RESEARCH ARTICLE

Determinants of preferred ground clearance during swing phase ofhuman walkingAmy R. Wu* and Arthur D. Kuo

ABSTRACTDuring each step of human walking, the swing foot passes close tothe groundwith a small but (usually) non-zero clearance. The foot canoccasionally scuff against the ground, with some risk of stumbling ortripping. The risk might be mitigated simply by lifting the foot higher,but presumably at increased effort, of unknown amount. Perhapsthe normally preferred ground clearance is a trade-off betweencompeting costs, one for lifting the foot higher and one for scuffing it.We tested this by measuring the metabolic energy cost of lifting andscuffing the foot, treating these apparently dissimilar behaviors aspart of a single continuum, where scuffing is a form of negative foot lift.We measured young, healthy adults (N=9) lifting or scuffing the footby various amounts mid-swing during treadmill walking, andobserved substantial costs, each well capable of doubling the netmetabolic rate for normal walking (gross cost minus that for standing).In relative terms, the cost for scuffing increased over twice as steeplyas that for lifting. That relative difference means that the expectedvalue of cost, which takes into account movement variability, occursat a non-zero mean clearance, approximately matching the preferredclearance we observed. Energy cost alone is only a lower bound onthe overall disadvantages of inadvertent ground contact, but it issufficient to show how human behavior may be determined not onlyby the separate costs of different trade-offs but also by movementvariability, which can influence the average cost actually experiencedin practice.

KEY WORDS: Biomechanics, Locomotion, Foot–ground clearance,Metabolic power, Energetic cost

INTRODUCTIONThe foot momentarily passes close to the ground about mid-waythrough each swing phase of walking. It does so with a peak speedover a stride, about three times walking speed (Winter, 1992), thuspresenting a risk of unexpected ground contact and thereforesusceptibility to tripping or stumbling, which are leading causes offalls among older adults (Barrett et al., 2010; Begg and Sparrow,2006). Inadequate foot–ground clearance may also be an issue forpersons with clinical conditions such as drop-foot or weakhamstrings (Cruz and Dhaher, 2009), leading to compensationssuch as hip hiking and swing leg circumduction (Cruz and Dhaher,2009; Kerrigan et al., 2000), which also have negativeconsequences. Even healthy individuals avoid unwanted groundcontact, for example on uneven terrain, by lifting the foot higher

mid-swing (Gates et al., 2012). Greater ground clearance may,however, also come with a cost, such as greater energy expenditure(Voloshina et al., 2013). There may thus be two competing trade-offs: a cost for making inadvertent ground contact (‘scuffing’) andone for lifting the foot mid-swing (‘lifting’). Together, these couldexplain the (non-zero) clearance humans normally prefer. Wetherefore sought to test the trade-offs between lifting the foot higherand allowing it to scuff against ground.

There are several reasons why lifting the foot could be costly(Fig. 1). For an otherwise normal gait, lifting the foot higher entailsgreater potential energy mid-swing, as well as a longer travel pathand thus greater kinetic energy, both entailing more muscular effort.The effort of swinging the leg could potentially be reduced with thehelp of elastic tendons (Kuo, 2002; Doke and Kuo, 2007; Dean andKuo, 2009), but simple walking models indicate that the elasticenergy for improved ground clearance would nevertheless requiremore muscular effort (Dean and Kuo, 2011). In fact, even if themodel is driven largely by passive dynamics and elastic tendons, itwould attain greatest economy if the swing foot could pass throughthe ground without stumbling (Dean and Kuo, 2009, fig. 7). Ofcourse, any model can only suggest how humans mighthypothetically behave. It is therefore important to test whetherlifting the foot higher actually requires more mechanical workperformed by the body, and whether that also increases themetabolic cost.

There are also likely costs to scuffing the ground mid-swing.These go beyond energy expenditure to include less quantifiablecosts such as the consequences of stumbling – for example, recoveryactions needed to maintain balance – and consequences of falling,such as pain and injury. Stumbling and lifting the foot thereforehave categorically different costs, and categorically differentmotions, making it difficult to compare their respective trade-offs.We therefore propose the simplification of treating the motionsalong a single continuum of vertical ground clearance, wherepositive values signify lifting the foot higher and negative valuessignify striking the ground harder (as if the foot could drop throughthe floor unimpeded). As for the costs, a typical optimizationapproach is to consider multiple contributions (e.g. Winters andHelm, 2000), each weighted and summed to yield a single objectivefunction with arbitrary units. A second simplification is that, ratherthan contend with the many costs of scuffing, we measure only themetabolic cost of repeated scuffing, and treat it as a lower bound onthe overall cost of unwanted ground contact. We therefore do notinclude stumbling and falling, which would only add to theincentive for greater ground clearance.

