the effects of pedestrian deceleration rates in roadside ... · stopping distance: 𝜇= 2 254 (4)...

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

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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 pedestrian’s

deceleration speed.

Well-established investigation methods [1, 2] have provided crash

reconstructionists with mathematical solutions to estimate a

pedestrian’s projectile speed based upon the pedestrian’s 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 ½ 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 pedestrian’s final

rest. The vehicle’s test speed is recorded using a police radar unit.

The radar operator is instructed to record the vehicle’s speed when

the pedestrian is released at the side of the moving ½ ton truck.

Based on the pedestrian stopping distance and the test vehicle’s

speed, the equivalent pedestrian’s 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 pedestrian’s 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 pedestrian’s takeoff angle is “zero” 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:

𝑉𝑚𝑖𝑛 = √2𝜇𝑔𝑆

1 + 𝜇2

(1)

Searle Maximum Formula:

𝑉𝑚𝑎𝑥 = √2𝜇𝑔𝑆 (2)

Searle Angle Formula:

𝑉 =√2𝜇𝑔𝑆

cos 𝜃 + (𝜇 × sin 𝜃) (3)



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Where 𝜇 is the actual friction value which exists between the

pedestrian and the ground surface on which the pedestrian is

sliding or tumbling, 𝑔 is the gravitational acceleration value

( 32.2 𝑓𝑝𝑠2 𝑜𝑟 9.81 𝑚/𝑠2 ), 𝑆 is the total throw distance the

pedestrian travels from impact to final rest, 𝜃 is the pedestrian

takeoff angle in degrees, and 𝑉𝑚𝑖𝑛 , 𝑉𝑚𝑎𝑥 , or 𝑉 represents the

projectile’s speed, expressed as feet-per-second ( 𝑓𝑝𝑠 ) or as

meters-per-second (𝑚/𝑠).

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:

𝜇 =𝑆2

254𝐷

(4)

Where 𝜇 is the calculated friction value based upon 𝐷 the

pedestrian’s stopping distance from first touchdown along the

ground surface to final rest and 𝑆 is the pedestrian’s 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 g’s.

This value is significantly higher than traditional pedestrian

frictional values in the order of 0.60 to 0.70 g’s.

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 pedestrian’s 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 pedestrian’s 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 pedestrian’s projectile

speed. This calculation requires the total throw distance from

impact to final rest. Here, we only deal with the pedestrian’s

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.

Searle’s 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:

�̅� = √𝑣2 + 2𝑔𝐻 (5)

Where 𝑣2 is the pedestrian’s vertical velocity on takeoff, or start

of airborne phase, 𝑔 is the gravitational acceleration

( 32.2 𝑓𝑝𝑠2 𝑜𝑟 9.81 𝑚/𝑠2 ), 𝐻 is the vertical height of the

pedestrian’s center-of-mass at impact in feet or meters, and �̅�

represents the vertical velocity of the pedestrian on landing and

expressed as feet-per-second (𝑓𝑝𝑠) or as meters-per-second (𝑚/𝑠).

In Equation 5, the upward vertical velocity component (𝑣 ) on

takeoff can be rewritten as:

𝑣 = 𝑣𝑜 × sin 𝜃 (6)

and 𝑣2 becomes:

𝑣2 = 𝑣𝑜

2 × sin2𝜃

(7)



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Then substitute Equation 7 into Equation 5:

�̅� = √𝑣𝑜2 × sin2 𝜃 + 2𝑔𝐻 (8)

Where 𝑣𝑜2 is the pedestrian’s takeoff velocity, or start of airborne

phase, sin2 𝜃 is the sine of the pedestrian’s takeoff angle in degrees,

𝑔 is the gravitational acceleration (32.2 𝑓𝑝𝑠2 𝑜𝑟 9.81 𝑚/𝑠2), 𝐻 is

the vertical height of the pedestrian’s center-of-mass at impact in

feet or meters, and �̅� represents the vertical velocity of the

pedestrian on landing and expressed as feet-per-second (𝑓𝑝𝑠) or as

meters-per-second (𝑚/𝑠).

