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The Effects of Pedestrian
Deceleration Rates in Roadside
Grass/Bushes on Projectile
Speed Analysis
Mike W. Reade
President/Senior Reconstructionist,
Forensic Reconstruction Specialists, Inc.
IPTM Symposium on Traffic Safety
Orlando, Florida, June 3-6, 2019
Page | 1
Pedestrian Deceleration Rates in Roadside Grass/Bushes;
How Does it Affect Projectile Speed Analysis?
Forensic Reconstruction Specialists Inc.
IPTM-UNF Adjunct Instructor
Mike W. Reade, CD
Abstract
Traffic crashes involving pedestrians will challenge investigators
to determine an appropriate pedestrian friction value as the
pedestrian slides, rolls, or tumbles along the ground surface. There
has been enough research to establish pedestrian frictional values
travelling upon a wide range of roadway surfaces. However, there
is limited research regarding decelerating rates for pedestrians
travelling through taller grass and bushes. Using traditional
deceleration values may underestimate the calculated pedestrianโs
deceleration speed.
Well-established investigation methods [1, 2] have provided crash
reconstructionists with mathematical solutions to estimate a
pedestrianโs projectile speed based upon the pedestrianโs frictional
value and throw distance from impact to final rest. Although there
are additional mathematical solutions, this research will focus on
the Searle [4] and Hague [8] research of establishing pedestrian
speed from stopping on a ground surface.
Introduction
For this research, a rescue randy crash test dummy (hereafter
referred to as: pedestrian) is carried in the rear cargo box of a
moving ยฝ ton truck. As the test vehicle reaches the pedestrian drop
zone, the pedestrian is dropped to the side of the moving vehicle.
Spotters positioned adjacent to the pedestrian drop area mark the
location where the pedestrian first enters the grass/bush area.
Pedestrian stopping distances are measured from where the
pedestrian first enters the grass/bush area to the pedestrianโs final
rest. The vehicleโs test speed is recorded using a police radar unit.
The radar operator is instructed to record the vehicleโs speed when
the pedestrian is released at the side of the moving ยฝ ton truck.
Based on the pedestrian stopping distance and the test vehicleโs
speed, the equivalent pedestrianโs deceleration value is calculated
for each drop test. Also, the horizontal speed loss is calculated for
each experiment as the pedestrian first strikes the ground surface.
These results are helpful for investigators to establish a more
appropriate frictional value as pedestrians travel to final rest
through taller grass and bush-like situations. The results of these
experiments are compared to previous research [3] conducted on
asphalt surfaces.
The purpose of this research is to determine whether investigators
should use traditional frictional values for situations involving
pedestrian travel through taller grass and bushes, or should
additional considerations be given to using a higher pedestrian
frictional value to account for the higher pedestrian deceleration.
However, using inappropriate frictional values may result in the
overestimating or underestimating the pedestrianโs slide to stop
speed. This research places the pedestrian travelling at the same
speed as the test vehicle when the pedestrian is released in the drop
zone. The pedestrianโs takeoff angle is โzeroโ degrees and
represents a forward projection trajectory.
This research is offered to assist investigators in situations where
the pedestrian decelerates through roadside taller grass and bushes
and to consider using a more appropriate frictional value for
pedestrians decelerating through similar conditions.
Mathematical Solutions
The formulae [1, 2, 4] used to analyze pedestrian crashes have been
widely used and accepted in the crash reconstruction community.
Searle Minimum Formula:
๐๐๐๐ = โ2๐๐๐
1 + ๐2
(1)
Searle Maximum Formula:
๐๐๐๐ฅ = โ2๐๐๐ (2)
Searle Angle Formula:
๐ =โ2๐๐๐
cos ๐ + (๐ ร sin ๐) (3)
IPTM Symposium on Traffic Safety
Orlando, Florida, June 3-6, 2019
Page | 2
Where ๐ is the actual friction value which exists between the
pedestrian and the ground surface on which the pedestrian is
sliding or tumbling, ๐ is the gravitational acceleration value
( 32.2 ๐๐๐ 2 ๐๐ 9.81 ๐/๐ 2 ), ๐ is the total throw distance the
pedestrian travels from impact to final rest, ๐ is the pedestrian
takeoff angle in degrees, and ๐๐๐๐ , ๐๐๐๐ฅ , or ๐ represents the
projectileโs speed, expressed as feet-per-second ( ๐๐๐ ) or as
meters-per-second (๐/๐ ).
In many cases it may be difficult for investigators to establish the
area of impact, while in most all cases it is not possible to
accurately measure a real-world takeoff angle. Investigators are
therefore challenged to determine the most appropriate method for
their crash analysis.
Frictional Values Based on Vehicle Speed and Pedestrian
Stopping Distance:
๐ =๐2
254๐ท
(4)
Where ๐ is the calculated friction value based upon ๐ท the
pedestrianโs stopping distance from first touchdown along the
ground surface to final rest and ๐ is the pedestrianโs travel speed
when released from the moving test vehicle.
Example:
If the pedestrian is released from a test vehicle travelling 33.5 mph
(54 km/h) and the pedestrian stops in tall grass/bushes in 10.50 feet
(3.2 meters), the calculated pedestrian frictional value is 3.58 gโs.
