Library / Automotive and vehicle dynamics / VEH-55
Automotive and vehicle dynamics
Front share of elastic roll moment
Share of the sprung-body roll moment M resisted at the front axle, from the front and rear roll stiffnesses Kf and Kr.
- Ref
- VEH-55
- Rev
- v1
- Field
- Automotive and vehicle dynamics
- Result
- Mφf [N m]
If both axles roll through the same angle φ, each resists roll in proportion to its roll stiffness, so the front share of the elastic roll moment Mφ is Kf/(Kf + Kr). The share sets the balance of lateral load transfer between the axles and hence the handling balance. The common roll angle is Mφ/(Kf + Kr) when the body is stiff in torsion.
Share of the sprung-body roll moment M resisted at the front axle, from the front and rear roll stiffnesses Kf and Kr. Both axles are taken to roll through the same angle, and geometric and unsprung load transfers need separate terms.
Calculator
- Rear roll moment, Mφ Kr/(Kf + Kr)1,600 N m
- Front share of the roll moment60 %
- Common roll angle, Mφ/(Kf + Kr)2.292 °
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 front axle resists 2,400 N m of the 4,000 N m roll moment, 60 %, and the body rolls 2.29°.
- Stiffening the front axle raises its share of the lateral load transfer, which loads the front outer tyre more and tends to produce understeer.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (N m) | Local step | Change in result |
|---|---|---|---|---|---|---|
| M_φ Roll moment on the sprung body | −50,000 to 50,000 N m | −30,000 | 30,000 | 60,000 | +2000 N m | +50 % |
| Kf Front roll stiffness | 1,000 to 500,000 N m/rad | 97.56 | 3,704 | 3,606 | +10% | +3.77 % |
| Kr Rear roll stiffness | 1,000 to 500,000 N m/rad | 428.6 | 3,934 | 3,506 | +10% | −3.85 % |
Sweep of Front roll stiffness
| Front roll stiffness (N m/rad) | Front roll moment (N m) |
|---|---|
| 1,000 | 97.56 |
| 63,380 | 2,452 |
| 125,800 | 3,035 |
| 188,100 | 3,299 |
| 250,500 | 3,449 |
| 312,900 | 3,547 |
| 375,300 | 3,615 |
| 437,600 | 3,665 |
| 500,000 | 3,704 |
Sweep one variable
Variables and how each one contributes
Front roll moment
What the equation gives you. Everything else feeds it.
Roll moment on the sprung body
The roll moment on the sprung body, in N m. Raises the front share in direct proportion. Raising it by 10 % (to 4,400) moves the result by +10 %, from 2,400 to 2,640 N m.
Front roll stiffness
The front roll stiffness, in N m/rad. Raises the front share, with diminishing returns as Kf grows. Raising it by 10 % (to 66,000) moves the result by +3.77 %, from 2,400 to 2,491 N m.
Rear roll stiffness
The rear roll stiffness, in N m/rad. Lowers the front share by taking more of the moment at the rear. Raising it by 10 % (to 44,000) moves the result by −3.85 %, from 2,400 to 2,308 N m.
Worked example with the values above
- Total stiffness: Kf + Kr = 60,000 + 40,000 = 100,000 N m/rad.
- Front share: Kf/(Kf + Kr) = 0.6.
- Mφf = 4,000 × 0.6 = 2,400 N m.
Assumptions and limits
- A linear suspension with small motion about the design ride height and a constant motion ratio.
- Rigid links and negligible bush compliance, and no preload or geometric stiffness unless stated.
Common mistakes
- Forgetting to square the motion ratio.
- Using the inverse motion ratio, wheel travel per spring travel, in place of spring travel per wheel travel.
- Adding spring and anti-roll-bar stiffness at different points without converting them to the same reference.
Statistics and uncertainty
Spring rates and installation ratios are usually known to about 3 % to 5 %, but the motion ratio enters squared, so a 3 % error in it becomes about 6 % in wheel rate.
Where it is used
- Converting spring and damper settings to wheel rate and wheel damping.
- Setting roll stiffness and front-to-rear roll balance.
Maths you need
- Motion ratio: spring travel per unit wheel travel
- Series springs: 1/k = 1/k₁ + 1/k₂
- Roll stiffness: roll moment per radian of roll