CRITICAL
SPEED OF A VEHICLE
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about critical velocity and its calculation. In this article, we have included
fundamentals of critical velocity and its calculation in the practical context.
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Critical speed of a vehicle is
the speed at which the vehicle will lose
lateral control on the roadway. There are different methods to calculate
the critical speed. It depends on friction force, elevation and radius of turn.
Calculation of critical speed of a vehicle plays a vital role in the field of accident
reconstruction.
Calculation of Critical speed
According to Newton’s 1st Law of motion, a body
moving in a straight line will continue in a straight line unless acted on by
an external force. A body moving on a circular path with constant speed will
have a changing velocity (directional speed) due to the body's changing
direction. This velocity change with time, called centripetal acceleration, has
a radial direction toward the center of the circular movement and is given by
the following equation:
a= V2 /R.............................................1
V:
velocity (m/s)
R =
Radius of Turn (m)
a =
Centripetal acceleration
Since Newton's second law tells
us that a force has to act on the body to produce an acceleration. Therefore,
F
= m a................................................2
m
= mass of vehicle
a
= centripetal acceleration
F
= Centripetal Force
Therefore,
F
= m v2/R...................................................3
Now, the lateral force on a vehicle moving in a circular motion
on a pavement surface is produced by the frictional force between the tires and
the roadway as follows :
F = µN.................................................4
Where,
N=Normal Reaction
Therefore,
F = µmg.........................................................5
Condition
for a vehicle to not to slip: Centripetal force should not exceed the
Frictional force. Therefore, equating both the forces will give the critical
velocity which should not be exceeded.
m v2/R
= µmg..............................................6
Solving
the equation will give, critical
velocity v,
V
critical = (µgR) 0.5 .............................7
Equal sign is important. g = 15 is used
for practical design (accident reconstruction).The formula is not valid for low
radial speeds. To calculate critical speed, equal sign is important. Converting
the above Equation to allow for the velocity, v, in mph, and accounting for the
roadway curve super-elevation, e, yields the familiar form of the centripetal
acceleration equation.
It is important to understand here, that above equation can be applied on the basis
of following assumptions and they are:
- Vehicle should be at its friction limit so that the slipping starts
- Vehicle follow a circular arc
- Vehicle should be within the tyre marks
- Speed of the vehicle is constant
Application of the above equation:
- Highway curve design
- Elevations
- Speed limit elevations
- Emergency turns by vehicle
From the above equation derived, we can
conclude many characteristics.They are:
Characteristics of Critical speed
- It depends on the friction between the road surface and tyre. Higher is the coefficient of friction, more is the critical velocity. But it is proportional to square root of the coefficient friction and value of coefficient of friction is not very high relative to other values (g, R) hence effect will not be more than the other parameters.
- It depends on the elevation or the banking of the road, as the normal reaction changes accordingly.
- It depends on the Turning Radius. Radius can hold any value hence it can have large values too thus, it will have higher influence on critical velocity. Thus, it is critical to design turns carefully or design vehicle for higher radius of turn.
- It is not affected by the position of CG. However, it affects Yaw, Pitch and Roll which is a different concept and seems to clash with this phenomenon.
- Does not depend on the vehicle geometry.
- CSF is valid for the assumptions described earlier in the article
- CSF is not applicable for low values of coefficient of friction.
- CSF does not take care of quantities such as steer angle, temperature effects, suspension etc.
- CSF should be calculated using the radius derived from earliest possible part of the tire marks as possible. Use curvature traced out by leading front tire for better results.
· There is always uncertainty in using CSF
formula and hence uncertainty or standard deviation should be taken care of while
designing using CSF.
In this article, we have tried to give
brief idea of the concept called as critical velocity. We can work to give more
detailed calculation and theories developed for measuring critical velocity in
practical context. We hope that this information will be useful for our users.
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