Development and Intensity of Tire Marks -

Analysis of Influencing Parameters

G. Seipel (formerly research associate at the Institute of Automotive Engineering, TU Darm-

stadt),

Continental AG, Chassis and Safety division

Gunther.Seipel@continental-corporation.com

H. Winner

Institute of Automotive Engineering, Technische Universität Darmstadt

Summary

Visible tire marks on the road induced by friction are important evidence during reconstruc-

tion of traffic accidents, since they allow conclusions to be drawn about the speed the vehicle

was traveling at when it made the marks. Since simulation tools are increasingly being used

for reconstruction purposes, knowledge of the pre-conditions for the development of tire

marks and the parameters which affect their intensity are decisive for the validity and trans-

ferability of the simulation results. There are hardly any comprehensive and valid results

available, or those that are available are contradictory. Within the context of the study pre-

sented, the causal relationship of tire mark development was analyzed systematically, and the

possible parameters were examined empirically on the basis of a categorization according to

vehicle dynamics, tire and road characteristics as well as visibility. As a result of the research

project described here, we have a validated physical model in a mathematically describable

form within the measuring accuracy currently attainable for implementation in simulation

tools as well as an objective method for its parameterization.

1 Introduction

During the reconstruction of traffic accidents, visible tire marks made by the vehicles involved

take on a special role within the accident data since they can provide a wide range of infor-

mation, particularly about the movement of the vehicle. The term "tire mark" describes, in

quite general terms, the contact marks left by the tire on the surface driven upon. A categori-

zation of tire mark types which can often be found in the literature is illustrated in Figure 1.

Figure 1: Tire mark types and their classification according to cause of development and proper-

ties of the surface (cf.[10])

Whereas tire imprint marks and driving marks are caused solely by contact between the road

and the tire by the tire tread penetrating a loose surface or an intermediate medium (e.g. wa-

ter or dirt) being applied to a compacted surface, the other mark types are caused by the fric-

tion between tires and the road.

In terms of determining the cause of accidents, brake and drift marks play a particularly im-

portant role among the tire marks, since they are caused in most cases in the phase before the

actual accident happens, and are used to calculate the speed prior to braking and the speed

around bends for accident reconstruction. A basic distinction is made between backward and

forward calculation. In the case of backward calculation, the vehicle speed is determined on

the basis of the tire mark characteristics (e.g. length of mark, radius of mark, angle of tread

texture depicted) measured at the accident spot, whereas with forward calculation the tire

marks are created using driving trials or simulation tools, depending on estimated initial

speeds and accelerations, and then compared with the tire mark patterns at the accident spot.

The advantage of driving trials is the high validity of the results, although implementation is

relatively time-consuming and cost-intensive, and a safety risk for the driver, depending on

the accident situation being investigated. Accident simulation represents a safe and low-cost

alternative, but the quality of its results depend to a large extent on the model assumptions

implemented in terms of the correlation between vehicle dynamics variables and the devel-

opment of tire marks. More recent studies (e.g. [3]) have determined significant differences

between the dynamic limits for tire mark development usually assumed for calculation and

the values actually measured. In addition, the influence of tires and roads on the intensity of

Tire MarksDue toFriction Force

Due toVertical Force

Unpaved Surface

Paved Surface

Tire Imprint Marks

Brake Marks

Dig Mark

Yaw MarksDrift Marks

Driving Mark

Tumble Marks

Scuff Marks

Acceleration Marks

Mark Interruptions

Skid Marks ABS MarksInterval Marks

tire marks is a well-known fact, but one that has not been taken into account in simulation to

date.

The aim of the investigation presented here was to clarify the question of whether and under

what conditions a mathematically describable correlation can be determined between vehicle

dynamics variables and the intensity of tire marks. The focus was on brake and drift marks.

2 Status of Research and Technology

Among the different methods of calculation used depending on the tire mark pattern found,

two cases which use brake and drift marks only are examined in more detail below using ex-

amples. Where brake marks are straight (no additional vehicle rotation), the calculation of the

speed prior to braking is made on the basis of their length according to the equation (1)

[4].Here, v0 is the speed prior to braking, vC the calculated impact speed at the time of the

crash, µx the friction coefficient in longitudinal direction, lB the length of the brake marks, g

the acceleration of gravity and ts the brake threshold time of the vehicle.

2

0 22

xc x B s

µ gv v µ g l t

(1)

Calculation of the speed around the bend vK using the radius r of a drift mark (from driving

round a bend without braking) is made using the friction coefficient µy in lateral direction ac-

cording to the equation (2) [5].

K yv µ g r (2)

Both for the simulation of tire marks and for backward calculation of speed on the basis of tire

marks found at the accident spot, it is assumed that tire marks are created when the wheel-

road adhesion limit between the tires and the road is exceeded. Accordingly, the maximum

friction coefficients are used for the calculation, which are either determined empirically from

the maximum deceleration of the accident vehicle under comparable conditions (e.g. load,

state of road, ambient temperature) or from value tables.