Another factor in the foot’s motion is the notion of risk orvariability (see probability distribution in Fig. 1). If the foot werecontrolled with perfect precision, a ground clearance of zero mightbe optimal, because it would entail no excess effort to lift the foot,while also avoiding scuffing. However, the actual foot motion isvariable from step to step, perhaps due to imperfect motor control,Received 15 January 2016; Accepted 22 July 2016

Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI48109, USA.

*Author for correspondence (amyrwu@umich.edu)

A.R.W., 0000-0002-1801-5716

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and behaves according to a slightly skewed normal distribution (e.g.mean about 1.56 cm, standard deviation about 0.25 cm; Begg et al.,2007). On some terrains, non-smoothness of the ground surface willalso present variability and occasionally cause insufficient groundclearance, and even contribute to a risk of falling (Best and Begg,2008). This can be accounted for with the expected value function(Papoulis and Pillai, 2002), which considers both the probabilitydistribution of the foot’s motion and the costs for various meanclearances, to yield an overall probabilistic cost for groundclearance.Here, we investigated the energetic cost and biomechanical

consequences of foot-to-ground clearance during swing. Wepropose that the preferred foot-to-ground clearance is governed byinteractions between the two hypothesized cost trade-offs of liftingand scuffing the foot, mediated by some probability distribution forthe step-by-step variability of foot motion. As much of gait appearsto be energetically optimal (e.g. Donelan et al., 2001; Doke et al.,2005; Elftman, 1966; Ralston, 1958), the preferred clearance heightmay closely match with the lowest metabolic cost. We expected thatlifting the foot higher should require more muscular effort and comeat greater metabolic cost. We also expected that negative foot lift,meaning greater amounts of scuffing, should require more effort andlead to greater metabolic cost as well. These costs, along with theprobability distribution of foot motion, may explain the preferredground clearance during normal walking.

MATERIALS AND METHODSGround clearance cost modelWe propose two simple models for the cost of lifting the foot and ofscuffing it against ground (Fig. 1). The cost of lifting the footCLH(z) is modeled as increasing with the maximum height z abovethe ground, and the cost of scuffing CSI(z) is modeled as increasingwith the opposite, a virtual negative lift where the foot would passbelow ground if unimpeded. Of course, with the ground as anobstacle, the actual result is a normal ground reaction force (GRF),and hence scuffing, modeled as a proportional drag force. Becausefoot motion is imperfect and exhibits variability, an additionalelement is added to represent the probability distribution pz(w) fordeviations w about a mean ground clearance z. The total, expected

cost for a mean lift height is the probability-weighted sum of thetwo individual costs,

_EðzÞ ¼ð1�1

ððCSIðzþ wÞ þ CLHðzþ wÞÞpzðwÞÞdw; ð1Þ

where _E represents the average metabolic energy expenditure rate,evaluated as the expected value of total cost.

A higher energetic cost is expected for either alternative, liftingthe foot higher or scuffing the foot harder as a function of verticalfoot lift (Eqn 1). The cost of increasingly positive lift z of the swingfoot could minimally be due to thework needed to lift the swing leg,but also include costs for the coordinative responses throughout thebody to produce that motion while maintaining balance and forwardgait. Regardless of the mechanism, the effort of lifting the footmight be such that least effort would be achieved with zero, or evennegative, foot lift, if not for the obstacle posed by the ground.However, in reality, negative lift is not usually achievable becauseof scuffing, which is also expected to be costly. There may bemultiple contributors to that cost, which is nonetheless expected toincrease with more negative lift as a consequence of the drag forceproduced by the ground against the foot, which the human mustcounteract to avoid stumbling. Indeed, any drag impulse must becounteracted with an equal and opposite positive impulse from therest of the body to recover the original walking speed.

We expect that both lifting and scuffing costs should beminimized near zero foot lift z. This alone would imply thathumans should prefer zero foot lift if not for variability of footmotion. Human motions are not perfectly repeatable, as a result ofimperfect motor control, noisy sensors, actuators and neurons, aswell as a number of variations in the surrounding environment. Withsome two-sided probability distribution pz(w) of deviations aboutthe nominal z, the minimum cost should typically be biased awayfrom the steeper of lifting and scuffing costs. Here, we posit that thecost of scuffing is steeper than the cost of lifting, therefore favoringslightly positive nominal foot lift.

The present study represents an extreme simplification of footscuffing. In real life, scuffing is often an unexpected and singularoccurrence, followed by multiple steps for recovery. Instead, weemployed purposeful, continuous scuffing during steady gait,which simplifies experimental control over the amount of scuffing,as well as measurement of the associated biomechanics andenergetics. Continuous scuffing might adequately reproduce theconsequences of relatively light scuffing, which does notnecessarily induce stumbling and recovery. The model (Eqn 1)therefore serves mainly as a conceptual basis for explaining thetrade-offs between lifting and scuffing the foot, rather than anaccurate representation of the complexities of the experimentalmeasurements. The main purpose here was to test and quantify thehypothesized costs of lifting and scuffing.

