For real this time: Mythbusters will air their challenge of the airplane on a conveyor belt puzzle this Wednesday at 9pm ET. (thx, darin)
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I didn't get to see the episode tonight, hopefully I can youtube or usenet it by tomorrow morning, but apparently the Mythbusters plane does take off:
The plane took off so easily. The laws of physics are proven correct once again. But I'm not sure this is going to settle anything. I'm getting email as we speak that the test was unfair. Plane was too light. Tarp was pulled too slowly. Etc. But the thing is, it doesn't matter how large the plane is...given enough runway and a strong enough conveyor belt, it will still take off. Ditto for the speed of the treadmill...it doesn't matter how fast the treadmill is moving. It could be going 300 mph in the opposite direction and as long as the bearings in the plane's wheels don't melt, it's gonna take off. For an explanation, try this one by my friend Mouser, who has a MIT Sc.D. in Nuclear Science and Engineering.
Gravity, oriented downwards, constant.
Lift, oriented upwards, function of airspeed.
Thrust, oriented forwards, assumed constant.
Drag, oriented backwards, superposition of air resistance and friction in the wheels.Obviously the plane will not take off until the force due to lift overcomes the force due to gravity. For this to happen, the plane must achieve some minimum forward velocity relative to the air. Forward acceleration will only occur as long as the force of thrust overcomes the drag force.
Because the conveyor belt speed is the inverse of the plane's airspeed, we can say that the conveyor belt does not move until the plane begins to accelerate forward. Thus, rolling resistance has already been overcome by thrust when this problem really begins.
Initially, the engine thrust is considerably higher than the drag—this is what allows aircraft to take off on regular runways. So the question is, once we start moving and the conveyor belt starts up, does it impose some force on the aircraft that can overcome the force of thrust?
Certainly not initially.
Which is what I've been saying, though perhaps not so clear:
Anyhow, here's what I've been thinking. Many people immediately think, and rightly so, that how fast the wheels spin doesn't matter, lift is produced by the air that goes over and under the wings. And I agree. But think a little further. Suppose you had a plane with a wheel system that had no internal friction. If you placed this plane on a conveyor belt straight down, the plane would not follow the direction of the conveyor belt. Rather, it would remain in place relative to the larger frame of reference (the ground) and the wheels would spin. Said plane would then turn on the engines and take off. Why? Because the engines would push the plane forward through the air. The plane is not in a wind tunnel, it is merely on a conveyor belt. That the surface it is on is moving doesn't matter since in this hypothetical, friction has been removed. (I did leave in friction enough that the rubber grips the ground. If there was no friction at that point, the plane would remain stationary, but the wheels wouldn't turn either, the conveyor belt would merely move below it.)
Now take a regular plane. Suppose it require the engines to operate at 80% of their collective power to take off. Place this plane on the conveyor belt. Turn the engines on slowly until the plane is now no longer moving relative to the ground. Suppose the engines are at 5% of their collective power. At this point, I'd suppose that if the engine power were increased to 85%, that the plane would take off, just as it did at 80% when on the ground. (The math is no where near this simple, this is just to illustrate a point.)
Anyhow, point is, while the conveyor belt may be going backwards at a rate of, say, 50 meters per second and the plane may need to approach a speed of 50 meters per second, relative to the air (called air speed), the force required to compensate for the 50 meters per second of the conveyor belt is far less (in the above example, sixteen times less) than the force required to get the plane moving at an air speed of 50 meters per second. Hopefully whatever plane they use is of the right mass to power ratio that it is capable of producing the required power.
Of course, I could totally be wrong.
(This of how this also relates to a plane taking off with a tail wind of 10 meters per second. It would need a ground speed of 60 meters per second to take off, right?)
For real this time: Mythbusters will air their challenge of the airplane on a conveyor belt puzzle this Wednesday at 9pm ET. (thx, darin)
Last night, I went to Allie's grandmother's house with her since she just had surgery. At 9, Allie asked if there was a show I wanted to watch. I told her not to worry since I only wanted to see one segment of it and could probably just download it today anyhow. I didn't want to make my TV watching a big deal.
Anyhow, she put on the Discovery Channel and we sat through an hour of Mythbusters. While not her favorite show, she did find it a bit amusing, though she was quite jealous of Kari Byron. Anyhow, the segment I wanted to see, whether a plane traveling in the opposite direction that a conveyor is running can take off, didn't air. (I'm glad to see my fellow internet nerds are angry, too.)
Anyhow, here's what I've been thinking. Many people immediately think, and rightly so, that how fast the wheels spin doesn't matter, lift is produced by the air that goes over and under the wings. And I agree. But think a little further. Suppose you had a plane with a wheel system that had no internal friction. If you placed this plane on a conveyor belt straight down, the plane would not follow the direction of the conveyor belt. Rather, it would remain in place relative to the larger frame of reference (the ground) and the wheels would spin. Said plane would then turn on the engines and take off. Why? Because the engines would push the plane forward through the air. The plane is not in a wind tunnel, it is merely on a conveyor belt. That the surface it is on is moving doesn't matter since in this hypothetical, friction has been removed. (I did leave in friction enough that the rubber grips the ground. If there was no friction at that point, the plane would remain stationary, but the wheels wouldn't turn either, the conveyor belt would merely move below it.)
Now take a regular plane. Suppose it require the engines to operate at 80% of their collective power to take off. Place this plane on the conveyor belt. Turn the engines on slowly until the plane is now no longer moving relative to the ground. Suppose the engines are at 5% of their collective power. At this point, I'd suppose that if the engine power were increased to 85%, that the plane would take off, just as it did at 80% when on the ground. (The math is no where near this simple, this is just to illustrate a point.)
Anyhow, point is, while the conveyor belt may be going backwards at a rate of, say, 50 meters per second and the plane may need to approach a speed of 50 meters per second, relative to the air (called air speed), the force required to compensate for the 50 meters per second of the conveyor belt is far less (in the above example, sixteen times less) than the force required to get the plane moving at an air speed of 50 meters per second. Hopefully whatever plane they use is of the right mass to power ratio that it is capable of producing the required power.
Of course, I could totally be wrong.
(This of how this also relates to a plane taking off with a tail wind of 10 meters per second. It would need a ground speed of 60 meters per second to take off, right?)