An approach path for an aircraft landing is shown in the figure on the next page and satisfies the following conditions:
i) The cruising altitude is h when descent starts at a horizontal distance L from touch down at the origin.
ii) The pilot must maintain a constant horizontal speed v throughout decent.
iii) The absolute value of the vertical acceleration should not exceed a constant k (which is much less than the acceleration due to gravity).
1) Find a cubic polynomial P(x)=ax^3 + bx^2 + cx + d
2) Use conditions (ii) and (iii) to show that (6hv^2)/L^2 less than or equal to K
3) Suppose that an airline decides not to allow vertical acceleration of a plane to exceed K = 800 mi/h^2. 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 in Problem 3 are satisfied?
The 4 pages solution shows a full derivation of the cubic polynomial required to describe the path of an aircraft as it approaches landing.