NOTE:

Because these experiments represent a zero-degree takeoff angle,

the 𝑣2 value in Equation 5 becomes zero (0) and both Equations 5

and 8 become:

�̅� = √2𝑔𝐻 (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:

𝑆𝑝𝑒𝑒𝑑 𝐿𝑜𝑠𝑠 𝑜𝑛 𝐿𝑎𝑛𝑑𝑖𝑛𝑔 = 𝜇�̅� (10)

or

𝑆𝑝𝑒𝑒𝑑 𝐿𝑜𝑠𝑠 𝑜𝑛 𝐿𝑎𝑛𝑑𝑖𝑛𝑔 = 𝜇√2𝑔𝐻 (11)

Where 𝜇 is the pedestrian’s sliding or tumbling friction value, 𝑔 is

the gravitational acceleration (32.2 𝑓𝑝𝑠2 𝑜𝑟 9.81 𝑚/𝑠2), 𝐻 is the

vertical height of the pedestrian’s center-of-mass at takeoff in feet

or meters, and �̅� represents the vertical velocity of the pedestrian

on landing and expressed as feet-per-second (𝑓𝑝𝑠) or as meters-

per-second (𝑚/𝑠).

After determining the pedestrian’s 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

pedestrian’s 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 pedestrian’s 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 – 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 pedestrian’s final rest.

The pedestrian’s 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 pedestrian’s

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) – [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 – [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 – [Table 4].

The difference between the two sets of 10 test values show a

significant increase in the pedestrian’s 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



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pedestrian is then dropped feet first for the second test resulting in

a calculated f-value of 2.00 – [Table 4].

To compare the drop test deceleration values [Table 3, Table 4]

with the pedestrian’s 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 pedestrian’s deceleration

distance along the ground surface, the pedestrian’s slide to stop

speed will always be conservative and underestimate the

pedestrian’s projectile speed, unless investigators consider a

different pedestrian deceleration value during the slide to stop

phase.

Therefore, investigators should include the pedestrian’s horizontal

speed loss with the pedestrian’s 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 pedestrian’s deceleration phase.

Although not adjusting the pedestrian’s frictional value can

underestimate the pedestrian’s slide to stop phase, investigators

must be mindful that using a high frictional value can falsely

overestimate the pedestrian’s projectile speed.

For crashes occurring on normal ground surfaces, the differences

in the pedestrian’s 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 – University of North Florida based out of

Jacksonville, Florida since 1993. His website is www.frsi.ca. and

he can be reached at [email protected].

Acknowledgements

I would like to thank members of CATAIR – 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) “The Trajectories of Pedestrians,

Motorcycles, Motorcyclists, etc., Following a Road Accident.”

SAE Technical #831622.

[2] Searle, J.A. (1993) “The Physics of Throw Distance in Accident

Reconstruction.” SAE Technical #9306759.

[3] Becker, T.L., Reade, M.W. (2008 to 2016) “Analysis of

Controlled Pedestrian / Cyclist Crash Testing Data.” IPTM-UNF

Pedestrian/Bicycle Crash Investigation Courses.

[4] Searle, J.A. (2009) “The Application of Throw Distance

Formulae.” IPTM Special Problems in Traffic Crash

Reconstruction, Orlando, Florida.

[5] Craig, A. (1999) “Bovington Test Results.” Impact Vol 8, No.

3, pp 83 – 85. ITA1, England, 1999.

[6] Hill, G. S. (1994) “Calculations of Vehicle Speed from

Pedestrian Throw.” Impact Vol. 4, No. 1, pp 18 – 20, ITA1,

England, 1994.

[7] Reade, M. W. (2011) “CATAIR Atlantic Region Pedestrian

Crash, Drop & Friction Testing.” Riverview, New Brunswick,

Canada, 2011.

[8] Hague, D.J. (2001) “Calculation of Impact Speed from

Pedestrian Slide Distance.” Metropolitan Laboratory Forensic

Science Service, ITAI Conference.

[9] Sullenberger, G. A. (2014) “Pedestrian Impact on Low

Friction Surface.” SAE Technical #2014-01-0470.

