MEASUREMENT OF ENGINEERING PARAMETERS
1. BASE UNITS - the SI – system of measurement is based on seven base units, three of these
being:
Metre
Kilogram
Second
What do these units look like and how would they be recognised?
Metre – one metre of length, or height/width, is not too difficult to recognise, for example:
The height of the doorway, to the nearest 0.1 metre, is _____ approximately.
The length of the room, to the nearest 0.1 metre, is _____ approximately.
The width of the image projected onto the wall screen, to the nearest metre, is _____
approximately.
Kilogram – one kilogram of mass can be recognised but size and shape can deceive, for example
all of the following have a mass of one kilogram:
A bag of sugar
Four blocks of butter
A steel bar 50 diameter x 65 long
An aluminium bar 50 diameter x 189 long
Second – one second of time is not as easy to recognise or visualise. A ‘rough and ready way’ of
assessing one second of time is to say the words “one thousand”. Hence to assess five seconds
of time these would be repeated five times and so on.
From the above it can be appreciated that some units are easier to recognise, or visualise or
assess, than others, but in all cases this recognition, or assessment, is only approximate.
2. MEASURING INSTRUMENTS - in engineering and science accurate measurements are usually
required and hence some form of measuring equipment has to be used. Typical examples include:
LENGTH Tape measure
Steel rule Increasing accuracy
Micrometer
Light of known wavelength
MASS Calibrated electronic balance.
TIME Stop watch
Electronic timer in conjunction with start/stop switches.
3. UNCERTAINTY AND ACCURACY - even when using measuring equipment of the type listed
above their will still be uncertainty about the accuracy of the measurement and the effect this has
on subsequent calculations. The uncertainty comes about due to the inherent accuracy (or
precision) of the measuring equipment. For example lengths measured with:
a tape measure are likely to be accurate to within ± 0.5mm
a steel rule to within ± 0.25mm and
a micrometer to within ± 0.01mm
So a length of 57mm measured using a tape measure has every chance of being somewhere
between 56.5 and 57.5mm.
1
, If possible, and time permits, several readings of the same measurement should be taken and a
mean value calculated. The spread (or range) of these readings is a measure of the uncertainty.
For example assume that the diameter of a circular bar is measured at five positions along its
length such that:
d1 = 16.50mm d2 = 16.51mm d3 = 16.50mm d4 = 16.52mm d5 = 16.51mm
The mean value is 16.508 or 16.51mm to 4 sf (see section 4 below).
Now since all of the readings are within 0.01mm of the mean value then a reasonable estimate of
the uncertainty of the diameter is 0.01mm (either way).
Diameter is 16.51± 0.01mm
If uncertainty cannot be calculated in this way then an 'educated guess' should be made.
4. DECIMAL PLACES AND SIGNIFICANT FIGURES - numbers may be written to either:
so many decimal places (dp) or
so many significant figures (sf)
and these two formats have an influence on uncertainty and accuracy. Examples of the two
formats are listed below.
NO. OF DECIMAL PLACES NO. OF SIGNIFICANT FIGURES
71.371 3 5
171.0007 4 7
0.017102 6 5
6720. 0 3
9 700 000. 0 2
9 700 001. 0 7
The first thing to note is that as a general rule answers to calculations should not contain more
significant figures than the least number of significant figures given amongst the numbers. The
following worked examples illustrate this.
EXAMPLE 1 – find the value of 7.231 x 1.24 x 1.3 = 11.656372
= 12 to 2 sf
4 sig.fig. 3 sig.fig. 2 sig.fig.
EXAMPLE 2 – find the value of 7.231 x 1.241 x 1.311 = 11.764483
= 11.76 to 4 sf
4 sig.fig.
The second thing to note is that when carrying out calculations using measured quantities the most
realistic answer is one that allows for the inherent accuracy of the measurements. The following
worked example illustrates this.
2
1. BASE UNITS - the SI – system of measurement is based on seven base units, three of these
being:
Metre
Kilogram
Second
What do these units look like and how would they be recognised?
Metre – one metre of length, or height/width, is not too difficult to recognise, for example:
The height of the doorway, to the nearest 0.1 metre, is _____ approximately.
The length of the room, to the nearest 0.1 metre, is _____ approximately.
The width of the image projected onto the wall screen, to the nearest metre, is _____
approximately.
Kilogram – one kilogram of mass can be recognised but size and shape can deceive, for example
all of the following have a mass of one kilogram:
A bag of sugar
Four blocks of butter
A steel bar 50 diameter x 65 long
An aluminium bar 50 diameter x 189 long
Second – one second of time is not as easy to recognise or visualise. A ‘rough and ready way’ of
assessing one second of time is to say the words “one thousand”. Hence to assess five seconds
of time these would be repeated five times and so on.
From the above it can be appreciated that some units are easier to recognise, or visualise or
assess, than others, but in all cases this recognition, or assessment, is only approximate.
2. MEASURING INSTRUMENTS - in engineering and science accurate measurements are usually
required and hence some form of measuring equipment has to be used. Typical examples include:
LENGTH Tape measure
Steel rule Increasing accuracy
Micrometer
Light of known wavelength
MASS Calibrated electronic balance.
TIME Stop watch
Electronic timer in conjunction with start/stop switches.
3. UNCERTAINTY AND ACCURACY - even when using measuring equipment of the type listed
above their will still be uncertainty about the accuracy of the measurement and the effect this has
on subsequent calculations. The uncertainty comes about due to the inherent accuracy (or
precision) of the measuring equipment. For example lengths measured with:
a tape measure are likely to be accurate to within ± 0.5mm
a steel rule to within ± 0.25mm and
a micrometer to within ± 0.01mm
So a length of 57mm measured using a tape measure has every chance of being somewhere
between 56.5 and 57.5mm.
1
, If possible, and time permits, several readings of the same measurement should be taken and a
mean value calculated. The spread (or range) of these readings is a measure of the uncertainty.
For example assume that the diameter of a circular bar is measured at five positions along its
length such that:
d1 = 16.50mm d2 = 16.51mm d3 = 16.50mm d4 = 16.52mm d5 = 16.51mm
The mean value is 16.508 or 16.51mm to 4 sf (see section 4 below).
Now since all of the readings are within 0.01mm of the mean value then a reasonable estimate of
the uncertainty of the diameter is 0.01mm (either way).
Diameter is 16.51± 0.01mm
If uncertainty cannot be calculated in this way then an 'educated guess' should be made.
4. DECIMAL PLACES AND SIGNIFICANT FIGURES - numbers may be written to either:
so many decimal places (dp) or
so many significant figures (sf)
and these two formats have an influence on uncertainty and accuracy. Examples of the two
formats are listed below.
NO. OF DECIMAL PLACES NO. OF SIGNIFICANT FIGURES
71.371 3 5
171.0007 4 7
0.017102 6 5
6720. 0 3
9 700 000. 0 2
9 700 001. 0 7
The first thing to note is that as a general rule answers to calculations should not contain more
significant figures than the least number of significant figures given amongst the numbers. The
following worked examples illustrate this.
EXAMPLE 1 – find the value of 7.231 x 1.24 x 1.3 = 11.656372
= 12 to 2 sf
4 sig.fig. 3 sig.fig. 2 sig.fig.
EXAMPLE 2 – find the value of 7.231 x 1.241 x 1.311 = 11.764483
= 11.76 to 4 sf
4 sig.fig.
The second thing to note is that when carrying out calculations using measured quantities the most
realistic answer is one that allows for the inherent accuracy of the measurements. The following
worked example illustrates this.
2