ExperimentWemeasured the costs of walking at different foot clearance heightsperformed by young, healthy adults. We used real-time visualfeedback to enforce varying amounts of foot lift and scuffing duringtreadmill walking. We measured metabolic energy expenditure asthe cost, and also characterized the associated gait kinematics andkinetics. Foot lift was measured relative to the ground, andadditionally characterized by the overall mechanical workperformed on the body center of mass (COM) and by the joints,while scuffing was characterized by the horizontal impulse (time-integral of fore–aft force) produced by the foot against the ground

Minimum

Expected cost

Foot liftFoot scuff

Cost o

f liftin

g

Normal

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Cost of scuffing

Mean

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Fig. 1. Proposed cost of ground clearance, in terms of metabolic power,including separate contributions for scuffing the foot on the ground andfor lifting the foot higher. Here, clearance is treated as if there were a singlerange of positive to negative foot lift, the latter causing foot scuff. The expectedcost is the sum of these contributions, mediated by variability of foot motion,described by a probability distribution function (inset) about amean foot lift. If thecost of scuffing is steeper than the cost of lifting near the origin, the average footlift with least cost should be positive, thus favoring non-zero average foot lift.

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surface mid-swing (75–100% of stride, defined as starting fromheel-strike). Eight subjects (N=8, 1 female, 7 male) walked atvarying levels of ground clearance during leg swing at a constantspeed of 1.25 m s−1 on an instrumented treadmill. Subjects walkednormally and with three levels of foot lifting and three levels ofscuffing during the swing phase of walking (Fig. 2). The thresholds,termed low, medium and high, to achieve during swing were 0.1, 0.2and 0.3 m for foot lift and 100, 200 and 300 N for scuff force. Liftthresholds were measured from the treadmill surface, and scuff forcewas defined as horizontal force produced by the foot, measured asthe drag GRFmid-swing. One subject’s scuffing datawere excludedbecause the scuff continued smoothly into heel-strike, making theimpulse indistinguishable from normal heel contact. Subjectsreceived visual feedback of toe marker height during foot liftconditions and fore–aft GRF during scuffing conditions. In eachcase, these were displayed in real time along with a target thresholdfor either scuff force or lift height. Trials were performed inrandomized order, and were 6 min in duration. Subjects’ age rangedfrom 18 to 29 years, and their body mass M was 73.8±11.1 kg(mean±s.d.) and leg length L was 0.93±0.05 m. All subjectsprovided written informed consent prior to the study, according toInstitutional Review Board procedures.Wemeasured metabolic power and gait mechanics using standard

procedures. Net metabolic rate (in W) was estimated from the rate ofoxygen consumption and carbon dioxide production using standardconversion factors (Brockway, 1987). Steady-state metabolic powerwas averaged over the last 2 min of each 6 min trial, and the rate forquiet standing (99.2±17.1 W, 0.0467±0.0123 dimensionless) wassubtracted from the gross rate to yield net metabolic power.Kinematic and kinetic data were also recorded over the same timewith motion capture (PhaseSpace, San Leandro, CA, USA), using astandard 24-marker set (Zelik and Kuo, 2010). Foot lift wasmeasured from the vertical height of the toe marker (fifthmetatarsal) during swing, relative to its height during quietstanding. The marker can exhibit one or two peaks – in particular,one peak when the foot is lifted – and so lift height zLH was definedas the first peak height after toe-off (Fig. 3D). For normal walking,we also measured the distribution of the minimum clearance(between the two peaks), as an indicator of pz(w). Scuffing wasmeasured and characterized by the scuff impulse F̂SI, defined as theintegral of drag force (aft GRF) during the swing phase (Fig. 3C),normally zero when there is no scuffing. As a point of comparison,we calculated the average total horizontal impulse generated perstride for normal walking (26.2±4.32 N s), which was many timesgreater than the scuff impulses induced experimentally. We alsomeasured the rate of work performed on the COM, termedinstantaneous COM work rate (Donelan et al., 2002), computedas the inner product of the GRFs of each leg and the COM velocity.Standard kinematics and inverse dynamics procedures (Visual3D,

C-Motion, Germantown, MD, USA) yielded ankle, knee and hipangles, and joint moments and powers. As a simple summary ofjoint actions, we defined summed joint power as the net power fromankle, knee and hip of one leg at each point in the stride. Thepositive intervals of COM work rate and summed joint powerduring a stride were integrated to yield positive COM work andsummed joint work per stride. Average positive COM and summedjoint work rates for both sides of the body were calculated from thecorresponding positive work per stride by dividing by stride timeand multiplying by 2. The same computation was performed fornegative work rates. Finally, step lengths and widths were alsocomputed, along with root-mean-square variabilities, for each trial.

