Share
Explore BrainMass

Explore BrainMass

Modeling the approach path of an aircraft

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?

Solution Summary

The 4 pages solution shows a full derivation of the cubic polynomial required to describe the path of an aircraft as it approaches landing.

$2.19