will it take off?

[rback33]

Sorry, sometimes I forget smilies. I express myself better in person. No offense was meant. Im having fun with this. Its frustrating but at the same time exercises my brain.
The above goes for everyone Ive offended. Well! almost everyone.

Not a problem. I am having fun with it too but was certainly guilty of starting to take things too seriously. I almost made the cardinal mistake of jumping to the wrong conclusion. It was a good wake up call for me. I'll be off till Monday.. Have a great Turkey Day all.

 

[NorthwestBlue]

Yes, I agree... with that part...... yer about to prop me back on the fence. now keep going.

Alright rback33,

Now hook up that same scale on the tail of the airplane. Turn the MCB off or tell it to take a chill or whatever. Fire up the engine on our trusty U-2 and firewall the thrust lever. The scale will read approx. 76kN.

 

[NorthwestBlue]

Did you fully read the post? Do you understand what I was saying? What questions do you have?
The locked brakes being able to hold the plane still was merely a requirement for showing that the coefficient of friction between the belt and the tires was sufficient so that the belt would not slip under the tires as it spun them up ever faster to resist the trust of the engine. The brakes were only used to verify sufficient traction. They are not used during the attempted takeoff.

Also there is a backward force on the plane as wheels touch down during landing. It takes energy to spin them up. That energy comes from the plane and is stored as rotational energy in the wheels. With the exception of the black mark on the pavement the system has the same energy before and immediately after landing, but the system has been slowed by some of that energy being stored rotationaly. The way that a plane could be held stationary on a conveyor is for the conveyor to force rotational energy into the wheels counterequal to the energy of the engines. How many hundred HP seconds can be stored in plane wheels? Not too many, but until the wheels exploded the plane could be held stationary.
Larry

Larry,

I read it all and agree with some of what you say. I wish you were here and we could hash this out with a few beers, you're really making me think (and I usually try to avoid doing that if at all possible).

If you look a the numbers again you'll see that the plane in my example is more than capable of accelerating with the brakes locked. Most high performance aircraft have more than enough thrust to overcome the friction of the tires. This U-2 has a turbojet engine which is actually fairly inefficient at low altitudes. A high bypass turbofan would perform much better.

The tires will slip depending on the acceleration of the belt. In order for the belt to have any chance of preventing forward motion of the aircraft it needs to maximize the frictional coefficient. This would require a slower acceleration to maintain a static frictional "connection" between the tires and belt. The wheels would certainly spin and gain rotational energy, but that centripital energy does not enter in into this force vector analysis. The aircraft is actually riding on bearings with a mu of .001 - negligible friction.

Now let's look at the landing analogy again. It is actually is very similar to the takeoff from the MCB. At landing there is indeed a transfer of rotational energy to the wheels and is does have a very small net affect of slowing the aircraft initially until the wheels are spun up to speed. After that the wheels try to keep the aircraft moving with the stored energy. Big brakes (and thrust reversers) and lots of heat slow the plane. Anti-skid also helps to maintain a high frictional coefficient.

You mentioned the "black mark on the pavement". That is what would happen with instantaneous acceleration of the MCB to counteract the movement of the airplane taking off. The belt can accelerate to minimize slippage, but the plane will move forward and rapidly.

 

[JimParker]

It comes down to how you interpret the problem - the wording is vague enough to allow differing interpretations. However, as I said in two earlier posts, if thrust is greater than the drag caused by the rotating wheels on the MCB, the plane will (eventually) fly. With "real world" bearings, wheels, and conveyor belts, a sailplane with an F16 engine would fly pretty quickly. The same sailplane using only an "auxiliary motor" (used while airborne to extend a sailplane's flight), the little motor would probably not provide enough thrust to accelerate the airframe to takeoff speeds.

Also as I said in two earlier posts, if thrust is less than or equal to the drag caused by the rotating wheels on the MCB, the plane will never fly. That's the simplest engineering exercise in the world...

For even a small lightplane (Cessna 150, Champ, Taylorcraft, or Cub), the minimal resistance of the wheel bearings and rubber tires means that the MCB would have to turn extremely fast to generate enough drag to counter the thrust of the prop/engine. In the "real world" - the plane would fly. In the "magic world" (required by the wording of the problem) - it depends on the plane's thrust relative to the drag generated by the bearings and wheels.

