A harmless riddle

Colleges & Universities Massachusetts Institute of Technology
21

<p>My boyfriend, who’s going into his senior year as an aero/astro major here, is very emphatic that the question as posed in the original post has no for an answer – he says, “No air speed, no takeoff.”</p>

<p>EDIT: He would like to direct you to [this</a> site](<a href=“Something to think about.....Will it Fly? - RC Groups”>Something to think about.....Will it Fly? - RC Groups) for airplane nerds like him, which has a 174-page thread on this very topic. The current vote there is 199 votes no and 169 votes yes, but he claims that “all the smart people” have voted no.</p>

22

<p>bmanbs2:</p>

<p>We are operating under the assumption that the speed of the treadmill will counteract any increase in velocity the plane might experience, so that, relative to the observer standing off the treadmill, the plane does not move. If we assume that, then at no point can the “thrust of the aircraft overcome the moving treadmill.”</p>

<p>For now, let’s not consider the landing gear. At some time t=0, treadmill and plane are completely still. Assume the thrust of the aircraft’s engines is capable of acclerating it forward at 5 m/s/s; assume that, at the same point, the treadmill starts to accelerate at 5 m/s/s the other direction (which is akeen to having another accelerative force being applied in equal magnitude but opposite direction as thrust). You agree with me that, regardless of whatever t it is, if these two acceleration vectors are constant, you will have the plane at 0 velocity relative to the man standing on the ground?</p>

<p>Give me a few minutes to think about the wheel.</p>

23

<p>Here is a 384 page thread at “physorg.com” about the same topic.</p>

<p><a href=“http://forum.physorg.com/index.php?showtopic=2417[/url]”>http://forum.physorg.com/index.php?showtopic=2417&lt;/a&gt;&lt;/p&gt;

24

<p>“An airplane is sitting on an enormous treadmill. As the plane starts its engines, the treadmill runs in the opposite direction at the same speed the plane is moving. Can the plane take off?”</p>

<p>The treadmill is running at the same speed as the plane WHEN THE ENGINES START (assume the plane starts with zero velocity). The riddle says nothing about the speed increasing to match plane speed. The treadmill is stationary and the plane will take off.</p>

25

<p>Dirt McGirt:</p>

<p>The problem is, the same speed as the plane is moving at what instant? You can’t define the velocity the instant it starts moving, because, you dont know what instant it starts moving, and it is impossible to tell.</p>

<p>Of course, if the treadmill is not accelerating and thrust provides acceleration to the frame of the aircraft, the aircraft will accelerate and might take off.</p>

<p>I did some speculation. “Positive” is forward, “negative” is backward</p>

<p>1.) Assume the engines are off. The treadmill is moving backward. The plane as a whole moves back with the treadmill, with no rotation in the landing gear wheels. See the airplane moving backward as inherent velocity, so that when we look at the system with engines on, we know the airframe already has a negative velocity due to the treadmill.</p>

<p>2.) Assume the engines are turned on. Assume frictionless connection between the gear leg and the gear wheel (I don’t think it matters that much). Remember, the treadmill is still running backward at constant velocity. As thrust increases, the aircraft begins to accelerate forward, negating it’s inherent rearward velocity and at some point turning that into positive velocity. Since there is a frictionless axle at the gear wheels, consider the gear legs part of the plane, and the wheels seperate. The wheels continue to spin due to Fs, but accelerate forward with the plane as thrust is also applied to it (since its connected to the gear leg). The wheels only spin if thrust is applied.</p>

<p>So really, if the treadmill is at constant velocity, the plane will overcome the initial backward velocity and might take off; if the treadmill accelerates to match the aircraft’s thrust, then the plane will never move relative to the ground. Whatever velocity at any instant the treadmill is moving back, that velocity is automatically inferred upon the airplane if we look at it from the frame of reference of the still ground; the thrust then works to counteract that with forward acceleration. If that is then immediately counteracted upon by the treadmill acceleration, you get a net a of 0 relative to the still ground.</p>

<p>Of course, if you’re sitting in the plane, you will feel like you are accelerating relative to any particular portion of the treadmill surface, but it’s not the plane moving forward, it’s the treadmill moving backward.</p>

<p>I wish we could just see it. Then everyone would be fine with it, whatever the answer might be. This is just gonna go on and on, just like it did those other places.</p>

26

<p>all my posts were under the assumption that the treadmill would be operated to stay at the same speed as the plane’s wheels. otherwise, this problem is more complicated and it would be plausible if it were to accelerate and take off.</p>

27

<p>

I’m pretty sure that is how it supposed to be interpreted Ben.</p>

28

<p>In that case, no is my final answer.</p>

29

<p>The kicker here is that the wheels do not provide the thrust.</p>

<p>In a frictionless wheel bearing, and say a rope is holding the airplane still, the same tension would be on the rope at 2 knots and 200 knots</p>

30

<p>Props generate thrust. They do not provide sufficient airflow over the wing to produce lift. The only factor that matters is airspeed. No airspeed = no lift. An aircraft can be stalled (loss of lift) at full throttle given the right loading and turn rate and angle of attack.</p>

31

<p>Exactly – thanks, 56.</p>

<p>bmanbs2 – it’s not about thrust. It’s about airflow over the wings, which is generated by the airplane *actually moving<a href=“or%20external%20wind”>/i</a>. I think the point of the riddle is to drive home that (fairly simple) fact.</p>

32

<p>Think of it this way.</p>

<p>Your walking down a treadmill like the one described. You accellerate positively, it acellerates negativley, you don’t move. Here, your thrust is provided by traction between you and the treadmill.</p>

<p>Now your wearing rollerblades with a fan on your back. You go forward, the wheels move, and the treadmill goes backwards. But since the thrust is provided by moving air, not traction, you can accellerate independent of the wheels. In short, the wheels are going backwards, but you go forwards. Just like a hula hoop you spin backwards. It goes forwards until it runs out of your force, then goes backwards because the traction force is greater.</p>

33

<p>bmanbs2:</p>

<p>I don’t understand. Your “thrust” when using a treadmill is not provided by “traction” or friction; it is provided by the component of the force parallel to the treadmill which is exerted when you forcefully push your leg off the of the treadmill. If you stand on a treadmill, there is static friction between your shoes and the treadmill (otherwise you’d slip), but that doesn’t cause you to magically move forward.</p>

34

<p>Yeah, you can’t push of the treadmill unless you have traction. Otherwise you’d just slip and fall, like on ice. Then you would go backwards</p>

35

<p>bmanbs2:</p>

<p>And this justifies force of friction as “thrust,” how?</p>

36

<p>Well, without something to push against (friction), the force would be neglagent.</p>

37

<p>If you push an airport cart the wrong way on a moving walkway at the same speed as the walkway, it won’t move anywhere with respect to the air.</p>

<p>You pushing is the same as the force of the engines, even though the wheels are free spinning.</p>

38

<p>Static friction just ensures that your feet do not slip when you push off of the ground. They are not responsible for the forward motion itself. That force is provided for by the muscles in your legs, using your analogy.</p>

<p>Spartan:</p>

<p>Good analogy.</p>

39

<p>Of course the airplane takes off… just assume that gravity is negligible.</p>

<p>Barring that, assume the treadmill is in a wind tunnel and/or the airplane has vertically placed propellors… such an easy riddle :-O</p>

40

<p>Yeah but when you push against the cart, you are still a force connected to the walkway.</p>

<p>put a model rocket engine on the cart, and it will go forward if it provides enough thrust</p>