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I'm thinking this question had to been asked before, but I did a search and couldn't find anything on it. It's really bugging me, because I never could find out the right answer.
Suppose you have a jet airplane sitting on a runway. But this runway acts like a treadmill. The jet starts it's thrusters and for every mile an hour the Jet's wheels move forward, the treadmill moves a mile an hour in the opposite direction.
ROB :: I need to be in this also ,:: #1- when a plane starts moveing forward from the (THRUST OF THE JET ENGINE) THE wind going past the wings, causes a low pressure on top side and a high pressure on bottom side, as the plane goes faster and LIFT EQUALS WEIGHT THE plane reaches lift (KNOWN BY PILOTS AS ROTATION POINT)IF its a prop it's the same except it pulls by the props., pulling air thru the props. Now the engines ARE what pushes or pulls the air craft forward, they always take off into the wind, on a aircraft carrier, they turn the ship, HEADING INTO THE WIND ONCE THE AIRCRAFT REACHES THE POINT OF ( LIFT EQUALLS WEIGHT < WHEN YOU PULL BACK ON THE STICK {OR YOUK} IT IS GOING TO LEAVE THE GROUND WITH FULL POWER ON::::::" WITH engines running ,that plane is going to move forward. Back ,I BElieve it was late 80's or 90's they redesigned the race car to work on the same princeable as a plane , except in reverse, LOW ON BOTTOM <HIGH PRESSURE ON TOP , this was done so they could hold to the road better ,go faster and not lose control as they used to . I KNOW because iv'e been a pilot since back in50's ive flpwn jet and prop ,I still hold pilots license ,WITH AIRCRAFT SINGLE <MULTI ENG> INSTRUMENT> I was AIR FORCE ,for 12years F.B.E.
Would everyone agree that a car on the same treadmill/tarmac would never get above zero mph?
No. Read the question more carefully.
Imagine a car moving at 40 MPH relative to the speed of the treadmill (i.e., the car's speedometer would read 40 MPH). But imagine also that the treadmill is only going at 20 MPH relative to the ground in the opposite direction. This means the car will move at 20 MPH relative to the ground, correct? Under these conditions the car is satisfying the condition of the question as originally posed, that is: "for every mile an hour the [car's] wheels move forward, the treadmill moves a mile an hour in the opposite direction." If we assume that these speeds are measured in a consistent way relative to the ground, then the car does indeed move forward.
The vehicle's speedometer may indicate a mechanical interpretation, but the key here is MPH, miles per hour, and if it's sitting still on the treadmill/dyno, it isn't covering any miles.
Going back to thte aircraft analogy... speed over ground (SOG) would be zero. Substitute the speedometer with GPS. I think your car is not moving.
lobroster, next time we want all of the variable, as much of the given info, upfront. OK, buddy?
The treadmill will match any speed of the plane's wheels.
The problem here is that this phrase is open to different interpretations, and the answer depends on how you think of "the speed of the plane's wheels." If this phrase means that the treadmill matches the forward horizontal velocity of the axle of the wheel, (i.e, the point of its average velocity relative to the ground) then the plane does move forward as I've shown before, and could take off. However, if the phrase means that the treadmill matches the speed of the contact point of the tire relative to the axle (i.e., its spinning velocity relative to the axle), then the plane stands still and it can't take off. By the way, the only way for this to physically work is for the frictional forces between tire and treadmill to exactly counter-balance the thrust of the engine, and if you ignore this rolling friction then it's easy to show that the treadmill must move infinitely fast. But that's another discussion.
There are too many variables to say whether the plane would take off or not. However, if you say there was NO wind at all and the platform on which the treadmill moves is stationary then the plane would defiantly NOT take off. As people have said, a plane takes off due to the lift under it's wings, it generates this lift by traveling at high velocity. The plane on the treadmill would have high speed, but no velocity. Velocity is movement in a direction. The plane would still be stationary.
If you imagine yourself running on an exercise treadmill, you can run very fast, but you will not feel a strong wind in your face. The same applies to the plane.
Since the wheels spin free. jet would move forward. As thrust increases, it will push jet forward, wheels would spin. Jet would jump off treadmill and at rotation speed, it would lift off.
The plane would take off. Unlike a car which pushes against the road, a plane pushes against the air.
Let's say the entire runway was a treadmill geared to the parameters discussed. The plane begins pushing the air and it moves against the ground at 1 mph. The treadmill goes at 1 mph but the plane is pushing against the air at 1 mph and IS moving over the ground. The thrust of the engines against the air isn't going to stop moving the airplane because of its wheels.
Ergo. If the plane is moving against the air at 1 mph, and the treadmill is moving at 1 mph, the treadmill is STILL 1 mph slower than the plane is moving over the ground, so the plane would begin its take off run normally.
As the speed of the plane against the air reaches say, 120 mph, the wheels would ordinarily be going 120 also, but because the treadmill is moving to match the wheels, the treadmill is still 120 mph slower than the air that is pushing the airplane - and the airplane would take off.
There is NO AIR PUSHING AGAINST THE PLANE.
Unless I've interpreted the question wrongly, the plane would not take off. If the plane was going 1000000mph on a completely flat, and infinitely long, surface in a vacuum the plan would still not take off. It would just keep going straight. SPEED makes no difference in this conundrum, it's the VELOCITY of the aircraft. Of course, like I said in my previous answer, there are too many variables which would change the output of this question, however we must say (for arguments sake) that 100% of the thrust generated by the engines is converted into kinetic energy in the wheels, and the forces active on the wheels and treadmill are balanced. If this is so then for each 1mph the planes wheels move forward, the treadmill reverses the effect my matching the speed in the reverse direction. Therefore, even when the plane is at max speed it is still standing stationary and there are no forces allowing the plane to take off.
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