race times
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recorded for the equivalent distance on level courses. This larger difference due to the
presence of hills (approx 12-15%) may be a consequence of the increased grades on the hill
used in the current courses; 8-12% compared with a constant 5% for Staab et al (123) as
well as the physical and psychological effect of carrying the extra monitoring equipment.
Accordingly, future research should attempt to elucidate the reasons for individual
variation in performance on courses involving hills. While ventilatory threshold (108) and
peak speed achieved during incremental treadmill tests (104) have been found to strongly
predict distance running performance on level courses, other factors may contribute to
performance when positive and negative gradients are a feature of courses. Paavolainen et
al (104) noted that VO2 max was found to contribute more to uphill than horizontal running
performance. As changes have been noted in the work performed around different joints
as a runner switches from level to uphill running (112), neuromuscular testing of strength
or endurance in the involved muscle groups may also explain inter-individual differences.
Examine the limits to downhill running speeds
In addition, there was a much larger variation in runners’ speeds on downhill sections in the
studies in Chapters Four and Five compared with other sections. Mercer et al (87) has
previously shown that runners change stride length rather than stride frequency to
attenuate shock when running downhill, while Baron et al (9) has shown that the degree of
eccentric loading influences pacing strategies during downhill sprints. Changes in
kinematics downhill have also been attributed to balancing shock attenuation with stability
of the upper extremities (32). Accordingly, future studies may benefit from including
assessments of eccentric force production and tests of balance and stability to investigate
whether inter-individual differences in downhill speeds may be due to differences in
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neuromuscular factors or motor control rather than cardiovascular capacities. It has been
shown that two brief bouts of downhill training are sufficient to protect against muscle
soreness in a subsequent downhill run (109). Accordingly, it may be beneficial to explore
the effect of incorporating specific downhill training to see if this can assist runners in
taking more advantage of potential improvements on these sections.
Investigate the efficiency of various gradient-speed trade-offs on hills
The studies in Chapters Four and Five assessed the various gradient-speed trade- offs
naturally chosen by runners. The methodology employed resulted in the use of a single
uphill/downhill section rather than a course of multiple hills. The length and relatively
constant grade of the hills used in the current studies thus enabled an improved prediction
of speed as a function of gradient. Future research however should investigate the
efficiency of a range of gradient-speed trade-offs. This could be accomplished in one of two
ways. Firstly, by using hills of varying grade and length to assess how changing these two
variables alters the speed to grade relationship, secondly, using a single grade for uphills
and downhills, numerous combinations of speed changes could be investigated using the
same runners, to evaluate the effect on energy cost, and/or performance in a subsequent
unpaced lap.
Further exploration of pacing strategies over hills
The study in Chapter Four found that runners adopted different pacing strategies at a
macro (lap) and micro (gradient) level, while the study in Chapter Five represents the first
pacing intervention in distance running to incorporate hills. As a result, future research is
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needed to examine these preliminary findings in this area. For example, while the present
study used a fairly homogenous group of runners, a broader description of pacing principles
may be apparent through the use of group comparisons. This could include younger vs.
older runners, males vs. females or comparing runners with widely varying levels of
fitness/ability. The ability to achieve adherence to the imposed pacing strategy limited
subject numbers in the Study in Chapter Five. Accordingly, it may also be advantageous to
revisit pacing in the laboratory setting in future studies to allow the researcher to more
accurately control pacing with larger numbers. This will enable the effect of different
strategies on performance to be gauged before their application is subsequently explored
in a field environment.
6.5 Summary Following the initial validation of a non-differential receiver across the full range of human
locomotion speeds, the second study provided the first characterization of how runners
alter speeds, gait parameters and oxygen consumption when running outdoors over hills.
These findings were subsequently used in the final study to assess the effect of providing an
individualised pacing strategy on running performance on an undulating outdoor course.
The collective findings of these studies suggest that the selection of speeds on hilly courses
requires a more specialized strategy than that previously proposed for running on level
ground. By examining the way in which runners self-regulate efforts in an environment
representative of those encountered in training and racing, the results presented
contribute an important step towards understanding the principles which influence
performance in distance running.