This value is significantly higher than traditional pedestrian
frictional values in the order of 0.60 to 0.70 gโs.
For those investigators using a more common pedestrian friction
value (0.70), the resulting speed calculation becomes 14.8 mph
(23.8 km/h). This result is significantly less than the test vehicle
speed of 33.5 mph (54 km/h) and therefore warrants further
consideration with additional research.
Previous Pedestrian Research
Previous research [3, 7, 8] shows the pedestrianโs slide to stop
speed is more conservative than the actual speed when released
from the moving test vehicle.
The field data collected during each experiment shows that
traditional pedestrian friction values result in a conservative speed
compared to the pedestrianโs airborne speed.
Pedestrian Friction Values
Pedestrian crashes require investigators to determine an
appropriate pedestrian frictional value between the pedestrian and
the surface on which it slides or tumbles [1]. There are many ways
to determine this value through testing, or investigators can refer
to previous research in this area [1, 3, 4, 5, 6, 7]. Regardless the
approach, an appropriate pedestrian friction value is required to
properly analyze the decelerating pedestrian.
Horizontal Speed Loss Upon First Ground Contact
Before, investigators have relied upon past research which
considers pedestrian throw distance, pedestrian friction values,
pedestrian takeoff angles and for some formulae, additional field
data as investigators attempt to calculate pedestrianโs projectile
speed. This calculation requires the total throw distance from
impact to final rest. Here, we only deal with the pedestrianโs
decelerating phase while in contact with the ground surface.
Although research [3, 4, 8] has suspected a horizontal speed loss is
occurring when the pedestrian first contacts the ground surface, the
horizonal speed loss is not required as part of a pedestrian throw
analysis.
Searleโs research [4] discusses the loss of pedestrian horizontal
speed when the pedestrian first impacts the ground and before the
pedestrian sliding/tumbling phase commences. Previous research
[3, 8] supports the discussion of a sudden loss of horizontal speed
as the pedestrian first contacts the ground surface.
Vertical Velocity on Landing:
๏ฟฝฬ ๏ฟฝ = โ๐ฃ2 + 2๐๐ป (5)
Where ๐ฃ2 is the pedestrianโs vertical velocity on takeoff, or start
of airborne phase, ๐ is the gravitational acceleration
( 32.2 ๐๐๐ 2 ๐๐ 9.81 ๐/๐ 2 ), ๐ป is the vertical height of the
pedestrianโs center-of-mass at impact in feet or meters, and ๏ฟฝฬ ๏ฟฝ
represents the vertical velocity of the pedestrian on landing and
expressed as feet-per-second (๐๐๐ ) or as meters-per-second (๐/๐ ).
In Equation 5, the upward vertical velocity component (๐ฃ ) on
takeoff can be rewritten as:
๐ฃ = ๐ฃ๐ ร sin ๐ (6)
and ๐ฃ2 becomes:
๐ฃ2 = ๐ฃ๐
2 ร sin2๐
(7)
IPTM Symposium on Traffic Safety
Orlando, Florida, June 3-6, 2019
Page | 3
Then substitute Equation 7 into Equation 5:
๏ฟฝฬ ๏ฟฝ = โ๐ฃ๐2 ร sin2 ๐ + 2๐๐ป (8)
Where ๐ฃ๐2 is the pedestrianโs takeoff velocity, or start of airborne
phase, sin2 ๐ is the sine of the pedestrianโs takeoff angle in degrees,
๐ is the gravitational acceleration (32.2 ๐๐๐ 2 ๐๐ 9.81 ๐/๐ 2), ๐ป is
the vertical height of the pedestrianโs center-of-mass at impact in
feet or meters, and ๏ฟฝฬ ๏ฟฝ represents the vertical velocity of the
pedestrian on landing and expressed as feet-per-second (๐๐๐ ) or as
meters-per-second (๐/๐ ).
NOTE:
Because these experiments represent a zero-degree takeoff angle,
the ๐ฃ2 value in Equation 5 becomes zero (0) and both Equations 5
and 8 become:
๏ฟฝฬ ๏ฟฝ = โ2๐๐ป (9)
Once investigators determine the vertical velocity of the pedestrian
on landing, the horizontal speed loss upon first ground contact is
calculated using Equation 10 or Equation 11:
Horizontal Speed Loss on Landing:
๐๐๐๐๐ ๐ฟ๐๐ ๐ ๐๐ ๐ฟ๐๐๐๐๐๐ = ๐๏ฟฝฬ ๏ฟฝ (10)
or
๐๐๐๐๐ ๐ฟ๐๐ ๐ ๐๐ ๐ฟ๐๐๐๐๐๐ = ๐โ2๐๐ป (11)
Where ๐ is the pedestrianโs sliding or tumbling friction value, ๐ is
the gravitational acceleration (32.2 ๐๐๐ 2 ๐๐ 9.81 ๐/๐ 2), ๐ป is the
vertical height of the pedestrianโs center-of-mass at takeoff in feet
or meters, and ๏ฟฝฬ ๏ฟฝ represents the vertical velocity of the pedestrian
on landing and expressed as feet-per-second (๐๐๐ ) or as meters-
per-second (๐/๐ ).
