Library / Automotive and vehicle dynamics / VEH-38
Automotive and vehicle dynamics
Front axle reaction under a horizontal drawbar pull
Front-axle reaction of a tractor on level ground pulling a horizontal draught force D at hitch height hd, with b the distance from the rear axle to the centre of gravity.
- Ref
- VEH-38
- Rev
- v1
- Field
- Automotive and vehicle dynamics
- Result
- Nf [N]
For a tractor on level ground pulling a horizontal draught force D at hitch height hd, moments about the rear contact patch give Nf·L = W·b − D·hd, where b is the distance from the rear axle to the centre of gravity. The pull acts above the ground and transfers load from the front axle to the rear. When Nf reaches zero the front wheels lift and steering is lost.
Front-axle reaction of a tractor on level ground pulling a horizontal draught force D at hitch height hd, with b the distance from the rear axle to the centre of gravity. Constant speed, no vertical hitch force. A positive result means the front wheels stay in contact.
Calculator
- Rear-axle reaction, W − Nf11,600 N
- Front share of the weight, Nf/W42 %
- Drawbar pull at which the front wheels lift, W·b/hd40,000 N
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.
- With a 5,000 N pull the front axle carries 8,400 N, 42 % of the weight.
- The front wheels would lift at a pull of 40,000 N, so 12.5 % of the way to tip-up. Lowering the hitch raises that limit directly.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (N) | Local step | Change in result |
|---|---|---|---|---|---|---|
| W Vehicle weight | 100 to 1,000,000 N | −1,152 | 478,800 | 480,000 | +10% | +11.4 % |
| D Horizontal drawbar pull | 0 to 500,000 N | −110,400 | 9,600 | 120,000 | +10% | −1.43 % |
| b Distance from rear axle to CG | 0.1 to 10 m | −400 | 78,800 | 79,200 | +10% | +11.4 % |
| L Wheelbase | 0.5 to 10 m | 2,100 | 42,000 | 39,900 | +10% | −9.09 % |
| hd Hitch height | 0.05 to 3 m | 3,600 | 9,500 | 5,900 | +10% | −1.43 % |
Sweep of Horizontal drawbar pull
| Horizontal drawbar pull (N) | Front-axle reaction (N) |
|---|---|
| 0 | 9,600 |
| 62,500 | −5,400 |
| 125,000 | −20,400 |
| 187,500 | −35,400 |
| 250,000 | −50,400 |
| 312,500 | −65,400 |
| 375,000 | −80,400 |
| 437,500 | −95,400 |
| 500,000 | −110,400 |
Sweep one variable
Variables and how each one contributes
Front-axle reaction
What the equation gives you. Everything else feeds it.
Vehicle weight
The vehicle weight, in N. Raises the front reaction in proportion to the weight times b. Raising it by 10 % (to 22,000) moves the result by +11.4 %, from 8,400 to 9,360 N.
Distance from rear axle to CG
The distance from the rear axle to the centre of gravity, in m. Moving the centre of gravity forward raises the front reaction. Raising it by 10 % (to 1.32) moves the result by +11.4 %, from 8,400 to 9,360 N.
Horizontal drawbar pull
The horizontal drawbar pull, in N. A bigger pull unloads the front axle in direct proportion. Raising it by 10 % (to 5,500) moves the result by −1.43 %, from 8,400 to 8,280 N.
Hitch height
The hitch height above the ground, in m. A higher hitch makes the same pull unload the front axle more. Raising it by 10 % (to 0.66) moves the result by −1.43 %, from 8,400 to 8,280 N.
Wheelbase
The wheelbase, in m. A longer wheelbase lowers the transfer for a given moment, but also changes the weight share. Raising it by 10 % (to 2.75) moves the result by −9.09 %, from 8,400 to 7,636 N.
Worked example with the values above
- Weight moment: W b = 20,000 × 1.2 = 24,000 N m.
- Pull moment: D hd = 5,000 × 0.6 = 3,000 N m.
- Nf = (24,000 − 3,000) / 2.5 = 8,400 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
- Using a hitch height measured from the axle instead of the ground.
- Treating a pull that is not horizontal as horizontal: a rising draw-bar angle also adds a vertical component.
- Forgetting that the front axle also carries the weight share, so a positive result alone does not guarantee steering grip.
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