Fitting in with the assumption of maximum friction coefficients, Danner and Halm [4], among

others, specify lower limits for the creation of visible tire marks of 8% to 10% longitudinal

slip or 5° to 10° slip angle. This corresponds to slip ranges where the maximum friction coeffi-

cient can usually be found. Studies by Simmermacher et al. [12], in which the visibility limits

were examined during, among other things, variation of lateral and longitudinal acceleration,

established visible tire marks from only 3% to 4% longitudinal slip.

There are different models available which consider the cause of development of tire marks as

visible black marks on the road surface. Basically, it is assumed that tire marks are the result

of tire wear particles on all compacted roads. According to Engels [6], for example, a high fine

roughness of the road (wavelength 10 µm to 1 mm) favors their development. In the case of

asphalt roads, the much more intensive characteristics of blocking marks, i.e. brake marks

from blocked wheels, compared with concrete surfaces are traced back to the thermal reac-

tion of the bitumen which melts and thus leads to blackening of the surface [1]. According to

Sakai and Araki, a tire-related effect, which leads to intensification of the marking due to tem-

perature [9] is the so-called "smearing" of tire rubber from a certain tire temperature on-

wards (approx. 200 °C).

Another factor of influence on the intensity of visible tire marks is the type of tire involved. In

this context, Simmermacher et al. [12] investigated the influence of different tire types and

established that the winter tires used made more intensive tire marks following the same

driving maneuvers than the summer tires used.

In addition to the factors listed, which influence the actual blackening of the road, optical pa-

rameters that influence the visibility of a tire mark (assessed on a purely subjective basis in

practice) are known. Ahlgrimm and Grandel, [2] among others, emphasize that the choice of

viewing direction, viewing angle and viewing height are decisive for the detectability of a tire

mark. The lighting conditions are a further important factor of influence. Metz and Ruhl [8]

assume, for example, that marks can be recognized better in diffuse light, in other words in

cloudy conditions, than in direct sunlight.

3 Modeling

In order to clarify the question as to which conditions visible tire marks occur under, the low-

er vehicle dynamics limits are of particular interest. Since it is known from the literature that

both the "bleeding" of bitumen and the "smearing" of tire rubber requires high friction and

thus slip values, primarily the abrasive wear of tire material is considered relevant for tire

marks at the visibility limit. In order to investigate the underlying model, it is assumed that

the intensity of a tire mark with any given tire-road combination is proportional to a certain

wear quantity related to the road area. The wear volume per area is designated in the follow-

ing as wear height hW and is the result of the equation (3) from the wear volume per distance s

covered VW/s and the width of the contact surface beff.

WW

eff

Vh

s b

(3)

According to wear models by Veith [13] or Grosch [7], the wear height of the work done by

the frictional force WR in the tread contact patch is proportional depending on the wear rate γ

specific to the friction partners. In relation to the distance s, this corresponds, according to the

equation (4), the product of the resulting tire guide force Fres and resulting gliding slip λs,res.

,

W Rres s res

V WF

s s (4)

Since slip is usually related to the rim and not the outer tire diameter, it is made up of the de-

formation slip considered irrelevant for the development of friction marks and the gliding

slip. In order to calculate the resulting gliding slip λs,res from the wheel slip λres, the linear part

of the µ-slip curve determined by the resulting tire slip resistance cres is subtracted from the

overall slip as in the equation (5).

,

ress res res

res

µ

c (5)

Using the "friction cake model" by Weber [14], according to which the resulting tire slip cor-

responds to the vectorial sum of the longitudinal and lateral slip, this representation can be

shown as a function of the longitudinal slip λ and slip angle α. This results in the product of

the resulting tire guide force Fres and resulting gliding slip λg,res, which is termed the gliding

frictional force FF,s below, according to the equation (6). Here, Fz is the wheel load, µx and µy

the frictional values at the edge of and across the tire, cλ the longitudinal and cα the slip angle

resistance of the tire.

2 2 2

2 2 2 2

, , sinx y

F s res s res z x y

µ µcF F F µ µ

c c

(6)

Alongside the distance-related wear, the width of the contact area beff is decisive for the wear

height (i.e. volume per area) shown in the equation (7). The width of the contact area is as-

sumed as the maximum width of the contact area, in other words minus the tread negative

share, perpendicular to the slip direction. This is illustrated in Figure 2 in the left-hand image

for the case of pure longitudinal slip using the example of a test tire (ContiSportContact3

225/45 R17). The image shows the so-called "footprint", in other words the pressure distribu-

tion over area in the tire contact area which was measured at a tire inner pressure of 2.5 bar

and a vertical load of 4.7 kN using a pressure-measuring film. While the maximum lateral

elongation of the contact area is 162 mm, the effective friction width under pure longitudinal

slip would only be 109 mm. In order to determine the effective friction width under any slip

direction, the tread contact patch is assumed to be an ellipse, the two half-axes of which cor-

respond to the maximum width and height of the actual contact area. This is shown in the

right-hand image in Figure 2. The angle β designates the directional angle of the resulting slip

according to the equation (7).

sin

arctan

(7)

The effective friction width is thus generally obtained from the equation (8) from the contact

patch height bL, the contact patch width bL and the slip angle β.

