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1.41 A manufacturer wants to quantify the expected average fuel mileage of a product line of automobiles.
They decide that they can put one or more cars on a chassis dynamometer and run the wheels at
desired speeds and loads to assess this, or they can use drivers and drive the cars over some selected
course instead. (a) Discuss the merits of either approach, considering the control of variables and
identifying extraneous variables. (b) Can you recognize that somewhat different tests might provide
answers to different questions? For example, discuss the difference in meanings possible from the
results of operating one car on the dynamometer and comparing it to one driver on a course. Cite
other examples. (c) Are these two test methods examples of concomitant methods?
1.42 We need to measure the coefficient of restitution of a volleyball by dropping the ball from a known
height H and measuring the height of the bounce, h. The coefficient of restitution, C R , is then
calculated as
C R ¼
ffiffiffiffi
h
H
r
a. Develop a test plan for measuring C R that includes the range of conditions expected in collegelevel volleyball play.
b. Identify extraneous variables that may affect the resulting values of C R .
1.43 Light gates may be used to measure the speed of projectiles, such as arrows shot from a bow. English
long bows made of yew wood in the 1400s achieved launch speeds of 60 m/s. Determine the
relationship between the distance between light gates and the accuracy required for sensing the times
when the light gate senses the presence of the arrow.
1.44 You estimate your car’s fuel use by comparing fuel volume used over a known distance. Your brother,
who drives the same model car, disagrees with your claimed results based on his own experience.
How might you justify the differences based on the concepts of control of variables, interference and
noises effects, and test matrix used?
1.45 In discussing concomitant methods, we cited an example of computing the volume of a cylindrical
rod based on its average dimensions versus known weight and material properties. While we should
not expect too different an answer with either technique, identify where noise and interference effects
will affect the result of either method.
1.46 When a strain gauge is stretched under uniaxial tension, its resistance varies with the imposed strain.
A resistance bridge circuit is used to convert the resistance change into a voltage. Suppose a known
tensile load were applied to the system shown in Figure 1.16 and the output measured on a voltmeter.
What are the independent and dependent variables in this calibration? Can you suggest any
extraneous variables? What would be involved in a replication?
1.47 For the strain gauge calibration of the previous problem, what would be involved in determining the
repeatability of the instrument? The reproducibility? What effects are different in the tests? Explain.
1.48 A major tennis manufacturer is undertaking a test program for shoes, tennis balls, and tennis
strings. Develop a test plan for the situations described below. In each case provide details for how
the test should be conducted, and describe expected difficulties in interpreting the results. In each
case the tests are to be conducted during college tennis matches. Four teams of six players each are
to test the products under match (as opposed to practice) conditions. A tennis team consists of six
players, and a match consists of six singles matches and three doubles matches.
a. Tennis shoes: Two different sole designs and materials are to be wear tested. The life of the soles
are known to be strongly affected by court surface and playing style.
38 Chapter 1 Basic Concepts of Measurement Methods
15:40:39 Page 38
1.41 A manufacturer wants to quantify the expected average fuel mileage of a product line of automobiles.
They decide that they can put one or more cars on a chassis dynamometer and run the wheels at
desired speeds and loads to assess this, or they can use drivers and drive the cars over some selected
course instead. (a) Discuss the merits of either approach, considering the control of variables and
identifying extraneous variables. (b) Can you recognize that somewhat different tests might provide
answers to different questions? For example, discuss the difference in meanings possible from the
results of operating one car on the dynamometer and comparing it to one driver on a course. Cite
other examples. (c) Are these two test methods examples of concomitant methods?
1.42 We need to measure the coefficient of restitution of a volleyball by dropping the ball from a known
height H and measuring the height of the bounce, h. The coefficient of restitution, C R , is then
calculated as
C R ¼
ffiffiffiffi
h
H
r
a. Develop a test plan for measuring C R that includes the range of conditions expected in collegelevel volleyball play.
b. Identify extraneous variables that may affect the resulting values of C R .
1.43 Light gates may be used to measure the speed of projectiles, such as arrows shot from a bow. English
long bows made of yew wood in the 1400s achieved launch speeds of 60 m/s. Determine the
relationship between the distance between light gates and the accuracy required for sensing the times
when the light gate senses the presence of the arrow.
1.44 You estimate your car’s fuel use by comparing fuel volume used over a known distance. Your brother,
who drives the same model car, disagrees with your claimed results based on his own experience.
How might you justify the differences based on the concepts of control of variables, interference and
noises effects, and test matrix used?
1.45 In discussing concomitant methods, we cited an example of computing the volume of a cylindrical
rod based on its average dimensions versus known weight and material properties. While we should
not expect too different an answer with either technique, identify where noise and interference effects
will affect the result of either method.
1.46 When a strain gauge is stretched under uniaxial tension, its resistance varies with the imposed strain.
A resistance bridge circuit is used to convert the resistance change into a voltage. Suppose a known
tensile load were applied to the system shown in Figure 1.16 and the output measured on a voltmeter.
What are the independent and dependent variables in this calibration? Can you suggest any
extraneous variables? What would be involved in a replication?
1.47 For the strain gauge calibration of the previous problem, what would be involved in determining the
repeatability of the instrument? The reproducibility? What effects are different in the tests? Explain.
1.48 A major tennis manufacturer is undertaking a test program for shoes, tennis balls, and tennis
strings. Develop a test plan for the situations described below. In each case provide details for how
the test should be conducted, and describe expected difficulties in interpreting the results. In each
case the tests are to be conducted during college tennis matches. Four teams of six players each are
to test the products under match (as opposed to practice) conditions. A tennis team consists of six
players, and a match consists of six singles matches and three doubles matches.
a. Tennis shoes: Two different sole designs and materials are to be wear tested. The life of the soles
are known to be strongly affected by court surface and playing style.
38 Chapter 1 Basic Concepts of Measurement Methods