Library / Automotive and vehicle dynamics / VEH-39
Automotive and vehicle dynamics
Axle load changes from a vertical tongue load
Change in front-axle load caused by a downward hitch load P applied a distance d behind the rear axle, for a level two-axle vehicle in static equilibrium.
- Ref
- VEH-39
- Rev
- v1
- Field
- Automotive and vehicle dynamics
- Result
- ΔNf [N]
A downward load P applied a distance d behind the rear axle, as with a trailer tongue, acts at a lever arm L + d about the front axle. Moments about the rear axle show that the front axle is unloaded by P·d/L, while the rear axle gains P(1 + d/L). The two changes sum to P, as vertical equilibrium requires.
Change in front-axle load caused by a downward hitch load P applied a distance d behind the rear axle, for a level two-axle vehicle in static equilibrium. The rear axle gains P(1 + d/L), and the two changes add up to P. Add them to the unhitched axle loads.
Calculator
- Change in rear-axle load, P(1 + d/L)1,200 N
- Sum of the two changes (equals P)1,000 N
- Front unloading as a share of P20 %
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.
- A 1,000 N tongue load changes the front-axle load by −200 N and loads the rear axle with 1,200 N.
- The rear axle takes more than the tongue load itself, by the factor 1 + d/L = 1.2, so a long overhang on a short wheelbase is hard on the rear tyres.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (N) | Local step | Change in result |
|---|---|---|---|---|---|---|
| P Downward tongue load | 0 to 100,000 N | −20,000 | 0 | 20,000 | +10% | +10 % |
| d Hitch distance behind the rear axle | 0 to 5 m | −1,667 | 0 | 1,667 | +10% | +10 % |
| L Wheelbase | 0.5 to 10 m | −1,200 | −60 | 1,140 | +10% | −9.09 % |
Sweep of Hitch distance behind the rear axle
| Hitch distance behind the rear axle (m) | Change in front-axle load (N) |
|---|---|
| 0 | 0 |
| 0.625 | −208.3 |
| 1.25 | −416.7 |
| 1.875 | −625 |
| 2.5 | −833.3 |
| 3.125 | −1,042 |
| 3.75 | −1,250 |
| 4.375 | −1,458 |
| 5 | −1,667 |
Sweep one variable
Variables and how each one contributes
Change in front-axle load
What the equation gives you. Everything else feeds it.
Downward tongue load
The downward tongue load, in N. Scales both axle changes in direct proportion. Raising it by 10 % (to 1,100) moves the result by +10 %, from −200 to −220 N.
Hitch distance behind the rear axle
The distance from the rear axle back to the hitch, in m. A longer overhang increases the lever arm and unloads the front axle more. Raising it by 10 % (to 0.66) moves the result by +10 %, from −200 to −220 N.
Wheelbase
The wheelbase, in m. A longer wheelbase reduces the front-axle unloading for a given overhang. Raising it by 10 % (to 3.3) moves the result by −9.09 %, from −200 to −181.8 N.
Worked example with the values above
- Lever ratio: d/L = 0.6 / 3 = 0.2.
- Front change: ΔNf = −P × d/L = −1,000 × 0.2 = −200 N.
- Rear change: P(1 + d/L) = 1,200 N, which together with the front change gives P = 1,000 N.
Assumptions and limits
- A rigid vehicle in static equilibrium, with no braking, driving or aerodynamic loads unless the page names one.
- Flat tyres contact patches treated as single points on a plane road, and suspension deflection that does not move the centre of gravity.
Common mistakes
- Measuring the centre-of-gravity height or hitch height from the wrong datum (axle centre instead of the road).
- Mixing the distance from the front axle with the distance from the rear axle.
- Using the vehicle weight where the road-normal component W cos θ is needed.
Statistics and uncertainty
Axle scales read to about 0.5 % to 1 %, but the geometry inputs (wheelbase, centre-of-gravity height, hitch height) are often known only to a few centimetres, and on short wheelbases that is a visible fraction of the result.
Where it is used
- Setting axle loads, tongue weight and drawbar loads for tractors and trailers.
- Checking tip-up and wheel lift-off limits before field tests.
Maths you need
- Static equilibrium: forces and moments each sum to zero
- Moment about a contact point: a force times its perpendicular distance
- Centre of gravity: the point where the weight acts