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- Knowing: uncertainty, complete measurement, errors, steps in handling calipers
- Abilities: calculate uncertainties and absolute/relative errors, handling calipers, choosing the correct measurement instrument
- Understand: measurement accuracy and being able to assess it, review of measurement method
3. Literature
[1] DIN 1319-4. Grundlagen der Meßtechnik. Teil 3: Auswertung von Messungen - Meßunsicherheit (9.2). Ausgabe 2, Februar 1999.
[2] Puente León, Messtechnik. Berlin, Heidelberg: Springer Berlin Heidelberg, 2019.
[3] Fornasini, The Uncertainty in Physical Measurements. New York, NY: Springer New York, 2008.
[4] Kameke, Messwerte und Messunsicherheit. Hamburg, TUHH, 2019.
[5] Lectures: MT-Motivation, Measurement Theory
Necessary further reading: how to use a caliper!, error propagation, rounding to significant figures!
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Errors that can influence a measurement can be either systemic or statistic. Systemic errors are dependent e.g. on the instrument and always have the same amount and sign and are reproducible, so they appear every time the measurement is conducted. Some kind of offset can be used to compensate for systemic errors, but there could also be unknown systemic errors that therefore can’t be compensated. Statistic errors cannot be corrected because they are random by definition, but they can be described by average values and standard deviation, if multiple measurements were conducted. The standard deviation then is a measure of the scattering of the values around the average, for a big standard deviation, the values scatter very far from the average. It can therefore be concluded, that a single measurement doesn’t have any implications as no knowledge about the statistic error exists! [2]
Example systemic error: a scale always shows a few grams, although nothing is on the scale.
Example statistic error: when reading a scale with an indicator needle, the reader makes small mistakes
(Serious/major errors: errors due to the experimenter, e.g. improper instrument handling/arrangement, can be easily and generally avoided with some care and preparation. E.g. reading the ammeter as a voltage)
It can therefore be concluded, that a single measurement doesn’t have any implications as no knowledge about the statistic error exists!
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There are four types of measurements that can be made with a vernier caliper gauge: Inside measurements, outside measurements, depth and steps.
When the vernier caliper is closed, the scale should read exactly 0. To take a measurement of an inside dimension, the jaws of the caliper are now opened until they exactly cover the area to be measured. To measure an outside dimension, the caliper jaws are opened and then closed again until they touch the object. For measuring depths (e.g. drilled holes), the depth gauge at the end of the caliper can be used - the main element of the caliper is pressed against the higher surface and the depth gauge is positioned at the deepest point of the hole.
For reading, the main scale in mm is now used first to read the digit before the decimal point. This can be read at the position in front of the dash of zero on the slider. In order to read the decimal place, the position in the vernier scale (german: Nonius-Skala) must be found where the line of the large scale exactly coincides with one of the smaller scale.
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Significant figures are figures in a number, that carry meaning. To avoid misunderstandings, only significant ending zeroes are written, non significant zeros are omitted by using the scientific notation with power of ten. Leading zeros are always non significant!
Some examples:
| number | significant figures |
|---|---|
| 34.22 | 4 |
| 0.0043 | 2 |
| 0.120 | 3, due to the last zero being written, we define it as a significant zero |
| 2,345 · 106 | 4 |
| 2 345 000 | 7, due to the last zero being written, we define it as a significant zero |
| 1.003 | 4 |
| 50 | 2 |
| 50.0 | 3 |
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- Gather all the necessary measurement objects and instruments:
- Caliper
- Ruler
- 10 cylinders of type A
- 2 flat objects -> Unterlegscheiben!
- 1 O-ring
- Prepare a table to record all your measurements.
- Familiarize yourself with the caliper and its function.
6. Experiment Procedure
1.0 Go to one of the teststands and open the Matlab App for Experiment 1. Enter your matriculation number and the number of the Experiment Kit you are working with.
1.1 O-ring measurements:
1.1.1 Measure the inner diameter of the o-ring using the caliper and the ruler. Note both values.
1.1.2 Which value is more exact?
1.2 Find out, which of the two flat objects is thicker, A or B.
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1.4 Measure the volume of one of the cylinders by carrying out the following steps:
1.4.1 Measure every size of the cylinder that is needed to find the volume. What accuracy does your measuring instrument have?
1.4.2 Calculate the propagated error and supply a complete measurement of the volume (rounded to significant figures and including the uncertainty)!
1.5 Measure at least 10 beans from the central container.
1.5
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.1 Measure the length and the diameter of the cylinder and submit a complete measurement of the length and the diameter
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of beans.
1.5.2 Calculate the amount of beans that fit into the container (47 x 39 x 55 mm) you took them from. Assume that a bean's volume V equals its diameter multiplied with its length:
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1.6 (creative) Find a way to measure the weight of your hand (only the hand, not the arm) at home volume of a very irregular shape (e.g. your hand) and describe your steps.???
7. Evaluation of Experiment Results
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- Matriculation number
- Value for 1.1 caliper
- value for 1.1 ruler
- value for 1.1.2 which value is more exact?
- the thicker object (A or B)
- value for cylinder - length (1.3.1)
- value for cylinder - diameter: measurement (1.3.1)
- value for cylinder - length (1.3.2)
- value for cylinder - diameter: measurement (1.3.2)
- value for cylinder - length (1.3.3)
- value for cylinder - diameter: measurement (1.3.3)
- reproducibility
- repeatability
- complete measurement of the volume of the cylinder 1.4
- complete measurement result for 1.5 - length and diameter
- (free text) explain your measurement steps and the final result of 1.6
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