For those of you having trouble with the "drag" part of the equation, think about the extra power required to drive your car down the road with four tires that have only about 5 psi of air pressure in them. The friction of the rolling tire supporting the weight of the vehicle causes tremendous drag, requiring a lot more power. That's why one of the most important things you can do to improve your gas milage is to raise the air pressure in your tires (up to the rated limit, of course). However, even when fully inflated, there is some drag caused by deflecting the shape of the tire as it rolls.

Ditto the wheel bearings. Properly lubricated bearings have very low rolling resistance. Dry bearings, on the other hand, would generate a lot of heat from - you guessed it - friction. That friction increases the drag of the rolling tire. Combine higher friction bearings with higher friction tires, and you get higher drag... and greater thrust required to fly. How much greater? I'm too tired to do the math...

But in his analysis (very intersting take on things, by the way) I don't see where NorthwestBlue accounted for the drag coefficient of the deflecting tire surface. It wouldn't make a hill of beans in his U-2 example (where there is an overwhelming thrust advantage), but it would make a big impact on an underpowered Cessna 150 or Taylorcraft. (Seems like I recall reading that under-inflated tires can extend the takeoff distance by up to 50% on a small lightplane - but I could be mistaken.)

Enough already... I refuse to look at this thread any more. ('Course, I said that last time, too! Dang!)

 

[joerocker]

Do you ALL agree that a ROCKET or missle on wheels on the MCB WOULD take off?





OK then, a plane is the SAME thing! The ONLY difference is the TYPE of engine.




In reality (excepting some SLIGHT friction in wheel bearings) your MCB is nothing more than nothing. A neutral "thing" that the plane is sitting on. It's the same as it being suspended in air. Crank up the engines and it WILL take off.

Remember...it's not moving forward BECAUSE the wheels are turning. The wheels are turning BECAUSE it's already moving forward. If the plane didn't move, the wheels and the MCB wouldn't move. Remember it's all relative. Only when the plane is ACTUALLY moving through the air CAN the wheels on the MCB move too. Remember...it's NOT a CAR. The wheels don't drive the plane, the planes movement makes the wheels turn. Without forward movement there is NO tire movement.

 

[Paddy]

Jim,

You said it in your first line, "It comes down to how you interpret the problem -"

The No fly camp is still entrenched in the understanding the MCB is matching the wheel rotation speed, not the plane speed as clearly stated. All the engineering calculations are irelivent if they are stuck on wheel speed. In fact lets go down that road for a bit. A plane, or any object moving through and along the surface of the earth, uses very little force at low velicity due to air resistance. The force by air is not lineair, velocity squared x surface area. So again following the No fly camp that has assumed wheel speed not plane speed. The only resistance the thrust of the plane will counter is wheel bearing resistance. This is drag/friction is extreamly low. The engine will creat tremendus wheel speed for very little thrust. No fancy calculation required!

Clearly the "will fly" camp has assumed the problem meant the MCB will match the plane's speed. In this case, when the MCB is moving West at xx mi/hr, the plane is moving East at xx mi/hr. The plane flys at speeds above it's required speed for lift. Again, no fancy calculations required.

So it all comes down to returning to the first post and re-reading the question. Wheel speed?? Plane speed?? When I first read the problem, I too was tricked mentally in to missunderstanding the the problem (first cute thing about this problem) But after reading the first few following posts where I saw the other assumption, I realized I had been tricked. What is amazing is this trick question has been presented many times in the past and even though the trick part of the question eventually shows up in discussions, some folks hold on to their first assumption.(That's the second cute thing about this problem, peaple can't let go!)

So, let's all re-read the problem and give your justification of YOUR assumption of wheel speed vs. plane speed. Because I do belive 95% of us would agree on Fly/No Fly IF the question was stated in such a way to have had not debate on wheel speed/plane speed.

OK so I start, Problem states "...CB matches plane speed..." Nothing said about wheels at all.