After determining the pedestrianโs total sliding/tumbling distance
through the tall grass/bushes, the vertical height of center-of-mass
before release, and the takeoff angle (zero for these experiments),
the horizontal speed loss is calculated then added to the
pedestrianโs slide to stop speed as the pedestrian decelerates to a
stop through tall grass/bushes. Application of the horizontal speed
loss is discussed by Searle [4] and Hague [8].
So, when the only physical evidence available to investigators is
the pedestrianโs deceleration distance along the ground surface,
investigators can figure out a more accurate pedestrian travel speed
based upon the start of the ground impact and slide to final rest
phase.
Current Pedestrian Research (Tall Grass/Bushes)
Assisted by members of the CATAIR โ Atlantic Region Chapter,
22 pedestrian drop tests were performed in Riverview, New
Brunswick Canada - June 2017.
Those participating assisted by taking video and photographs of
each experiment while others recorded vehicle speed and measured
pedestrian stopping distance from first contact with the ground to
the pedestrianโs final rest.
The pedestrianโs vertical height to center of mass for all 22
experiments is between 4.42 feet (1.35 meters) and 4.92 feet (1.5
meters). These values are used to calculate the pedestrianโs
horizontal speed loss upon first contact with the ground surface.
The resulting horizontal speed loss for all tests ranges between
11.82 fps (3.6 m/s) and 12.46 fps (3.8 m/s) or 8.05 mph (12.94
km/h) and 8.49 mph (13.66 km/h) โ [Table 5, Table 6].
NOTE:
For the drop test experiments and horizontal speed loss
calculations an f-value of 0.70 and a vertical height to center of
mass of between 4.43 feet (1.35 meters) and 4.92 feet (1.5 meters)
are used.
The first set of 10 drop tests was conducted in a waist-high
grass/bush drop zone. The pedestrian is dropped head first during
the first five tests resulting in a calculated average f-value of 3.70.
The pedestrian is then dropped feet first for the second set of five
tests resulting is a calculated average f-value of 3.47 โ [Table 3].
During testing, it is clear the pedestrian stops quickly once
entangled in the tall grass/bushes.
The second set of 10 drop tests was conducted in a knee-high grass
drop zone. The pedestrian is dropped head first for the first five
tests resulting in a calculated average f-value of 1.91. The
pedestrian is then dropped feet first for the second set of five tests
resulting in a calculated average f-value of 1.63 โ [Table 4].
The difference between the two sets of 10 test values show a
significant increase in the pedestrianโs decelerate rate through tall
grass/bushes compared to shorter grass and no bushes. Even so, the
pedestrian deceleration values of between 1.91 and 1.63 are much
higher than traditional pedestrian frictional values in the order of
0.60 to 0.70.
Finally, a third set of 2 drop tests was conducted in the same area
as the second set of drop tests. However, the test vehicle is
travelling in the opposite direction. The pedestrian is dropped head
first for the first test resulting in a calculated f-value of 1.87. The
IPTM Symposium on Traffic Safety
Orlando, Florida, June 3-6, 2019
Page | 4
pedestrian is then dropped feet first for the second test resulting in
a calculated f-value of 2.00 โ [Table 4].
To compare the drop test deceleration values [Table 3, Table 4]
with the pedestrianโs drag test values [Table 7], testing was
conducted along the edge of the tall grass/bush area. The resulting
average pedestrian friction value from these tests resulted in a
calculated f-value of 0.89.
So, how does the actual pedestrian friction testing between the
pedestrian and the surface along which it is travelling compare
with traditional drop testing calculations? [Appendix 1]
If an investigator can only document the pedestrianโs deceleration
distance along the ground surface, the pedestrianโs slide to stop
speed will always be conservative and underestimate the
pedestrianโs projectile speed, unless investigators consider a
different pedestrian deceleration value during the slide to stop
phase.
Therefore, investigators should include the pedestrianโs horizontal
speed loss with the pedestrianโs slide to stop speed in order to
provide in a more accurate speed estimate.
Conclusions
This research shows investigators cannot rely upon traditional
frictional values when pedestrians are thrown into and travel to a
stop in taller grass and bush-like terrain. In such cases,
consideration need be given to choosing an appropriate frictional
value when dealing with the pedestrianโs deceleration phase.
Although not adjusting the pedestrianโs frictional value can
underestimate the pedestrianโs slide to stop phase, investigators
must be mindful that using a high frictional value can falsely
overestimate the pedestrianโs projectile speed.
For crashes occurring on normal ground surfaces, the differences
in the pedestrianโs friction value does not significantly affect the
final speed calculations, unless there is a low-friction surface [9]
or a high-friction situation as shown in this research.
Continued research in this area should be encouraged.
About the Author
Mike W. Reade, CD is the owner of Forensic Reconstruction
Specialists Inc., a collision reconstruction consulting firm located
in Riverview, New Brunswick Canada. Mike has been an Adjunct
Instructor with the Institute of Police Technology and
Management โ University of North Florida based out of
Jacksonville, Florida since 1993. His website is www.frsi.ca. and
he can be reached at reademw@gmail.com.
