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DanRow93
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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 take-off weight. Assume that the distance covered during the climb is always 100km. Consider the typical payload-range 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 take-off) = 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 take-off 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 take-off) - W(fuel, climb) = (m(max take-off)*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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