Dynamic Weight Transfer

Before you can understand this you have to know about Vehicle Motion Resistances

Calculation of dynamic weight transfer (axle load during acceleration on incline)

The weight transfers to rear axle or rear axle load increases due to inertial resistance (at the time of acceleration), aerodynamic drag, due to incline of uphill and also a very little with rolling resistance.

Terms used in above free body diagram

Centre of gravity=CG

Distance from CG to front axle=Lb1

Distance from CG to rear axle=Lb2

Wheel base=L

Height of CG=Hb

Static radius of tyre= Rst

Eccentricity of rolling resistance=Ew

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

Tangential forces due to frictional resistance=Fx,1 , Fx,2

Gravitational force on body only without axles=Gb=mg

Front and rear axle gravitational forces=Ga,1 , Ga,2

Resultant of inertia forces including axles Fi,1 and Fi,2=Fi,r

Acceleration of vehicle=a

Gravitational acceleration=g

Angle of slant or uphill= θ

Moment of inertia of front and rear axle (as it will in direction opposite to tyre rotation)=Mi.1 , Mi,2=I* α (I is inertia of tyre and alpha is angular acceleration of tyre)

Assuming no pitching in car hence no moment of inertia at CG

Aerodynamic drag and lift force by air=Fa,x,Fa,z (both will act on centre of pressure hence we taking correction moment factor=Ma)

Calculating summation of moments=0 at contact patch of rear wheel for front axle loading and vice versa for rear axle loading

DYNAMIC FRONT AXLE LOAD

Fz,1 = 1/L [ (Ga,1*L+Gb*Lb,2)*cos θ - ( (Ga,1+Ga,2)*Rst+Gb*Hb)*sin θ - Fa,x*Hb - Fa,z*Lb,2 -Ma -(  (Ga,1+Ga,2)*Rst + Gb*Hb) *a/g - (Ia,1* α1 + Ia,2* α2) - Fr*Rst]

DYNAMIC REAR AXLE LOAD

Fz,2 = 1/L [ (Ga,2*L+Gb*Lb,1)*cos θ + ( (Ga,1+Ga,2)*Rst+Gb*Hb)*sin θ +      Fa,x*Hb - Fa,z*Lb,1 +Ma +       (  (Ga,1+Ga,2)*Rst + Gb*Hb) *a/g + (Ia,1* α1 + Ia,2* α2) +      Fr*Rst]

You can see the formula is separated with spaces by which i want to denote that

First part is the static loading on incline

Second part is the aerodynamic part

Third part is the inertial or acceleration part

And, fourth part is the rolling resistance parts

As you can see that all parts get added in rear axle loading formula hence it proves all those parts increase the rear axle load and decreases the front axle load (in short transfers weight from front to rear axle)