We expected that the increasing levels of each condition wouldaffect the corresponding measure and metabolic cost. Thus, scuffimpulsewas expected to increasewith the amount of scuffing, and liftheight with the amount of foot lifting. We also tested for simplerelationships between these measures and metabolic rate. Forscuffing, we expected its metabolic cost to be an odd function ofscuff impulse F̂SI, meaning the cost should decrease as scuffingapproaches zero and would continue to decrease past the origin if anegative (i.e. assistive) drag force were possible. We thereforeperformed a linear fit between scuff impulse F̂SI and net metabolicrate. For foot lift, it was less clear how it should determine energeticcost, and so we tested for net metabolic rate increasing both linearlyand quadratically with lift height zLH. Fits were performed for all ofthe data from each condition simultaneously, allowing each subject tohave an individual constant offset. Statistical tests were performed onthe coefficients, with a significance level of α=0.05. The effect ofeach condition on corresponding measures (F̂SI and zLH) was alsotested (ANOVA followed by post hoc t-tests with Holm–Sidakcorrection for multiple comparisons; Glantz, 2005).

To facilitate comparison between the relative costs of scuffingand lifting, we devised a scaling factor to translate between the two.Scaling foot lift zLH to scuff impulse F̂SI requires a transformationfrom units of distance to units of momentum.We defined the scalingfactor mfg/vf, where g is acceleration due to gravity, and mf is themass of the lower leg and vf is its speed, approximated as 16.1% ofbody mass M (Winter, 2004) and 3.75 m s−1 (three times walkingspeed; Winter, 1992), respectively. This may be interpreted astransforming the gravitational potential energy of the lifted foot andlower leg into work as the foot is scuffed against the ground. Suchscaling is used to examine the relative metabolic costs of scuffingand lifting, where scuffing and lifting are plotted opposite each otheron a common, scaled axis. This allows the costs to be compared interms of the slope of metabolic rate versus either scuffing or lifting.

Dimensionless measurements are reported here, using the baseunits of body mass M, standing leg length L and gravitationalacceleration g. Force was non-dimensionalized by Mg (mean723.6 N), moment and work by MgL (mean 670.8 N m), power

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Fig. 2. Experimental set-up. Subjects (N=8)walked with varying levels of foot lift and scuffforce on a split-belt treadmill at 1.25 m s−1.During scuffing conditions (left), subjects wereasked to produce a drag force against the ground(aft ground reaction force, GRF, plotted in thepositive direction) during swing phase walking,indicated by two target thresholds, one for eachfoot. In the foot lift conditions (right), they wereasked to clear a target threshold for the height ofthe lateral toe marker. Visual feedback of bothreal-time data and thresholds was projected ontoa screen visible to the subject.

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by Mg1.5L0.5(mean 2182 W), step length and width by L (mean0.9265 m), and step time by

ffiffiffiffiffiffiffiffiL=g

p(mean 0.3072 s).

RESULTSWe found each of the experimental conditions to yield varyinglevels of scuff impulse or lift height (Fig. 3). The conditions alsoresulted in substantial changes in metabolic energy expenditure, aswell as alterations to gait biomechanics. Net metabolic rateincreased substantially within the range of conditions, to about1.9 and 2.3 times the normal expenditure rate for scuff and foot lift,respectively. The increase was less steep for increasing lift height(treated as a continuous variable), than for increasing scuff impulse.Positive and negative joint and COM work rate also increased withgreater foot lift. In contrast, foot scuffing had less obvious effects onbiomechanical measures despite its relatively high energetic cost.Significant changes resulted from each of the discrete walking

conditions for foot scuffing and lifting (Fig. 3, Table 1). These wereobservable in the form of aft-directed GRFs for scuffing and higherfoot trajectories for lifting, summarized by significant changes inscuff impulse F̂SI and lift height zLH, respectively (all P<0.05). Thescuffing conditions resulted in aft-directed impulses up to 2.13±0.46 N s for the high condition, equivalent to about 8.6% the aft-directed impulse for an entire normal stride. The lifting conditions

resulted in heights about 1.62 to 3.41 times greater than the normallift of 0.0886 m, referring to the first peaks in toe clearance.

As expected, the preferred, normal lift height approximatelycoincided with minimummetabolic cost (Fig. 4). Net metabolic rateincreased with a greater magnitude of lift height or scuff impulse,treating the two measures as continuous variables (see Table 2).There was an approximately linear trend for scuff impulse, withslope −7.03±1.99 (metabolic rate per unit impulse, mean±95%confidence interval, CI) and offset 0.088±0.0316 (mean±s.d.,equivalent to about −69.0 W N−1 s−1 and 183 W, respectively),with R2=0.747 (P=3.95e−7). With the aforementioned scalingfactor to convert scuff impulse to negative height, this slope isequivalent to −0.9097±0.2571. There was also a significant trendfor lift height with quadratic coefficient 0.9876±0.2363 and offset0.0877±0.0409 (equivalent to about 2517 W m−2 and 185 W,respectively), with R2=0.77 (P=1.10e−8). Alternatively, applying alinear rather than quadratic fit for lift height, the trend remainedsignificant, with linear coefficient 0.4395±0.0928 (metabolic rateper unit lift height) and offset 0.0472±0.0410, with R2=0.8116(P=1.12e−9), with approximately half the steepness of theanalogous slope for scuffing (0.9097 after scaling to metabolicrate per negative lift height). Thus, the cost of scuffing was farsteeper than that for lifting, regardless of the fitting method. As a