2 2

cos sineff L Lb b h (8)

Figure 2: Model for effective friction width beff.

From the basic assumption that the intensity of a tire mark is proportional to the wear volume

per surface area, the assumption follows from the equations (3) and (4) that the intensity is

also proportional to the width-related gliding slip force. One proportionality factor is repre-

sented by the wear rate γ according to the equation (4) which describes the correlation be-

tween wear and gliding slip force and is mainly influenced by the tribological characteristics

of the friction pairing (e.g. wear resistance of the rubber compound, road roughness). What

has not been considered so far, however, is the factor which describes the correlation be-

tween wear height and intensity. This is termed the blackening rate ξ below. This results in

the correlation shown in the equation (9) between the friction mark intensity I and the gliding

friction force FF,s related to the effective width beff..

bL

hLbeff

β

λ λres

sinα.

b = 162 mm

h = 105 mm

bL = 109 mm

, ,F s F s

eff eff

F FI

b b (9)

As far as the blackening rate is concerned, it is assumed that this mainly depends on the opti-

cal characteristics of the road and the worn tire material. For this reason, the wear and black-

ening rate is summarized in the marking sensitivity ζ which describes the tire-road influence

on the intensity of tire marks.

The thus defined correlation only takes the factors of influence on the actual blackening of the

road into account and hereby assumes that the intensity of tire marks is an objective meas-

ured variable. However, the literature knows no objective method for determining the intensi-

ty of tire marks. There is a large number of empirical values available which demonstrate the

extent to which the subjectively evaluated contrast of marks to the road changes depending

on visibility and light conditions (e.g. direction of light and viewing, color temperature, view-

ing distance, illumination). Derived from this, the basic model assumes that even with possi-

ble objective determination of the intensity, there is a further influencing factor κ resulting

from the given visibility and light conditions which represents the ratio of intensity under the

given conditions to the intensity under reference conditions (ideally optimum visibility condi-

tions). For this reason, the experimental investigation of the model predictions should strive

to achieve constant visibility and light conditions for the results to be comparable.

4 Testing Methods and Tools

The central approach of the investigation consists of the isolated investigation of the possible

parameters which influence the development of friction marks and their intensity. On the ba-

sis of the basic model, these parameters are divided into three disjunctive categories as shown

in Figure 3:

Vehicle dynamics parameters which influence the width-related gliding friction force,

influences of tire and road characteristics on the sensitivity of marking and

optical parameters which influence the visibility.

Figure 3: Categorization of parameters [10]

With regard to the vehicle dynamics parameters, two major hypotheses are derived from the

model:

1. Tire marks can develop as soon as gliding slip occurs between the tires and the road.

2. The intensity of a tire mark with constant marking sensitivity and constant visibility

and light conditions only depends on the amount of width-related gliding friction force

and is thus independent of the direction of slip.

In order to investigate these hypotheses, the tire measuring trailer PETRA (German acronym

for Personenwagen-Reifen-Traktions-Messanhänger = passenger car tire traction measuring

trailer) was used, which, unlike a conventional passenger car, makes the independent varia-

tion of wheel load, longitudinal slip, slip angle and vehicle speed possible (cf. section 4.1). This

way, tire marks were produced under different longitudinal slip and slip angle values at con-

stant wheel load and vehicle speed, and the tests were repeated for different tire-road combi-

nations (cf. sections 4.4 and 4.5).

The transferability of the results to a real passenger car under lateral and longitudinal slip

were carried out using a test vehicle and an identical tire-road combination (cf. section 4.2).

The driving maneuvers chosen were straight braking and steady-state cornering testing. What

is common to both driving maneuvers is that the acceleration acting on the vehicle and thus

the tire forces are almost constant. In the case of straight braking, this ideally leads to con-

stant brake slip and with steady-state cornering testing to constant slip angles at the wheels,

whereby lateral slip only occurs at the non-driven axis. The driving maneuvers were designed

so that maximum longitudinal or lateral accelerations are reached, in order to produce tire

marks which are as visible as possible.

