Library / Automotive and vehicle dynamics / VEH-14
Automotive and vehicle dynamics
Rear axle load during acceleration
Normal load on the rear axle while accelerating: the static rear load plus the weight transferred rearward.
- Ref
- VEH-14
- Rev
- v1
- Field
- Automotive and vehicle dynamics
- Result
- Fz,r [kN]
m is the vehicle mass, L the wheelbase, a the distance from the centre of gravity to the front axle, h the height of the centre of gravity and ax the forward acceleration in g. Accelerating shifts a load m ax h / L from the front axle to the rear axle, on top of the static rear load m g a / L. The loads are totals for the axle, on a level road with no aerodynamic forces. If the front load reaches zero the front wheels have lifted and the equation no longer applies.
Normal load on the rear axle while accelerating: the static rear load plus the weight transferred rearward. Level road, no aerodynamic forces.
Calculator
- Static rear axle load, m g a / L7.085 kN
- Load transferred rearwards, m ax h / L1.199 kN
- Front axle load6.431 kN
- Rear axle share of the weight56.3 %
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- At rest the rear axle carries 7.085 kN; accelerating at 0.4 g moves 1.199 kN rearwards, taking it to 8.284 kN (56.3 % of the weight).
- This is why rear-wheel drive launches harder than front-wheel drive at high acceleration: the load on the driven wheels increases. A front-wheel-drive car loses load on its driven axle in the same acceleration, which limits its launch.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (kN) | Local step | Change in result |
|---|---|---|---|---|---|---|
| m Vehicle mass | 500 to 5,000 kg | 2.761 | 27.61 | 24.85 | +10% | +10 % |
| a Distance from the centre of gravity to the front axle | 0.9 to 1.8 m | 6.104 | 11.01 | 4.905 | +10% | +8.55 % |
| L Wheelbase | 2.2 to 3.5 m | 6.391 | 10.17 | 3.776 | +10% | −9.09 % |
| ax Forward acceleration | 0.05 to 0.8 g | 7.235 | 9.483 | 2.248 | +10% | +1.45 % |
| h Centre of gravity height | 0.4 to 0.9 m | 7.957 | 9.047 | 1.09 | +10% | +1.45 % |
Sweep of Forward acceleration
| Forward acceleration (g) | Rear axle load (kN) |
|---|---|
| 0.05 | 7.235 |
| 0.1437 | 7.516 |
| 0.2375 | 7.797 |
| 0.3312 | 8.078 |
| 0.425 | 8.359 |
| 0.5188 | 8.64 |
| 0.6125 | 8.921 |
| 0.7063 | 9.202 |
| 0.8 | 9.483 |
Sweep one variable
Variables and how each one contributes
Rear axle load
What the equation gives you. Everything else feeds it.
Vehicle mass
The vehicle mass, in kg. Directly proportional: both the static load and the transfer scale with mass. Raising it by 10 % (to 1,650) moves the result by +10 %, from 8.284 to 9.112 kN.
Wheelbase
The wheelbase, in m. A longer wheelbase lowers the static rear load (for a fixed a) and reduces the transfer. Raising it by 10 % (to 2.97) moves the result by −9.09 %, from 8.284 to 7.531 kN.
Distance from the centre of gravity to the front axle
The distance from the centre of gravity to the front axle, in m. A larger a puts more weight on the rear axle. Raises the static rear load in proportion, so a rear-heavy vehicle starts with more rear load. Raising it by 10 % (to 1.43) moves the result by +8.55 %, from 8.284 to 8.992 kN.
Centre of gravity height
The height of the centre of gravity above the ground, in m. Raises the weight transferred in direct proportion, so taller vehicles squat more. Raising it by 10 % (to 0.605) moves the result by +1.45 %, from 8.284 to 8.404 kN.
Forward acceleration
The forward acceleration, as a multiple of g. Raises the weight transferred in direct proportion; a harder launch loads the rear tyres more. Raising it by 10 % (to 0.44) moves the result by +1.45 %, from 8.284 to 8.404 kN.
Worked example with the values above
- Static rear load: m g a / L = 1,500 × 9.81 × 1.3 / 2.7 = 7,085 N.
- Load transfer: m ax h / L = 1,500 × (0.4 × 9.81) × 0.55 / 2.7 = 1,199 N.
- Fz,r = 7,085 + 1,199 = 8,284 N = 8.284 kN. The front axle carries 6.431 kN.
Assumptions and limits
- A level road, a rigid vehicle and constant acceleration, with no aerodynamic forces and no pitching acceleration.
- The centre of gravity is on the centre line, and the loads are totals for both wheels on an axle.
Common mistakes
- Using the distance b (to the rear axle) in place of the distance a to the front axle.
- Using the result when the front wheels have lifted: if the front load is negative, the equation no longer holds.
Statistics and uncertainty
As in braking, the weakest input is the height of the centre of gravity, which is known only to about 5 to 10 %. The weight transfer is directly proportional to it, so a 10 % error in h gives a 10 % error in the transferred load and a smaller error in the rear axle load. Suspension squat, tyre compliance and aerodynamic lift also move the real loads by a few per cent.
Where it is used
- Traction calculations for rear-wheel-drive vehicles and launch analysis.
- Choosing the weight distribution and driven axle for a performance or off-road vehicle.
Maths you need
- Moments about an axle: balance of moments in a statics problem
- Newton’s second law: inertial force m a at the centre of gravity