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Fig. 3. Measures of foot scuffing and lifting observed in experimental conditions. (A) Foot scuff GRFs. Fore–aft GRFs versus time in gait cycle (% of fullstride starting from heel-strike) from a representative subject indicate greater drag (aft) force achieved from low to high scuff threshold levels (rectangle). (B) Footlift swing trajectories. Fore–aft and vertical trajectory of the lateral toe marker from a representative subject for various lift height thresholds from the treadmill.(C,D) Mean ground clearance levels across subjects measured through (C) scuff impulse (N=7) and (D) lift height (N=8). All levels of ground clearance weresignificantly different from normal (*P<0.05). Left-hand axes are dimensionless, using body mass, leg length and gravitational acceleration as base units; SI unitsare given in the right-hand axes. Bars denote means across subjects and error bars denote s.d.

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simple indicator of magnitude, dragging the foot with 11% of thenormal stance phase ground reaction impulse caused anapproximate doubling of metabolic cost. A similar doubling ofcost resulted from lifting the foot about 23 cm higher than normal.Minimum clearance during normal walking, as measured from thetrough of the marker trajectory, was 0.0157±0.0046 m (mean±s.d.).The major costs above were associated with relatively minor

changes in step parameters for foot lift, and even smaller changes forscuffing (Table 2). Subjects exhibited slightly longer step length,step width, and step period and shorter double support duration withincreasing lift height (for each 1 m additional lift: 0.53 m longer,0.17 m wider, and 0.43 s more time, and −0.11 s more time; allP<0.05). There were also small increases in step length and widthRMS variability (0.0504 m and 0.0588 m per 1 m lift, respectively,P<0.05). However, the only changes in step parameters for scuffingwere slightly increased step width and step length variability(−0.0093 m and −0.0036 m per 1 N s additional scuff impulse,respectively, P<0.05).The effects of foot lifting and scuffing were somewhat more

evident in the mechanics of walking, particularly for lifting.Qualitatively examining force and power trajectories (Fig. 5),

greater foot lift appeared to magnify the first peak of the verticalGRF, the positive and negative peaks of the fore–aft GRF, and themagnitudes of COM and summed joint power. In contrast, scuffingseemed to have much less effect, perhaps slightly reducing thesecond peak of the vertical GRF and push-off power (see Fig. 3 forrepresentative data, and Fig. 5 for across-subject average data). Interms of joint kinematics (Fig. 6), lifting the foot appeared to requiremore flexion in the knee and hip during swing, while scuffingproduced relatively minor changes. Lift height also producedchanges in joint power while only ankle push-off seemed to reducefor scuffing.

These observations are supported by quantitative differences inthe work performed by the body (see Fig. 7). Scuffing resulted inonly minor or non-significant changes in average work rates on theCOM and by the summed joints, whereas foot lifting resulted inmuch greater and significant increases in work (see Table 2 fordetails and individual joint results). In particular, greater foot liftentailed more positive and negative work on the COM and by thejoints, particularly the ankle and knee for positive work, and hip fornegative work.

DISCUSSIONWe hypothesized that humans compromise between the additionaleffort to lift the foot higher during swing, and that associated withscuffing of the foot on the ground. We found both types ofdeviations to be energetically more costly than the normal swing,with scuffing particularly sensitive to even small amounts ofcontact. These costs could in part explain the preferred groundclearance, if movement variability is also taken into account. This isbecause the average cost of clearing the ground by a nominal andpositive amount can also depend on relatively infrequent but costlyscuffing. Another aspect of this study is the treatment of twodissimilar options, lifting versus scuffing the foot, in a continuousfashion. We next consider the implications of this approach, forexamining not only limb swing but also more general movements.

One notable finding was that the costs of scuffing or lifting thefoot can be quite high (Fig. 4). Within the range of conditionsconsidered, both were well capable of doubling the normal netmetabolic rate. In the case of foot lifting, the cost is partiallyattributable to mechanical work, as indicated by two measures:work performed on the body COM (which the swing leg contributesto) and work performed by the lower extremity joints (Fig. 7 andTable 2). Work is needed to lift the leg, direct it on a longer path, andslow its descent as it nears the ground (Fig. 3) with each swingphase. It also appears that other adjustments take place throughoutthe stride, including a greater overall amplitude of COM power andsummed joint power (Fig. 5). The apparently simple act of raisingthe swing foot therefore entails a coordinated action affecting theentire stride. The same is true for scuffing, albeit more subtly, with