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APPENDIX ONE- Adherence to an imposed pacing strategy
Introduction
Previous experimental pacing studies have only rarely discussed the ability of participants
to adhere to the prescribed strategy (8, 57). A review of the pacing literature shows that
this is primarily due to the exclusive use of ergometers in studies of cycling (3, 51, 65) or
treadmills in running (55) which place limits on how far a participant can stray from the
required speed. Consequently, few studies have mentioned issues of non-adherence in
pacing interventions. Thompson et al (128) found that trained swimmers were able to
follow an even paced strategy more closely than a fast/slow or slow/fast strategy; while
Atkinson et al (8) reported that two of their seven cyclists were unable to fully adhere to a
5% variation in power in parallel with gradient variation. In the very few outdoor pacing
interventions in running, adherence is either not reported (20) or is defined by the ability to
maintain close proximity to a pacing cyclist circling a level track at a set constant pace (15,
38). Ensuring adherence to a pacing strategy which accounts for gradients thus presents a
unique methodological challenge which has never previously been attempted in
experimental pacing studies of running. The challenge of maintaining adherence was thus
twofold: firstly, the ability of the runner to achieve the required intensity and secondly, the
accuracy with which they could make the necessary adjustments to achieve the required
pace.
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Methods
Experimental design
During the first field session, runners ran a solo time trial with the aim of minimizing their
overall time but were free to select their own pacing strategy and were not given any
feedback on times to prevent external pacing. For the second and third field trials, runners
were paced for the first three laps according to two different pacing regimes, Intervention
(INT) and Control (CON), while maintaining the same overall time as that for the first three
laps in the initial spontaneous (SPON) trial. (For a full description of runners, and the course
(including gradients, section lengths and subdivisions for delivery of pacing information) the
reader is referred to Chapter Five)
The specific goal of the pacing was to regulate the runners’ pace at frequent intervals, to
account for both the effect of gradient as well as the gradual changes in speed when
transitioning between new gradients. The inclusion of gradients, the use of a natural
outdoor environment and the use of frequent pace changes (66 in ≈ 7500m) precluded the
use of a “pacing vehicle” in this study. Instead, pacing was managed by informing runners
of their split time when each subsection for the paced laps was completed (90-165 m), a
goal time for the next section (of equal grade and length) and precise instructions to vary
their pace (speed up, slow down or maintain pace) in order to achieve the desired goal time
for the next subsection. A researcher rode a moped ahead of the runner in order to sight
the runner crossing a marked line on the course which designated the end of each section
and split times were recorded manually using a stopwatch mounted on the front of the
vehicle. This enabled the researcher to deliver immediate feedback to the runner on their
split time and goal time for the following section.
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Assessment criteria
A range of criteria were considered to assess the level of individual adherence to the pacing
strategy (Table A1.1 & A1.2). Initially, the root mean square error (RMSE) was determined
based on the percentage deviation from the required time. This was calculated at the level
of gradient and section (part of gradient). In addition to RMSE, two other criteria were also
applied in order to assess adherence more robustly. These are detailed below. Ideally,
adherence scores would be high across the range of such measures.
In order to examine how consistently runners were able to adhere to the strategy across
the course, the proportion of sections and gradients that were within nominated thresholds
were also calculated. As required speed changes were given to runners in whole numbers,
rather than fractional times, the threshold for adherence at a section level was errors of
less than 10% as a lower percentage would result in a classification of non-adherence when
the runner was less than 1 second away from the goal time on the shortest sections (14-15
seconds duration). Individual gradients represented a longer duration (approx 90 seconds
to 3 minutes), thus at this level a more stringent target of 5% error was able to be used as
the criteria against which to measure adherence.
