Public Domain Aeronautical Software (PDAS)

The calculation of skin friction on an airplane from first principles is an incredibly complex task and requires powerful methods of computational fluid mechanics. Engineering estimates are usually made from formulas that were developed to provide an empirical fit to extensive sets of wind tunnel data on flat plates with no external pressure gradient.

From the vast collection of measurements of skin friction, there have been many attempts to make a simple formula which fits the observed data. All of these formulas are in some sense successful, and the student of aerodynamics may choose from among them. The formula developed by Sommer and Short has one feature that is not found in most other equations. Sommer and Short were primarily concerned with the large amount of scatter in the data at low hypersonic Mach numbers, and Reynolds numbers of about one million or less. They found that better correlations could be obtained if the temperature of the flow is included as a variable. As a result, the function supplied here has three arguments, Reynolds number, Mach number and freestream temperature. From a few numerical experiments, the user can see that for low Mach numbers (say < 3) the value of skin friction coefficient returned is quite independent of temperature. Temperature is of little importance at high Reynolds number, regardless of Mach number. But, if you are designing a trans- atmospheric vehicle for high altitudes at hypersonic speeds, you may want this added variable.

For the great majority of flight problems, the variation of friction with temperature is of little importance. I have modified the Fortran function to show you how to use optional arguments. In the general case, you would use the function in your program in the form

cf = TurbulentSkinFriction(rn, mach,temperature)

and you would be expected to provide inputs for all three arguments. For ordinary flight problems, temperature is not important, and you may use the function in the form

cf = TurbulentSkinFriction(rn, mach)

If you are working on a low speed problem, you may use the function in the form

cf = TurbulentSkinFriction(rn)

and the cf returned will be for zero Mach number.

Using the code in these different formats is not something flaky that may break when you move from one machine to another. This is a robust, fully conforming feature of Fortran 95 and you may use optional arguments with confidence.

If you are trying to impress people, you can tell them that your new code exhibits polymorphism, which is one of the features of modern object-oriented programming. And you didn't have to learn C++ to do it. For those of you who have succumbed, I have provided a copy of the function in C++.

This program was not released by NASA through COSMIC.

Public Domain Aeronautical Software (PDAS)