High School Mathematics
Meets Accident Reconstruction
Louis Roodt PrEng
Civil Engineering
Road design and safety
July 2014
PURPOSE OF LECTURE
To show how high school
physics and mathematics
are applied in engineering
specifically in
accident reconstruction
Physical science looks at both statics and
dynamics: things that are in balance and
things that move.
Statics plays an important role in the
designs of structures such as bridges.
Dynamics are of importance in the
reconstruction of accidents, as movement
is required for crashes to occur.
Statics: things in balance
Dynamics: things that move
Basic equations of motion:
constant speed
Equations of motion
Assumption: constant acceleration
v = u + at … (1)
s = ½(u + v)t … (2)
s = ut + ½at2 … (3)
v2 = u2 + 2as … (4)
The severity of an accident is,
amongst other factors,
a function of the speed of collision.
The kinetic energy of a body in motion is
KE = ½ m v2
At 100 km/h the KE of a 1000 kg vehicle is
½ x 1000 x 27,772 = 386 kJ
At 120 km/h the KE of a 1000 kg vehicle is
½ x 1000 x 33,332 = 555 kJ
20 % increase in speed, 44 % increase in energy
The purpose of an accident reconstruction
is to understand how the accident was
caused, the factors that contributed and
the damage that resulted.
This calls for team work!
The accident reconstruction team will
consist of experts in
human behaviour,
road environment design,
vehicle construction and dynamics,
trauma and medical specialists and
mathematicians
The mathematican’s task
is to determine the
speeds of the vehicles
Brake skid marks shows the length over which
maximum deceleration occurred. Deceleration
is a function of many variables, but the
dominant factor is the coefficient of friction µ
between the tyre and the road surface.
v2 = 2as
Skid mark length (average of 4 tyres marks) = 20 m
µ = 0,6 to 0,8 for a dry road, good tyres and level surface
Speed = 0 at end of brake mark
a = µg = 0,7 x 9.8 = 6.86 m/s2
v = (2 x 6.86 x 20) 0.5
v = 16,56 m/s = 60 km/h
The Coefficient of Friction between two
surfaces such as the tyre and road is
determined in experiments where the skid
marks are measured at known speeds
Use CAR magazine’s road tests to
determine the deceleration of modern cars:
100 – 0 km/h in 3,5 seconds!
For accident reconstruction we are
interested in the values for CoF of
•
•
•
•
•
good and bald tyres
dry and wet roads
roads with different surfacing
such as concrete, asphalt and gravel
polluted roads
Circular yaw marks show that the vehicle did
not skid as under braking, as there was
directional control. A braking skid mark forms
a straight line, dictated by momentum.
The yaw marks can also indicate speed.
From circular motion: centrifugal acceleration
ac = v2 / R
ac = µg
The radius is estimated to be 20 m.
From circular motion: centrifugal acceleration
v2 = R x ac
ac = µg = 6.86 m/s2
v = (6.86 x 20) 0.5
= 11.7 m/s = 42 km/h
This is the critical curve speed. If this speed is
exceeded the vehicle will skid to the outside in
the momentum vector direction
Some crashes are, however, difficult to
reconstruct based only on measurements and
photographs taken after the fact.
The next video illustrates
the unexpected movements of the vehicles
involved in crashes.
Where is my boat???
Mathematics and Physics
are the tools with which we take problems
apart to work on them in solvable portions.
The basis of our technical skills
is formed in school.
Therefore, dedicate yourselves to
understanding and applying this knowledge.
And develop your communications skills!
You must write the report.
YOU CAN DO IT!
WITH SUPPORT OF
YOUR FAMILY,
FRIENDS AND HARD
WORK
DANKIE
THANK YOU
ENKOSI KAHKULU