I'm studying for my ATP written and for the life of me I can't find an easy way to convert Mach number to TAS as is required for some of the flight plan calculations.
In my previous life I was an engineer so I know how to calculate it if I have the speed of sound at a given temperature. So I guess the question is there an easy way to calculate speed of sound at given temperatures?
The gleim book says the following :
To obtain TAS from .78 Mach, use the calculator side of your flight computer and set OAT at -41C over the Mach index. Find the Mach number on the "minutes" scale, and read TAS above on "miles" scale, or 463kts.
The problem is my E6B doesn't appear to have a Mach index probably becuase my E6B is the one I used for my private and not many 172's in GA use Mach number. I also have an electronic e6b I bought ages ago which will convert TAS to mach number but can't convert mach number back to TAS. Doh!
Refering to the old faithful Aerodynamics by Naval Aviators you get the following:
M=V/a
M=Mach number
V=TAS in kts
a=speed of sound in kts=a
o(theta)**(1/2)
ao=speed of sound at standard see level (661kts)
theta=tempertature ratio T/T
o (temperatures in Kelvin)
btw **(1/2) is math speak for square root of theta as I couldn't be arsed working out how to put in a proper square root symbol.
So in the case of the gleim problem:
theta = T/To = (273-41)/(273+15) = .806
(theta)**(1/2) = .896
a = 661*.896 = 593.26kts
V = M*a = 593.26 * .78 = 462.8kts
Great I get the correct answer but there must be a quicker way .... anybody got the magic formula?