Of course that's where the answer lies -- it takes airspeed to the wing for a plane to takeoff ... we agree perfectly. Please explain what keeps the airplane from accelerating down the runway and gaining airspeed to the wing. JB
do you feel any airspeed relative to your "wings" running on a treadmill? the problem assumes the the velocity of the air molecules are equal to that of the ground. the plane must move relative to the ground to move its wing relative to the air because the air molecule to ground speed are equal, ie zero. the plane cannot move relative to the ground while on the belt, so it cannot generate any airspeed for lift
I agree. With further thought, the sliding friction would theoretically be possible, but not likely in practice. The rolling friction example is correct. The question is really whether or not you can get forward movement to create lift. The answer is yes. Try putting a wheelchair on a treadmill (preferably without anyone on it). No matter what speed you have the treadmill going at, you can still push the wheelchair forward due to the thrust you create independent of the wheels.
Just so you know Max, I agree with your conclusion that in the above scenario, the plane hasn't taken off -- but the above isn't a valid representation of the stated problem. To make your problem come into line with the stated problem let's continue it ... Above you have achieved a steady state situation -- that is the plane is sitting still relative to the surrounding earth. (Incidently, it will take no more than an idle of the engine to achieve enough thrust to make the plane sit still as you describe) Now, throttle up and continue adding thrust. The plane will begin to move and there ain't a damn thing that the treadmill can do to stop it. JB
Max: >do you feel any airspeed relative to your >"wings" running on a treadmill? Of course not, but the point you're missing is that the plane isn't "running on a treadmill" -- it's "running through the air" and happens to just be sitting on a treadmill. >the problem assumes the the velocity of the air >molecules are equal to that of the ground. the >plane must move relative to the ground to move >its wing relative to the air because the air molecule >to ground speed are equal, ie zero. you've got this part down perfectly. >the plane cannot move relative to the ground >while on the belt, so it cannot generate any >airspeed for lift Of course it can -- what's gonna stop it? (see wheelchair example above and below) JB
Macal's example is so excellent that I'm gonna expand on it for a moment. Put a guy in a wheel chair and ask him to propel himself in the normal wheelchair manner (through the wheels). Put the guy out on this giant runway treadmill and the dude who controls the runway will DOMINATE the wheelchair dude -- poor wheelchair dude can't do ANYTHING but sit still no matter how hard he tries. Now, macal walks up beside this runway treadmill (but doesn't stand on it) reached out and grabs our wheelchair dude and starts pushing him -- walking along beside the treadmill as he goes. Treadmill dude gets *pissed* and keeps turning up the treadmill -- macal just keeps walking alongside up the runway pushing the wheelchair as he goes, it's wheels spinning faster and faster. Unless the treadmill guy can crank up the treadmill sooooo high that he blows out the wheels/bearings of the wheelchair, there isn't a thing he can do to keep macal from walking up the runway pushing the wheelchair. (remember, macal isn't walking on the moving runway, but just to the side of it on the unmoving earth) Same with the plane -- the thrust is coming from a source separated from the moving surface. Just as macal and his wheelchair don't care how fast treadmill dude moves the runway, the plane's propeller doesn't give a shit either. JB
maybe i am missing smthg.. place a wheelchair on a moving treadmill, you must push the treadmill till its speed is equal to that of the belt for it to remain motionless in space, right? its wheels are rotating at a specific speed at this point. at this point, relative to the quiet air the wheelchair is motionless. now, certainly, at this point you can push the wheelchair with more force or greater thrust. but this results in a greater speed to the wheelchair relative to the treadmill and, equally, to the surrounding air. no shit, or in other words so what??! the wheelchair is no longer moving equal to the treadmill and is now moving relative to the air
Max: >maybe i am missing smthg.. You are. >place a wheelchair on a moving treadmill, you >must push the treadmill till its speed is equal to >that of the belt for it to remain motionless in >space, right? its wheels are rotating at a specific >speed at this point. You keep getting stuck in this world you created for yourself where the plane/wheelchair must not move relative to the surrounding world. there's nothing in the original problem (nor in any of my subsequent versions) stating such . Get that thought out of your head pronto and you will have a much easier time with the problem. The problem only states that the treadmill speed will be set to the same speed as the wheels and in an opposite direction. If macal is pushing the wheelchair at 5mph up the runway, the runway speed is then set at 5mph in the other direction -- macal and his wheelchair friend continue up the runway at 5mph and the wheelchairs wheels happily spin along as if they're moving 10mph. >... or in other words so what??! the wheelchair >is no longer moving equal to the treadmill. Of course it is -- the wheelchair and it's wheels are moving forwards at 5mph (relative to the ground), and the treadmill is moving backwards at 5mph (relative to the ground) -- how do you come up with their speeds not being equal? Pound a stake in the ground and wheelchair moves away from the stake to the right, while the runway moves away from the stake to the left -- both moving away from the stake at the same speed. JB