[10] Reade, M. W., Rich, A. S. (2016) “The Effects of Carry

Distance, Takeoff Angle, Friction Value, and Horizontal Speed

Loss Upon First Ground Contact on Pedestrian/Cyclist Crash

Reconstruction.” WREX2016 (World Reconstruction Exposition

2016) Conference, Orlando, Florida, 2016.

http://www.frsi.ca/



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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 – 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



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Table 3: First Set of Pedestrian Drop Tests (Calculated Pedestrian f-Value – 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)



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Table 4: Second & Third Sets of Pedestrian Drop Tests (Calculated Pedestrian f-Value – 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)



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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



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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)



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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

pedestrian’s travel distance through the tall grass/bush-filled ditch.

The pedestrian’s 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 pedestrian’s 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.

𝑉 = √2𝜇𝑔𝑑 (1)

𝑉 = √2 × 0.79 × 32.2 × 16.01 (2)

𝑉 = √814.52 (3)

𝑉 = 28.53 𝑓𝑝𝑠 (4)

Convert “fps” to “mph”:

𝑆 =28.53

1.466 (5)

𝑺 = 𝟏𝟗. 𝟒𝟕 𝒎𝒑𝒉 (6)

2. Next, calculate the pedestrian’s 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 pedestrian’s slide to stop result and becomes 28.56

mph (45.91 km/h).

𝑉 = 𝜇√2𝑔𝐻 (7)

𝑉 = 0.79√2 × 32.2 × 4.43 (8)

𝑉 = 0.79√285.29 (9)

𝑉 = 0.79 × 16.89 (10)

𝑉 = 13.34 𝑓𝑝𝑠 (11)


𝑆 =13.34

1.466 (12)



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𝑺 = 𝟗. 𝟎𝟗 𝒎𝒑𝒉 (13)

Speed Addition: (Slide to Stop + Horizontal Speed Loss)

𝑆 = 𝑆𝑙𝑖𝑑𝑒 𝑡𝑜 𝑆𝑡𝑜𝑝 + 𝐻𝑜𝑟𝑖𝑧𝑜𝑛𝑡𝑎𝑙 𝑆𝑝𝑒𝑒𝑑 𝐿𝑜𝑠𝑠 (14)

𝑆 = 19.47 𝑚𝑝ℎ + 9.09 𝑚𝑝ℎ (15)

𝑺 = 𝟐𝟖. 𝟓𝟔 𝒎𝒑𝒉

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).

𝑉 = √2𝜇𝑔𝑑 (16)

𝑉 = √2 × 0.89 × 32.2 × 16.01 (17)

𝑉 = √917.62 (18)

𝑉 = 30.29 𝑓𝑝𝑠 (19)


𝑆 =30.29

1.466 (20)

𝑺 = 𝟐𝟎. 𝟔𝟔 𝒎𝒑𝒉 (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 pedestrian’s 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.

𝑉 = 𝜇√2𝑔𝐻 (22)

𝑉 = 0.89√2 × 32.2 × 4.43 (23)

𝑉 = 0.89√285.29 (24)

𝑉 = 0.89 × 16.89 (25)

𝑉 = 15.03 𝑓𝑝𝑠 (26)


𝑆 =15.03

1.466 (27)



Page | 12

𝑺 = 𝟏𝟎. 𝟐𝟓 𝒎𝒑𝒉 (28)



𝑆 = 20.66 𝑚𝑝ℎ + 10.25 𝑚𝑝ℎ (30)

𝑺 = 𝟑𝟎. 𝟗𝟏 𝒎𝒑𝒉 (31)

5. If investigators use a pedestrian friction value of 1.2 or greater, there is a good chance the calculated speed overestimates the

pedestrian’s 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:

𝑉 = √2𝜇𝑔𝑑 (32)

𝑉 = √2 × 1.2 × 32.2 × 16.01 (33)

𝑉 = 35.17 𝑓𝑝𝑠 (34)


𝑆 =35.17

1.466 (35)

𝑺 = 𝟐𝟑. 𝟗𝟗 𝒎𝒑𝒉 (36)

Horizontal Speed Loss:

𝑉 = 𝜇√2𝑔𝐻 (37)

𝑉 = 1.2√2 × 32.2 × 4.43 (38)

𝑉 = 1.2√285.29 (39)

𝑉 = 1.2 × 16.89 (40)

𝑉 = 20.26 𝑓𝑝𝑠 (41)


𝑆 =25.33

1.466 (42)

𝑺 = 𝟏𝟑. 𝟖𝟏 𝒎𝒑𝒉 (43)



