The importance of physical models: how not to shoot yourself in the foot or elsewhere

We take shortcuts all the time with our physical models. We rarely consider wire to have resistance, for example, or batteries to have source impedance. That's fine to the point where it's not. Take the case of the Navy's Grumman F11F Tiger aircraft. The supersonic aircraft was impressive, although it suffered from some fatal flaws. But it also has the distinction of being the first plane to be shot down.

So here is the simple math. An aircraft traveling at Mach 1 is traveling at around 1,200 km/h - the exact number depends on a few factors like your altitude and the humidity. Let's say about 333 m/s. Bullets from a 20 mm cannon, on the other hand, travel at over 1000 m/second. So when the ball leaves the plane, it would take more than three seconds for the plane to catch up with it, after which it got further and further away, right?

Who shot you?

No. In 1956, Tom Attridge took off from Long Island to carry out a weapons test over the Atlantic. He climbed to 20,000 feet, began a Mach 1 dive, and fired his guns which ran out of ammunition at approximately 13,000 feet.

Around the 7,000 foot mark, something hit her windshield - presumably a bird. The aircraft began to lose power and crashed, leaving a 300ft fiery path through a wooded area near the airstrip. Attridge survived but had a broken leg and a broken vertebra.

But it wasn't a bird that hit the naval aviator's plane. They were his own bullets. The problem is that the bullet left the gun at a high speed. However, they immediately encountered air resistance, causing them to slow down. By the time the bullets slowed to 643 m/s, the aircraft was traveling at 1,400 m/s. Three bullets hit the aircraft, one through the nose cone, one through the windshield, and one hit the starboard engine intake. All this took only 11 seconds. You can see the whole story in the video below.

The aircraft proved to be less reliable than other contemporary fighter aircraft. It had other undesirable features, but it was used as a training aircraft and the Blue Angels used them until 1968.

Lesson learned?

You might think that's proof enough that something was wrong, but no. It was dismissed as a "fluke". Of course, in 1973 an F-14 Tomcat also went down with a dummy missile. A Dutch F-16 also went down in 2019 in a very similar incident. You have to wonder if there are any other examples that haven't been pointed out.

However, there is a lesson here. Common sense is not always engineering sense. Think a two-micron gap isn't important? Think again. Or maybe you want to check for air leaks using a candle in a nuclear power plant? Engineering history is full of stories where any reasonable person would think something was right, when in retrospect it was anything but.

There is an old Russian saying "trust but verify". It's a good adage for us too. Trust your instincts, but verify with solid mathematical models that take everything into account.