Although the pacing regimes distributed speeds in different manners, they were designed
so that runners still arrived at the end of the paced section (laps 1-3) in the same overall
time. Accordingly, adherence to this overall goal was also assessed. It is important to note
that this could not be used as an exclusive measure of adherence, as a low overall error
could mask large variations from the intended paces for each section. For example, a
participant who ran too fast on some sections and too slow on others could have a low
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overall deviation from the three lap goal, when in fact they had not adhered closely to any
of the goals for the individual gradients and subsections. Accordingly, although indicative of
adherence at a macro-level, a high level of adherence needed to be coupled with
acceptable scores in the other measures.
Statistical Analysis
Errors in pacing were calculated as deviations from the goal time for each gradient and
expressed in relative terms as a percentage of the goal time. These deviations were then
entered into a three way analysis of variance which was used to determine the effects of
the independent variables of condition (INT or CON trial), lap and gradient on group level
adherence to the pacing strategy. To rank individual adherence deviations were assessed at
both the gradient and section (part of gradient) level and the root mean square error
calculated at each level. The percentage of gradients with less than 5% mean error and
sections under 10% were also determined to assess the consistency of pacing errors at a
higher level of resolution.
Results
The adherence results are broken into two parts. First the effect of condition, lap and
gradient is outlined on group level adherence. Next individual adherence is assessed
according to all criteria.
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Group level adherence
There was a significant overall effect of lap and gradient on runners’ adherence to the
imposed pacing strategies. The lap effect was restricted to lap one where mean deviations
from the pacing schedule were significantly larger than laps two or three (lap one: -1.21%,
lap two +0.18%, lap three +0.21%, p < 0.05). Adherence did not differ between laps two and
three (p= 1.00). The gradient effect was confined to the downhill sections, where the mean
error (2.0%) was significantly larger than any of the other three sections (uphill: 0.27%, level
after uphill: 0.88%, level after downhill -0.25%, p < 0.05). Errors did not differ significantly
between any of these three gradients. Group adherence as a function of gradients for each
of the pacing conditions is outlined in Table A1.4. While there was no significant effect of
condition on adherence (p = 0.89), there was a strong interaction effect between condition
and gradient (p < 0.01). This was primarily due to INT downhill where the mean error (3.2%)
was almost double that of any other gradient on either of the two conditions.
Individual adherence
Individual adherence is outlined in Table A1.1 and A1.2 with adherers ordered from highest
to lowest adherence based on the RMSE. Three runners (C, F and B) achieved an acceptable
level of adherence across all criteria for the INT trial (Table A1.1). Conversely, Runner A had
the highest level of errors when analysed at a section level, while the low level of
adherence for Runners D and E was due to a high error rate on downhill sections. There
was also a clear distinction between adherers on the CON trial (Table A1.2) with Runners D,
F and B the only runners to meet all the required criteria.
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Table A1.1- Pacing adherence on Intervention trial using different criteria
(n = refers to number of gradients or sections respectively)
NB: Negative values represent a slower pace than required goal Lap 3 goal time.
Adherence
measure
Root Mean
Square Error (%)
Percentage within 5% (gradient) and 10% (section) of goal time
Overall
3 lap error
Condition/
Runner Gradient Section
Gradients
(n =12)
Sections (n =66)
(%)
C 1.60 3.52 100 98.5 0.19
F 1.96 3.92 100 97 1.12
B 2.63 3.95 91.7 97 1.56
A 2.84 6.79 91.7 80.3 -0.16
D 3.79 5.21 83.3 92.4 -0.29
E 4.22 5.83 83.3 92.4 -1.44
Average 2.84 4.87 91.7 92.9 0.16
SD 1.02 1.29 7.5 6.7 1.07
150
Table A1.2-Pacing adherence on Control trial using different criteria
(n = refers to number of gradients or sections respectively)
NB: Negative values represent a slower pace than required goal Lap 3 goal time.