𝑆 = 23.99 𝑚𝑝ℎ + 13.81 𝑚𝑝ℎ (45)



Page | 13

𝑺 = 𝟑𝟕. 𝟖𝟎 𝒎𝒑𝒉 (46)

Difference (Calculated Speed vs. Drop Test Speed)

Difference = Calculated Speed − Drop Test Speed (47)

Difference = 37.80 𝑚𝑝ℎ − 33.56 𝑚𝑝ℎ (48)

Difference = + 4.24 𝑚𝑝ℎ (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 pedestrian’s total throw distance from impact to final rest whereas this research deals with the pedestrian’s stopping

distance along the ground surface.

Our research [3] shows that the use of high friction values will overestimate both the pedestrian’s projectile speed and the vehicle’s

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 pedestrian’s 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 pedestrian’s deceleration speed in a tall grass/bush-like situation.



Page | 14

Appendix 2: Derivation of throw distance formulae [4] – (Reproduced with permission).

Variables:

𝑣 = Vertical velocity at takeoff in feet-per-second (𝑓𝑝𝑠) or meters-per-second (𝑚/𝑠) and 𝑣 = 𝑉 sin 𝜃.

𝑣𝑜 𝑜𝑟 𝑉 = Pedestrian’s original takeoff velocity in feet-per-second (𝑓𝑝𝑠) or meters-per-second (𝑚/𝑠).

𝑢 = Horizontal velocity at takeoff in feet-per-second (𝑓𝑝𝑠) or meters-per-second (𝑚/𝑠) and 𝑢 = 𝑉 cos 𝜃.

ℎ = Maximum height above takeoff height measured upward, or positively in feet (𝑓𝑡) or meters (𝑚) above 𝐻.

𝐻 = Vertical height to pedestrian’s center-of-mass measured upward, or positively in feet (𝑓𝑡) or meters (𝑚).

𝑔 = Gravitational acceleration in feet-per-second2 (𝑓𝑝𝑠2) or meters-per-second2 (𝑚/𝑠2).

�̅� = Vertical velocity at landing in feet-per-second (𝑓𝑝𝑠) or meters-per-second (𝑚/𝑠).

𝑡 = Time to landing in seconds.

𝜇 = Pedestrian friction value.

𝜃 = Pedestrian’s takeoff angle measured between 𝑢 and 𝑣𝑜 𝑜𝑟 𝑉 measured in degrees.

NOTE:

The 𝐶𝑎𝑟𝑟𝑦 𝐷𝑖𝑠𝑡., 𝑆1(𝐴𝑖𝑟𝑏𝑜𝑟𝑛𝑒), 𝑆2(𝑆𝑙𝑖𝑑𝑒), and 𝑆 (𝑇𝑜𝑡𝑎𝑙 𝑇ℎ𝑟𝑜𝑤) distances are measured in feet (𝑓𝑡) or meters (𝑚).



Page | 15

Maximum Height Above Takeoff Height:

ℎ = 𝑣2

2𝑔 (1)

Vertical Velocity on Landing:

�̅� = √𝑣2 + 2𝑔𝐻 (2)

Time to Landing:

𝑡 = 𝑣 + �̅�

𝑔 (3)

Distance Travelled Before Landing:

𝑆1 = 𝑢𝑡 = 𝑢 (𝑣 + �̅�

𝑔) (4)

Horizontal Speed Loss on Landing:

𝑆𝑝𝑒𝑒𝑑 𝐿𝑜𝑠𝑠 𝑜𝑛 𝐿𝑎𝑛𝑑𝑖𝑛𝑔 = 𝜇�̅� (5)

Wrap Trajectories:

𝑆𝑝𝑒𝑒𝑑 𝐿𝑜𝑠𝑠 𝑜𝑛 𝐿𝑎𝑛𝑑𝑖𝑛𝑔 = 𝜇√𝑣2 + 2𝑔𝐻 (6)

or:

𝑆𝑝𝑒𝑒𝑑 𝐿𝑜𝑠𝑠 𝑜𝑛 𝐿𝑎𝑛𝑑𝑖𝑛𝑔 = 𝜇√𝑣𝑜2 × sin2 𝜃 + 2𝑔𝐻 (7)

