Physics Question for you.....

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  • Anna
    Senior Member
    • Feb 2006
    • 728
    • CA, USA.
    • BT3100

    Originally posted by DaveSur
    Just think how a sea plane takes off. It relies entirely on the propeller to pull it through the air to gain enough speed to take off. There are no little outboard motors strapped to the pontoons to give it thrust. A regular airplane needs wheels only to roll and not to drive. It also relies only on the propeller or jet engine to move forward. It does not matter what the conveyor belt is doing as long as the wheels are free to rotate.
    How about a seaplane on a river with a really strong current going in the opposite direction. How easy will it be for the seaplane to take off? How much more power does the plane need to overcome the river current? Any seaplane pilots out there to give a definitive answer and put this whole matter to rest?

    It's true that the plane on a tarmac needs some way to thrust it forward. Whether with a propeller or jet engine, it doesn't really matter. The thrust moves the plane on a regular tarmac. It can roll, like on wheels, or it can slide/skid, like on pontoons. Either way, in normal circumstances, the plane moves forward.

    As it moves forward, with constant thrust, we get constant acceleration so that we go from zero speed to a critical speed that allows the plane to take off.

    We all agree on that, I think. So on to the controversy with the conveyor belt.

    Now let's say we have a thrust that normally allows for an acceleration of 1 m/s^2. Starting from rest, in 1 second, the plane would have traveled 0.5 meters (that's from x = x0 + v0t + (1/2)at^2). The conveyor belt, in that time, also travels 0.5 meters in the opposite direction (say to the right).

    Result: To someone standing on the tarmac, the plane is in the same position it started with and has not moved. To someone standing on the conveyor moving to the right, the plane just moved 0.5 meters to the left.

    After the next second, the plane would have normally moved a total of 2 meters. But so did the conveyor. Again, to an observer on the tarmac, the plane still has not moved; to an observer on the conveyor, the plane moved 2 meters to the left, with an instantaneous speed of 2 m/s. (That's from v = v0 + at.)

    So, depending on who's doing the observing, the plane is either moving or it's not.

    The key then is the air flow around the plane. On a still day, an observer on the tarmac will see a wind speed of zero. To a guy on the conveyor belt moving to the right, the wind speed (after 2 seconds) will be 2 m/s to the left.

    What about the plane? 2 seconds after we started the exercise:

    To an observer on the tarmac, the plane is not moving. The wind is also not moving. So the plane sees no motion of the wind.

    To an observer on the conveyor belt, the plane is moving to the left at 2 m/s. The wind is also moving to the left 2 m/s. Since the plane and the wind are moving with the same speed, in the same direction, then an observer on the plane sees no motion of the wind.

    We can keep incrementing time, we can change the values of the acceleration, and we'll still get the same result. There is no relative motion between the plane and the wind.

    If there is no wind, as far as the plane is concerned, there is no lift. No lift, no takeoff.

    With the MythBuster guys, the "conveyor belt" did not match the speed of the plane. What they should have done, to approximate the hypothetical, is to have the "conveyor belt" - which looked like just a very long piece of cloth - hooked up to a similar plane with the same engine as the test plane, but going in the opposite direction. Then, with the equal thrust, one can probably get similar accelerations. That would have been far more convincing to me than using a truck and a plane.
    Last edited by Anna; 02-03-2008, 02:17 PM.

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    • Anna
      Senior Member
      • Feb 2006
      • 728
      • CA, USA.
      • BT3100

      Originally posted by tjmac44
      Three forces:
      1. Down (GRAVITY, weight of the plane).
      2. Forward (Engine thrust).
      3. Backward (Conveyer).

      Is the forward motion cancelled by the backward motion?
      Don't forget normal forces (perpendicular to surface).

      Comment

      • niki
        Senior Member
        • Nov 2006
        • 566
        • Poland
        • EB PK255

        Lets make an experiment.
        Take your car, remove the engine and the gear so the wheels can rotate free forward or back.

        Put your car on the conveyer. Put some barrier behind the car just not to let it go backward, the barrier will be anchored to the ground, not to the conveyer.

