Question 1 (Total: 15 marks) a) The following diagram shows the forces acting on the aircraft during a climb performance. The governing equation is: dh T-D dt W Assume that the

aircraft is climbing at a constant speed of V = 150 m/s If the mass of the aircraft is 50,000 kg, the thrust T and drag D varies with altitude h, with the following function: K Rate of Climb = T = 119770-11.15 h D=52890 - 4.3977 h +0.001 h² Time (s) 0 60 i) Formulate a numerical procedure to Calculate the aircraft climb performance using forward difference method. (i.e. to find a numerical expression for h at different t) 120 180 -V ii) Based on the numerical method formulated in (i), Compute the aircraft altitude at different time, using At = 60 sec (hints: complete the following table) where the initial height is 500 m Aircraft altitude h (m) 500 iii) Analyse the accuracy and efficient of the numerical formulation used, by commenting the effect of dt on the accuracy of the result and efficiency of the algorithm. Appraise three possible methods that to verify and validate the result of your computation