Acknowledgements
I would like to thank members of CATAIR โ Atlantic Region
Chapter, members of the RCMP, and all volunteers who either
assisted or participated in this research.
References
[1] Searle, J.A., Searle, A. (1983) โThe Trajectories of Pedestrians,
Motorcycles, Motorcyclists, etc., Following a Road Accident.โ
SAE Technical #831622.
[2] Searle, J.A. (1993) โThe Physics of Throw Distance in Accident
Reconstruction.โ SAE Technical #9306759.
[3] Becker, T.L., Reade, M.W. (2008 to 2016) โAnalysis of
Controlled Pedestrian / Cyclist Crash Testing Data.โ IPTM-UNF
Pedestrian/Bicycle Crash Investigation Courses.
[4] Searle, J.A. (2009) โThe Application of Throw Distance
Formulae.โ IPTM Special Problems in Traffic Crash
Reconstruction, Orlando, Florida.
[5] Craig, A. (1999) โBovington Test Results.โ Impact Vol 8, No.
3, pp 83 โ 85. ITA1, England, 1999.
[6] Hill, G. S. (1994) โCalculations of Vehicle Speed from
Pedestrian Throw.โ Impact Vol. 4, No. 1, pp 18 โ 20, ITA1,
England, 1994.
[7] Reade, M. W. (2011) โCATAIR Atlantic Region Pedestrian
Crash, Drop & Friction Testing.โ Riverview, New Brunswick,
Canada, 2011.
[8] Hague, D.J. (2001) โCalculation of Impact Speed from
Pedestrian Slide Distance.โ Metropolitan Laboratory Forensic
Science Service, ITAI Conference.
[9] Sullenberger, G. A. (2014) โPedestrian Impact on Low
Friction Surface.โ SAE Technical #2014-01-0470.
[10] Reade, M. W., Rich, A. S. (2016) โThe Effects of Carry
Distance, Takeoff Angle, Friction Value, and Horizontal Speed
Loss Upon First Ground Contact on Pedestrian/Cyclist Crash
Reconstruction.โ WREX2016 (World Reconstruction Exposition
2016) Conference, Orlando, Florida, 2016.
IPTM Symposium on Traffic Safety
Orlando, Florida, June 3-6, 2019
Page | 5
Table 1 - Summary of Pedestrian Friction Value Research. [3]
Clothing / Surface Friction Values Mean Low High Std. Dev. (s)
Hill [6] (Jacket, Trousers, Nylon, Leather, Jeans, Woolen suit) 0.695 0.567 .750 0.073
Bovington [5] (Nylon, Leather, Fabric, Jeans) 0.584 0.532 0.633 0.039
Searle [4] (Sandbag on Various Surfaces) 0.63 0.30 0.78 0.134
Becker/Reade [3] (Cotton, Nylon, Woolen, Jeans) 0.590 0.440 0.690 0.085
Sullenberger [9] (Mean Low-Friction, Winter Conditions) 0.36 0.237 0.549 0.122
Reade [7] (Low-Friction, Winter Conditions) 0.52 0.45 0.58 0.03
Research Average Values (* Summary of above.) * 0.56 (avg.) * 0.42 (avg.) * 0.66 (avg.) 0.06
Table 2 โ Summary of Horizontal Speed Loss Upon First Ground Contact & Vertical Drop Testing Research. [3]
Experiment Type Mean Low High Std. Dev. (s) No. of Tests
All Crash Tests
6.47 mph
(10.41 km/h)
3.18 mph
(5.13 km/h)
10.85 mph
(17.46 km/h)
1.11 mph
(1.78 km/h)) 139
Pedestrian Only Tests
6.53 mph
(10.51 km/h)
4.38 mph
(7.05 km/h)
10.85 mph
(17.46 km/h)
1.04 mph
(1.68 km/h) 94
Cyclist Tests
6.54 mph
(10.52 km/h)
4.51 mph
(7.25 km/h)
9.30 mph
(14.97 km/h)
1.11 mph
(1.78 km/h) 32
Wrap Trajectory Tests
6.53 mph
(10.51 km/h)
4.38 mph
(7.05 km/h)
10.85 mph
(17.46 km/h)
1.06 mph
(1.70 km/h) 126
Forward Projection Tests
5.20 mph
(8.37 km/h)
3.18 mph
(5.13 km/h)
6.51 mph
10.48 km/h)
1.11 mph
(1.79 km/h) 8
Crash Test Dummy Drop Testing
7.08 mph
(11.39 mph)
5.32 mph
(8.56 km/h)
8.21 mph
(13.22 km/h)
0.78 mph
(1.26 km/h) 39
IPTM Symposium on Traffic Safety
Orlando, Florida, June 3-6, 2019
Page | 6
Table 3: First Set of Pedestrian Drop Tests (Calculated Pedestrian f-Value โ Waist-High Grass/Bushes)