Adherence
measure
Root Mean
Square Error (%)
Percentage within 5% (gradient) and 10% (section) of goal time
Overall
3 lap error
Condition/
Runner Gradient Section
Gradients
(n =12)
Sections (n =66)
(%)
D 1.64 1.12 100 97 -0.06
F 1.69 3.80 100 97 -0.05
B 1.92 3.72 100 98.5 1.21
A 2.85 5.12 83.3 93.9 1.04
E 2.91 4.89 92 97 -2.60
C 3.03 4.26 83.3 97 -0.68
Average 2.34 3.82 95.8 96.7 -0.19
SD 0.66 1.44 7.00 1.50 1.38
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Table A1.3- Individual pacing adherence across different gradients
C = control condition, I = intervention condition
LD: level after downhill, UP: uphill, LU: level after uphill, DOWN: downhill
NB: Differences represent unsigned errors averaged across laps.
Labels refer to individual runners.
Difference from goal time (%)
Gradient LD UP LU DOWN
Condition C I C I C I C I
A 2.1 3.9 3.0 1.0 1.5 2.3 2.3 2.3
B 1.8 0.9 1.2 4.5 1.7 1.9 2.1 1.4
C 1.9 0.7 3.7 1.4 2.8 1.2 1.8 1.5
D 1.6 1.6 0.7 1.3 0.8 2.7 0.9 6.1
E 2.2 2.0 4.7 1.5 1.9 1.6 1.5 6.8
F 1.9 1.9 1.5 1.3 1.0 2.1 0.9 1.9
152
Table A1.4-Group pacing adherence as a function of gradients
C = control condition, I = intervention condition
LD: level after downhill, UP: uphill, LU: level after uphill, DOWN: downhill
NB: Negative values in mean error represent a slower pace than required goal.
Standard Gradients within
5% of goal (%)
Subsections within
10% of goal (%)
Mean error
(% of goal time)
Gradient C I C I C I
Total 94.4 91.7 96.5 92.7 -0.30 -0.20
LD 100 94.4 95.8 90.3 -0.47 -0.29
UP 83.3 94.4 98.1 97.2 -0.42 1.07
LU 94.4 100.0 99.1 100 -0.32 1.64
DOWN 100 77.8 92.6 82.4 -0.62 -3.20
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Table A1.5- Wet Bulb Globe Temperature for each trial.
Means and standard deviations are shown for conditions (columns) and individual runners
(rows). All values are reported in degrees Celsius
Runner/Condition SPON CON INT Runner
average
A 27.1 27.5 28.8 27.8 ± 0.9
B 24.6 26.0 22.1 24.2 ± 2.0
C 24.0 21.6 26.9 24.2 ± 2.7
D 19.6 20.3 18.0 19.3 ± 1.2
E 19.7 11.1 23.2 18.0 ± 6.2
F 17.0 15.1 16.7 16.3 ± 1.0
Condition average 22.0 ± 3.8 20.3 ± 6.3 22.6 ± 4.8 21.6 ± 4.4
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Table A1.6-Assessment of adherence to pacing by different criteria: INT trial
Runner/Criteria
RMSE
< 4% for section
RMSE < 3% for gradient
90% of sections within 10% of goal time
90% of gradients within 5% of goal time
Overall 3 lap error
< 2%
A
B
C
D
E
F
Table A1.7-Assessment of adherence to pacing by different criteria: CON trial
Runner/Criteria
RMSE
< 4% for section
RMSE < 3% for gradient
90% of sections within 10% of goal time
90% of gradients within 5% of goal time
Overall 3 lap error
< 2%
A
B
C
D
E
F
155
Discussion
The study in Chapter Five imposed two pacing strategies on a group of runners in order to
gauge their effects on performance and the accompanying physiological responses.
Accordingly, a secondary aim of this study was to assess the ability of runners to adhere to
these pacing strategies. The main finding was that adherence was much lower on downhill
sections where runners were instructed to go faster than on equivalent sections on their
SPON trial. There was also much larger individual variation in pacing adherence on the
downhill compared with uphills and level sections.
