analysis, interpretation, and the presentation of experimental data. The 

 most important advantage gained in dimensional analysis techniques is the 

 reduction of the number of variables in a problem. If only two variables 

 are involved in a problem, a single curve can be used to describe the 

 functional relationship; if three variables are involved, a family of 

 curves relating two of the variables with constant values of the third 

 variable (the varying parameter) is required. As the number of variables 

 increase further, the number of families of curves also increases. Thus, 

 without dimensional analysis to group the variables into a smaller number 

 of dimensionless terms (the values can be used to plot curves for analysis 

 and presentation of the data in a more precise form), it would be impossi- 

 ble in many cases to perform model tests economically or to present experi- 

 mental data in a way that would allow easy interpretation. The application 

 of functional relationships can also facilitate the detection of random 

 errors in test data, as contrasted to the less likely situation where a 

 complete set of data may be erroneous because of faulty recording appara- 

 tus or the use of an incorrect datum. 



The correct interpretation of a set of measurements from an engineer- 

 ing or scientific experiment is often more difficult than performing the 

 tests and obtaining the observations. The accuracy of the measurements 

 depends on the precision of the instruments used and on the observers 

 dependability and skill. "Precision" refers to the degree of mutual 

 agreement among independent measurements of a single quantity when meas- 

 urements are repeated; "accuracy" refers to the agreement of the measure- 

 ments with the absolute or true value. When a large number of observations 

 are made of quantities that are supposedly identical, such as the still- 

 water depth in a wave flume, these data can be plotted as a frequency 

 graph (number of observations versus the measured value of water depth) , 

 to derive a normal distribution curve from which, with certain necessary 

 assumptions, the standard deviation from the mean and the probable error 

 can be calculated (Murphy, 1950). The curves and indexes of precision 

 can be obtained, for example, for the weight and specific weight of armor 

 units in rubble-mound stability tests, and the heights and periods of test 

 waves. However, the wave height can vary considerably with respect to 

 time and from test to test due to transverse oscillations, circulation 

 due to mass transport, reflected waves from the test structure, and dif- 

 ferences in starting positions of the wave machine plunger. In wave 

 pressure measurements, the pressures due to nonbreaking waves can also 

 vary considerably because of variations of wave height with respect to 

 time and variations in the reflection coefficients due to variations in 

 overtopping. The variations in pressures caused by breaking waves can 

 be large because of the nature of the phenomena itself, as well as the 

 variations of the wave heights with respect to time as noted above. 

 Therefore, the interpretation of these data must consider the precision 

 of the instruments used in the observations, and the degree to which the 

 variations are inherent in the prototype phenomena. 



The interpretation of test results from rubble-mound stability models 

 is difficult even when care is taken in the construction of the test sec- 

 tions and the measurements of the wave conditions. The construction of 



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