Compressible Aerodynamics

The topic of one of my Compressible Aerodynamics lectures last semester was determining Mach number though the use of a body’s Mach Cone angle. Guess what I did when I got home! ^_^

EDIT: Made a notation goof in the picture. The Mach number (“M”) is still 2.92, but I don’t multiply it by the local sound speed (“a”) unless I want to find Rainbow Dash’s velocity (“v”) in meters/second.

v = M*a

where a = √ (ɣ * gas constant * local air temperature in Kelvin)

ɣ for air = 1.4
gas constant = 287 J/(kg*K)
Kelvin temperature = (local air temperature in °C) + 273.15



To complete this calculation, we need the local air temperature. RD performed the maneuver at the altitude of Cloudsdale, which I’ll assume to be a standard cumulus cloud. Cumulus clouds usually form around 3,000 meters (10,000 feet) in altitude.

Using a standard atmosphere calculator [link] , I find that the temperature at that altitude is 268.650 K. (In normal people units, this is -4.5 °C or 23.9 °F. Brrrr!)

So now:
a = √ (ɣ * gas constant * local air temperature in Kelvin)
a = √ (1.4 * 287 J/(kg*K) * 268.650 K)
a = 328.548 m/s

v = M*a

v = 2.92 * 328.548 m/s
v = 959.359 m/s
v = 2,146.02 mph