The correct answer is (b) 37.8 ton

To EXPLAIN: Given, a jet aircraft, crew and payload = 6500 kg.

Since, mission profiles are given we need to FIND mission segment fuel weight fraction for each.

For take-off, climb and LANDING it is given as 0.98.

For cruise,

Range R 1500 nm= 9114000ft, C =0.5 1/hr. =0.0001389 1/s, L/D =13.2, velocity V=570 ft/s

Now cruise weight fraction is given by Range formula. For, prop-driven aircraft it is given by,

Wcruise / W0 = \(e^{\left(-\frac{R*C}{V*\frac{L}{D}}\right)}\) = \(e^{(-\frac{9114000*0.0001389}{570*13.2})}\) = 0.8451

LOITER: loiter of 2 hour is given hence,

Endurance E = 2*3600 = 7200 s

Now, loiter fuel fraction

Wloiter / W0 = \(e^{\left(-\frac{E*C}{\frac{L}{D}}\right)}\) = \(e^{(-\frac{7200*0.0001389}{13.2})}\) = 0.9270

Now from fuel fraction method,

Wx / W0 = multiplication of each phase fraction

= 0.98*0.98*0.8451*0.9270*0.98

= 0.7373

Now,

Wf / W0 = 1.06 * [1 – (Wx / W0)] = 1.06 * [1-0.7373] = 0.2784

Empty weight fraction We / W0 = 0.55

Gross weight of aircraft is,

W0 = Wcrew + Wpayload + WFUEL + Wempty

By re-arranging,

W0 = Wcrew + Wpayload / [1 – (Wf / W0) – (We / W0)]

= 6500 / [1-0.2784-0.55] = 37880 kg = 37.8