1. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
INTERNATIONAL JOURNAL OF MECHANICAL ENGINEERING
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 6, November - December (2013) © IAEME
AND TECHNOLOGY (IJMET)
ISSN 0976 – 6340 (Print)
ISSN 0976 – 6359 (Online)
Volume 4, Issue 6, November - December (2013), pp. 69-77
© IAEME: www.iaeme.com/ijmet.asp
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IJMET
©IAEME
IMPLEMENTATION OF GRAPHICAL - ANALYTICAL METHOD IN
DETERMINATION OF SPEED OF VEHICLE IN CASE OF ROAD
ACCIDENT AND COMPARING OF RESULTS WITH THE
SOFTWARE METHOD
1
1,2
Gëzim HOXHA,
2
Nijazi IBRAHIMI
University of Prishtina, Faculty of Mechanical Engineering, Department of Traffic and
Transport, St. Sunny Hill, n.n., 10 000 Prishtina, Kosovo
ABSTRACT
In this paper is treated the problem of determining the speed of movement of vehicles in case
of road accident. One frequent cause of accidents in road is the speed of movement and adaptation
conditions with circumstances of the road. For determination of speed is used the graphic-analytical
method which based in maintaining the quantity of movement of the vehicles before and after the
collision. This method takes into account several factors such as: measures of vehicles involved in
the accident, angle between the directions of movements of the vehicles before and after the
collision, the displacement distance of vehicle after the collision. Results obtained with graphicalanalytical method are compared with software method - through PC Crash software.
Keywords: Velocity, Vehicle, Road, Angle, Distance, Collision, Simulations.
1. INTRODUCTION
Determination of velocities of motion of vehicles participating in the accident constitutes the
most important analysis in the delivery of final results to finding the cause of truly accident.
Implementation of graphical –analytical method for determination of speed of vehicle in the case of
accident is treated for three different cases of accidents.
In each of the accidents have been involved two vehicles with different technical features.
Technical characteristics of vehicles involved in the accidents which have been subjected to
treatment in this paper and the road conditions which are causing accidents are presented in Table1.
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2. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 6, November - December (2013) © IAEME
Table.1. Technical characteristics of vehicles involved in the accidentsand the road conditions
First case of road accident
Second case of road
accident
(Vehicle)
(Vehicle)
Technical
Characteristics
Toyota Land
Cruiser
VW Golf3
TDI
Truck
DAF
Mercedes
Benz 200
Land Cruiser
3.0 D-4D
1HXO
2700 ATI
124
Engine type:
Engine power
[kW]:
Diesel
Diesel
Diesel
96
81
Weight [kg]:
2080
Length [m]:
Third case of road
accident
(Vehicle)
Opel Astra
Ford
Eskort
X16SZR
Escort 1.6
16V
Benzin
Benzin
Benzin
295
80
55
66
1055
6100
1321
1070
1145
4.72
4.15
5.63
4.74
4.11
4.3
Width [m]:
1.88
1.74
2.5
1.74
1.71
1.7
Height [m]:
1.85
1.44
-
1.44
1.43
1.46
Track width [m]:
1.57
1.51 / 1.49
2.10 / 2.10
1.49
1.485 /
1.46
1.44 / 1.46
Wheelbase [m]:
2.79
2.51
4.4
2.8
2.61
2.52
265/65R17S
195/65R15V
295/80R22C
185/65R14
185/65R15
175/70R13
13.1
10.8
-
9.6
16.5
12.7
-
-
0.71
0.9
1.35
0.82
0.81
Type
Tire dimensions :
Accel. 0-100
[km/h]:
Rear overhang
[m]:
Front overhang
[m]:
Type of road
Number of
lanes
Vehicle traffic
Road condition
Visibility
0.780000
1.08
0.72
0.840000
0.860000
Regional road
Highways
Regional road
1 lanes for directions
2 lanes for directions
1 lanes for directions
average
asphalt and dry
good - sunny day
average
asphalt and wet
rainy weather
average
asphalt and wet
rainy weather
2. ANALYSIS OF FIRST CASE OF ROAD ACCIDENT
In this accident are involved two vehicles:“Toyota Land Cruiser” and “VW Golf”.Vehicles
before the crash have been moving in the opposite direction with one another. Collision between
vehicles is made at the angle 21○ .After crash, vehicle " Toyota Land Cruiser " stopped in the
distance of 11[m] from collision position, vehicle " VW Golf " stopped near collision position
turned at 140○from direction of motion before the crash .
