# Why is that max-Q doesn't occur in transonic regime?

Is there any reason why the maximum dynamic pressure should not occur in the transonic regime. It is clear from this answer that the max-Q for various rockets occur outside the transonic region

Do the rocket scientists design the launch in a way that the max-Q always occur outside transonic region?

Max-Q is a function of both altitude and velocity. There isn't any reason in particular that it needs to fall at a particular Mach number. It's just the point at which the rate that atmospheric density is falling outpaces the rate at which the square of the velocity is increasing. Nothing more.

• Concur, for shuttle first stage flight design there was no specific constraint about when max q needed to happen. – Organic Marble Feb 26 '19 at 2:20

Here's a very simple model of a Faux Falcon 9 launched vertically, with no turn towards horizontal. That doesn't matter so much at the altitude at max-Q but the final altitude at MECO is higher than in the videos because it hasn't turned towards horizontal. There are several simplifications, but it should reproduce most things in a qualitative way.

The final velocity is a little high but that may be related to the model not throttling back near max Q, or to other approximations.

I chose a scale height model for density $$\rho(h) = \rho_0 \exp(-h/h_{scale})$$ and a trans-sonic drag coefficient $$C_D$$ of 0.6 (from here) which matters mostly near mach 1 when max-Q is happening. I assumed the first stage fuel is 70% of the total launch mass of 550,000 kg.

Answer: Max-Q happens around mach 1 because the Earth's atmosphere and gravity and structural materials are what they are. Rockets are designed to make due with our atmosphere and gravity to get the most mass to orbit or beyond, with the caveat that they don't fall apart under crushing forces at max-Q.

If we lived on a planet with a lower surface pressure, it would happen earlier. If we lived on planet with different mass or diameter, that would affect both gravity on the rocket and the scale height, and max-Q would also happen earlier or later.

Luckily we don't live here! def deriv(X, t):
h, v   = X
acc_g  = -GMe / (h + Re)**2
m      = m0 - mdot * t
acc_t  = vex * mdot / m
rho    = rho0 * np.exp(-h/h_scale)
acc_d  = -0.5 * rho * v**2 * CD * A / m
return [v, acc_g + acc_t + acc_d]

import numpy as np
import matplotlib.pyplot as plt
from scipy.integrate import odeint as ODEint

Re      = 6378137. # meters
GMe     = 3.986E+14  # m^3/s^2
rho0    =  1.3 # kg/m3
h_scale = 8500.  # meters

# faux falcon-9 FT
vex     = 3600.  # m/s
tburn   = 160. # sec
m0      = 550000.  # kg
mdot    =  m0 * 0.70 / tburn  # kg/s
CD      = 0.6
A       = np.pi * (0.5*3.66)**2  # m^2

times = np.arange(0, tburn+1, 1)  # sec
X0    = np.zeros(2)    # initial state vector

answer, info = ODEint(deriv, X0, times, full_output=True)

hkm  = 0.001 * h
vkph = 3.6 * v
mach = v / 330. # roughly
rho  = rho0 * np.exp(-h/h_scale)
Q    = 0.5 * rho * v**2

if True:
plt.figure()
plt.subplot(2, 2, 1)
things = (hkm, vkph, mach, rho, Q)
names  = ('height (km)', 'velocity (km/h)', 'mach', 'density (kg/m^3)', 'Q')
for i, (thing, name) in enumerate(zip(things, names)):
plt.subplot(5, 1, i+1)
plt.plot(times, thing)
if i == 2:
plt.ylim(0, 3)
plt.plot(times, np.ones_like(times), '-k')
llim, ulim = plt.ylim()
plt.text(5, 0.7*ulim, name)
plt.xlabel('time (sec)', fontsize=16)
plt.show()

• Wow, two down votes but zero comments! – uhoh Sep 16 '19 at 10:15

No. Rockets need to be optimized for various, contradicting requirements:

1. Minimal mass of the hull ($$\rightarrow$$ should be so weak as possible)
2. Aerodynamics of the hull in sub-sonical regime
3. Aerodynamics of the hull in supersonical regime (very different from the sub-sonical aerodynamics)
4. Minimal gravity loss ($$\rightarrow$$ it needs to get to orbit quickly)
5. Minimal aerodynamical loss ($$\rightarrow$$ should not fly too quickly in dense athmosphere)

The planned trajectory of the vehicle is a compromise between them.

There is no direct reason to close out a sub-sonical max-Q. It simply didn't happen on engineering optimization reasons until now.