Library / Automotive and vehicle dynamics / VEH-60
Automotive and vehicle dynamics
Dynamic load coefficient of a tyre
Standard deviation of the vertical tyre load divided by its mean, from four sampled loads taken over equal time intervals (population standard deviation of the record).
- Ref
- VEH-60
- Rev
- v1
- Field
- Automotive and vehicle dynamics
- Result
- DLC
The dynamic load coefficient is the standard deviation of the dynamic tyre load divided by its mean, DLC = σ(Fz)/F̄z. It measures how much the contact load fluctuates: a value of 0 means a constant load and values of 0.2 to 0.3 mean a wheel regularly nearing lift-off, since a Gaussian load reaches zero three standard deviations below the mean. The page uses the population standard deviation of four samples.
Standard deviation of the vertical tyre load divided by its mean, from four sampled loads taken over equal time intervals (population standard deviation of the record). It measures road-holding variation; state the speed, road section and measurement bandwidth.
Calculator
- Mean load, F̄z4,000 N
- Standard deviation of the load707.1 N
- Largest deviation from the mean1,000 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.
- The load varies by 17.7 % of its mean, which is moderate.
- A Gaussian load would reach zero at a DLC of about 0.33, so 0.531 of that limit is used here.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing () | Local step | Change in result |
|---|---|---|---|---|---|---|
| Fz3 Vertical load, sample 3 | 100 to 100,000 N | 0.1149 | 1.503 | 1.388 | +10% | +22.4 % |
| Fz1 Vertical load, sample 1 | 100 to 100,000 N | 0.1027 | 1.466 | 1.364 | +10% | −15.9 % |
| Fz2 Vertical load, sample 2 | 100 to 100,000 N | 0.1768 | 1.485 | 1.308 | +10% | +0.445 % |
| Fz4 Vertical load, sample 4 | 100 to 100,000 N | 0.1768 | 1.485 | 1.308 | +10% | +0.445 % |
Sweep of Vertical load, sample 3
| Vertical load, sample 3 (N) | Dynamic load coefficient |
|---|---|
| 100 | 0.5757 |
| 237.1 | 0.5482 |
| 562.3 | 0.486 |
| 1,334 | 0.3534 |
| 3,162 | 0.1308 |
| 7,499 | 0.3695 |
| 17,780 | 0.8514 |
| 42,170 | 1.255 |
| 100,000 | 1.503 |
Sweep one variable
Variables and how each one contributes
Dynamic load coefficient
What the equation gives you. Everything else feeds it.
Vertical load, sample 1
The vertical tyre load in sample 1, in N. Raises or lowers the mean and the spread depending on its distance from the others. Raising it by 10 % (to 3,300) moves the result by −15.9 %, from 0.1768 to 0.1486.
Vertical load, sample 2
The vertical tyre load in sample 2, in N. Raises or lowers the mean and the spread depending on its distance from the others. Raising it by 10 % (to 4,400) moves the result by +0.445 %, from 0.1768 to 0.1776.
Vertical load, sample 3
The vertical tyre load in sample 3, in N. Raises or lowers the mean and the spread depending on its distance from the others. Raising it by 10 % (to 5,500) moves the result by +22.4 %, from 0.1768 to 0.2164.
Vertical load, sample 4
The vertical tyre load in sample 4, in N. Raises or lowers the mean and the spread depending on its distance from the others. Raising it by 10 % (to 4,400) moves the result by +0.445 %, from 0.1768 to 0.1776.
Worked example with the values above
- Mean: (3,000 + 4,000 + 5,000 + 4,000) / 4 = 4,000 N.
- Standard deviation: σ = 707.11 N, from squared deviations of 1,000,000, 0, 1,000,000 and 0 N².
- DLC = 707.11 / 4,000 = 0.17678.
Assumptions and limits
- Equally spaced samples of the vertical tyre load from one wheel on one road section at a steady speed.
- The population standard deviation (divide by n), with the mean load taken as the average of the same samples.
Common mistakes
- Using the sample standard deviation (divide by n − 1) when the population form is intended.
- Including the static weight in the deviation instead of only the variation about the mean.
- Comparing DLC values measured at different speeds, on different roads or with different filter bandwidths.
Statistics and uncertainty
With only four samples the standard deviation itself is uncertain by about 35 %, so a DLC from so few points is an illustration. Real tests use records of many seconds at a fixed speed, and the value depends on the measurement bandwidth.
Where it is used
- Ride, comfort and road-holding studies of passenger and off-road vehicles.
- Choosing spring and damper values for a quarter-car model.
Maths you need
- Newton’s second law: m z̈ = Σ forces
- Eigenvalue problem: natural frequencies from the system matrices
- Complex frequency response: amplitude and phase at a driven frequency