        Turn the conveyer to 500 MPH.
        Because the wheels can move free, they will rotate at 500 MPH but the force backward will be only the tire drag + bearing friction, I think that you can stop the car from moving backward only with your hand (lets say that you need 100 lbs to stop the car moving back)

        Now, on the roof of you car, install an engine with propeller or jet engine or a rocket than can produce 10,000 lbs of thrust (it will not have any connection to the car wheels that still can move free).

        Go back on the conveyer, turn it to 500 MPH, get into the car and start the engine/jet/rocket to maximum power.

        To overcome the tire and bearing friction you need only 100 lbs, the rest 9,900 lbs are pushing the car forward off the barrier. Of course the wheels speed will increase but you are pushed and accelerated forward.

        Another experiment.....
        Take a matchbox car, tie a string at the front and tie a fish-scale to the string.
        Put the car on your belt sander, switch it on, and measure the force required to hold the car in place, let's say that you measured 2 lbs, this force is the product of the tire and bearing friction.
        now, increase the belt speed, you shall still read 2 lbs (maybe a little more) but the tires are turning faster.

        Now, install on top of the car roof some propeller or jet engine that can produce 3 lbs or more. 2 lbs of thrust will be required to overcome the tire/bearing friction (without any connection to the tire speed) and the rest of the thrust will produce forward motion relative to the ground, or more correct, to the space.

        The wheels, are only medium between the plane and the belt, they are not tieing the plane to the belt and are free to rotate. They produce some drag force, but ones we overcome this drag force, the plane is like in the free air.

        niki
        Last edited by niki; 02-03-2008, 02:53 PM.

        Comment

        • williamr
          Forum Newbie
          • Dec 2006
          • 56
          • Mazatlan or Toronto
          • BT3000SX

          Originally posted by Anna
          How about a seaplane on a river with a really strong current going in the opposite direction. How easy will it be for the seaplane to take off? How much more power does the plane need to overcome the river current? Any seaplane pilots out there to give a definitive answer and put this whole matter to rest?



          With the MythBuster guys, the "conveyor belt" did not match the speed of the plane. What they should have done, to approximate the hypothetical, is to have the "conveyor belt" - which looked like just a very long piece of cloth - hooked up to a similar plane with the same engine as the test plane, but going in the opposite direction. Then, with the equal thrust, one can probably get similar accelerations. That would have been far more convincing to me than using a truck and a plane.

          In New Westminster BC -- on The Fraser River-- there is a seaport for light planes. They normally take off in the centre of the river and are considered a motor vessel while in the water. :-) IOW they have to follow the same rules I do in the water when I cruise past --- under sail, canoing or stink-potting. They are not required to clean my drawers when they pass with in a foot of the cabin. Not even when the fiberglass whip vibrates... ROW depends on who has the most maneuverability...

          Like any other pilots, they prefer to take off into the wind. They prefer to be airborne rather than waterborne.

          Yes there is more drag on the pontoons than on the wheels of an airplane.

          Yes they have to overcome the drag of the river -- upstream or down. Planes with pontoons on during the summer season are slower than when they fly with skis in the winter -- or wheels if they are "down south" near the Great Lakes. Ideally you want to take off downstream -- into the wind -- and with prevailing westerlies they almost always have their wish. The pontoons create a lot of drag in the fluid called air.

          Correctly designed pontoons form a planing hull. Thus defying the "dreaded Bernoulli's law". Sailboat hulls remain in the water and are captive to the dreaded law. Speed of an "in-water" hull is clearly definable, and the speed is thus a function of the length -- the longer the hull, the faster the boat could be -- IOW bigger engines won't help beyond this point.

          Speed boats are "planing hulls" -- water wings if you will...

          So, the faster the current, the sooner the plane will get the pontoons "on plane" -- defying the dreaded Bernoulli and the sooner the plane can reach flying speed.

          So yes the water is a "big conveyor" and yes they do overcome it. And with all the extra drag.

          When you look at a problem like this it is helpful to think of the "problem space". In this case you are dealing with an airplane in a fluid (air). The question is can the airplane archive flight speed in air -- despite any other "outside" influences.

