Library / Automotive and vehicle dynamics / VEH-61
Automotive and vehicle dynamics
Temporal frequency of a spatial road wave
Frequency in cycles per second at which a vehicle meets a sinusoidal road profile of wavelength λ, travelling at constant speed U along the measured wheel path.
- Ref
- VEH-61
- Rev
- v1
- Field
- Automotive and vehicle dynamics
- Result
- f [Hz]
A vehicle at speed U passes a sinusoidal road of wavelength λ in a time λ/U, so the frequency it feels is f = U/λ. This links the road’s spatial content to the vehicle’s frequency range: at a given speed, short wavelengths drive wheel hop and long wavelengths drive body bounce. The relation is exact for constant speed along the profile.
Frequency in cycles per second at which a vehicle meets a sinusoidal road profile of wavelength λ, travelling at constant speed U along the measured wheel path.
Calculator
- Speed in kilometres per hour54 km/h
- Angular frequency, 2πf31.42 rad/s
- Wavelength that excites a 12 Hz wheel-hop at this speed, U/121.25 m
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 3 m wave at 15 m/s excites the vehicle at 5 Hz.
- At this speed, wheel-hop around 12 Hz is excited by wavelengths near 1.25 m, and body bounce near 1.2 Hz by waves near 12.5 m.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (Hz) | Local step | Change in result |
|---|---|---|---|---|---|---|
| λ Road wavelength | 0.1 to 100 m | 0.15 | 150 | 149.8 | +10% | −9.09 % |
| U Vehicle speed | 0 to 60 m/s | 0 | 20 | 20 | +10% | +10 % |
Sweep of Road wavelength
| Road wavelength (m) | Excitation frequency (Hz) |
|---|---|
| 0.1 | 150 |
| 0.2371 | 63.25 |
| 0.5623 | 26.67 |
| 1.334 | 11.25 |
| 3.162 | 4.743 |
| 7.499 | 2 |
| 17.78 | 0.8435 |
| 42.17 | 0.3557 |
| 100 | 0.15 |
Sweep one variable
Variables and how each one contributes
Excitation frequency
What the equation gives you. Everything else feeds it.
Vehicle speed
The vehicle speed, in m/s. Raises the excitation frequency in direct proportion. Raising it by 10 % (to 16.5) moves the result by +10 %, from 5 to 5.5 Hz.
Road wavelength
The road wavelength, in m. A longer wavelength lowers the frequency in inverse proportion. Raising it by 10 % (to 3.3) moves the result by −9.09 %, from 5 to 4.545 Hz.
Worked example with the values above
- Speed: U = 15 m/s.
- Wavelength: λ = 3 m.
- f = U/λ = 15 / 3 = 5 Hz.
Assumptions and limits
- Constant vehicle speed along a straight wheel path, and a stationary, zero-mean road profile.
- One-sided PSDs, with spatial frequency in cycles per metre and temporal frequency in hertz.
Common mistakes
- Mixing cycles per metre with radians per metre, which differ by 2π.
- Mixing one-sided and two-sided spectra.
- Applying a spectral relation outside the wavelength band over which the road was measured.
Statistics and uncertainty
Measured road PSDs scatter by a factor of two or more between road sections, and a power-law fit describes only a limited band. Treat spectral levels as indicative of a road class, not of a specific road.
Where it is used
- Converting measured road roughness into inputs for ride simulations.
- Predicting which road wavelengths excite body bounce, pitch and wheel hop.
Maths you need
- Wavelength and frequency: f = U/λ
- Power spectral density: variance per unit frequency
- Parseval’s theorem: the area under the PSD equals the variance