km/h mph meters feet
54.00 33.56 3.20 10.50 3.58
53.00 32.94 2.50 8.20 4.41
54.00 33.56 4.55 14.93 2.52
49.00 30.45 2.35 7.71 4.01
51.00 31.70 2.55 8.37 4.00
54.00 33.56 2.10 6.89 5.45
53.00 32.94 4.08 13.39 2.70
51.00 31.70 2.78 9.12 3.67
54.00 33.56 4.88 16.01 2.35
52.00 32.32 3.33 10.93 3.19
Head First Avg f-Value: 3.70
Feet First Avg f-Value: 3.47
Test Speed Radar Ped Stopping DistanceCalculated f-Value
Photograph 1: First Set of Pedestrian Drop Tests (Photograph of Waist-High Grash/Bushes)
IPTM Symposium on Traffic Safety
Orlando, Florida, June 3-6, 2019
Page | 7
Table 4: Second & Third Sets of Pedestrian Drop Tests (Calculated Pedestrian f-Value โ Knee-High Grass)
km/h mph meters feet
55.00 34.18 4.63 15.19 2.56
51.00 31.70 5.47 17.95 1.87
52.00 32.32 6.70 21.98 1.58
56.00 34.80 6.10 20.01 2.02
51.00 31.70 6.65 21.82 1.53
53.00 32.94 5.64 18.50 1.95
52.00 32.32 6.88 22.57 1.54
52.00 32.32 6.59 21.62 1.61
51.00 31.70 6.16 20.21 1.66
51.00 31.70 7.25 23.79 1.41
53.00 32.94 5.90 19.36 1.87
55.00 34.18 5.95 19.52 2.00
Head First Avg f-Value: 1.91
Feet First Avg f-Value: 1.63
Third Set Avg f-Value: 1.93
Test Speed Radar Ped Stopping DistanceCalculated f-Value
Photograph 2: Second & Third Sets of Pedestrian Drop Tests Photograph of Knee-High Grass)
IPTM Symposium on Traffic Safety
Orlando, Florida, June 3-6, 2019
Page | 8
Table 5: First Set of Pedestrian Drop Tests (Calculated Minimum Pedestrian Horizontal Speed Loss)
km/h mph meters (min) feet (min) m/s fps
54.00 33.56 1.35 4.43 3.60 11.82
53.00 32.94 1.35 4.43 3.60 11.82
54.00 33.56 1.35 4.43 3.60 11.82
49.00 30.45 1.35 4.43 3.60 11.82
51.00 31.70 1.35 4.43 3.60 11.82
54.00 33.56 1.35 4.43 3.60 11.82
53.00 32.94 1.35 4.43 3.60 11.82
51.00 31.70 1.35 4.43 3.60 11.82
54.00 33.56 1.35 4.43 3.60 11.82
52.00 32.32 1.35 4.43 3.60 11.82
Head First (km/h): 12.96 Head First (mph): 8.06
Feet First (km/h): 12.96 Feet First (mph): 8.06
Test Speed Radar Pedestrian Drop Height Min. Horizontal Speed Loss
Table 6: Second Set of Pedestrian Drop Tests (Calculated Maximum Pedestrian Horizontal Speed Loss)
km/h mph meters (min) feet (min) m/s fps
54.00 33.56 1.50 4.92 3.80 12.46
53.00 32.94 1.50 4.92 3.80 12.46
54.00 33.56 1.50 4.92 3.80 12.46
49.00 30.45 1.50 4.92 3.80 12.46
51.00 31.70 1.50 4.92 3.80 12.46
54.00 33.56 1.50 4.92 3.80 12.46
53.00 32.94 1.50 4.92 3.80 12.46
51.00 31.70 1.50 4.92 3.80 12.46
54.00 33.56 1.50 4.92 3.80 12.46
52.00 32.32 1.50 4.92 3.80 12.46
Head First (km/h): 13.66 Head First (mph): 8.50
Feet First (km/h): 13.66 Feet First (mph): 8.50
Test Speed Radar Pedestrian Drop Height Min. Horizontal Speed Loss
IPTM Symposium on Traffic Safety
Orlando, Florida, June 3-6, 2019
Page | 9
Table 7: Pedestrian Drag Tests(Along Edge of Tall Grass/Bush Area)
lb kg lb kg
35.00 15.91 26.00 11.82 0.7435.00 15.91 30.00 13.64 0.8635.00 15.91 35.00 15.91 1.0035.00 15.91 37.00 16.82 1.0635.00 15.91 33.00 15.00 0.9435.00 15.91 35.00 15.91 1.0035.00 15.91 32.00 14.55 0.9135.00 15.91 26.00 11.82 0.7435.00 15.91 28.00 12.73 0.8035.00 15.91 32.00 14.55 0.91
Calculated Mean: 0.914Calculated Average: 0.897Standard Deviation: 0.11
Pedestrian Weight (W) Pull Force (F)Calculated f-Value
Photograph 3: Pedestrian Drag Sled Tests (Edge of Tall Grass/Bushes)
IPTM Symposium on Traffic Safety
Orlando, Florida, June 3-6, 2019
Page | 10
Appendix 1: Pedestrian Drop Test Analysis.
