Question

During a routine flight in 1956, test pilot Tom Attridge put his jet fighter into a$\mathbf{20}\mathbf{°}$dive for a test of the aircraft’s 20 mmmachine cannons. While traveling faster than sound at 4000 m altitude, he shot a burst of rounds. Then, after allowing the cannons to cool, he shot another burst at 2000 m; his speed was then344 m/s, the speed of the rounds relative to him was 730 m/s, and he was still in a dive. Almost immediately the canopy around him was shredded and his right air intake was damaged. With little flying capability left, the jet crashed into a wooded area, but Attridge managed to escape the resulting explosion. Explain what apparently happened just after the second burst of cannon rounds. (Attridge has been the only pilot who has managed to shoot himself down.)

Short answer

After the second burst of cannon rounds, the actual velocity of the cannon rounds became less than the speed of the plane so the plane hits the cannon before the explosion happens.

Step-by-step solution

The given data

1. A jet fighter puts a $20°$dive for a test of 20 mm machine cannons.
2. With a speed greater than the speed of light at 4000 m altitude, he shot the burst.
3. After cooling, he shot the next burst at 2000m altitude, his speed was 344 m/s.
4. Speed of the rounds relative to him was 730 m/s.
5. Then immediately, the canopy was shredded and his right air intake got damaged.

Understanding the concept of the drag force

For decreasing altitude, the density of the air increases accordingly. Now, using the concept of drag force, and the given value of the speed of the cannon rounds, we can get the reason for the hit with the plane before the explosion happens.

Formula:

The drag equation relating the force to speed and density,

${\mathbf{F}}_{\mathbf{D}}\mathbf{=}{\mathbf{C}}_{\mathbf{D}}\mathbf{A}\frac{{\mathbf{pV}}^{\mathbf{2}}}{\mathbf{2}}$ (1)

where${\mathbf{F}}_{\mathbf{D}}$ is the drag force,

${\mathbf{C}}_{\mathbf{D}}$is the drag coefficient,

A is the reference area,

pis the density of the fluid,

Vis the flow velocity relative to the object.

Calculation of the state of the cannon rounds after the second burst

Initially when Tom Attridge was at 4000 m altitude shot for the first time but after that, he was at 2000 m altitude in the 2nd case. At this altitude, the air is denser than at the altitude 4000 m. As the plane was flying at supersonic speed, the drag force due to the air on the bullet is greater considering equation (1). Thus, within moments the actual velocity of bullets became less than the plane and the plane hit those bullets therefore the explosion happens.