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3. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 6, November - December (2013) © IAEME
Figure 1. Positions of vehicles “Toyota Land Cruiser” and “VW Golf” before and after crash
2.1. IMPLEMENTATION OF GRAPHIC - ANALYTICAL METHOD IN CALCULATION
OF SPEED VEHICLES “TOYOTA LAND CRUISER” AND “VW GOLF”
This method is based on the law on maintaining the quantity of motion for vehicles “Toyota
Land Cruiser” and “B” before and after the crash. According to this law have:
K T + K VW = K 'T + K 'VW ,
K 'T − K T = I T
dhe
d K
dt
s
= F = 0 → K '− K = I,
K 'VW − K VW = I VW ,
(1)
I T = − I VW
(2)
K T = mT ⋅ vT - quantity of motion of “Toyota Land Cruiser” before collision,
(3)
K 'T = mT ⋅ v 'T - quantity of motion of “Toyota Land Cruiser” after collision,
(4)
KVW = mVW ⋅ vVW - quantity of motion of “VW Golf” before collision,
(5)
K 'VW = mVW ⋅ v'VW - quantity of motion of “VW Golf” after collision.
(6)
mT = m aT + m n + 2 ⋅ m p = 2080 + 75 + 2 ⋅ 75 = 2305[ kg ] -weight of
passangers.
“Toyota Land Cruiser” with
mVW = m aM + m n + 4 ⋅ m p = 1055 + 75 + 4 ⋅ 75 = 1430 [ kg ] - weight of “Toyota Land Cruiser” with
passangers.
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4. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 6, November - December (2013) © IAEME
K VWx = mVW ⋅ vVWx = mVW ⋅ vVW ⋅ cos 90 = 0
K VWy = mVW ⋅ vVWy = mVW ⋅ vVW = 1715 ⋅ vVW
(7)
,
(8)
K Tx = m T ⋅ v Tx = m T ⋅ v T ⋅ sin 21 o = 2305 ⋅ v T ⋅ 0 . 35 = 806 . 75 ⋅ v T ,
(9)
K Ty = m T ⋅ v Ty = m T ⋅ vT ⋅ cos 21 o = 2305 ⋅ vT ⋅ 0 . 93 = 2143 . 6 ⋅ v T .
(10)
a’2Tasf=5.0 [m/s2]- break of “Toyota Land Cruiser ” after collision in asphalt
a’2Tdh=4.0 [m/s2]- break of “Toyota Land Cruiser ” after collision in street earthy.
Speed of “Toyota Land Cruiser” and “VW Golf” after collision :
v 'T =
v 'VW =
2 ⋅ a ' 2 asf ⋅S Tasf + 2 ⋅ a ' 2 dh ⋅S T dh =
2 ⋅ a ' 2 asf ⋅ S VWasf
=
2 ⋅ 5 ⋅ 4 + 2 ⋅ 4 ⋅ 7 ≈ 10 [ m / s ] = 36 [ km / h ]
(11)
2 ⋅ 5 ⋅ 2 = 4 . 4 [ m / s ] = 15 [ km / h ],
(12)
K 'Tx = mT ⋅ v 'Tx = mT ⋅ v 'T ⋅ cos 30 o = 2305 ⋅ 10 ⋅ 0 .86 = 198213 [ kg ⋅ m / s ]
K 'Ty = mT ⋅ v 'Ty = mT ⋅ v 'T ⋅ sin 30 o = 2305 ⋅ 10 ⋅ 0 .5 = 11525 [ kg ⋅ m / s ]
,
(13)
,
(14)
K 'VWx = mVW ⋅ v 'VWx = mVW ⋅ v 'VW ⋅ cos 50 o = 1430 ⋅ 4 .4 ⋅ 0 .64 = 4026 [ kg ⋅ m / s ]
K 'VWy = mVW ⋅ v 'VWy = mVW ⋅ v 'VW ⋅ sin 50 = 1430 ⋅ 4 .4 ⋅ 0 .76 = 4782 [ kg ⋅ m / s ]
72
.
,
(15)
(16)

5. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 6, November - December (2013) © IAEME
Figure 2. Graphics of maintaining quantity of motion for vehicles
From grafics is measured KVW=331cm= 33100[kg·m/s] and KT = 638cm = 63800[kg·m/s].
