An aircraft has Crew and payload of 180kg. It has empty weight fraction of 0.48 and fuel weight is 0.7 times empty weight. What will be the gross weight of aircraft?

Correct Answer : Option (C) :   4430kg

Explaination : Given crew weight = 150kg, payload weight = 600kg
Fuel weight fraction W_f / W₀ = 1.06[1 – W_x/W₀],
Now from fuel fraction method,
W_x / W₀ = multiplication of each phase fraction
= 0.975*0.98*0.96*0.8*0.96*0.97
= 0.6833
Now,
W_f / W₀ = 1.06 * [1 – (W_x / W₀)] = 0.3357
Empty weight fraction W_e / W₀ = 0.481
Gross weight of aircraft is,
W₀ = W_crew + W_payload + W_fuel + W_empty
By re-arranging,
W₀ = W_crew + W_payload / [1 – (W_f/ W₀) – (W_e / W₀)]
= 150 + 600 / [1-0.3357-0.495] = 4430kg

Correct Answer : Option (C) :   fuel, crew, payload and empty weight

Explanation : Total take-off gross weight is nothing but the sum of all the possible aspects of an aircraft. Hence, it will depend on fuel weight, crew and payload weight and also on empty weight.

Correct Answer : Option (D) :   2157lb

Explanation : Given crew and payload = 180kg,
Empty weight fraction W_e / W₀ = 0.48
Fuel weight is 0.7 times empty weight.
Hence, W_f = 0.7*W_e
Hence, W_f / W₀ = 0.7*W_e / W₀ = 0.7*0.48 = 0.336
Gross weight of aircraft is,
W₀ = W_crew + W_payload + W_fuel + W_empty
By re-arranging,
W₀ = W_crew + W_payload / [1 – (W_f/ W₀) – (W_e / W₀)]
= 180 / [1-0.336-0.48] = 978.26kg = 2157.06lb.