One major requirement for the investigation of the parameters influencing the marking sensi-

tivity - in the sense of a transfer function between width-related gliding friction and friction

mark intensity - was that the measurement of input and output variables should be as direct

as possible. As far as the width-related gliding friction force is concerned, this is only possible

to a very limited extent with the tire measuring trailer, since the gliding friction force is calcu-

Vehicle DynamicsTire and Road

SurfaceVisibility

Friction Force /Friction Width

Tire Marking Sensitivity

Visibility Factor

Characteristical Parameter

Categories of Influences

,F s

eff

F

b

lated model-based using the rim-related forces and the slip, whereby local differences in forc-

es and gliding speeds over the contact patch are left unconsidered to a major extent. During

tests with PETRA, the effective friction width is not measured during the drive either, but ra-

ther is determined from static footprint measurements for comparable wheel loads. For this

reason, the linear friction test stand VERINA (German acronym for Versuchseinrichtung zur

Reifenspur-Intensitäts-Analyse = test equipment for the analysis of tire mark intensity) was

developed. Here, only tread sections are used rather than a whole tire, which allows friction

force and friction movement to be measured and controlled very close to the contact zone (cf.

section 4.3).

For evaluation of the friction mark intensity, an objective method was developed under re-

producible visibility and light conditions (cf. 4.6). This was used for investigating the parame-

ters in all three categories and thus created the base for comparability of the results.

4.1 Tire Measurement Trailer PETRA

The main structure of PETRA is shown in Figure 4. The slip angle is adjusted in accordance

with the target value specification at the measuring wheel (left-hand side) by means of an

electric motor, while the reference wheel on the right-hand side compensates the yaw mo-

ments induced by the measuring wheel and keeps the float angle of the trailer constant at al-

most 0°. The brake slip at the measuring wheel is produced by the wheel driving a pump by

means of a transmission; this pump pumps hydraulic oil against a throttle. The drive torque is

controlled via the flow volume by means of a proportional valve depending on the wheel

speed. The pumping moment and the brake moment transmitted via the measuring wheel on

account of traction are in a stable state of balance.

Figure 4: Tire measurement trailer PETRA [10]

The important technical key data related to the possible variation range and the sensor sys-

tem installed are listed in Table 1 and Table 2.

Table 1: PETRA sensor system

Sensor Measured variable Measuring

range

Resolution

Datron V2 Correvit-Sensor Path difference - N/A

Speed 0.25 – 250 km/h

Direction of movement ± 40°

Pepperl & Fuchs TRD-J-

1000 Speed Sensor

Wheel rotation angle,

wheel speed

- 0.36° (1000

increments)

Kistler KST 223000

Measuring rim

Longitudinal force ± 20 kN 20 N

Lateral force ±15 kN 15 N

Vertical force 0 – 20 kN 20 N

Moment around the x-axis ± 6 kNm

Moment around the y-axis ± 6 kNm

Moment around the z-axis ± 2.5 kNm

ASM BA-30TV IR-Sensor Temperature 0 – 500 °C 0.2 °C

SICK WL12-2P-130-Light

Barrier

Light reflection impulse 1.5 kHz

HBM U2 Load Cell Axial force < 491 N N/A

IR TemperatureSensor

CorrevitTM-Sensor

Light Barrier

Power Supply

Mess- und Steuerelektronik

Wheel LoadAdjustment

Gearbox(Covered)

Axial Piston Pump with Valve (Covered)

Throttle(Covered)

Reference Wheel

(Covered)

Measurement Wheel with Force

Transducer

Table 2: PETRA variation range

Variation parameter Value range

Speed max. 90 km/h

Longitudinal slip 0% – 90%

Slip angle ± 8°

Camber angle ± 5°

Wheel load 4.6 – 5.8 kN

Tire dimension 14 – 17", 175 – 225 mm

4.2 Test Vehicle

The test vehicle used was a Mercedes C-Class (type C 180, model series W 204), on which two of

the test tires of dimension 225/45 R17 were used. The main requirement on the test vehicle was to

be able to record the same parameters as with PETRA to calculate the gliding friction force FF,s,

according to the equation (10), on the four tires.

2 2 2

, ,2 2 2 2

, , , ,

,

sinx i y i

F s i x i y i i i

z i

F FcF F F

c F c

(10)

In particular, these include:

the tire longitudinal force Fx,i,

the tire lateral force Fx,i,

the longitudinal slip λi, which is calculated using the wheel speed ωi, dynamic tire radi-

us rdyn and wheel hub speed vi according to the equation (11) for every wheel,

,

,max ,

i dyn i i

i

i dyn i i

r v

r v

(11)

and the tire slip angle αi.

The longitudinal rigidity cλ and lateral rigidity cα of the tires were determined for every tire-

road combination using the characteristic curves measured with PETRA and assumed to be

constant.

This requirement was implemented by equipping the vehicle with respective sensors. An

overview of the main components of the measuring system is shown in Figure 5. The forces in

all three spatial directions were measured on the four wheels using force measuring hubs.

These also have wheel speed sensors. There is a CorrevitTM-sensor mounted to the trailer

coupling hitch which directly measures the vehicle or wheel hub speed (only applicable for

straight driving).