The crash test dummy (pedestrian) is travelling the same speed as the test vehicle (33.56 mph/54 km/h) when dropped to the side of the
vehicle. The pedestrian lands in a tall grass/bush-filled ditch and decelerates to a stop. Evidence shows where the grass/bushes are laid
down as the pedestrian lands and continues to final rest position in the ditch. The measured distance of flattened-down grass/bush is
16.01 feet (4.88 meters). There is no roadway evidence to locate the area of impact. The only crash data available to investigators is the
pedestrianโs travel distance through the tall grass/bush-filled ditch.
The pedestrianโs center of mass height (H) at takeoff is between 4.43 feet (1.35 meters) and 4.92 feet (1.50 meters). This experiment is
a level takeoff trajectory with a zero-degree takeoff angle.
Steps:
1. First, measure the pedestrianโs travel distance in the tall grass/bush ditch as the pedestrian comes to final rest. The stopping
distance in this example is 16.01 feet (4.88 meters). Currently we would refer to previous research [1] and a pedestrian frictional
value of 0.79 in grass conditions. Here, the pedestrian stopping speed is 19.47 mph (31.29 km/h). Considering the crash test
data, the calculated value is conservative because of the lower pedestrian frictional value.
๐ = โ2๐๐๐ (1)
๐ = โ2 ร 0.79 ร 32.2 ร 16.01 (2)
๐ = โ814.52 (3)
๐ = 28.53 ๐๐๐ (4)
Convert โfpsโ to โmphโ:
๐ =28.53
1.466 (5)
๐บ = ๐๐. ๐๐ ๐๐๐ (6)
2. Next, calculate the pedestrianโs horizontal speed loss. Here, we use the pedestrian friction of 0.79 and a vertical height to center
of mass as 4.43 feet (1.35 meters). A horizontal speed loss of 13.34 fps (9.09 mph) or 4.06 m/s (14.62 km/h) is determined.
From previous research [3, 4, 7, 8] the horizontal speed loss is added to the pedestrianโs slide to stop result and becomes 28.56
mph (45.91 km/h).
๐ = ๐โ2๐๐ป (7)
๐ = 0.79โ2 ร 32.2 ร 4.43 (8)
๐ = 0.79โ285.29 (9)
๐ = 0.79 ร 16.89 (10)
๐ = 13.34 ๐๐๐ (11)
Convert โfpsโ to โmphโ:
๐ =13.34
1.466 (12)
IPTM Symposium on Traffic Safety
Orlando, Florida, June 3-6, 2019
Page | 11
๐บ = ๐. ๐๐ ๐๐๐ (13)
Speed Addition: (Slide to Stop + Horizontal Speed Loss)
๐ = ๐๐๐๐๐ ๐ก๐ ๐๐ก๐๐ + ๐ป๐๐๐๐ง๐๐๐ก๐๐ ๐๐๐๐๐ ๐ฟ๐๐ ๐ (14)
๐ = 19.47 ๐๐โ + 9.09 ๐๐โ (15)
๐บ = ๐๐. ๐๐ ๐๐๐
Compared to the pedestrian release speed (33.56 mph / 54 km/h) in experiment # 9, our calculation is 5 mph (8 km/h) lower
than the drop test field data. This is still a reasonable comparison and conservative. So, what would happen if we used a higher
pedestrian friction value?
3. Let us substitute the pedestrian friction value calculated value from testing 0.89 [Table 7] which represents the travel of the
pedestrian in the tall grass/bush conditions. The pedestrian deceleration speed becomes 20.66 mph (33.24 km/h).
๐ = โ2๐๐๐ (16)
๐ = โ2 ร 0.89 ร 32.2 ร 16.01 (17)
๐ = โ917.62 (18)
๐ = 30.29 ๐๐๐ (19)
Convert โfpsโ to โmphโ:
๐ =30.29
1.466 (20)
๐บ = ๐๐. ๐๐ ๐๐๐ (21)
4. Using the higher pedestrian friction value of 0.89 results in a higher horizonal speed loss of 15.03 fps (10.25 mph) or 4.58 m/s
(16.47 km/h). This result is added to the pedestrianโs stopping speed in step 3 and becomes 30.91 mph (49.73 km/h). This result
compares favorably to the actual drop test speed recorded in experiment # 9.
