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14:36:30 Page 199
We advise the reader that test uncertainty by its very nature evades exact values. But the
methodology presented gives reasonable estimates provided that the engineer has used sound,
impartial judgment in its implementation. The important thing is that the uncertainty analysis be
performed during the design and development stages of a test, as well as at its completion to assess
the stated results. Only then can the engineer use the results with appropriate confidence and
professional and ethical responsibility.
REFERENCES
1. International Organization for Standardization (ISO), Guide to the Expression of Uncertainty
in Measurement, Geneva, Switzerland, 1993.
2. ANSI/ASME Power Test Codes-PTC 19.1, Test Uncertainty, American Society of Mechanical
Engineers, New York, 2005.
3. Smith, R. E., and S. Wenhofer, From measurement uncertainty to measurement communications, credibility and cost control in propulsion ground test facilities, Journal of Fluids
Engineering 107: 165–172, 1985.
4. Kline, S. J., and F. A. McClintock, Describing uncertainties in single sample experiments,
Mechanical Engineering 75: 3–8, 1953.
5. Epperson, J.F., An Introduction to Numerical Methods and Analysis, Wiley-Interscience,
New York, 2007.
6. Moffat, R. J., Uncertainty analysis in the planning of an experiment, Journal of Fluids
Engineering 107: 173–181, 1985.
7. Taylor, B.N., and C. Kuyatt, Guidelines for Evaluating and Expressing the Uncertainty of NIST
Measurement Results, NIST Technical Note 1297, Gaithersburg, MD, 1994.
8. Kestin, J., A Course in Thermodynamics, revised printing, Hemisphere, New York, 1979.
9. Coleman, H., and W.G. Steele, Experimentation and Uncertainty Analysis for Engineers,
2nd ed., Wiley-Interscience, New York, 1999.
10. Dieck, R., Measurement Uncertainty: Methods and Applications, 3rd ed., Instrumentation,
Systems and Automation Society (ISA), Research Triangle Park, NC, 2002.
11. Monsch, S., Figliola, R.S., Thompson, E., Camberos, J., Induced Drag for 3D Wing with
Volume Integral (Trefftz Plane) Technique, AIAA Paper 2007-1079, AIAA, New York, 2007.
NOMENCLATURE
a
lower bound
b
upper bound; generic systematic standard
uncertainty
b x
systematic standard uncertainty in x
e k
kth elemental error
f()
general functional relation
p
pressure ml
À1
t
À2
À
Á
q
offset factor
s x
sample standard deviation of x
s x
random standard uncertainty in x; sample
standard deviation of the means
s yx
standard deviation of a fit
t v,95 t variable (at 95% probability)
t
time (t); t-variable
u x
uncertainty of a measured variable
u d
design-stage uncertainty
u c
instrument calibration uncertainty
u 0
zero-order uncertainty
u i
ith-order uncertainty
u N
Nth-order uncertainty
x
measured variable
x
0
true value of the population of x
Nomenclature 199
14:36:30 Page 199
We advise the reader that test uncertainty by its very nature evades exact values. But the
methodology presented gives reasonable estimates provided that the engineer has used sound,
impartial judgment in its implementation. The important thing is that the uncertainty analysis be
performed during the design and development stages of a test, as well as at its completion to assess
the stated results. Only then can the engineer use the results with appropriate confidence and
professional and ethical responsibility.
REFERENCES
1. International Organization for Standardization (ISO), Guide to the Expression of Uncertainty
in Measurement, Geneva, Switzerland, 1993.
2. ANSI/ASME Power Test Codes-PTC 19.1, Test Uncertainty, American Society of Mechanical
Engineers, New York, 2005.
3. Smith, R. E., and S. Wenhofer, From measurement uncertainty to measurement communications, credibility and cost control in propulsion ground test facilities, Journal of Fluids
Engineering 107: 165–172, 1985.
4. Kline, S. J., and F. A. McClintock, Describing uncertainties in single sample experiments,
Mechanical Engineering 75: 3–8, 1953.
5. Epperson, J.F., An Introduction to Numerical Methods and Analysis, Wiley-Interscience,
New York, 2007.
6. Moffat, R. J., Uncertainty analysis in the planning of an experiment, Journal of Fluids
Engineering 107: 173–181, 1985.
7. Taylor, B.N., and C. Kuyatt, Guidelines for Evaluating and Expressing the Uncertainty of NIST
Measurement Results, NIST Technical Note 1297, Gaithersburg, MD, 1994.
8. Kestin, J., A Course in Thermodynamics, revised printing, Hemisphere, New York, 1979.
9. Coleman, H., and W.G. Steele, Experimentation and Uncertainty Analysis for Engineers,
2nd ed., Wiley-Interscience, New York, 1999.
10. Dieck, R., Measurement Uncertainty: Methods and Applications, 3rd ed., Instrumentation,
Systems and Automation Society (ISA), Research Triangle Park, NC, 2002.
11. Monsch, S., Figliola, R.S., Thompson, E., Camberos, J., Induced Drag for 3D Wing with
Volume Integral (Trefftz Plane) Technique, AIAA Paper 2007-1079, AIAA, New York, 2007.
NOMENCLATURE
a
lower bound
b
upper bound; generic systematic standard
uncertainty
b x
systematic standard uncertainty in x
e k
kth elemental error
f()
general functional relation
p
pressure ml
À1
t
À2
À
Á
q
offset factor
s x
sample standard deviation of x
s x
random standard uncertainty in x; sample
standard deviation of the means
s yx
standard deviation of a fit
t v,95 t variable (at 95% probability)
t
time (t); t-variable
u x
uncertainty of a measured variable
u d
design-stage uncertainty
u c
instrument calibration uncertainty
u 0
zero-order uncertainty
u i
ith-order uncertainty
u N
Nth-order uncertainty
x
measured variable
x
0
true value of the population of x
Nomenclature 199