What is the correct glide distance?

Question

An experienced captain of an airline took off from Peking for Heathrow and used his discretion to fly with marginally less fuel to optimise fuel consumption by reducing the all up weight of the airliner. 45 minutes before landing at Heathrow the captain and co- pilot discussed the fuel situation and decided that they would land the aircraft at Heathrow because the fuel situation they thought was not so acute as to warrant an unplanned landing on an enroute airfield and therefore the captain in good faith decided to take the chance to land the aircraft as per flight plan to avoid unnecessary press attention etc.

Half an hour before landing when the fuel warning lights started blinking you were asked to advise the pilots about how to get the best range should the fuel starvation to the engines took place.

What range the aircraft is expected to cover if both the engines fail at a height of 1500m and pilots select a glide angle of 3.5 degrees The plane now is185000kg. Pls show workin

Answer 1

Without power, the aircraft is just a glider and this becomes a simple trigonometry question.

Let a = glide angle = 3.5 degrees

Let h = altitude = 1500 m

Let R = range

R = h / tan(a) = 1500 / tan(3.5 degrees) = 24524 m = 24.5 km

Note that the mass of the aircraft is irrelevant and so is most of the information in the question. It's designed to throw you off.

Answer 2

tan 3.5 = h/d = 0.06116

d = h/0.06116 = 1500/0.06116 = 24500 m