A harmless little riddle

<p>The way I read it: the conveyer belt is simulating the normal expected ground speed of the airplane in relation to the amount of thrust thus moving the belt in the opposite direction to match the plane’s expected ground speed.</p>

<p>Unfortunetly, the wording opens the riddle to interpretation.</p>

<p>I consulted my brother, who’s been reading the Space Shuttle Manual since before he could actually read. Reads the Jane’s Guide for fun. Here’s what we decided, as per our AIM conversation…</p>

<p>(14:35:17) aibarr’s brother: “makes no difference, because the wheels on a plan are free-rolling, the thrust of the plane whether it be from a propeller or a jet engine would push the plane forward until it reached take-off velocity and lifted off.”
(14:35:19) aibarr’s brother: that guy’s right.
(14:36:00) aibarr’s brother: it will take off. however, if the airplane is fixed to the treadmill, it won’t unless it’s a very specific type of airplane.
(14:37:10) aibarr: So essentially, you’ve got free-rolling wheels, and so long as the bearings can withstand the extra difference in speed and friction that the added speed-relative-to-belt contributes, then it can thrust as normal and achieve the necessary windspeed to take off…
(14:37:19) aibarr’s brother: exactly.
(14:37:25) aibarr: But if the plane is stationary relative to the ground, then it won’t work.
(14:37:40) aibarr: Because you don’t get any airspeed.
(14:37:51) aibarr’s brother: unless it’s got what are known as “blown flaps”, where the airflow out the engines goes over the flaps.
(14:38:01) aibarr: Which is why you can’t have magical VTOL conveyor belts.
(14:38:15) aibarr’s brother: and even then, you’d have to be very light and have a LOT of thrust.
(14:38:17) aibarr: ok, understood.</p>

<p>The point is, the treadmill runs opposite of the wheels, not the whole plane. Since the bearings relatively seperate the two, the plane can accellerate</p>

<p>My prop thing wasn’t completely wrong though. It would take off faster with a puller thrust system</p>

<p>And Sky, this question was posed under the same title at the MIT forum. I’ve tried to explain it too them but I don’t think they buy it. Might go over there and tell them.</p>

<p>bmanbs2, </p>

<p>As much as I would like to, I don’t think I’d have the energy to enter another debate on this topic. :slight_smile: </p>

<p>All the debate in the MIT thread is meaningless. The simple fact of the matter, this problem can be simply solved using the first thing they teach you in high school physics… using a free body diagram. An airplane will have 4 forces acting on it, thrust, drag, lift, and weight (due to gravity). Lift can be ignored for this problem. Let’s assume a stationary airmass along the “runway.” Obviously if you have a headwind, you can take off with a lower ground speed, but assuming it is stationary will make things easy (and is a perfectly fine assumption. Zero wind is a great condition for pilots). Aerodynamic drag will not become a significant force during the initial roll, so that can be ignored at first. Thrust of the engine will be assumed constant as a function of velocity. The only remaining forces we are looking at are the thrust of the engine and the frictional forces due to the landing gear. Without even looking at the mechanics of the frictional forces, I think it is pretty clear that the forces due to friction will be much much less than the forces due to the propulsion system. The net force in the longitudinal direction can mean only one thing in Newtonian physics: an acceleration. The airplane will continue to accelerate until the forces balance (no net force = no acceleration). Aerodynamic drag will certainly increase with velocity (squared), but the frictional forces at the tire and in the wheel bearings are dependent primarily upon forces acting normal to them (based on the weight), which will decrease as the airplane starts producing lift that opposes the weight. These frictional forces generally are independent of velocity. “Startup” forces that get bearings spinning are much higher than any friction that is caused by spinning the bearings faster (as what would happen when the treadmill speed increases). </p>

<p>Remember how we assumed a stationary airmass? As the airplane velocity increases (since it is accelerating down the runway), there is now a airflow over the wings which produces lift. Even if you don’t assume a stationary airmass, then you will get another velocity component between the wing and the airmass, but regardless, the airplane’s velocity is generally much higher than the airmass. </p>

<p>And with respect to your puller prop statement… It could help… but only in a certain configuration. The prop wash in a tractor (ie. puller) configuration can increase the lift a wing generates if the wing is in the slipstream of the propeller. Most pilots will know that the “power-on” approach can result in a lower airspeed as compared to the “power-off” approach. This is because a propeller does increase the airflow over the wings, and therefore does produce a bit more lift. However, for this problem, this fact is pretty much irrelevant.</p>

<p>Well… dang! It looks like in the time that it took me to write this, I could have posted the same message in the MIT forum. Regardless, if you want, you can link them to this post, or cut and paste it yourself.</p>

<p>I’ll also add my credentials as a pilot and aerospace engineer if it helps add any weight to my argument.</p>

<p>Sweet, another pilot. I was hoping I wasn’t the only one (though I’m only a student pilot), and I am planning on becoming an aerospace engineer. Did you get your flight certifications from a flight school or educational institutions, and what certifications do you have?</p>

<p>BTW, I’ll go ahead and copy and paste ^ over there.</p>

<p>This was on basically every internet forum worth a damn about 6 months ago.</p>

<p>Yes, it is made its way to a Camaro forum on which I post. Heh.</p>

<p>You on LS2.com?</p>

<p>Yea… I actually heard it on an AM talk show host like about 9 months ago… although I never heard their explanation… the talk show host (a pilot) was actually claiming that the airplane wouldn’t take off… </p>

<p>I tried as hard as I could to stay out of this one… but I couldn’t help it… harmless riddle my a$$… I am having a nervous breakdown reading the garbage that some people are saying… hehe… I’m ready to go hire some Indian and Chinese engineers! Just kidding… but seriously… I hope most of the people posting here are still sophomores in highschool and haven’t taken physics yet…</p>

<p>Sky, just think about how big a leg up you have on everyone. :)</p>

<p>No. I’m on camaroz28.com and ls1tech.com</p>

<p>Do you have a C6 or GTO?</p>

<p>Nah, about 95% of the people on LS2.com have LS1s. It’s basically the remainder of ls1.com.</p>