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Tony's Intertwingled Memex • Reference Manual

Rocket Drag and Aerodynamic Deceleration (Aerospace Engineering)

Formulas & Definitions

An aerospace propulsion engineer is modeling the aerodynamic drag force FDF_D experienced by a sounding rocket ascending through the lower stratosphere. The aerodynamic drag (in kilonewtons) depends on the flight velocity vv (in m/s\text{m/s}) and atmospheric density scale factors according to the empirical relationship:

FD(v)=0.002v2+180v3+0.05v32F_D(v) = 0.002 v^2 + \frac{180}{\sqrt[3]{v}} + 0.05 v^{\frac{3}{2}}
for operational velocities v∈[50,1000] m/sv \in [50, 1000]\text{ m/s}.

  1. Pre-process the radical denominator term 180v3\frac{180}{\sqrt[3]{v}} into explicit power form c⋅vnc \cdot v^n.
  2. Compute the derivative dFDdv\frac{dF_D}{dv}, which represents the velocity sensitivity gradient of aerodynamic drag.
  3. Factor out the lowest power from the resulting fractional terms to simplify the post-derivative expression, and evaluate dFDdv∣v=64 m/s\left.\frac{dF_D}{dv}\right|_{v = 64\text{ m/s}}.