From (3) ⇒ vT =
vT =
KT
,
mT
KT
63800 [ kg ⋅ m / s ]
=
≈ 27 [ m / s ] ≈ 97 [ km / h ]
mT
2305 [ kg ]
From (5) ⇒ vVW =
V VW =
(17)
KVW
,
mVW
K VW
33100 [ kg ⋅ m / s ]
=
= 23 [ m / s ] ≈ 83 [ km / h ].
m VW
1430 [ kg ]
(18)
2.2. RESULTS OBTAINED WITH SOFTWARE METHOD FOR CALCULATION OF
SPEEDS OF VEHICLES“TOYOTA LAND CRUISER” AND “VW GOLF”
With simulations software “PC-crash” based in final positions of vehicles “Toyota Land
Cruiser” and “VW Golf” after crash, are acquired results of velocities as follows :
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6. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 6, November - December (2013) © IAEME
Figure 3. Speeds and final positions of vehicles “Toyota Land Cruiser” and “VW Golf” after
collision- by software
3. ANALYSIS OF SECOND CASE OF ROAD ACCIDENT
In the second case of accident are involved two vehicles“DAF” (truck) and “Mercedes
200”. Vehicles before the crash have been moving in the opposite direction with one another.
Collision between vehicles is made as in figure.4.
Fig.4. Positions of vehicles “DAF” and “Mercedes 200” at the moment of collision
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7. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 6, November - December (2013) © IAEME
Figure. 5. Final positions of vehicles “DAF” and “Mercedes” before and after collision
Results obtained for this vehicles by graphical-analytical method and software method are showed in
table2.
Table 2.
Results of speeds
v [km/h]
Graphicalanalytical method
Software method
Vehicles
DAF
Mercedes
75
108
75
105
4. ANALYSIS OF THIRD CASE OF ROAD ACCIDENT
In the third case of accident are involved two vehicles: “Opel Astra” and “Ford
Eskord”. Vehicles before the crash have been moving in the direction as a fig.6. Position of
collision and positions of vehicles after collision are showed in figure 7.
Figure 6. Positions of vehicles “Opel Astra” and “Ford Escord” at the moment of collision
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8. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 6, November - December (2013) © IAEME
Figure 7. Final positions of vehicles “Opel Astra” and “Ford Escort”after collision
Results obtained for this vehicles by graphical-analytical method and software method are showed in
table 3.
Table 3.
Results of speeds
v [km/h]
Graphicalanalytical method
Software method
Vehicles
Ford Escort
Opel Astra
79.9
25
79.4
20.4
5. CONCLUSIONS
Results of velocities by graphical-analytical method and software method , for the three cases
of accidents analysis, summary are showed in table 4.
Table.4. Results of velocities by graphical-analytical method and software method , for the three
cases of accidents analysis
Vehicles
Case
1
Case
2
Case
3
Toyota Land Cruiser
Results of speeds V[km/h]
Graphical- analytical method
Softwaremethod
97
100
VW Golf
DAF
Mercedes
Opel Astra
83
75
108
25
82
75
105
20.4
Ford Escort
79.9
79.4
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9. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 6, November - December (2013) © IAEME
Differences between results obtained of velocities through two methods used (graphicalanalytical method and software method) for vehicles with different technical characteristics and
involved in different cases of fatal road accidents are shown on Diagram 1.
Diagram1. Comparing the results
As seen from the comparison of results obtained in diagram 1, deviations between the results
obtained by graphical-analytical method and software method are quite small. Based of this may
conclude that graphical-analytical method is a quite accurate method for calculating the velocities of
motion of vehicles before the crash. Especially in case of accidents when lacking sufficient data for
the way that the accident occurred and when and when known only the final positions of vehicle,
graphics method is more advantageous to use.
5. REFERENCES
[1]
[2]
Prof.dr. Frankko Rotim “Elementi sigurnosti cestovog prometa”, svenska 3, Zagreb, 1991.
Prof.dr. Franko Rotim “Elementi sigurnosti cestovog prometa” (Kinetika vozila), sveska 2,
Zagreb, 1991.
[3] Dr.sc.Ahmet Geca “Siguria në komunikacion,” , Prishtinë, 2009.
[4] Dr.sc.Heset Cakolli “Teoria e lëvizjes së automjeteve”, Prishtinë, 2010.
[5] Dr. Steffan Datentechnik “PC-CRASH - A Simulation Program for Vehicle Accidents”,
Linz, Austria, November 2008 .
[6] Forbes, T. W.: Human Factors in Highway Traffic safety Research, Toronto, 1972.
[7] Ing. Artur Sulçe, ing. Edmond Kazazi: Metodika e llogaritjes së aksidentit rrugor, Tiranë,
2006.
[8] Dhimitër Sotja “Mekanika e automjeteve”, Tiranë, 2005.
[9] Mr.ing. Ahmet Geca: Nelinearne oscilacije vozila “Zaztava 101” u nestacionarnim uvjetima
kretanja (Doktorska disertacija), Prishtinë, 1987.
[10] Sanjay H. Sawant and Dr. J. A. Tamboli, “Analysis and Comparison of Vehicle Dynamic
System with Nonlinear Parameters Subjected to Actual Random Road Excitations”,
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