Adherence lower on downhills
Assessment at a group level, showed no overall effect of condition on adherence to the
pacing strategies. A closer inspection of adherence by gradient, however showed that
adherence on the INT trial was clearly lowest on the downhill sections with a mean error
(3.2%) almost double that of the other gradients and the lowest number of gradients and
subsections completed within 5% and 10% of their respective goals (Table A1.4).
Conversely, during the CON trial, mean errors were consistent across all gradients (range
0.30-0.62%). This may suggest that runners are less able or willing to vary their speeds on
downhill sections according to an alternative pacing regime when compared with level or
uphill sections. It has been shown in an earlier study that spontaneous speeds on downhill
sections had a higher variability between runners than level or uphill sections (131). As
oxygen cost does not limit downhill speed other factors such as a need to minimise impact
shock (87), or maximise stability (32) may determine maximum speeds. Examination of
individual adherence shows that the higher pacing error on the downhill is primarily due to
two runners (D and E) whose mean errors were more than 2.5 times higher than the next
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lowest adherer (Table A1.3). The perceptions of these athletes as to their inability to match
speeds on these sections are addressed further in Chapter Five (see Discussion-effect of
pacing on speed and oxygen consumption).
Control trial adherence
As the CON trial used the runners’ original splits from their SPON trial, it was expected that
adherence would be higher under this condition and any variance would be a combination
of day to day variability and an ability to replicate speed changes. During level track trials,
experienced collegiate runners were shown to match goal speeds more accurately
compared with recreational runners (57). As runners in this study were both highly
experienced and had high levels of fitness (see runner characteristics, chapter Five), this
reduced the possibility that errors would be due to significant errors in adjusting speeds
accurately. Day to day variability has also been shown to be low in experienced runners,
with values of 2.7% (117) and 1.4% (113) reported in spontaneous speeds using manual and
feedback controlled treadmill trials respectively. While the inclusion of gradients hinders
direct comparisons with these values, adherence was shown to be higher on the CON trial
compared with INT for the majority of runners (Tables A1.1& A1.2) with five of six runners
having a lower RMSE at a section level and four of six at a gradient level (with one runner
approximately equal).
Environmental factors
In contrast to the other runners, Runner E was consistently slower than the prescribed split
times for his CON trial, arriving at the end of the three laps with by far the largest deficit in
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time compared to the overall goal (Table A1.2). His inability to match his original split times
may be partly explained by an analysis of daily weather conditions. In addition to the effect
of gradient, environmental factors such as temperature may affect a runner’s ability to
adhere to an imposed strategy. A difference in temperatures between runners was partially
due to seasonal variations in temperatures as trials were conducted from late summer to
late autumn. More important was the variability between the three trials for each runner.
Though assigning trials to the early morning hours (0600 to 0800) minimised inter-trial
temperature fluctuations for most runners, runner E experienced an unseasonably cold day
on the morning of his CON trial compared with his SPON and INT trials (Table A1.5). Post
trial comments from this runner reflected his perceptions of its adverse affects on his speed
and it is possible that this may have contributed to his inability to match his split times from
the original SPON trial.
Conclusion
Adherence to a pacing strategy needs to be assessed relative to the frequency with which
changes in speed are imposed. For the majority of studies, paces have been changed at
relatively infrequent intervals but a reliance on treadmills and ergometers has ensured
adherence, so deviations from goal paces are practically impossible. The current study was
unique to pacing studies of running in that it involved positive and negative gradients and
involved frequent pace changes to account for the effect of gradient transitions and
extended durations. Based on this type of pacing delivery, RMSE was found to provide the
single best indicator of adherence as it assessed adherence continually. Using this index,
individual variation was found in the ability to adhere to the imposed strategy which could
be based on a range of physiological, biomechanical and psychological factors. Adherence
158
may be improved in future studies through preliminary examinations of these factors to
exclude potential non-adherers, and through the development of high precision methods
for providing continuous speed feedback.
159
APPENDIX TWO - Differences in displacement of the GPS receiver at three different locomotion speeds.
Lean angles were 0, 3 and 10.5 ° for walk, run and sprint respectively. Nominal course is
represented by shaded circle.
