...
where v_2 - v_1 = v_2 * cos(Lambdaλ)
where c_p = 1004.5 for air and Lambda is the sweep angle of the fins
Assuming the rocket reaches a target of 30K ft AGL:
T_static = 59F - .00356(F/ft) * h_{max_v} (ft)
Therefore,
T_stag = (59F - .00356(F/ft) * h_{max_v} (ft)) + (4.9776*10^{-4}) * (v_2 * cos(λ))^2
v_2 = Mach 2 = 2*343 (m/s) = 686 (m/s)
T_stag = (59F - .00356(F/ft) * h_{max_v} (ft)) + (4.9776*10^{-4}) * (686 (m/s) * cos(λ))^2
Note that the first half of the sum is in degrees F whereas the second half of the sum will be in degrees K.
Dynamic Pressure
Dynamic pressure (q) represents the aerodynamic pressure exerted on a vehicle in motion through a fluid (air). It is defined by the equation:
...
Structural integrity of the rocket must be maximized to withstand the peak load at Max Q.
Dynamic Stability
Dynamic Stability is how systems respond to disruptions over time. Defined by:
d^2x/dt^2+2𝞯⍵(n)(dx/dt)+⍵(n)^2x=0
In which:
x: displacement
𝞯: damping ratio = (c/c_c): actual damping/ critical damping
⍵(n): natural frequency