I hope I'm posting this in the right section. This isn't a homework problem, but rather a curiosity. Please move it if you wish.(adsbygoogle = window.adsbygoogle || []).push({});

I have been goofing around with the flight characteristics of the Me-163 Komet (a rocket-powered fighter plane) for my class and something isn't jiving. Maybe I'm making a mistake and would appreciate it if someone can fill me in.

According to all my sources, the Me-163 had a level flight speed on the order of 500 mph. When intercepting enemy bombers it would fly at roughly this horizontal speed and then immediately pull up into about a 70 degree attack, climbing to 39000 ft in 3 minutes (which was a record at the time).

I cannot see how this is possible.

To make it to 39000 ft altitude at 70 degrees the plane would need to travel a total distance of about 50,000 ft, which is roughly 13,000 meters. If it's initial speed is close to 500 mph (220 m/s), its final speed when traveling 13,000 meters would be about -80 m/s, which means it has already passed the maximum altitude and is on its way down. (This would correspond to an acceleration of about -1.7 m/s^{2}.)

The initial speed of 500 mph is perhaps a little unrealistic, but even at 300 mph the plane is barely moving when it gets to its maximum altitude. The Komet had good stall characteristics, but notthatgood.

This all assumes a constant acceleration. The thrust of the rocket will be pretty constant throughout the flight. The weight of the plane decreases because of the spent fuel, but the drag also decreases because the density of the air lessens. Given all this, I would think that the acceleration of the Komet should be fairly constant.

The issue is the flight time. It should take far less than 3 minutes to travel 50,000 ft if your initial speed is 500 mph. If we lower the flight time to 1 minute we get more realistic final speeds.

Problems also appear when finding the drag force acting on the plane. With a thrust of 17,000 newtons and a mass of 3950 kg, the drag force actually has to point forward to sufficiently accelerate the Komet to reach 39,000 ft in 3 minutes. Naturally this is nonsense.

What am I doing wrong?

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# Characteristics of the Me-163 Komet

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