# Appendix 12.1 — Bird-impact Forces — The Physics

###### Introduction

This book features a series of tables that assist readers in understanding the impact forces that are generated by birds of various weights at a variety of speeds:

• Table 12.1 — Bird Impact Forces vs. Speed
• Table 12.2 — FAR 33 Engine Certification Standard Bird Weights
• Table 5.5 — FAR 23, 25 & 29 Airframe Certification Standard Bird Impact Forces
• Table 5.6 — FAR 33 Engine Certification Standards (Old) Bird Impact Forces

Knowledge of impact force and the potential for aircraft damage are critical in the design and certification of aircraft components. This section summarizes the methodology applied in the calculation of bird-impact forces.

###### Impact-force calculation assumptions

There are a number of factors that affect the impact of a bird strike. These include:

• impact speed,
• bird weight,
• bird density,
• bird rigidity,
• angle of impact,
• impact-surface shape, and
• impact-surface rigidity.

To simplify the calculation, the following assumptions were made:

• impact speed is equal to the speed of the aircraft;
• impact angle is 90 degrees;
• bird shape is spherical;
• bird is deformed by one half of its size on impact;
• aircraft impact surface does not deform; and
• aircraft impact surface is flat.
###### Bird-impact force mathematical equation

The bird-strike impact-force equation was developed with the assistance of Mr. A.C. Tribble of the Advanced Technology Center at Rockwell Collins. The equation was derived as follows:

1. The energy transfer — or pressure — that results from a bird strike to an aircraft hull can be estimated through relatively simple calculations. Taking the simplest approximation — where the bird is at rest and 'sticks' to the aircraft after the collision — the change in a bird's kinetic energy is

where W is the work, F is the force, d is the distance over which the force is delivered, m is the mass of the bird and v is the velocity of the aircraft.

2. The force that the bird felt — the same force that the airplane felt — is given by

We can estimate the bird's mass, m, and the aircraft speed, v, with ease. The key parameter then is the distance d over which the impact is delivered.

3. As a first approximation, let's assume it is half the distance traveled by the aircraft in moving through the bird-impact event. If we further assume that the bird can be represented as a sphere, we end up with

4. If we assume the bird is spherical, then the bird's size depends on its mass according to the relation

where is the bird's density.

5. Combining the two previous expressions gives

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