Originally Posted by Jane-DoH
Does anybody here have a mach-number to KEAS conversion table for altitudes above 65,000 feet, or a mathematical formula to help perform the conversion?
Jane, you seem to me to be plenty smart enough to figure it out for yourself without a program, but it does need some mathematical background, and I don't know how much you have.
First, a caveat. The speed of sound is functionally dependent only on the square root of temperature in Kelvin. So you need to know what the temperature is at a given altitude - and of course temperature can vary. So speed of sound is not a function of altitude per se and your program is not giving you that. It is probably assuming you are in an International Standard Atmosphere (ISA). Let's make that assumption below.
The speed of sound is sqrt(gamma x R x T), where gamma is the ratio of the specific heat of air at constant pressure to the specific heat of air at constant volume and is usually taken to be about 1.4; R is the gas constant, whose value for "ideal" air is 287 Joules per kilogramm per Kelvin in SI units (or 1716 ft-lb per slug per degree Rankine in English units); T is temperature in Kelvin (you'll have to apply a degrees-Rankine conversion factor in this formula if you are working in English units).
Now, you just need the distribution of temperature with altitude in the ISA. I'm sure there is a nice graph seomwhere on the WWW (it is a linear spline, which is a name for a number of straight line segments joined together at their ends), but I didn't find it. You can get it pointwise from the standard atmospheric calculator at
Standard Atmosphere Calculator, but then you can get the speed of sound from it, too, up to 86,000m (about 180,000 ft). To my mind, understanding the relationships of the quantities and using an arithmetic calculator is more fun than plugging numbers into some special computer program.
There is a very nice explanation of the standard atmosphere in Chapter 3 of John D. Anderson Jr.'s Introduction to Flight (6th Edition, McGraw-Hill 2008). This includes the definition of ISA temperature in terms of altitude, given in a graph in Figure 3.4. (Preceding that is a discussion of what "altitude" means!).
You may be wondering about gamma, the ratio of specific heats at constant pressure and volume. That is a matter of (what is called) elementary thermodynamics. Let me spare you the details here, although I seem to remember Pugilistic Animus was inspired to write it down on some other thread, which I forgot. The issue is dealt with quite nicely in Section 4.5 of Anderson. The speed of sound is discussed in Section 4.9.
I think you'll find Anderson quite helpful. If you don't have easy access to a copy, you might think of buying it. It is comprehensive, and Anderson has gone to a lot of trouble over the editions to make it so (it is over thirty years since the first edition). If you need to follow something from very first principles on, you can do it with Anderson. You'll need some facility in following reasoning using differential calculus - I don't know whether you have that.
PBL