Library / Automotive and vehicle dynamics / VEH-40
Automotive and vehicle dynamics
Load transfer ratio from left and right wheel loads
Normalised difference between the right and left vertical loads of an axle (or of the whole vehicle).
- Ref
- VEH-40
- Rev
- v1
- Field
- Automotive and vehicle dynamics
- Result
- LTR
The load transfer ratio LTR = (NR − NL)/(NR + NL) is the normalised left–right load difference. It is zero when the loads are equal and reaches ±1 when one side carries no load, which is wheel lift. It is measured from wheel loads and is independent of the cause of the transfer, so it works as a rollover indicator in tests and in controllers.
Normalised difference between the right and left vertical loads of an axle (or of the whole vehicle). It is 0 for equal loads and ±1 when all load sits on one side, the point at which the opposite wheels lift. State whether axle or vehicle totals were used.
Calculator
- Total load, NR + NL10,000 N
- Load moved across from the equal-load split, (NR − NL)/21,500 N
- Load on the lighter side, as a share of the total35 %
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.
- The ratio is 0.3: 1,500 N has moved to the heavier side compared with an equal split.
- At ±1 the lighter wheels would carry no load. This one is 30 % of the way to lift-off.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing () | Local step | Change in result |
|---|---|---|---|---|---|---|
| NR Right-side vertical load | 0 to 1,000,000 N | −1 | 0.993 | 1.993 | +10% | +14.2 % |
| NL Left-side vertical load | 0 to 1,000,000 N | −0.9871 | 1 | 1.987 | +10% | −14.7 % |
Sweep of Right-side vertical load
| Right-side vertical load (N) | Load transfer ratio |
|---|---|
| 0 | −1 |
| 125,000 | 0.9455 |
| 250,000 | 0.9724 |
| 375,000 | 0.9815 |
| 500,000 | 0.9861 |
| 625,000 | 0.9889 |
| 750,000 | 0.9907 |
| 875,000 | 0.992 |
| 1,000,000 | 0.993 |
Sweep one variable
Variables and how each one contributes
Load transfer ratio
What the equation gives you. Everything else feeds it.
Right-side vertical load
The vertical load on the right-hand wheels, in N. A heavier right side raises the ratio towards +1. Raising it by 10 % (to 7,150) moves the result by +14.2 %, from 0.3 to 0.3427.
Left-side vertical load
The vertical load on the left-hand wheels, in N. A heavier left side lowers the ratio towards −1. Raising it by 10 % (to 3,850) moves the result by −14.7 %, from 0.3 to 0.256.
Worked example with the values above
- Difference: NR − NL = 6,500 − 3,500 = 3,000 N.
- Sum: NR + NL = 10,000 N.
- LTR = 3,000 / 10,000 = 0.3.
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