Relative uncertainty [
]
Sometimes one wants to improve the precision of the measurement. In the example of the speed measurement from before, the measurement uncertainty of the distance and the time measurement influence the uncertainty of the measurement. To find out which change will mostly affect the uncertainty of the speed the relative uncertainty or percentage uncertainty can be calculated, see Tab. 5. This can be calculated by first making an overview of all input and output quantities, their value, and their uncertainty from which the percentage uncertainty can be calculated.
Table 5: All the quantities, their value, uncertainty, and relative uncertainty for a speed measurement.
| Quantity | Value | Uncertainty | Relative uncertainty |
|---|---|---|---|
| Input: | |||
| Distance | 50.00 m | 0.50 m | 1% |
| Time | 20.0 s | 1.0 s | 5% |
| Output: | |||
| Speed | 2.50 m/s | 0.13 m/s | 5.2% |
By looking at the relative uncertainties and how they propagate, one can quickly identify the quantity that has the biggest impact on the uncertainty of the calculated quantity. In this case, decreasing the uncertainty of the time measurement (5% relative uncertainty) will decrease the uncertainty of the speed much more than measuring the distance to a higher precision (1% relative uncertainty).
Further reading [
]
It can sometimes be useful to estimate the uncertainties before an experiment. Setting this goal for the uncertainty will affect the experimental procedure: [1].
Literature
- Priemer, B. (2023). Wie präzise soll's denn sein—Eine einfache Abschätzung von Messunsicherheiten vor einem Experiment. MNU Journal, 76(4), 320–323.