Table 1. Effects of experimental conditions

Lift height (zLH) Scuff impulse (F̂SI) Net metabolic rate

SI Dimensionless SI Dimensionless SI Dimensionless

Normal 0.0886±0.0146 0.0956±0.0144 0.0273±0.0518 −1.264e−4±2.417e−4 176.93±32.357 0.0833±0.0228Lift low 0.1436±0.0293* 0.1553±0.0325* −0.0565±0.0557 −2.462e−4±2.385e−4 254.96±67.680* 0.1204±0.0399*Lift medium 0.2236±0.0147* 0.2416±0.0150* −0.0320±0.1335 −8.451e−5±6.874e−8 325.08±94.062* 0.1527±0.0503*Lift high 0.3018±0.0330* 0.3259±0.0321* −0.1044±0.1371 −4.490e−4±5.833e−4 411.27±114.818* 0.1920±0.0572*Scuff low 0.0823±0.0154 0.0888±0.0154 0.7736±0.2669* 0.0037±0.0016* 223.27±66.037* 0.1074±0.0313*Scuff medium 0.0861±0.0185 0.0861±0.0185 1.4229±0.3006* 0.0067±0.0015* 290.30±64.790* 0.1394±0.0314*Scuff high 0.0804±0.0219 0.0867±0.0231 2.1282±0.4629* 0.0102±0.0033* 339.34±88.586* 0.1650±0.0503*

Lift height, scuff impulse and net metabolic rate are given in both dimensional SI units and dimensionless form (means±s.d.). Asterisks indicate statisticalsignificance versus normal swing values (P<0.05).

0−0.02 0.2 0.4Scuff impulse Lift height

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Fig. 4. Net metabolic cost as a function of measured scuff impulse and liftheight.Netmetabolic rate increased with greater scuff impulse (N=7) at a rate of−69.0 W N−1 s−1 (R2=0.75, P<0.05) and with greater lift height (N=8) at2517 W m−2 (R2=0.77, P<0.05). The distribution of minimum toe clearanceduring swing indicates movement variability during normal walking. Differentcolors denote each subjects’ data (squares for scuffing, circles for foot lift). Netmetabolic rate for normal walking is also indicated (dashed line), defined asgrossmetabolic rateminus quiet standing rate.Metabolic rate, scuff impulse andlift height are shown in dimensionless units, using body mass, leg length andgravitational acceleration as base units; equivalent SI units are also indicated.

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force imparted on the ground through the swing knee and hip(Fig. 6, Table 2). However, this had only a modest effect on overallwork rates (small or non-significant effects, Fig. 7), suggesting thatscuffing is primarily an action peripheral to the COM, perhapsaccompanied by additional coordination throughout the body andpotentially observable at the muscle level. In fact, both lifting andscuffing appear to entail a complex series of compensations that aredifficult to predict and subtle to measure. It would be challenging topredict a more than doubling of metabolic cost from gait analysismeasurements alone. The gait analysis presented here thereforeserves mainly to illustrate possible indicators of the increasedenergetic cost, rather than being a comprehensive explanation.

During normal walking, the foot does not undergo the extremesof lifting or scuffing, but rather clears the ground with a small andusually positive amount. Although the experiment entailed largeextremes, these were intended to reveal continuous trends inmetabolic cost from discrete experimental conditions. Theindividual costs for lifting and scuffing are difficult to separatefrom one another near zero ground clearance, and so thesurrounding trends were used to extrapolate the costs close to thatboundary. Here, it is evident that, even though the energetic costswere only slightly elevated above normal, they increased moresharply with scuffing than with lifting. These relative sensitivitiesare proposed to determine the optimum clearance, mediated by the

Table 2. Quantitative results for fits to metabolic rate, step parameters, and work and work rate as a function of lift height and scuff impulse

Lift height (zLH) Scuff impulse (F̂SI)

Slope (mean±CI) Offset (mean ±s.d.) R2 P Slope (mean±CI) Offset (mean ±s.d.) R2 P

Net metabolic rate (quadratic fitcoefficient)

