Critical Speed of Vehicle: Calculation and other important considerations

CRITICAL SPEED OF A VEHICLE

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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 1^st 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. Please let us know whether this was useful or not. Thanks for believing in us...and yes don't forget to like..for our efforts...