Question

An aircraft starts gliding in power-off condition at an altitude of 4 km. Given that the maximum lift to drag ratio of the aircraft is 15, the maximum glide range that the aircraft can cover, measured along the ground, is _______ km (rounded off to the nearest integer).

Hint:

Maximum glide range = altitude lost multiplied by the maximum lift to drag ratio, since \(\tan\gamma_{min}=1/(L/D)_{max}\).

Answer 1

Correct Answer: 60

Step 1: Set up the glide relation.
In power-off (engine idle/off) gliding flight, the aircraft is in equilibrium under lift \(L\), drag \(D\) and weight \(W\), descending along a straight glide path at angle \(\gamma\) below the horizontal. Resolving forces along and perpendicular to the flight path gives \(L=W\cos\gamma\) and \(D=W\sin\gamma\), so \(\tan\gamma = D/L\).

Step 2: Relate glide angle to lift to drag ratio.
Since \(\tan\gamma = D/L = 1/(L/D)\), the glide angle is smallest, and hence the horizontal distance covered for a given loss of altitude is largest, when \(L/D\) is at its maximum value. Using \((L/D)_{max}=15\):
\[ \tan\gamma_{min} = \frac{1}{(L/D)_{max}} = \frac{1}{15} \]

Step 3: Relate glide range to altitude.
If the aircraft glides from height \(h\) down to the ground, the horizontal distance \(R\) (glide range) and \(h\) form the two legs of the glide-path triangle, so \(\tan\gamma = h/R\), which gives \(R = h/\tan\gamma\). For the maximum range case, this becomes \(R_{max} = h \times (L/D)_{max}\). This is the well known result that maximum glide range equals altitude lost multiplied by the best lift to drag ratio (independent of aircraft weight or air density).

Step 4: Substitute the numbers.
The aircraft starts at \(h = 4\) km and \((L/D)_{max}=15\):
\[ R_{max} = 4 \times 15 = 60 \text{ km} \]

Final Answer:
The maximum glide range measured along the ground is 60 km. \[ \boxed{60 \text{ km}} \]