§AERE 261 Homework 8 Corrections

Sep 25, 2025

§1.

−1≤nstruct≤2.6 -1\leq n_{struct}\leq 2.6
V∞=46m/s V_\infty=46m/s
W=16481N W=16481N
S=22.9m2 S=22.9m^2
CL,max=1.37 C_{L,max}=1.37
ρ∞=1.156kg/m3 \rho_\infty=1.156kg/m^3
g=9.81m/s2 g=9.81m/s^2

§1. (a) i.

IMPORTANT
Rpull up=V∞2g(n−1)=(46m/s)29.81m/s2∗(2.6−1)=134.8m R_{pull\ up}=\frac{V_\infty^2}{g(n-1)}=\frac{(46m/s)^2}{9.81m/s^2 * (2.6 - 1)}=\boxed{134.8m}
ωpull up=g(n−1)V∞=9.81m/s2∗(2.6−1)46m/s=0.3412rad/s=19.549deg⁡/s \omega_{pull\ up}=\frac{g(n-1)}{V_\infty}=\frac{9.81m/s^2 * (2.6 - 1)}{46m/s}=0.3412rad/s=\boxed{19.549\deg/s}

§1. (a) ii.

IMPORTANT
Rturn=V∞2gn2−1=(46m/s)29.81m/s2∗2.62−1=89.87m R_{turn}=\frac{V_\infty^2}{g\sqrt{n^2-1}}=\frac{(46m/s)^2}{9.81m/s^2 * \sqrt{2.6^2 - 1}}=\boxed{89.87m}
ωturn=gn2−1V∞=9.81m/s2∗2.62−146m/s=0.5118rad/s=29.324deg⁡/s \omega_{turn}=\frac{g\sqrt{n^2-1}}{V_\infty}=\frac{9.81m/s^2 * \sqrt{2.6^2 - 1}}{46m/s}=0.5118rad/s=\boxed{29.324\deg/s}

§1. (b)

The maneuvering velocity of the pull-up maneuver does not exceed the velocity in which the aircraft is flying at.
Vmaneuvering, pull up=ωR=0.3412/s∗134.8m=46.00m/s=V∞ V_{maneuvering,\ pull\ up}=\omega R=0.3412/s * 134.8m=46.00m/s=V_\infty
The maneuvering velocity of the turn maneuver does not exceed the velocity in which the aircraft is flying at.
Vmaneuvering, turn=ωR=0.5118/s∗89.87m=46.00m/s=V∞ V_{maneuvering,\ turn}=\omega R=0.5118/s * 89.87m=46.00m/s=V_\infty

§1. (c)

The turn maneuver will be the right choice here as it offers a smaller turn radius of 89.87m89.87m which is superior to the pull-up maneuver even though the instantaneous turn rate is lower because the benefit of a smaller turn radius trumps the benefit of a faster instantaneous turn rate.
Yes, I took 7 years of art. How can you tell?

§2.

A (top): accelerated stallA (bottom): inverted accelerated stall; the same thing as A where pulling up too much makes you stall but instead now pulling the nose too downB (top): positive structural limitB (bottom): negative structural limit; once again, the kinda of deal with stall; this one will deform you pulling downC: airspeed limit after which structural damage may occur; calm down, you are not Chuck Yeager