AER1216- Assignment # 3 Solved

An unmanned aircraft has the following characteristics: CLmax = 1.2, S = 20 m2, W = 10,000 N, with an installed jet engine, TFSC is 0.7 hr−[1]. We also know that CD0 = 0.03, ε = 0.7, AR = 10. We also assume at sea level, the thrust available is 5,000N.Plot in a velocity-altitude envelope, the minimum flight speed Vmin (corresponding to CLmax, and the optimum flying speed for minimum thrust required VTR,min, with respect to different altitudes (up to 15 km). One may refer to standard atmosphere model for the air density calculations.1 
Draw the plot of maximum climbing rate with respect to altitude,and estimate the ceiling for this UAS to operate.
Let’s assume the UAS is flying with constant angle of attack anda constant velocity of M = 0. Prove that range R of the UAS is given by
where W0 = W, W1 = W − Wf, Wf being the fuel weight.

Based on the assumption in (c), if we would like to give the UASof range of 100 km, calculate the required fuel weight at sea level.
 

Consider a Quadrotor at sea-level with a total weight of 8 N and a frameCD=0.7 based on the reference area S = 0.01m2 that is powered by motors with a Kv = 1050 V/rpm, i0 = 0.4 amps, rm = 0.12 ohms, and Kt = 1/Kv. The quadrotor uses four APC 8x3.8 Slow Flyer propellers. The ESC internal resistance is re = 0.05 ohms. The battery is a 3 cell 1300mA-hr 30◦C battery. The coefficients for the battery discharge curve are (for discharge in mA-hr):
a
=
12.3063
b
=
−0.000328
c
=
−0.008112
d
=
−4.7809 × 10−7
e
=
−7.7835 × 10−7
f
=
1.4086 × 10−10
 

What is the power required to hover from momentum theory, assuming no motor or ESC losses? 
What is the hover endurance from momentum theory assumingno motor and ESC losses and using the 0th order model for the given battery
What is the hovering power considering the APC propellers measured characteristics (instead of momentum theory), assuming no motor or ESC losses? 
Using the same assumptions as part (c), what is the hover endurance using the 0th order battery model?
Using the same assumptions as part (c), what is the hoveringendurance if the motor is 85% efficient and the ESC is 95% efficient using the 0th order battery model? 
Now considering the given propellers, motor, ESC and batterydischarge characteristics (i.e. use the 1st order battery model) what is the hover endurance? Assume the initial discharge state is at 1 mA-hr and use a ∆t = 0.1 s.
Using momentum theory for forward fight (steady-state, level flightat sea-level) calculate and plot the following for speeds from 0 to 20 m/s in increments of 0.5 m/sThrust
Induced Po

[1] There are many references for this subject, e.g. Anderson, Introduction to Flight

Induced Power
Total Power Requirediv. Total Power/Velocity
(h) Using the 0th order battery model and assuming the motor is 85% efficient and the ESC is 95% efficient, what is the maximum endurance and maximum range? What forward speed does the quadrotor need to fly to get these values?