Forward Projection Trajectories:

𝑆𝑝𝑒𝑒𝑑 𝐿𝑜𝑠𝑠 𝑜𝑛 𝐿𝑎𝑛𝑑𝑖𝑛𝑔 = 𝜇√2𝑔𝐻 (8)

Distance Travelled After Landing:

𝑆2 = (𝑢 − 𝜇�̅�)2

2𝜇𝑔 (9)

Total Throw Distance:

𝑆 = 𝑆1 + 𝑆2 (10)

𝑆 = 𝑢 (𝑣 + �̅�

𝑔) +

(𝑢 − 𝜇�̅�)2

2𝜇𝑔 (11)

𝑆 = [(2𝜇𝑢𝑣 + 2𝜇𝑢�̅� ) + (𝑢2 − 2𝜇𝑢�̅� + 𝜇2�̅�2)]

2𝜇𝑔 (12)



Page | 16

𝑆 = 𝑢2 + 2𝜇𝑢𝑣 + 𝜇2𝑣2 + 2𝜇2𝑔𝐻

2𝜇𝑔 (13)

𝑆 = (𝑢 + 𝜇𝑣)2

2𝜇𝑔+ 𝜇𝐻 (14)

The extra distance travelled is due to the initial height of the pedestrian’s (cyclist’s) center-of-mass and is equal to 𝜇𝐻

Recall that 𝑣 = 𝑉 sin 𝜃 and 𝑢 = 𝑉 cos 𝜃 therefore, Equation 14 can be written as [1, 4]:

𝑆 = 𝑉2

2𝜇𝑔(cos 𝜃 + 𝜇 sin 𝜃)2 + 𝜇𝐻 (15)

2𝜇𝑔(𝑆 − 𝜇𝐻)

(cos 𝜃 + 𝜇 sin 𝜃)2= 𝑉2 (16)

Rearranged to represent the Searle formula [1, 4] which considers an adjustment for the pedestrian’s center-of-mass height at impact

and requires a projectile takeoff angle:

𝑉 = √2𝜇𝑔(𝑆 − 𝜇𝐻)

(cos 𝜃 + 𝜇 sin 𝜃) (17)

Since reconstructionists normally cannot determine a takeoff angle, an investigator can consider an appropriate value for 𝜃, the

projectile’s takeoff angle, to establish an upper (maximum) and a lower (minimum) limit for the projection velocity.

To find the maximum value for 𝑉, where 𝜃 = 0, the Searle Maximum [4] formula becomes:

𝑉𝑚𝑎𝑥 = √2𝜇𝑔(𝑆 − 𝜇𝐻) (18)

To find the minimum value for 𝑉, note that:

1 − sin2 𝜃 − cos2 𝜃 = 0 (19)

Expand (cos 𝜃 + 𝜇 sin 𝜃)2 in Equation 16 by putting in extra zero (0) terms:

(cos 𝜃 + 𝜇 sin 𝜃)2 = cos2 𝜃 + 2𝜇 sin 𝜃 cos 𝜃 + 𝜇2 sin2 𝜃 + (1 − sin2 𝜃 − cos2 𝜃) + 𝜇2(1 − sin2 𝜃 − cos2 𝜃) (20)

(cos 𝜃 + 𝜇 sin 𝜃)2 = 1 + 𝜇2 − [sin 𝜃 − μ cos 𝜃]2 (21)

Because [sin 𝜃 − cos 𝜃]2 is squared and cannot go negative, its minimum value is zero (0). Therefore, the maximum value of

(cos 𝜃 + 𝜇 sin 𝜃)2 is:

(cos 𝜃 + 𝜇 sin 𝜃)2 = 1 + 𝜇2 (22)

After substituting 1 + 𝜇2 for (cos 𝜃 + 𝜇 sin 𝜃)2 in Equation 16, we find the well-known Searle Minimum [1, 2] formula which

considers an adjustment for the pedestrian’s (cyclist’s) height of center-of-mass. [4] That is:

𝑉𝑚𝑖𝑛 = √2𝜇𝑔(𝑆 − 𝜇𝐻)

1 + 𝜇2 (23)

the effects of pedestrian deceleration rates in roadside ... · stopping distance: 𝜇= 2 254 (4)...

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