§AERE 261 Homework 7

Sep 25, 2025
Refer the adjacent Python file for the code. Refer to the provided CLI per section to run the script.

§1. (a)

py index.py --plot=temperature

§1. (b)

py index.py --plot=pressure

§1. (c)

py index.py --plot=density

§2. (a)

py index.py --plot=v_stall

§2. (b)

py index.py --plot=v_r_c_max

§2. (c)

Yes, it is.

§3. (a)

py index.py --plot=p_r

§3. (b)

py index.py --plot=p_a

§3. (c)

py index.py --plot=p_e

§4. (a)

py index.py --plot=r_c_max

§4. (b)

py index.py --plot=ceilingsService ceiling is about 16.8km16.8km and the absolute ceiling is about 17.5km17.5km.

§5. (a)

CD,0=0.017 C_{D,0}=0.017
K=0.056 K=0.056
(CL)max=1.37 (C_L)_{max}=1.37
Swing=22.9m2 S_{wing}=22.9m^2
ηpr=90%=0.9 \eta_{pr}=90\%=0.9
W0=16481N W_0=16481N
P=180000W P=180000W
h=7000ft=2134m h=7000ft=2134m
ρ∞=0.993kg/m3 \rho_\infty=0.993kg/m^3
tan⁡θmin=1(L/D)max=1(CL/CD)max \tan\theta_{min}=\frac{1}{(L/D)_{max}}=\frac{1}{(C_L/C_D)_{max}}
θmin=arctan⁡1(CL/CD)max \theta_{min}=\arctan\frac{1}{(C_L/C_D)_{max}}
(CL/CD)max=14KCD,0=14∗0.056∗0.017=16.21 (C_L/C_D)_{max}=\sqrt{\frac{1}{4KC_{D,0}}}=\sqrt{\frac{1}{4 * 0.056 * 0.017}}=16.21
θmin=arctan⁡116.21=3.53° \theta_{min}=\arctan\frac{1}{16.21}=\boxed{3.53\degree}

§5. (b)

dmax=htan⁡θmin=2134mtan⁡3.53°=34590m d_{max}=\frac{h}{\tan\theta_{min}}=\frac{2134m}{\tan3.53\degree}=\boxed{34590m}

§5. (c)

V∞=2Wρ∞SKCD,0=2∗16481N0.993kg/m3∗22.9m20.0560.017=51.29m/s V_\infty=\sqrt{\frac{2W}{\rho_\infty S}\sqrt{\frac{K}{C_{D,0}}}}=\sqrt{\frac{2 * 16481N}{0.993kg/m^3 * 22.9m^2}\sqrt{\frac{0.056}{0.017}}}=\boxed{51.29m/s}

§5. (d)

Vs=V∞sin⁡θmin=51.29m/s∗sin⁡3.53°=3.158m/s V_s=V_\infty\sin\theta_{min}=51.29m/s * \sin 3.53\degree=\boxed{3.158m/s}