Figure 5: Test car (Mercedes C-Class, W 204)

A further CorrevitTM-sensor on the front right-hand wheel was used to measure the slip angle

and the wheel hub speed with an additional steering angle on the front right-hand wheel. Ac-

cordingly, only the measured data at the front right-hand wheel and its markings were used

for the comparison with PETRA marks under lateral slip.

The light barrier also mounted on the trailer coupling hitch was used for local assignment of

the measured data with the aid of light barrier reflectors. The important technical key data

related to the sensor system used are listed in Table 3.

Measurement Equipment

Wheel Force Sensor

Light Barrier

CorrevitTM-Sensor

CorrevitTM-Sensor

Computer

Incremental Encoder

Table 3: Sensor system in the test vehicle

Sensor Measured variable Measuring range Reversals

Datron SL CorrevitTM

-Sensor Path difference - 2.5 mm

Speed 0.5 – 250 km/h

Direction of movement ± 40° ± 0.1°

Datron SFII CorrevitTM

-Sensor Path difference - 2.08 mm

Speed 0.3 – 250 km/h

Direction of movement ± 40° ± 0.1°

A&D WFS Wheel Force Sensor Longitudinal force ± 24 kN

6 N Lateral force ±15 kN

Vertical force ± 24 kN

Moment around the x-axis ± 4.5 kNm

1.8 Nm Moment around the y-axis ± 4.0 kNm

Moment around the z-axis ± 4.5 kNm

SICK WL12-2P-130 Light Barrier Light reflection impulse 1.5 kHz

4.3 Linear Friction Test Stand VERINA

The linear friction test stand VERINA (cf. [11]) mainly comprises a frame which is permanent-

ly installed on the road and a slide which moves horizontally, on which the tire tread elements

are pressed onto the road by means of spring pre-tension. The normal force and the gliding

speed are prescribed. The forces at the tread element are measured using a 3D load cell. The

main components are shown in Figure 6.

Figure 6: Friction test stand VERINA [10]

IR-Temperature Sensor

Tread Part Holder (dismounted)

Normal Force Cylinder

3D-Force Transducer

Temperature Measuring Gap

Sled

Motor

The possible variation range with regard to friction path, gliding speed, normal force and di-

mensions of the tread sections are summarized in Table 4. Table 5 contains the main technical

data of the sensor system installed.

Table 4: VERINA variation range

Variation parameter Value range

Friction path ≤ 1.78 mm

Normal force 60 N – 613 N

Friction speed 1 mm/s – 3 m/s

Dimension of the tread elements 10 x 10 – 100 x 100 mm²

Table 5: VERINA sensor system

Sensor Measured variable Measuring range Resolution

ME K3D-120 force sensor Longitudinal force

± 1 kN 0.8 N Lateral force

Vertical force

Optris CT laser LT Temperature -50 – 975 °C 0.1 °C

4.4 Test tires

Four tires with differing characteristics and purposes of application were used as test tires. An

overview of the tires used can be seen in Figure 7. Table 6 lists the exact designation, dimen-

sion and UTQG classification (Uniform Tire Quality Grade) of the tires.

Figure 7: Test tires used and corresponding tread sections [10].

Goodyear Excellence

ContiSportContact 3ContiEcoContact 3

Pirelli Sottozero W210

Table 6: Test tires used

Designation

Manufacturer Tire type Dimension UTQG mark-

ing

Tre

ad

wea

r

Tra

ctio

n

Tem

per

atu

re

ContiSportContact 3

MO

Continental Summer tires 225/45 R 17 91

Y

280 AA A

ContiEcoContact 3 MO Continental Summer tires,

with optimized rolling

resistance characteris-

tics

185/65 R 15 88

T

280 A A

Excellence MOE Goodyear Summer tires, with

run-flat characteristics

225/45 R 17 91

W

240 A A

Sottozero W210 MO Pirelli Winter tires 225/45 R 17 91

H

- - -

In order to determine the effective friction width, footprint measurements were carried out

for all four tires, during which the tire was pressed vertically onto a pressure-measuring film

using constantly increasing normal force (0 – 10 kN). This makes the pressure distribution

over area and contact surface depending on the wheel load available for each tire. Figure 8

shows the pressure distribution over area for the four tires and the respective contact surfac-

es at the tire inner pressure of 2.5 bar (differential pressure) and wheel load of 4.7 kN (corre-

sponds to the static wheel load of the tire measurement trailer PETRA at the measuring

wheel) used in the tests. From the contact patch areas AL measured, it can be seen that despite

the larger tread pitch, the winter tire (Pirelli Sottozero W210) has the smallest tread negative

share and thus the largest contact area of the four tires, while the ContiSportContact3 has the

smallest contact area due to the very wide peripheral grooves.