          You have to "draw the box" around the correct system. You can of course draw boxes around sub problems (sub-systems) of the complete problem space. The contact with ground or water is a sub-space of the entire problem space.

          Rockets lift off easiest near the equator... Higher rotational velocity of the earth... There is a lot of related stuff you can think of. (Pardon me -- of which you can think.)

          Hope that helps Anna. The rest is just small stuff... :-)

          I will leave it to mpc to provide any math. His post is correct -- regardless of what we would like to think. This is the best I can do without a few boring equations -- and It's Sunday -- my day of rest. No math permitted on Sundays.

          ---
          Will

          Comment

          • Russianwolf
            Veteran Member
            • Jan 2004
            • 3152
            • Martinsburg, WV, USA.
            • One of them there Toy saws

            The seaplane on a river is not really a good experiment. The effec of the current on the pontoons would create much more drag than the wheels a regular airplane experiences.


            A skiplane would be a better experiment since the wheels would be totally removed from the equation, butagain, they produce more friction/drag.

            But the mythbusters experiment could be effect if not perfect. If they measure the distance the plane needs to take off at 100% throttle, then compare it to that needed to takeoff at 100% with the conveyor moving (speed of the conveyor is actually irrelevent). If the needed distance is substantially greater, then the doubt of a matched speed takeoff would increase. If the distance didn't substantially increase hen the match speed takeoff would be proven likely.

            Another way to do the same thing.
            1)Start the plane at taxiing speed 10mph let's say. Then start the conveyor. What speed is the plane doing relative to the ground now?
            2) start the conveyor, then start the planes engines to the rpm needed to taxi at 10mph. What id the speed of the plane relative to the ground now?

            I'll wager that both would show the plane moving at 9-10 mph. Meaning the conveyor speed has little effect on the planes relative speed.
            Mike
            Lakota's Dad

            If at first you don't succeed, deny you were trying in the first place.

            Comment

            • williamr
              Forum Newbie
              • Dec 2006
              • 56
              • Mazatlan or Toronto
              • BT3000SX

              Originally posted by Russianwolf
              The seaplane on a river is not really a good experiment. The effec tof the current on the pontoons would create much more drag than the wheels a regular airplane experiences.


              I'll wager that both would show the plane moving at 9-10 mph. Meaning the conveyor speed has little effect on the planes relative speed.
              Gotcha!

              Correctly formed pontoons are planing hulls. A planing hull has low drag -- otherwise speed boats would not exist. :-)

              Going upriver would mean high initial drag, but the plane would become "on-plane" sooner.

              A smooth lake is another issue... :-) But rivers almost always have some chop...

              It's just a sub-case of your original problem. And the friction is only nominally higher than wheels or skis -- once the plane is "on-plane".

              You have to first solve the equation on the fluid medium of air. Then look at other drag sources -- and you know that. :-)

              Are you sorry you asked the original puzzle? lol

              It is a lot of fun tho...


              ---
              Will

              Comment

              • williamr
                Forum Newbie
                • Dec 2006
                • 56
                • Mazatlan or Toronto
                • BT3000SX

                Originally posted by leehljp
                Are we forgetting about gliders? When the tow cable is released, gliders don't drop straight to the ground.

                Some of you Canadians will remember the commerical jet about 15 years ago in which there was a mix up in liters/gallons for the American pilot. He ordered gallons/ they put in liters. The plane was somewhere near 30,000 feet or so and the engines quit - fuel starvation. No Fuel. They glided 50 or 60 kilometers and did a dead stick landing safely at an abandoned airfield where there was a lot of Sat/Sun afternoon crowd, jsut missing them.

                Gimli Glider...



                Interesting... but

                ---
                Will

                Comment

                • MilDoc

                  I've been reading this post since it started. All I can say now is ....


                  I HAVE A HEADACHE!!!

                  Comment

                  • cabinetman
                    Gone but not Forgotten RIP
                    • Jun 2006
                    • 15218
                    • So. Florida
                    • Delta

                    Originally posted by MilDoc
                    I've been reading this post since it started. All I can say now is ....