0.9876±0.2363 0.0877±0.0409 0.7707 1.1e−8* – – – –

Net metabolic rate (linear fit) 0.4395±0.0928 0.0472±0.0410 0.8116 1.1e−9* −7.0288±1.9864 0.0881±0.0316 0.7475 4.0e−7*Step length 0.5319±0.1585 0.7032±0.0580 0.6837 4.5e−7* −1.0911±3.0302 0.7479±0.0576 0.0297 0.46Step width 0.1733±0.0823 0.1532±0.0215 0.4598 2.3e−4* −2.1181±1.0521 0.1663±0.0248 0.4893 4.4e−4*Step length RMS 0.0504±0.0205 0.0148±0.0083 0.5367 3.8e−5* −0.8175±0.6207 0.0218±0.0079 0.2908 0.012*Step width RMS 0.0588±0.0196 0.0181±0.0070 0.6338 2.4e−6* −0.2118±0.4866 0.0238±0.0065 0.0428 0.37Step period 1.2822±0.3793 1.6959±0.1539 0.6869 4.0e−7* −2.6384±7.2691 1.8043±0.1548 0.0302 0.46Double support duration −0.3217±0.0890 0.5539±0.0203 0.7148 1.3e−7* 0.3518±2.0775 0.5432±0.0147 0.0067 0.73COM work (pos.) 0.1178±0.0239 0.0200±0.0076 0.8231 5.4e−10* 0.0850±0.2843 0.0325±0.0068 0.0207 0.54COM work (neg.) −0.1518±0.0239 −0.0248±0.0080 0.8854 3.6e−12* −0.3095±0.3977 −0.0390±0.0108 0.1252 0.12COM work rate (pos.) 0.0448±0.0076 0.0131±0.0041 0.8685 1.8e−11* 0.0874±0.1214 0.0181±0.0038 0.1093 0.15COM work rate (neg.) −0.0585±0.0078 −0.0164±0.0053 0.9151 1.1e−13* −0.2079±0.1955 −0.0217±0.0065 0.2110 0.038*Joint work (pos.) 0.2018±0.0394 0.0358±0.0136 0.8344 2.5e−10* −0.7226±0.4046 0.0587±0.0056 0.4299 0.0013*Joint work (neg.) −0.1335±0.0236 −0.0276±0.0079 0.8601 3.6e−11* 0.1598±0.4520 −0.0408±0.0115 0.0287 0.4693Joint work rate (pos.) 0.0802±0.0217 0.0230±0.0096 0.7241 9.2e−8* −0.3471±0.1585 0.0326±0.0041 0.5315 1.9e−4*Joint work rate (neg.) 0.0501±0.0084 −0.0176±0.0049 0.8719 1.3e−11* 0.0530±0.2150 −0.0226±0.0068 0.0142 0.61Ankle work (pos.) 0.0659±0.0271 0.0258±0.0095 0.5321 4.3e−5* 0.4780±0.5282 0.0335±0.0102 0.1622 0.0737Ankle work (neg.) −0.0272±0.0107 −0.0125±0.0043 0.5512 2.6e−5* 0.2016±0.2246 −0.0157±0.0037 0.1600 0.0759Knee work (pos.) 0.1053±0.0160 0.0059±0.0098 0.8933 1.6e−12* −0.5130±0.3447 0.0177±0.0084 0.3436 0.0056*Knee work (neg.) −0.0479±0.0197 −0.0264±0.0030 0.5305 4.4e−5* 0.2234±0.3180 −0.0299±0.0053 0.1045 0.1583Hip work (pos.) 0.0438±0.0349 0.0209±0.0144 0.2323 0.016* −1.3926±0.4001 0.0247±0.0086 0.7412 5.0e−7*Hip work (neg.) −0.0717±0.0180 −0.0054±0.0101 0.7534 2.5e−8* 0.4399±0.2541 −0.0125±0.0083 0.4147 0.0017*

Fit parameters include trend value (means±95% confidence interval, CI) and offsets (means±s.d.) and are linear unless otherwise noted. R2 values indicategoodness of fit, and P-values indicate statistical significance of the trend (*P<0.05). Quantities are reported in dimensionless form, with body mass, gravitationalacceleration and leg length as base variables. RMS, root mean square; pos., positive; neg., negative.

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Fig. 5. Force and power measures versus time withingait cycle for varying levels of ground clearance.(A) Vertical and (B) fore–aft GRF, (C) center of mass (COM)power and (D) summed joint power from the sum of ankle,knee and hip power from one leg. More qualitative changesare observed in lift conditions than in scuff conditions,compared with the normal condition. Vertical axes areshown in both dimensionless (left axes) and SI form (rightaxes); horizontal axes are shown as a fraction of gait cycle(% of stride) beginning with heel-strike, with acorresponding time scale for each condition shown in A.Each trace is a filtered average across subjects; see Fig. 3Afor representative trials.

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variability of foot motion. The typical variability of foot motionadmits the possibility of occasional scuffing with only a 2 degchange in swing ankle angle (Winter, 1992). Scuffing may thereforebe costly enough to make it preferable to avoid it by lifting the foothigher on average. Most humans probably scuff infrequently on flat,smooth floors, but the incidence likely increases on unevensurfaces. That scuffing does occasionally happen may besurmised by the wear pattern on shoe soles, or the marks left ontiled floors. We speculate that scuffing happens occasionallybecause it would be costlier to completely avoid it.To address movement variability, we treated scuffing as if it could

lie along a continuum with lifting the foot. We thus introducedscuffing as a consequence of negative virtual clearance of the foot,along with a scaling factor between lift height and scuff impulse. Itis only with such a conversion that the relative sensitivities ofmetabolic cost with respect to lifting and scuffing can be compared(see opposing sides of Fig. 4). While similar results could have beenachieved with summed joint work, this provides a means to compareotherwise dissimilar options, which are not easily incorporated intoan optimization framework. Here, they are treated as convertibleinto a single independent variable. However, the actual cost ofscuffing in the real world is likely considerably greater than the