Figure 8: Tread imprint, pressure distribution over area and contact patch area AL for the four

tires (pi = 2,5 bar, Fz = 4.6 kN)

4.5 Test Road

Depending on the purpose of the examination, the tests were carried out on up to three differ-

ent road surfaces, the textures of which are illustrated in Figure 9:

a) Old rough asphalt

b) New mastic asphalt

c) Concrete

Figure 9: Surface texture of the roads tested.

yR

in mm

x R in m

m

-100 -80 -60 -40 -20 0 20 40 60 80-60

-40

-20

0

20

40

60

80

100

pN

in b

ar

0

2

4

6

8

10

12

14

16

yR

in mm

x R in m

m

-100 -80 -60 -40 -20 0 20 40 60 80-60

-40

-20

0

20

40

60

80

100

pN

in b

ar

0

2

4

6

8

10

12

14

16

yR

in mm

x R in m

m

-100 -80 -60 -40 -20 0 20 40 60 80-60

-40

-20

0

20

40

60

80

100

pN

in b

ar

0

2

4

6

8

10

12

14

16

Goodyear Excellence, AL = 1,08 ∙ 104 mm²

ContiSportContact 3, AL = 1,00 ∙ 104 mm²ContiEcoContact 3, AL = 1,12 ∙ 104 mm²

Pirelli Sottozero W210, AL = 1,20 ∙ 104 mm²

4.6 Evaluation of Intensity

The method of evaluating intensity developed during the study comprises the photo image of

the marks produced under reproducible visibility and light conditions and digital image anal-

ysis for the objective determination of an intensity value. The photo was taken in a mobile and

lightproof tent (2.6 m ⋅ 1,25 m ⋅ 1.6 m) made of a truck tarpaulin which was aligned centrally

and in longitudinal direction above the mark area in question. Within the tent, a digital reflex

camera as well as an external flash with a reflection shade (for indirect diffuse exposure) are

attached at a fixed height and angle. This is shown in Figure 10.

Figure 10: Photo tent for reproducible photo taking [10].

The photos were taken in the direction of travel or friction under constant camera settings

(aperture, exposure time, focal length, ISO sensitivity). The main imaging parameters are

summarized in Table 7.

ReflectorFlash

Camera

Table 7: Camera and flash settings [10]

Camera model Nikon D90

Number of pixels of the image sensor

in tire mark direction

max. 4288 (crosswise) x

2848 (lengthwise)

Lens AF-S DX VR Zoom-

NIKKOR 18-200 mm

1:3.5-5.6G IF-ED

Focal length 18 mm

Camera height 60 cm

Angle of the camera to the roadway -30°

f-number 11

ISO value 400

Exposure time 1/80 s

Flash unit Nikon SB-28DX

Flash capacity 1/1

Max. guide number 42 (24 mm) at ISO 200

The evaluation of photos taken in this way was performed by a MATLAB® routine, the im-

portant steps of which are shown in Figure 11. In the first step, the perspectively distorted

photos are rectified so that an image from vertically above is produced. For this step, red

markings are fixed in the photo tent which are detected on the photos and used to transform

the photo according to the actual relative positions of the points. In the second step, the inho-

mogeneous lighting in the longitudinal direction, which is the result of the angled illumina-

tion, is balanced out.

Figure 11: Important steps of the evaluation algorithm

In the third step, the position of the mark in the photo (angle and distance to the center of the

image) is detected. This is done by evaluating the image histograms, in other words the gray

scale distribution, over the image width under different angles of rotation. The result of this

analysis represents the average gray value determined over the height of the image depend-

ing on the distance and angle to the center of the image. Under the assumption that the mark

represents a line-shaped area of lower gray values compared to the road, the position of the

mark is determined from the minimum gray value distribution. In the fourth step, the mark

intensity is calculated as a standardized contrast value in that the difference between the av-

erage gray value FbG of the road and the average gray value SpG of the friction mark is divided

by the average gray value of the road according to equation (12).

Fb Sp

Fb

G GI

G

(12)

1. Rectification

2. Compensation of Inhomogeneous Lighting in Longitudinal Direction

÷ =

3. Angle and Edges Detection

4. Contrast Calculation, ,

,

n Fb n Sp

rel

n Fb

G GI

G

5 Results

5.1 Vehicle dynamics

Figure 12 shows the comparison of the friction values measured using PETRA at the visibility

limit and the maximum friction values of the four tires on the old asphalt with separate varia-

tion of the longitudinal slip and the slip angle. The diagram shows the friction value in longi-

tudinal direction over the friction value in lateral direction for each tire. It can be seen that in

the case of the ContiEcoContact3 in particular, the friction value at the visibility limit both un-

der longitudinal and lateral slip is significantly below the maximum friction value of the tire

on the road. The visibility limit only correlates approximately with the tire-road adhesion lim-

it with one of the four tires. In other words, the widely accepted assumption that tire marks

are only produced at the tire-road adhesion limit is clearly revoked by these results.

Figure 12: Comparison of the friction values measured at the visibility limit (blue) and the max-

imum friction values (red) of the four tires on the old asphalt road [10].