                    I HAVE A HEADACHE!!!

                    Paul

                    How about: Dee-Dee-Dee.
                    .

                    Comment

                    • MilDoc

                      Has anyone ever done a Google search on this problem? I just did. Hundreds of sites have debated this (one has close to 1,000 posts?) including a physics site, an airliner site, and others. Guess what? Their conclusions are the same as here:

                      1. Yes, it takes off
                      2. No, it doesn't

                      Oh well. I guess I'll go with the Mythbusters since that is apparently the only "test" done on this problem using a real plane.

                      Lots of folks posted their own videos with scale models;

                      Myth is: 737 passenger jet airplane gains lift on a conveyor belt moving opposite to plane's forward motion...What Do You Think?...Now simply put it- THE PLA...


                      And I still like cecil's explanation;

                      Last edited by Guest; 02-03-2008, 05:16 PM.

                      Comment

                      • Anna
                        Senior Member
                        • Feb 2006
                        • 728
                        • CA, USA.
                        • BT3100

                        William, I know it's really tempting to turn this into a Second Law problem, but it's really a kinematics problem.

                        And although it's been three years since I last taught calculus physics, I think I can probably handle the equations and free body diagrams just fine.

                        One last attempt, then I'll call it a day.

                        When an object "moves," it's usually relative to something. We have three components in our system: the plane, the ground, and the conveyor belt. We're assuming that the air is "still" with respect to the ground, where most of us are watching.

                        Case 1: Conveyor belt does not move. This is the same case as when the belt does not exist at all, and the plane taxies off the ground.

                        For the plane to take off, it has to move with respect to the ground in order to create a lift. That is, the motion of the plane allows the air to move against the plane (although to us sitting on the ground, the air is still not moving) which allows the plane to fly.

                        Does it matter if the plane has wheels or skids or pontoons? Not really because what's important is the relative motion of the plane to the ground. With still air, the speed of the plane is also its air speed, and when it reaches a critical air speed, it takes off.

                        Case 2: The conveyor belt is moving. This is basically when the "ground" on which the plane is sitting on is moving in the opposite direction.

                        If the speed of the plane is matched by the conveyor belt but in the opposite direction, then the resulting motion is zero. Honest. Go ask your physics teacher. It doesn't matter if the plane is going full throttle, as long as the conveyor belt is going full throttle in the opposite direction. It's still zero.

                        The only way that the plane will take off with respect to the ground is if the speed of the plane is greater than the speed of the belt. But the statement of the problem denies that.

                        In the Mythbusters episode, the acceleration of the plane beat the acceleration of the truck. The instantaneous speed of the plane was therefore different from that of the truck, and there's a net speed for the plane. Therefore, it moved with respect to the ground with enough speed to take off.

                        Another important point: we're talking about matching speeds between the conveyor belt and the plane. If the conveyor belt runs at CONSTANT speed, it loses because there is a net force on the plane, and therefore a net acceleration. Constant speed implies ZERO net force (or zero acceleration). So the case with the matchbox or car or whatever is not the same as the original problem either.

                        Okay, that's all for me. I don't really know how many other ways to explain that there is no relative motion to the ground and therefore no relative motion to the air with the way the problem is originally defined. I don't buy the wheels-have-nothing-to-do-with-motion argument either. Well, it's really not an argument. And it's pretty common to conflate motion with forces.

                        P.S. Husband's comment: "Is there a pilot in the plane? Because, you know, whether the conveyor belt matches the plane's speed or not, the FAA won't allow the plane to take off."
                        Last edited by Anna; 02-03-2008, 05:22 PM.

                        Comment

                        • williamr
                          Forum Newbie
                          • Dec 2006
                          • 56
                          • Mazatlan or Toronto
                          • BT3000SX

                          Originally posted by Anna
                          William, I know it's really tempting to turn this into a Second Law problem, but it's really a kinematics problem.

                          And although it's been three years since I last taught calculus physics, I think I can probably handle the equations and free body diagrams just fine.


