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Homework Statement
Assume that m(fuel, climb) = 1300kg is the mass of fuel required for the climb to the cruising altitude of 10,000m, independently of the takeoff weight. Assume that the distance covered during the climb is always 100km. Consider the typical payloadrange diagram shown and calculate the values of the payload and range at points P1, P2 and P3. Ignore the descent phases.
https://imgur.com/tgdNBUC
Some necessary variables:
TSFC = 0.63 h^(1)
m(empty) = 8600kg
m(max takeoff) = 14000kg
m(max fuel) = 5200kg
m(max payload) = 1400kg
AR = 11.02083
CD(0) = 0.016
CL(max) = 1.4
e = 0.84
S = 48 m^(2)
p (density) = 0.414 at 10,000m
g = 10 m/s^(2)
W0 = Initial weight of aeroplane (with fuel)
W1 = Final weight of aeroplane (all fuel used)
Homework Equations
R = (1/TSFC)*(√(8/(pS)))*((CL^(0.5))/CD)*(√W0  √W1)
CL: This is where I may have made a mistake, I assumed that because the Range formula above contains "((CL^(0.5))/CD)", I should calculate CL using the bottom formula in this image: https://imgur.com/DpAFSEJ
CL = √((Pi/3)*e*AR*CD(0))
CD = CD(0) + (CL^(2))/(Pi*e*AR)
The Attempt at a Solution
Firstly, these are the places where I have possibly gone wrong:
1. Question states that m(fuel, climb) is independent of the takeoff weight. Does this mean that I ignore it and don't use it at all in finding the value of W0?
2. CL in the Range formula. Possible that I just use the given value CL(max) to find the points (the points on the diagram are maximum ranges)?
3. I may have worked out W0 and W1 wrong. I believe W0 = W(max take off)  W(fuel climb), and W1 = W(empty) + W(payload).
Attempt:
P1 is the point at which range is maximum with W(max payload).
Payload = m(max payload) = 1400kg
W0 = W(max takeoff)  W(fuel, climb) = (m(max takeoff)*10)  (m(fuel,climb)*10)
= 140000  13000 = 127000N
W1 = W(empty) + W(max payload)
= (8600*10) + (1400*10) = 100000N
CL = √((Pi/3)*e*AR*CD(0))
= √((Pi/3)*0.84*11.02083*0.016) = 0.39384
CD = CD(0) + (CL^(2))/(Pi*e*AR)
= 0.016+(0.39384^(2))/(Pi*0.84*11.02083) = 0.02133
R = (1/TSFC)*(√(8/pS))*((CL^(0.5))/CD)*(√W0  √W1)
= (1/0.63)*(√(8/(0.414*48)))*((0.39384^(0.5))/0.02133)*(√127000  √100000)
= 1189.48966 km
+100km (distance covered during climb) = 1289.48966 km
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