Run- 3.3 m/s
Sprint- 5.6 m/s
Walk- 1.2m/s
10m
10m
160
APPENDIX THREE - Spatial distribution of GPS positions relative to known geodetic point
-2 -1.5 -1 -0.5 0 0.5 1 0.5
0.9 1.3
1.7
2.1
0
200
400
600
800
1000
Longitude error (m)
Latitude
error
(m)
Num
ber o
f Obs
erva
tions
161
APPENDIX FOUR –Validation studies of GPS and DGPS for speed (A) and distance/position (B) SA = Selective Availability, GPS = non-differential Global Positioning system, DGPS = differential Global Positioning System, WAAS= Wide Area Augmentation System
A. Validation studies of speed during human locomotion
Study Receiver type Sampling Frequency Modality Range of speeds (km/hr)
Speed estimation error (SD unless otherwise stated)
Schutz et al (1997) GPS Not specified Walking 2-6 0.7
Running 6-20 1.1
Cycling 20-40 0.8
Schutz et al (2000) DGPS 0.5 Hz Walking 2.9- 6 0.08 (Δ distance/time); 0.15 (Doppler)
Running 6-25.2 0.11 (Δ distance/time); 0.25 (Doppler)
Larsson et al (2001) DGPS 0.5 Hz
Running 6.6-20.1 Correlation with chronometry (Doppler: r = 0.9996)
Correlation with chronometry (Δ distance: r = 0.9995)
Witte et al (2004) GPS 1 Hz Cycling 3.4 – 38.9 Overall: 45% < 0.2m/sec
Straights 57% < 0.2m/sec
Witte et al (2005) GPS-WAAS enabled 1 Hz Cycling 10-35 Overall 59% < 0.2m/sec
Straights 67% < 0.2m/sec
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B. Validation studies of distance or position
Study Receiver type Sampling Frequency
(Hz)
Modality Distance/position estimation error
Larsson et al (2001) DGPS 0.5 Running Mean error for 115m section: 0.8 ± 2.8m
Static For 2 fixed points (2.13 ± 0.42m, 1.94 ± 0.19m)
Adrados et al (2002) GPS
DGPS
0.0028
0.0033
Static GPS: 78m with SA, 11.9m without SA
DGPS: 11.3m with SA, 5.2m without SA
Rodriguez et al (2005) GPS-WAAS enabled 0.0333 Static 3.02 ± 2.51m
163
APPENDIX FIVE - Summary of regression weightings for group and individual subjects VO2 max, maximal oxygen consumption; VT, ventilatory threshold;
vVO2 max, speed at maximal oxygen consumption; vVT, speed at ventilatory threshold.
* p < 0.001
NB: All individual variables significant, p < 0.001.
Group
Variable Beta B Intercept Adjusted R2 SEE
Gradient -0.898 -8.265 3.948 0.825* 0.239
Lap -0.147 -0.103
Modified gradient -0.934 -9.743 3.979 0.891* 0.189
Lap -0.164 -0.114
Individual
Variable Beta B Intercept Adjusted R2 SEE
Modified gradient -0.765 -9.743 2.340 0.651* 0.411
Lap -0.134 -0.114
VO2 max 0.228 0.024
Modified gradient -0.765 -9.743 2.003 0.656* 0.408
Lap -0.134 -0.114
VT 0.239 0.032
Modified gradient -0.765 -9.743 0.649 0.733* 0.360
Lap -0.134 -0.114
vVO2 max 0.365 0.684
Modified gradient -0.765 -9.743 -1.504 0.721* 0.368
Lap -0.134 -0.114
vVT 0.349 1.247
164
APPENDIX SIX - Circle Earth Formula
Δ displacement = r Δσ
Δσ = arccos (sinΦ1 sinΦ2 + cos Φ1 cos Φ2 cosΔλ). Where Φ1, λ1; Φ2, λ2 are the latitude and
longitude of two points respectively, Δλ the longitude difference, Δσ the angular difference
and r = Earth radius (6378800m)
