How can I calculate ground speed (and TAS) when in the air with a specific mach number and no wind?

Question

i mean, let's imagine we are flying at FL370 with mach .86, we know that ground speed (with no wind) is something around 500 kts, but can I calculate exactly the speed?

(and is the ground speed at FL370 greater than at for example FL320 with the same mach number)?

Answer 1

Without OAT you can't compare mach and knots since knots are static and mach varies greatly with air temperature and density. Also whats the point in finding ground speed with no wind when ground speed is nothing more than air speed compensated FOR wind.

To get true air speed you really need to know the outside temperature.

the equation would be

Vt = Ao • M√(T/To)

where

Ao is the speed of sound at standard SLP

M is mach number

T is outside air temp

To is standard temperature at sea level

then you can compensate for the wind and get your ground speed.

Answer 2

TAS and ground speed are the same with no wind, so let's toss out ground speed and say you just want to calculate TAS based on a percentage of the speed of sound. Wind won't matter so we can toss out the assumption of no wind.

So your question is, what is the speed of sound at various altitudes? (You could've just asked that in the first place.) That question is answered at a lot of sites. This is one:

http://www.grc.nasa.gov/WWW/K-12/airplan...

Answer 3

The speed of sound varies with altitude (air density and air temperature).  

http://www.aerospaceweb.org/question/atm...

Additionally, if you want to be "exact" you are going to have to take into account the radius of ground and the radius the flight level with respect to center of the earth.