Library / Vibration exposure / VIB-03
Vibration exposure
Weighted RMS acceleration over three segments
Single weighted RMS level for a journey made of three stretches at different vibration levels.
- Ref
- VIB-03
- Rev
- v1
- Field
- Vibration exposure
- Result
- aw [m/s²]
For a journey made of three stretches with weighted RMS levels a1, a2 and a3 lasting T1, T2 and T3, the overall weighted RMS is the square root of the time-weighted mean of the squares. This equals the equal-sample sum when the sampling interval is constant and no samples are missing. A frequency weighting is a filter applied to the signal, not a constant multiplier of a result, so aw must come from the weighted acceleration history of each stretch.
Single weighted RMS level for a journey made of three stretches at different vibration levels. Each level is squared and weighted by how long it lasts, so a long moderate stretch can matter more than a short severe one.
Calculator
- Total duration3.5 h
- Share of the mean square from stretch 357.14 %
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.
- Levels of 0.5, 1 and 2 m/s² for 2, 1 and 0.5 h combine to 1 m/s². The shortest stretch, at 2 m/s², supplies 57.1 % of the mean square, even though it lasts only 14.3 % of the time.
- A single weighted RMS hides how the levels are distributed in time. For shocks, use the vibration dose value, which is much more sensitive to short severe events.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (m/s²) | Local step | Change in result |
|---|---|---|---|---|---|---|
| a1 Weighted RMS, segment 1 | 0 to 3 m/s² | 0.9258 | 2.449 | 1.524 | +10% | +1.49 % |
| a2 Weighted RMS, segment 2 | 0 to 3 m/s² | 0.8452 | 1.813 | 0.9675 | +10% | +2.96 % |
| T3 Duration, segment 3 | 0.1 to 8 h | 0.7829 | 1.745 | 0.9622 | +10% | +2.09 % |
| a3 Weighted RMS, segment 3 | 0 to 3 m/s² | 0.6547 | 1.309 | 0.6547 | +10% | +5.83 % |
| T1 Duration, segment 1 | 0.1 to 8 h | 0.7255 | 1.375 | 0.6495 | +10% | −2.05 % |
| T2 Duration, segment 2 | 0.1 to 8 h | 1 | 1 | 0 | +10% | 0 % |
Sweep of Weighted RMS, segment 3
| Weighted RMS, segment 3 (m/s²) | Weighted RMS acceleration (m/s²) |
|---|---|
| 0 | 0.6547 |
| 0.375 | 0.6698 |
| 0.75 | 0.7134 |
| 1.125 | 0.7806 |
| 1.5 | 0.866 |
| 1.875 | 0.9648 |
| 2.25 | 1.073 |
| 2.625 | 1.189 |
| 3 | 1.309 |
Sweep one variable
Variables and how each one contributes
Weighted RMS acceleration
What the equation gives you. Everything else feeds it.
Weighted RMS, segment 1
The weighted RMS acceleration in the first stretch, in m/s². Raises aw by a share given by that stretch’s part of the total mean square. Raising it by 10 % (to 0.55) moves the result by +1.49 %, from 1 to 1.015 m/s².
Duration, segment 1
The duration of the first stretch, in hours. Pulls aw towards that stretch’s level. Raising it by 10 % (to 2.2) moves the result by −2.05 %, from 1 to 0.9795 m/s².
Weighted RMS, segment 2
The weighted RMS acceleration in the second stretch, in m/s². Raises aw by a share given by that stretch’s part of the total mean square. Raising it by 10 % (to 1.1) moves the result by +2.96 %, from 1 to 1.03 m/s².
Duration, segment 2
The duration of the second stretch, in hours. Pulls aw towards that stretch’s level. Raising it by 10 % (to 1.1) moves the result by +0 %, from 1 to 1 m/s².
Weighted RMS, segment 3
The weighted RMS acceleration in the third stretch, in m/s². Raises aw by a share given by that stretch’s part of the total mean square. Raising it by 10 % (to 2.2) moves the result by +5.83 %, from 1 to 1.058 m/s².
Duration, segment 3
The duration of the third stretch, in hours. Pulls aw towards that stretch’s level. Raising it by 10 % (to 0.55) moves the result by +2.09 %, from 1 to 1.021 m/s².
Worked example with the values above
- Each mean square times its time: 0.5 + 1 + 2 = 3.5.
- Divide by the total time 3.5 h: 1.
- aw = 1 m/s².
Assumptions and limits
- Each stretch has a steady weighted RMS level, with the same axis and weighting throughout.
- Constant sampling interval and no missing data in each stretch.
Common mistakes
- Averaging the RMS values directly instead of averaging their squares.
- Applying a frequency weighting as a single multiplier on an unweighted RMS.
Statistics and uncertainty
RMS levels measured over a short sample have a statistical error of a few per cent that falls with record length; a record of at least 1 to 2 minutes per stretch is common practice. Frequency-weighting filter errors add a further few per cent.
Where it is used
- Describing a whole journey over mixed terrain with one weighted RMS number.
- Feeding that number into a daily exposure or a ride comfort assessment.
Maths you need
- Root mean square: square root of the mean of squares
- Frequency weighting: a filter emphasising the frequencies the body feels