๐ = ๐โ2๐๐ป (22)
๐ = 0.89โ2 ร 32.2 ร 4.43 (23)
๐ = 0.89โ285.29 (24)
๐ = 0.89 ร 16.89 (25)
๐ = 15.03 ๐๐๐ (26)
Convert โfpsโ to โmphโ:
๐ =15.03
1.466 (27)
IPTM Symposium on Traffic Safety
Orlando, Florida, June 3-6, 2019
Page | 12
๐บ = ๐๐. ๐๐ ๐๐๐ (28)
Speed Addition: (Slide to Stop + Horizontal Speed Loss)
๐ = ๐๐๐๐๐ ๐ก๐ ๐๐ก๐๐ + ๐ป๐๐๐๐ง๐๐๐ก๐๐ ๐๐๐๐๐ ๐ฟ๐๐ ๐ (29)
๐ = 20.66 ๐๐โ + 10.25 ๐๐โ (30)
๐บ = ๐๐. ๐๐ ๐๐๐ (31)
5. If investigators use a pedestrian friction value of 1.2 or greater, there is a good chance the calculated speed overestimates the
pedestrianโs actual speed once added to the horizontal speed loss. So, based on the same information above and a frictional
value of 1.2, the results become:
๐ = โ2๐๐๐ (32)
๐ = โ2 ร 1.2 ร 32.2 ร 16.01 (33)
๐ = 35.17 ๐๐๐ (34)
Convert โfpsโ to โmphโ:
๐ =35.17
1.466 (35)
๐บ = ๐๐. ๐๐ ๐๐๐ (36)
Horizontal Speed Loss:
๐ = ๐โ2๐๐ป (37)
๐ = 1.2โ2 ร 32.2 ร 4.43 (38)
๐ = 1.2โ285.29 (39)
๐ = 1.2 ร 16.89 (40)
๐ = 20.26 ๐๐๐ (41)
Convert โfpsโ to โmphโ:
๐ =25.33
1.466 (42)
๐บ = ๐๐. ๐๐ ๐๐๐ (43)
Speed Addition: (Slide to Stop + Horizontal Speed Loss)
๐ = ๐๐๐๐๐ ๐ก๐ ๐๐ก๐๐ + ๐ป๐๐๐๐ง๐๐๐ก๐๐ ๐๐๐๐๐ ๐ฟ๐๐ ๐ (44)
๐ = 23.99 ๐๐โ + 13.81 ๐๐โ (45)
IPTM Symposium on Traffic Safety
Orlando, Florida, June 3-6, 2019
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๐บ = ๐๐. ๐๐ ๐๐๐ (46)
Difference (Calculated Speed vs. Drop Test Speed)
Difference = Calculated Speed โ Drop Test Speed (47)
Difference = 37.80 ๐๐โ โ 33.56 ๐๐โ (48)
Difference = + 4.24 ๐๐โ (49)
(Speed Overestimate = + 4.24 mph) (50)
6. Therefore, investigators should be aware that using a high pedestrian friction value, such as 1.5, can overestimate the actual
speed for a pedestrian decelerating though similar roadside conditions.
NOTE:
This research only discusses the portion of the crash scenario where the pedestrian travels in contact with the ground surface. This
research does not suggest using higher pedestrian friction values in pedestrian projectile or throw formulae. Pedestrian projectile
formulae require the pedestrianโs total throw distance from impact to final rest whereas this research deals with the pedestrianโs stopping
distance along the ground surface.
Our research [3] shows that the use of high friction values will overestimate both the pedestrianโs projectile speed and the vehicleโs
impact speed. Although care should be used in low-friction situations [9] to not overestimate pedestrian/vehicle speed, we know that
care should be used when pedestrians travel through high-friction situations.
Using pedestrian frictional values greater than 1.0 can overestimate the pedestrianโs projectile speed. The practice of arbitrarily assigning
high pedestrian friction values when investigators can determine the area of impact and a total throw distance should be discouraged. In
those situations, it is recommended to select an appropriate friction value based on other research [1, 3, 4, 5, 7, 9].
However, when investigators are only dealing with a pedestrian stopping distance and not a total pedestrian throw distance, it is more
appropriate to consider using a higher friction value to determine the pedestrianโs deceleration speed in a tall grass/bush-like situation.
IPTM Symposium on Traffic Safety
Orlando, Florida, June 3-6, 2019
Page | 14
Appendix 2: Derivation of throw distance formulae [4] โ (Reproduced with permission).
Variables:
๐ฃ = Vertical velocity at takeoff in feet-per-second (๐๐๐ ) or meters-per-second (๐/๐ ) and ๐ฃ = ๐ sin ๐.
๐ฃ๐ ๐๐ ๐ = Pedestrianโs original takeoff velocity in feet-per-second (๐๐๐ ) or meters-per-second (๐/๐ ).
๐ข = Horizontal velocity at takeoff in feet-per-second (๐๐๐ ) or meters-per-second (๐/๐ ) and ๐ข = ๐ cos ๐.
โ = Maximum height above takeoff height measured upward, or positively in feet (๐๐ก) or meters (๐) above ๐ป.
๐ป = Vertical height to pedestrianโs center-of-mass measured upward, or positively in feet (๐๐ก) or meters (๐).
๐ = Gravitational acceleration in feet-per-second2 (๐๐๐ 2) or meters-per-second2 (๐/๐ 2).
๏ฟฝฬ ๏ฟฝ = Vertical velocity at landing in feet-per-second (๐๐๐ ) or meters-per-second (๐/๐ ).
๐ก = Time to landing in seconds.
๐ = Pedestrian friction value.
๐ = Pedestrianโs takeoff angle measured between ๐ข and ๐ฃ๐ ๐๐ ๐ measured in degrees.
NOTE:
The ๐ถ๐๐๐๐ฆ ๐ท๐๐ ๐ก., ๐1(๐ด๐๐๐๐๐๐๐), ๐2(๐๐๐๐๐), and ๐ (๐๐๐ก๐๐ ๐โ๐๐๐ค) distances are measured in feet (๐๐ก) or meters (๐).
