Braking Weight Transfer

Calculation of weight transfer at the time of braking and brake force

Terms used in diagram

Distance from CG to front axle=Lb1

Distance from CG to rear axle=Lb2

Wheel base=L

Height of CG=h

Braking inertia (direction is opposite to acceleration as at the time of braking its deceleration and is –a) =ma

Weight of vehicle without rotating mass=W=mg

Brake force or friction force that stops the car, for front wheels and rear wheels (the friction force direction is to front when car is accelerating and its direction is toward back when car is decelerating)=B1,B2

Section forces or weight on axles=Fz,1, Fz,2

Calculating moment at rear tyre patch

Fz,1*L-W*Lb2-m*a*h=0

WEIGHT ON FRONT WHEELS AT THE TIME OF BRAKING

Fz,1 = 1/L [W*Lb2 + m*a*h]

WEIGHT ON REAR WHEELS AT THE TIME OF BRAKING

Fz,2 = 1/L [W*Lb2 - m*a*h]

Calculation of braking force

As you can see from the diagram

B1 + B2 = ma

Brake force on individual wheel depends upon its normal force. The weight transfers to the front wheels at the time of braking so B1>B2

The coefficient of friction can be adhesion coefficient (static friction coefficient) or less than that depending upon tyre slip as shown in figure

So,B1 <= fa*Fz,1

B2 <= fa*Fz,2

Let’s consider ideal braking force when coefficient of friction is max i.e. adhesion coefficient

Max B1 = fa*Fz,1

Max B2 = fa*Fz,2

B1 + B2 = ma

 fa*Fz,1+ fa*Fz,2=ma

fa (Fz,1+ Fz,2)=m*a*g/g

fa*mg=mg *a/g

fa=a/g=Z

Also taking ratio

B1/B2= Fz,1/ Fz,2=Lb2+Z*h/Lb1-Z*h