Fundamentals of Aerodynamics
Fundamentals of Aerodynamics
6th Edition
ISBN: 9781259129919
Author: John D. Anderson Jr.
Publisher: McGraw-Hill Education
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Chapter 9, Problem 9.1P

A slender missile is flying at Mach 1.5 at low altitude. Assume the wave generated by the nose of the missile is a Mach wave. This wave intersects the ground 559 ft behind the nose. At what altitude is the missile flying?

Expert Solution & Answer
Check Mark
To determine

The altitude of flying missile.

Answer to Problem 9.1P

The altitude of flying missile is 499.98ft .

Explanation of Solution

Given:

The Mach number of slender missile is M=1.5 .

The horizontal distance is H=559ft .

Formula Used:

The expression for the relation between Mach angle and Mach number is given as,

  sinβ=1M

Here, β is the Mach angle and M is the Mach number.

The expression for the tan function can be given as,

  tanθ=PB

Here, θ is the angle, P is the perpendicular length, and B is the base length.

Calculation:

The Mach angle can be calculated as,

  sinβ=1Msinβ=11.5β=sin1(1 1.5)β=41.81°

The vertical distance can be calculated as,

  tanβ=VHtan41.81°=V559ftV=499.97ft

Conclusion:

Therefore, the altitude of missile is flying is 499.98ft .

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