An unmanned aerial vehicle (aircraft) () is required to travel for a horizontal

Question

An unmanned aerial vehicle (aircraft) () is required to travel for a horizontal distance of 500 m from point A to point B at fixed flying height of 1 km with respect to the sea surface height (). Three types of aircrafts (X, Y and Z) are designed using three different approaches to meet this requirement. Each type is tested and the measurement of the aircraft flying height for each 100 meter distance travelling from point A to point B is registered as following: Flying height in (Km) of Type X = [0.90 0.95 1.00 1.05 1.05 1.00] Flying height in (Km) of Type Y = [0.80 1.00 1.10 1.00 1.05 1.00] Flying height in (Km) of Type Z = [1.10 1.05 1.05 1.00 1.05 1.00] Suggest mathematical method to determine which one of these three types of aircraft is better meets the requirements of flying height.

Explanation / Answer

We can develop a very simple methamatical model:

Measured heights of aircraft are given for each 100 m distance travelled , .

Average flying height for 500 m distance

For Type X : [0.90+0.95+1+1.05+1.05]/5 = 0.99 km

For Type Y: [ 0.80+1+1.10+1+1.05]/5= 0.99

For TypeZ : [1.10+1.05+1.05+1+1.05]/5 = 1.05 km

The better model is for type X as height is in increasing mode and become 1 km(required) just after traveling 500 m horizontal distance.

TypeX aircraft is better according to requirement.

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