In Figure 13, the measured intensity of the marks over the width-related gliding friction force

are superimposed, which were produced using PETRA and the ContiSportContact3 on old as-

phalt, varying the slip direction and height. In the diagram, the blue circles represent the tire

marks produced under longitudinal slip, the green squares the ones produced under com-

bined slip and the red triangles the ones under lateral slip. The black line maps the course of

the model function, the slope of which corresponds to the marking sensitivity of the respec-

tive tire-road combination from the VERINA measurements. The vertical error bars indicate

the scatter range of the intensity values ΔIrel = 0.03 on the basis of roadway inhomogeneity.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

y

x

grenz

(Goodyear Excellence)

grenz

(Pirelli Sottozero W210)

grenz

(ContiSportContact 3)

grenz

(ContiEcoContact 3)

max

(Goodyear Excellence)

max

(Pirelli Sottozero W210)

max

(ContiSportContact 3)

max

(ContiEcoContact 3)

x =

y

The horizontal error bars correspond to the uncertainty in calculating the width-related glid-

ing friction force from the measured slip values due to the possible fluctuation in the actual

tire rigidities of ± 20 % compared to the assumed constant values. It can be seen that within

the uncertainty range, the intensities of the tire marks produced at identical width-related

gliding friction force are independent of the slip direction. In addition, there is a rise in inten-

sity values from a width-related gliding friction force of 6 N/mm which correlates with the

linear model function within the context of the scatter range of intensity values. No clear in-

crease in intensity values with width-related gliding friction force can be established below

about 4 N/mm. With decreasing width-related gliding friction force, the intensity values re-

main at approx. 0.02 – 0.04. This can be explained by the fact that the road has a certain back-

ground emission due to its inhomogeneity which corresponds to the standard deviation of the

road gray value distribution around its average value. The results thus support the hypothesis

that the intensity of a tire mark under constant tire-road combination can be exclusively ex-

plained on the basis of the width-related gliding friction force, independently of the direction

of slip.

Figure 13: Mark intensity over the width-related gliding friction force for different directions of

slip using PETRA measurements of the ContiSportContact3 on old asphalt

The results of the transferability of the model to a real passenger car are shown in Figure 14

and Figure 15. Figure 14 shows the contrast intensity of the marks produced during straight

braking with the test vehicle (W204) over the width-related gliding friction force compared

with the model function as well as marks from PETRA under longitudinal slip and the VERINA

reference marks. The marks made by the front axle of the test vehicle are shown as lilac dia-

monds (front left-hand wheel) and red circles (front right-hand wheel), the PETRA marks as

0 2 4 6 8 10 12 14 160

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

Friction Force per Width FF,s

/beff

in N/mm

Tir

e M

ark

Inte

nsity I

rel

Longitudinal Slip

Combined Slip

Lateral Slip

Model Function

green squares and the VERINA marks as blue triangles. It can be seen that the intensities of

the marks made by the test vehicle (passenger car) in the uncertainty range – represented by

the error bars – are shown in good proximity by the model function parameterized with

VERINA measurements. The intensities of the PETRA marks under longitudinal slip and the

VERINA marks correspond to the intensities of the marks made by the test vehicle at the same

width-related gliding friction force.

Figure 14: Mark intensity over the width-related gliding friction force at full brake application

with the test vehicle compared to marks from VERINA and PETRA under longitudinal slip.

Figure 15 shows the intensity of the mark made by the front right-hand wheel during steady-

state tirepad testing over the width-related gliding friction force compared to the model func-

tion and the marks produced with PETRA under lateral slip. It can be seen in this case too that

the mark intensity is well approximated by the model function within the framework of un-

certainties, and the intensities of the PETRA and VERINA marks correspond to the intensities

of the test car under identical width-related gliding friction force. This proves that the model

prediction for the driving maneuvers and environmental conditions tested can be transmitted

to a real passenger car.

0 5 10 15 20 250

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Friction Force per Width FF,s

/beff

in N/mm

Tir

e M

ark

Inte

nsity I

rel

VERINA

PETRA

W 204, VR

W 204, VL

Model Function

Figure 15: Mark intensity over the width-related gliding friction force at steady-state tirepad

testing with the test vehicle (passenger car) compared to marks from VERINA and PETRA under

lateral slip.