purely energetic cost measured here (on a flat, constant-speedtreadmill), making its steepness (left side of Fig. 4) greater thanmeasured here. The steeper that cost, the greater the incentive forhigher average ground clearance, despite its higher metabolic cost. Itis also possible that many other human behaviors depend in part onmovement variability when determining an optimum or preference.For example, Begg et al. (2007) speculated that less effort may beneeded to increase the skewness of the distribution (i.e. only tightlycontrol the variability closer to the ground) than to decrease itsvariability.

There are a number of limitations to this study. We attempted toinduce lifting and scuffing of the foot as deviations from normalgait, but this does not necessarily reproduce the adjustments thatoccur in real-world situations. For example, actual scuffing isusually unintentional, and could induce fear, injury avoidance andrecovery actions not examined here. We also did not address thepotential cost of controlling movement variability, or consider theeffect of treadmill speed on the cost of ground clearance. Previousstudies have shown that preferred ground clearance increases withwalking speed (De Asha and Buckley, 2015; Schulz et al., 2010). Athigh walking speeds, scuffing would be expected to induce greaterdrag force, and therefore become costlier, thus favoring more

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A BExt

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Fig. 6. Joint angle, moment and power for foot scuff and foot lift conditions. (A) Foot scuff and (B) foot lift trajectories versus time for ankle, knee and hip, withgait cycle starting at heel-strike. Left-hand axes for moment and power are in dimensionless units and right-hand axes are SI units. Ext, extension; Flx, flexion.

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Fig. 7. Mechanical work rate againstscuff impulse and lift height. (A) MeanCOM work rate per stride and (B) meansummed joint work rate per stride for ankle,knee and hip. Lift height had a greaterimpact on work rate than scuff impulse.Greater lift contributed towards significantincreases in positive and negative COMwork rate and joint work rate. However,scuff impulse only affected negative COMwork rate and positive joint work rate, bothto a lesser extent than for lift height.Different colors denote each subjects’ data(squares for scuffing, circles for foot lift).Trend significance is indicated by solidlines (P<0.05) and non-significance bydashed lines.

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clearance. Conversely, it is possible that scuffing becomes lesscritical at very low walking speeds, when it might even be helpful toscuff at the end of the swing to bring the foot to rest. We have alsoassumed that scuffing is adequately characterized by the drag forceit produces against the ground and have not explored other possibleeffects. For example, scuffing may also entail some collision workagainst the ground, assumed here to be small as a result of therelatively low vertical GRF (Fig. 5). Another consideration is thepossibility of unintended effects from experimental controls; forexample, cognitive effort from visual feedback conditions. Thepresent study therefore only represents a simple characterization ofpossible contributing factors that determine the average foot–ground clearance.There are also several possible implications from our findings.

One is a potential explanation for the increased clearance observedon uneven terrain (Gates et al., 2012; Voloshina et al., 2013).Uneven ground would be expected to increase the cost of scuffing,and perhaps shift it in the direction of positive foot lift (Fig. 1). Itmay also affect balance and gait steadiness, and cause a wider, andperhaps skewed, probability distribution for foot motion. Both ofthese effects would cause the optimum average foot clearance toincrease. There may also be other factors in the opposite direction.For example, walking on surfaces with low friction could be moreforgiving of scuffing, as humans anecdotally appear more willing toscuff when wearing slippers or walking on sand, grass or light snow,conditions where the drag force appears low. This also suggests apotential opportunity to lift the swing foot less when traversingstepping stones raised above ground. A reduced amount orprobability of drag would be expected to favor reduced foot lift.The approach applied here may also affect other scenarios, such asthe effects of fatigue or age. Older adults tend to walk at slowerspeeds and with increased clearance variability compared withyounger adults (Begg et al., 2007), which may be due to differingbiomechanics or control, and result in differing costs for scuffing orlifting the foot, and perhaps contribute to increased risk forstumbling or falling. Although we have explored a relativelyinnocuous situation here, the trade-offs between scuffing and liftingthe foot may affect the overall energetic cost of walking as well asrisks for injury.

AcknowledgementsThe authors thank Daniel J. Bertoni for assistance in data collection.

Competing interestsThe authors declare no competing or financial interests.

Author contributionsA.R.W. and A.D.K. conceived the study and drafted the manuscript. A.R.W.designed and carried out the experiments and data analyses. Both authors read andapproved the final manuscript.

FundingThis work was supported in part by the Office of Naval Research (ETOWL program),National Institutes of Health (AG030815), and US Department of Defense

(W81XWH-09-2-0142, National Defense Science & Engineering GraduateFellowship Program). Deposited in PMC for release after 12 months.

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