# How to calculate the TAT (total air temperature) when a rocket is flying to space? [closed]

I checked this answer and I used the formula this answerer provided, but I couldn't get the data he/she presented in the graph. Did I do something wrong?

• How can we address "did I do something wrong" when you don't show us what you did? As they teach in 6th grade math, show your work.
– Ralph J
Commented Aug 24, 2022 at 2:43

Since you didn't show your calculation / results I can only assume what went wrong. Something easily missed is using the correct units for the calculation. The formula

$$\frac{\text{TAT}}{\text{SAT}} = 1 + \frac{\gamma - 1}{2} M^2 = 1 + \frac{1}{5} M^2$$

only works for TAT and SAT as absolute temperatures. You have to use Kelvin (or degrees Rankine), not degrees Celsius (or Fahrenheit), for the calculations.

For the plots shown in the answer, I did all the calculations in Kelvin and then converted the results to degrees Celsius. Try repeating your calculation in Kelvin and see if you get consistent results.

Additional Note: since you want to use this calculation for a rocket flying to space, note that the formula only really works when air can be approximated as an ideal gas. Additionally, $$\gamma = 7 / 5$$ only holds for diatomic gases. At some altitude, these assumptions are no longer useful approximations, so you cannot use this formula all the way to space.