# Weight Transfer During Braking When a vehicle brakes, there is a transfer of weight from the rear to the front wheels. This is due to inertia: as the vehicle decelerates, the center of gravity (CG) tends to continue moving forward, increasing the normal force on the front wheels and decreasing it on the rear wheels. ## Assumptions - Flat, level road - Four-wheel braking - No aerodynamic effects - The vehicle is a rigid body - Brakes are applied uniformly ## Variables - \( m \): Mass of vehicle - \( g \): Acceleration due to gravity - \( a \): Deceleration (braking acceleration, positive value) - \( h \): Height of center of gravity above the ground - \( L \): Wheelbase (distance between front and rear axles) - \( b \): Distance from CG to rear axle - \( a_f \): Distance from CG to front axle (\( a_f = L - b \)) ## 1. Static Load on Axles (No Braking) - **Front axle load:** \( W_{f, static} = \frac{b}{L} mg \) - **Rear axle load:** \( W_{r, static} = \frac{a_f}{L} mg \) ## 2. During Braking: Dynamic Load Transfer When braking, a moment is created about the contact patches due to deceleration. The additional load transferred forward (\( \Delta W \)) is: \[ \Delta W = \frac{mh}{L} a \] - **Direction:** From rear to front axle - **Magnitude:** Proportional to mass, CG height, deceleration, and inversely to wheelbase ### **Derivation** #### Step 1: Forces and Moments - **Sum of vertical forces:** \( N_f + N_r = mg \) - \( N_f \): Normal force on front wheels - \( N_r \): Normal force on rear wheels - **Sum of moments about rear axle:** \[ N_f \cdot L = mg \cdot a_f + m a \cdot h \] The term \( m a \cdot h \) is the moment due to braking force acting at the CG height. #### Step 2: Solving for Normal Forces - **Front axle:** \[ N_f = \frac{mg \cdot a_f + m a \cdot h}{L} \] - **Rear axle:** \[ N_r = mg - N_f \] Alternatively, \[ N_r = \frac{mg \cdot b - m a \cdot h}{L} \] #### Step 3: Weight Transfer The **increase in front axle load** due to braking is \( \Delta W = \frac{mh}{L} a \). - **Front axle load:** \( W_f = W_{f, static} + \Delta W \) - **Rear axle load:** \( W_r = W_{r, static} - \Delta W \) ## 3. Final Weight Transfer Formula \[ \boxed{ \Delta W = \frac{mh}{L} a } \] - **Where:** - \( \Delta W \): Weight transferred from rear to front during braking - \( m \): Mass of vehicle - \( h \): Height of CG - \( L \): Wheelbase - \( a \): Deceleration (braking acceleration) ## 4. Physical Meaning - **Higher CG (\( h \)) or more aggressive braking (\( a \)) increases weight transfer.** - **Longer wheelbase (\( L \)) reduces weight transfer.** --- **Diagram (for reference):**  *Figure: Forces and moments acting on a braking vehicle (CG, wheelbase, normal forces).*