 

[SPYDERLK]

NorthwestBlue et al,
Pls take a look back at post#233 by MossRoad. Read the links he has provided. By the time I got there I was wondering if this part of the physics was going to come up in the thread, and, if not, how was I going to introduce it with enuf lucidity to convey the phenomenon. I wasrelieved to see it introduced and explained in the second of MossRoads links. Then in reading onward in the link I was surprised that no one picked up on it. I finally reintroduced the concept independently. It still isnt clicking with anyone that I can identify with surety. When I see posters going thru analyses with bearing friction, tire flex losses, skids, pontoons etc, I know the point has been missed.
The only things absolutely necessary to hold the plane still are tiretraction in excess of thrust, wheels, NON zero wheel mass, and a magical conveyor that can continuously accelerate the rotation of magical wheels that can be spun up to relativistic tangential velocity without exploding. In such case, the composite plane continues to gain energy but doesnt move at all. If the conveyor stopped, this energy, stored in the mass of the rotating wheels, would be coupled back to the airframe thru axles, and with adequate strength of materials and traction the plane would take off like a bullet.
This theoretic truth could be demonstrated in the real world by optimizing parameters to remain within strength of materials. The plane thrust would have to be marginal, the wheels should be heavier than usual, and demonstration time should be fairly short - - otherwise wheel or conveyor failure would end the experiment violently.
Larry

 

[NorthwestBlue]

It comes down to how you interpret the problem - the wording is vague enough to allow differing interpretations. However, as I said in two earlier posts, if thrust is greater than the drag caused by the rotating wheels on the MCB, the plane will (eventually) fly. With "real world" bearings, wheels, and conveyor belts, a sailplane with an F16 engine would fly pretty quickly. The same sailplane using only an "auxiliary motor" (used while airborne to extend a sailplane's flight), the little motor would probably not provide enough thrust to accelerate the airframe to takeoff speeds.

Also as I said in two earlier posts, if thrust is less than or equal to the drag caused by the rotating wheels on the MCB, the plane will never fly. That's the simplest engineering exercise in the world...

For even a small lightplane (Cessna 150, Champ, Taylorcraft, or Cub), the minimal resistance of the wheel bearings and rubber tires means that the MCB would have to turn extremely fast to generate enough drag to counter the thrust of the prop/engine. In the "real world" - the plane would fly. In the "magic world" (required by the wording of the problem) - it depends on the plane's thrust relative to the drag generated by the bearings and wheels.

For those of you having trouble with the "drag" part of the equation, think about the extra power required to drive your car down the road with four tires that have only about 5 psi of air pressure in them. The friction of the rolling tire supporting the weight of the vehicle causes tremendous drag, requiring a lot more power. That's why one of the most important things you can do to improve your gas milage is to raise the air pressure in your tires (up to the rated limit, of course). However, even when fully inflated, there is some drag caused by deflecting the shape of the tire as it rolls.

Ditto the wheel bearings. Properly lubricated bearings have very low rolling resistance. Dry bearings, on the other hand, would generate a lot of heat from - you guessed it - friction. That friction increases the drag of the rolling tire. Combine higher friction bearings with higher friction tires, and you get higher drag... and greater thrust required to fly. How much greater? I'm too tired to do the math...

But in his analysis (very intersting take on things, by the way) I don't see where NorthwestBlue accounted for the drag coefficient of the deflecting tire surface. It wouldn't make a hill of beans in his U-2 example (where there is an overwhelming thrust advantage), but it would make a big impact on an underpowered Cessna 150 or Taylorcraft. (Seems like I recall reading that under-inflated tires can extend the takeoff distance by up to 50% on a small lightplane - but I could be mistaken.)

Enough already... I refuse to look at this thread any more. ('Course, I said that last time, too! Dang!)

Well Jim if you happen to be tempted once again to look at this thread you can see this rebuttal to your statement "I don't see where NorthwestBlue accounted for the drag coefficient of the deflecting tire surface".

I used the coefficient of friction for rolling resistance for a hard "rubber" tire
Crr = mu = .015. This takes into account the deflection of the tire on an asphalt surface. I don't think anyone has tested the rolling resitance on the MCB or else I could have used this value. Anyway the value was more conservative than what the actual value would have been.

And if anyone is at all wondering. I'm just having fun with this whole hypothetical. The deal with engineering is that if somebody says something is impossible then you find a way to make it possible. I'll never try to prove why something can't be done, just find a way to do it.

