(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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)

2. Relevant 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)

3. 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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# Homework Help: Flight Mechanics - Range and Payload calculations

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