5.2 Marking Sensitivity

During tests with the friction test stand VERINA, reference marks were produced using tread

sections from the four tires on three different roads under varying friction force. The course of

the loss in mass of the tread elements under friction force, which was determined using an

analysis scale, was used to determine the wear rate γ for each tire-road combination through

linear regression, while the course of intensity of reference marks over the loss of mass was

used to determine the blackening rate ξ. Figure 16 shows the blackening rate determined this

way over the wear rate for each of the tire-road combinations considered. Since the marking

sensitivity ζ is the product of the blackening rate and wear rate, all the combinations of identi-

cal marking sensitivity are on one of the parallels to the straight lines marked in the diagram

with double logarithmic representation. The marking sensitivity decreases towards the origin

of the diagram. The result shows that no statement about the marking sensitivity can be made

solely on the basis of a tire-road combination. It can be seen, for example, that the old rough

asphalt has the highest wear rate on all tires compared to the other roads, as can be expected,

but due to the low contrast produced by the wear on the road, it has the lowest blackening

rate and thus a lower marking sensitivity than the other two types of road. On the other hand,

the concrete road has the lowest wear rates, but has the highest blackening rate due to its

light color, since here even a little wear leads to a significant contrast. This means that there is

no clear correlation between the blackening rate and wear rate, and that the connection be-

0 5 10 15 20 250

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Friction Force per Width FF,s

/beff

in N/mm

Tir

e M

ark

Inte

nsity I

rel

VERINA

PETRA

W 204, VR

Model Function

tween width-related gliding friction force and friction mark intensity can therefore only be

determined when the marking sensitivity of the tire-road combination is known.

Figure 16: Blackening rate ξ over wear rate γ and straight line of constant marking sensitivity ζ

[10].

5.3 Visibility

Figure 17 shows extracts of the result of investigating optical influences on friction mark in-

tensity. It shows the visibility factor κ of a mark with variation in camera and flash angle in the

photo tent. The visibility factor is calculated from the ratio of the intensity measured in each

case to the maximum intensity which occurred during the test. The result shows that the mark

contrast is at its highest of all the combinations studied at a camera angle of 30° in the direc-

tion of travel and the same direction of exposure, which is why these settings were also cho-

sen for the objective method of intensity evaluation.

101

102

101

102

Wear Rate in mg/Nm

Bla

ckenin

g R

ate

in m

m2/g

ContiEcoContact 3, Aged Asphalt

ContiEcoContact 3, New Asphalt

ContiEcoContact 3, Concrete

ContiSportContact 3, Aged Asphalt

ContiSportContact 3, New Asphalt

ContiSportContact 3, Concrete

Pirelli Sottozero W210, Aged Asphalt

Goodyear Excellence, Aged Asphalt

Goodyear Excellence, New Asphalt

Goodyear Excellence, Concrete

Tire Marking Sensitivity = const.

Figure 17: Standardized contrast of the mark with variation of camera and light angle [10]

Experience from the literature, which reports particularly good contrast ratios when the

marks are considered at a flat viewing angle in the direction of travel with the sun behind the

observer (e.g. [8]) have thus been confirmed for the first time by objective measurements.

6 Conclusion and Outlook

Within the context of the study presented, the pre-conditions for the production of visible fric-

tion marks on compacted roads as well as the parameters of influence on their intensity were

analyzed. The study was based on a physically motivated model which led to the categoriza-

tion of the possible parameters of influence in three disjunctive areas. These are vehicle dy-

namics parameters, tire and road characteristics as well as optical conditions. In terms of ve-

hicle dynamics parameters, it is assumed that only the extent of the width-related gliding fric-

tion force, which corresponds to the product of the resulting tire guide force and resulting

gliding slip, influences the friction mark intensity. A proportional correlation is only assumed

if the wear and blackening characteristics of tire and road, termed marking sensitivity, can be

considered as constant. Since the mark contrast perceived varies solely on the basis of optical

factors of influence, a minimization of the relevant interference factors is required.

The assumptions made were examined empirically using a tire measurement trailer, a pas-

senger car and a friction test stand for tread elements. A photometric method was developed

for the objective evaluation of the mark contrast on the road, which makes measurement of

the intensity possible on the basis of photos under reproducible visibility and light conditions.

The results of tests with the tire measurement trailer confirmed the assumption that the in-

tensity of a tire mark under constant tire-road combination depends on the degree of width-

20 40 60 80 100 120 140 1600

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

11

Light Angle in °

Vis

ibili

ty F

acto

r

Camera Angle = 30°

Camera Angle = 90°

Camera Angle = 150°

related gliding friction force and is independent of the direction of slip. Pre-condition for the

production of a mark is a minimum width-related gliding friction force, the extent of which is

determined by the marking sensitivity of tires and road. The investigation of ten different tire-

road combinations with the friction test stand in terms of their wear rate and blackening rate

showed that the light color of the road in particular has a significant influence on marking

sensitivity. For this reason, a quality-related statement concerning the marking behavior of a

tire-road combination cannot be made solely on the basis of the wear rate. The transferability

of the results to a real passenger car was proved using a longitudinal and lateral dynamic

driving maneuver.

As the next step towards using the findings for accident reconstruction, the mathematical cor-

relation found between the forces as well as the slip at the tire and the friction mark intensity

could be implemented in accident reconstruction tools. As far as the marking sensitivity re-

quired for parameterization of the model is concerned, the extent to which general tendencies

can be derived for certain tire and road types on the basis of the consideration of further tire

and road combinations should be investigated. These tendencies could be stored in the form

of a database for representative cases.

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