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Orlando, Florida, June 3-6, 2019
Page | 15
Maximum Height Above Takeoff Height:
โ = ๐ฃ2
2๐ (1)
Vertical Velocity on Landing:
๏ฟฝฬ ๏ฟฝ = โ๐ฃ2 + 2๐๐ป (2)
Time to Landing:
๐ก = ๐ฃ + ๏ฟฝฬ ๏ฟฝ
๐ (3)
Distance Travelled Before Landing:
๐1 = ๐ข๐ก = ๐ข (๐ฃ + ๏ฟฝฬ ๏ฟฝ
๐) (4)
Horizontal Speed Loss on Landing:
๐๐๐๐๐ ๐ฟ๐๐ ๐ ๐๐ ๐ฟ๐๐๐๐๐๐ = ๐๏ฟฝฬ ๏ฟฝ (5)
Wrap Trajectories:
๐๐๐๐๐ ๐ฟ๐๐ ๐ ๐๐ ๐ฟ๐๐๐๐๐๐ = ๐โ๐ฃ2 + 2๐๐ป (6)
or:
๐๐๐๐๐ ๐ฟ๐๐ ๐ ๐๐ ๐ฟ๐๐๐๐๐๐ = ๐โ๐ฃ๐2 ร sin2 ๐ + 2๐๐ป (7)
Forward Projection Trajectories:
๐๐๐๐๐ ๐ฟ๐๐ ๐ ๐๐ ๐ฟ๐๐๐๐๐๐ = ๐โ2๐๐ป (8)
Distance Travelled After Landing:
๐2 = (๐ข โ ๐๏ฟฝฬ ๏ฟฝ)2
2๐๐ (9)
Total Throw Distance:
๐ = ๐1 + ๐2 (10)
๐ = ๐ข (๐ฃ + ๏ฟฝฬ ๏ฟฝ
๐) +
(๐ข โ ๐๏ฟฝฬ ๏ฟฝ)2
2๐๐ (11)
๐ = [(2๐๐ข๐ฃ + 2๐๐ข๏ฟฝฬ ๏ฟฝ ) + (๐ข2 โ 2๐๐ข๏ฟฝฬ ๏ฟฝ + ๐2๏ฟฝฬ ๏ฟฝ2)]
2๐๐ (12)
IPTM Symposium on Traffic Safety
Orlando, Florida, June 3-6, 2019
Page | 16
๐ = ๐ข2 + 2๐๐ข๐ฃ + ๐2๐ฃ2 + 2๐2๐๐ป
2๐๐ (13)
๐ = (๐ข + ๐๐ฃ)2
2๐๐+ ๐๐ป (14)
The extra distance travelled is due to the initial height of the pedestrianโs (cyclistโs) center-of-mass and is equal to ๐๐ป
Recall that ๐ฃ = ๐ sin ๐ and ๐ข = ๐ cos ๐ therefore, Equation 14 can be written as [1, 4]:
๐ = ๐2
2๐๐(cos ๐ + ๐ sin ๐)2 + ๐๐ป (15)
2๐๐(๐ โ ๐๐ป)
(cos ๐ + ๐ sin ๐)2= ๐2 (16)
Rearranged to represent the Searle formula [1, 4] which considers an adjustment for the pedestrianโs center-of-mass height at impact
and requires a projectile takeoff angle:
๐ = โ2๐๐(๐ โ ๐๐ป)
(cos ๐ + ๐ sin ๐) (17)
Since reconstructionists normally cannot determine a takeoff angle, an investigator can consider an appropriate value for ๐, the
projectileโs takeoff angle, to establish an upper (maximum) and a lower (minimum) limit for the projection velocity.
To find the maximum value for ๐, where ๐ = 0, the Searle Maximum [4] formula becomes:
๐๐๐๐ฅ = โ2๐๐(๐ โ ๐๐ป) (18)
To find the minimum value for ๐, note that:
1 โ sin2 ๐ โ cos2 ๐ = 0 (19)
Expand (cos ๐ + ๐ sin ๐)2 in Equation 16 by putting in extra zero (0) terms:
(cos ๐ + ๐ sin ๐)2 = cos2 ๐ + 2๐ sin ๐ cos ๐ + ๐2 sin2 ๐ + (1 โ sin2 ๐ โ cos2 ๐) + ๐2(1 โ sin2 ๐ โ cos2 ๐) (20)
(cos ๐ + ๐ sin ๐)2 = 1 + ๐2 โ [sin ๐ โ ฮผ cos ๐]2 (21)
Because [sin ๐ โ cos ๐]2 is squared and cannot go negative, its minimum value is zero (0). Therefore, the maximum value of
(cos ๐ + ๐ sin ๐)2 is:
(cos ๐ + ๐ sin ๐)2 = 1 + ๐2 (22)
After substituting 1 + ๐2 for (cos ๐ + ๐ sin ๐)2 in Equation 16, we find the well-known Searle Minimum [1, 2] formula which
considers an adjustment for the pedestrianโs (cyclistโs) height of center-of-mass. [4] That is:
๐๐๐๐ = โ2๐๐(๐ โ ๐๐ป)
1 + ๐2 (23)
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