Library / Vibration exposure / VIB-05
Vibration exposure
Motion sickness dose value at a steady level
Motion sickness dose value for a steady weighted vertical acceleration lasting a given time.
- Ref
- VIB-05
- Rev
- v1
- Field
- Vibration exposure
- Result
- MSDVz [m/s^1.5]
MSDVz is the square root of the time integral of the squared motion-sickness-weighted vertical acceleration. For a steady weighted RMS level awf,z lasting T seconds it is awf,z√T. The result is in m/s1.5. It uses the appropriate motion-sickness weighting (not the weighting used for health). The duration is entered in hours and converted to seconds inside the formula. Because the exponent is the square root of time, a long journey adds up gradually.
Motion sickness dose value for a steady weighted vertical acceleration lasting a given time. Unlike the vibration dose value, it grows with the square root of time, so a long journey adds up gradually.
Calculator
- Duration in seconds7,200 s
- MSDV after one hour at this level12 m/s^1.5
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 weighted level of 0.2 m/s² maintained for 2 h gives an MSDV of 16.97 m/s1.5. Four times the journey time only doubles it: 33.94.
- Halving the vibration level halves the MSDV for any duration, so a smoother route or a better suspension pays off linearly, while shortening the journey pays off only with the square root.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (m/s^1.5) | Local step | Change in result |
|---|---|---|---|---|---|---|
| awf,z Motion-sickness-weighted vertical RMS | 0.02 to 1 m/s² | 1.697 | 84.85 | 83.16 | +10% | +10 % |
| T Duration | 0.1 to 8 h | 3.795 | 33.94 | 30.15 | +10% | +4.88 % |
Sweep of Duration
| Duration (h) | Motion sickness dose value (m/s^1.5) |
|---|---|
| 0.1 | 3.795 |
| 1.088 | 12.51 |
| 2.075 | 17.29 |
| 3.063 | 21 |
| 4.05 | 24.15 |
| 5.037 | 26.93 |
| 6.025 | 29.46 |
| 7.013 | 31.78 |
| 8 | 33.94 |
Sweep one variable
Variables and how each one contributes
Motion sickness dose value
What the equation gives you. Everything else feeds it.
Motion-sickness-weighted vertical RMS
The motion-sickness-weighted vertical RMS acceleration, in m/s². Journeys on land usually have 0.05 to 0.5 m/s². Raises the MSDV in proportion. Raising it by 10 % (to 0.22) moves the result by +10 %, from 16.97 to 18.67 m/s^1.5.
Duration
The duration of the journey, in hours. Raises the MSDV with the square root of time: a 10 % longer journey gives about 4.9 % more. Raising it by 10 % (to 2.2) moves the result by +4.88 %, from 16.97 to 17.8 m/s^1.5.
Worked example with the values above
- Convert the time to seconds: 2 h × 3600 = 7,200 s, with square root 84.85.
- Multiply by the level: 0.2 × 84.85.
- MSDVz = 16.97 m/s1.5.
Assumptions and limits
- A steady motion-sickness-weighted vertical acceleration level.
- The motion-sickness weighting is used, not the health weighting.
Common mistakes
- Entering the duration in seconds when the formula expects hours.
- Using a health-weighted acceleration instead of the motion-sickness weighted one.
Statistics and uncertainty
Individual susceptibility to motion sickness varies greatly, so a dose value predicts the proportion of passengers affected, not whether a given person will be sick. The weighting filter itself has tolerances of a few per cent.
Where it is used
- Estimating how likely passengers are to feel sick on a long ride at a roughly constant level.
- Comparing routes and vehicles for passenger comfort.
Maths you need
- Root mean square: square root of the mean of squares
- Frequency weighting: a filter emphasising the frequencies the body feels