Question: An approach path for an aircraft landing
An approach path for an aircraft landing is shown in the figure and satisfies the following conditions:
(i). The cruising altitude is h when descent starts at a horizontal distance from touchdown at the origin.
(ii). The pilot must maintain a constant horizontal speed throughout descent.
(iii). The absolute value of the vertical acceleration should not exceed a constant (which is much less than the acceleration due to gravity).
1. Find a cubic polynomial P (x) = ax3 + bx2 + cx + d that satisfies condition (i) by imposing suitable conditions on P (x) and P'(x) at the start of descent and at touchdown.
2. Use conditions (ii) and (iii) to show that 6hv2/l2 3. Suppose that an airline decides not to allow vertical acceleration of a plane to exceed k = 860 mi/h2. If the cruising altitude of a plane is 35,000 ft and the speed is 300 mi/h, how far away from the airport should the pilot start descent?
4. Graph the approach path if the conditions stated in Problem 3 are satisfied.
Transcribed Image Text:
y y = P(x) e-
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