                          P.S. Husband's comment: "Is there a pilot in the plane? Because, you know, whether the conveyor belt matches the plane's speed or not, the FAA won't allow the plane to take off."
                          And it's been about the same since I taught docs, and post docs in eng. math <grin> -- so we're even there. lol The only reason I responded was I thought -- that person knows how to present a analysis -- and clearly that's true -- I actually admired your case.

                          Regardless -- I will go for the guy from Boeing and his solution. (mpc)

                          And I feel better since I read all his posts -- I got suckered for a few minutes too -- till I remembered the plane is sitting in air, the engines work in the fluid system of the air, and the conveyor and the wheels are just a distraction for the real issue...

                          There is nothing wrong with your conveyor analysis. I stand by the statement that it is "the wrong problem space".

                          As to you husbands comment -- he's probably right -- so all the science in the world don't matter. FAA has grounded "The Flight of the BT3" -- end of discussion.

                          And I still won't do math today. And I will stick to NP problems from now on -- simpler to wrap your head around. :-) :-)

                          ---
                          Will

                          Comment

                          • Russianwolf
                            Veteran Member
                            • Jan 2004
                            • 3152
                            • Martinsburg, WV, USA.
                            • One of them there Toy saws

                            Anna, in your second case you are assuming that the speed of the plane is influenced by the contact with the conveyor. Why would this be the case?

                            The airplane is not driven forward by it's wheels. It is the engine pushing against the air behind it that moves the plane. The wheels are freespinning.
                            Mike
                            Lakota's Dad

                            If at first you don't succeed, deny you were trying in the first place.

                            Comment

                            • williamr
                              Forum Newbie
                              • Dec 2006
                              • 56
                              • Mazatlan or Toronto
                              • BT3000SX

                              Originally posted by Russianwolf
                              Anna, in your second case you are assuming that the speed of the plane is influenced by the contact with the conveyor. Why would this be the case?

                              The airplane is not driven forward by it's wheels. It is the engine pushing against the air behind it that moves the plane. The wheels are free spinning.
                              There is no question there is an initial influence -- but then you are right the influence rapidly dwindles to small significance.

                              Once you get a short time beyond the startup phase the plane is working in it's native media -- the fluid air... i.e once the "inertia" of the plane is overcome -- friction of the wheels etc... So a second or two or three (and even if it's 10 -- it doesn't affect the final outcome) after windup and the brakes are released...

                              Maybe you should do the force vector analysis for all of us -- and show that the vectors are working (primarily) in a fluid media. <grin>

                              I think that's the difficulty with the analysis for most.

                              ---
                              will

                              Comment

                              • Anna
                                Senior Member
                                • Feb 2006
                                • 728
                                • CA, USA.
                                • BT3100

                                Well, as usually the case, I can't stay away from a good debate unless I completely turn the computer off. So here goes:

                                I've been thinking about the proposition that planes act on the air around them and not on the ground. And that's true... when the plane is in flight.

                                In our case, the plane is in contact with the ground. Now there are two cases:

                                1. The "real world" case where the plane's wheels roll on the ground which means there's friction, which means there's a force in the opposite direction to the plane's thrust, which can make the plane's effective acceleration zero. Hence no motion. That's what I've been proposing because I assumed that the plane's wheels kept in contact with the ground. After all, if it's not in contact with the ground, it's already in flight and what's the point of all the argument anyway?

                                2. The second case is a completely frictionless system. Imagine the plane on ice skates and the conveyor belt is made of ice. Either that or the air already rests on a cushion of air (like the super trains in Japan). In this case, there is no drag to the plane's motion when the jets or props are fired up, and the plane flies! This is the same scenario as when the wheels have no traction on the ground or conveyor belt. In other words, the net force on the plane is equal to the thrust, and the plane accelerates.

                                So, I think all this debate is really based on two different assumptions. I assumed a real-world case where the plane's wheels stay in contact with the ground without slipping. I think the others assumed that everything is frictionless.

                                Seen that way, everyone is right. Although, being a woman and all, I'll have to say I'm never wrong.

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