 

[turnkey4099]

Ok. Here is an experiment you can do that will show you how the conveyor can counter the thrust of the plane via the wheels:
* take a wheel with bearings and put it on an axle
* put the axle on 2 level rails with enuf room so the wheel is suspended between
* attach something to the wheels outer perimeter that will give you some purchase to push against - - this is your traction
* push on this "thing" gently and parallel to the rails - with just a little force the wheel will turn and your traction handhold will slip by you hand - the axle will probably not move at all
* now push on the thing hard - you will probably have to strike it to be able to deliver the force before the thing rotates out of the way - the axle will move along the rails
* Now imagine that you could continue delivering the instant force of your blow continuously as the wheel turned. The continuous rotational acceleration imparted to the wheel would continue to deliver force to the axle, pushing the axle along the rails.

The accelerating conveyor can do this to the wheel. The force it exerts to continue accelerating the wheel is transmitted to the plane via the axle. With a high enuf rate of acceleration this force can completely counteract the planes thrust. -- So, in the realm of what ifs - If the wheel to conveyor traction were great enuf to impart the needed force to accelerate the wheel(s) that fast, and if the conveyor were physically capable of doing so, then the plane would not move. Until the wheels exploded - - but if they didnt..........?
Larry

Wrong. Get off the idea that the motor is driving the wheels or the wheels driving the plane. For your theory to work you have to picture the plane sitting stationary on the WCB in still air with the engine wound up having no effect at all on the air.

Look at it backwards. The airplane is flying when it encounters a WCB exactly matching the speed in reverse. Per your theory, the airplane suddenly stops and drops vertically down on the belt.

The only difference between the two is the minimal friction in the axles.

Remeber that prop is thrashing away at the air and something has to give, the airplane moves _through the air_. It doesn't care one wit what the wheels are doing.
Harry K

 

[NorthwestBlue]

NorthwestBlue et al,
Pls take a look back at post#233 by MossRoad. Read the links he has provided. By the time I got there I was wondering if this part of the physics was going to come up in the thread, and, if not, how was I going to introduce it with enuf lucidity to convey the phenomenon. I wasrelieved to see it introduced and explained in the second of MossRoads links. Then in reading onward in the link I was surprised that no one picked up on it. I finally reintroduced the concept independently. It still isnt clicking with anyone that I can identify with surety. When I see posters going thru analyses with bearing friction, tire flex losses, skids, pontoons etc, I know the point has been missed.
The only things absolutely necessary to hold the plane still are tiretraction in excess of thrust, wheels, NON zero wheel mass, and a magical conveyor that can continuously accelerate the rotation of magical wheels that can be spun up to relativistic tangential velocity without exploding. In such case, the composite plane continues to gain energy but doesnt move at all. If the conveyor stopped, this energy, stored in the mass of the rotating wheels, would be coupled back to the airframe thru axles, and with adequate strength of materials and traction the plane would take off like a bullet.
This theoretic truth could be demonstrated in the real world by optimizing parameters to remain within strength of materials. The plane thrust would have to be marginal, the wheels should be heavier than usual, and demonstration time should be fairly short - - otherwise wheel or conveyor failure would end the experiment violently.
Larry

Larry,

I do understand everything that you wrote and with the Mossroad link. My premis to overcome the "Magic" is to minimize and trivialize its only strength - instant and endless acceleration. The only way that it can transfer energy to the airplane is through friction (the contact between tires and belt). The reason that the links theory fails is TIME. The reason I chose the plane that I did was to emphasize the fact that it would take very little time to create lift and therefore reduce friction and belt induced drag. I chose a design that can accelerate regardless of the state of the wheels. Rotating, stopped (brakes on), or even rotating in reverse has no bearing on the outcome.

I agree that given enough time that the MCB would prevent the airplane from taking off. Given enough friction or as you say "traction" then the MCB wins. My idea is to reduce friction or traction and to overpower any negative effects of that friction. My airplane has Teflon wheels. It can out accerate its own wheels. It will accelerate fast enough, and lift will occur fast enough that its own wheels will not be able no maintain the friction to spin up without slipping. Add additional rearward acceleration (MCB) and the wheels just slip faster. Then its just a force drag equation. The plane will fly. If you're still not convinced... I just picked up a few gallons of synthetic oil for my truck and tractor. I could use a little tubing and route a continuous drip on my Teflon wheels. Yee Haw! Come on Mr. ME -three tractor man... Git 'er done.

Oh, and happy Thanksgiving.