Characteristics of the Me-163 Komet

[JPierce]

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.

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/s².)

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 not that good.

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?

 

[K^2]

First of all, your calculator is set to radians. It's closer to 17,000m.

Secondly, the deceleration is far from constant. It will decelerate a lot more rapidly early on, which increases time required to reach altitude.

I tried to make a simple estimate using quadratic drag, but the numbers aren't working out exactly right. I'll try to get a better estimate.

 

[JPierce]

First of all, your calculator is set to radians. It's closer to 17,000m.

Secondly, the deceleration is far from constant. It will decelerate a lot more rapidly early on, which increases time required to reach altitude.

EDIT: Bad physics in my response removed.

BTW, I checked the distance, and from what I have the total distance of travel is 12,650 meters (with an overall vertical altitude of 11,887 meters). I don't think I entered the distance wrong, but I'll check again but 17,000 meters doesn't look right.

 

[JPierce]

One more question: Would a linear drag force (F=bv) be sufficient?

 

[K^2]

Woah, I entered something wrong. Never mind about the altitude.

Anyways, no, quadratic drag must be used. Doesn't matter, though. I don't see how it can climb at 70°. It doesn't have enough thrust. Even if it starts out at 500mph, it will come to a stop in under 40 seconds, traveling only about 4km in that time. So it must switch to the shallower angle rather early.

 

[JPierce]

Woah, I entered something wrong. Never mind about the altitude.

Anyways, no, quadratic drag must be used. Doesn't matter, though. I don't see how it can climb at 70°. It doesn't have enough thrust. Even if it starts out at 500mph, it will come to a stop in under 40 seconds, traveling only about 4km in that time. So it must switch to the shallower angle rather early.

Oddly enough, the 60-70 degree angle of attacks are widely quoted and video footage of the plane indicates that it can gain altitude very readily at such a steep angle. But I think you're right -- something on the order of 45 degrees was probably more likely. I guess I'll play around with the angle of attack and see if I can come up with something. Thanks for your time -- much appreciated.

 

[RobK13]

The 70 degree climb rate is at the very end of its fuel load, when thrust to weight is approaching a 1:1 ratio, so that is entirely plausible, e.g. in the last 8 - 10 seconds before all of the fuel is expended.

From my research, the general angle appears to be in the 45 - 60 degree range during most of its flight.

Also, rocket engines get more efficient at altitude, and the drag will be much less in the thinner atmosphere, so the climb rate increases considerably over time, e.g. from around 9,000 - 12,000 Ft./Min. to 16,000 at very high level. The Komet is a slippery 0.012 in terms of drag.

I was puzzled by this aircraft's climb rate as well, given all the conflicting info published.

I now believe the time to various altitudes are from a standing start, including the roll on the runway from brake release. I just watched a bit of footage on-line, and the time to roll down the runway, level off, drop the trolley, and then pull up takes about 45 seconds, or so. The plane then builds up a bit more speed, supposedly to 420 MPH, and is then put into a steep climb. (Liftoff from the runway is at about 225 MPH).

The fighter then climbs at anywhere from 45 - 60 degrees, 50 - 60 degrees seems to be mentioned the most, at around 500 MPH, or so. The steepest climb mentioned is at a speed of 420 MPH, at a 70 degree angle, but I think that can only be managed when most of the fuel is gone, and it can pull into the steeper climb.

Also, I've read accounts of the aircraft overspeeding in a climb, while attempting to intercept a Mosquito - happened to both pursuing pilots, which presumably means they exceeded 623 MPH in a climb.

Most climb rates mentioned are in the 420 - 525 MPH range, so I presume they have throttled back a bit to increase their endurance from full thrust, and so they don't exceed their critical Mach speed.

I hope that helps.

I'd love to see a climb profile of this fighter, if anyone knows of one in print.

I'm also interested in its unpowered speed, and dive speeds, while both powered, and unpowered.