will it take off?

[daTeacha]

What, no possibility even quite remote for rapture?

Pat

Not to get too far afield from the topic of tractors or anything, but yesterday my pastor -- a very fundamentalist kind of guy -- gave me a magazine from the ICR and asked me to evaluate it. Among various articles was one which discussed a computer simulation done at that institution which explained the great flood by having the earth slowly rotate (10 or 20 times per year) on an axis perpendicular to the N-S spin axis while still maintaining the 24 hour day-night spin we all know and love. Since you brought up rotational inertia and fundamentalist beliefs and are somewhat of a science guy, how about explaining how that rotation could happen. I can't imagine simultaneous rotation on two perpendicular axes of an object as small as a basketball, much less a planet. If it could happen, who knows? The plane might take off and land simultaneously.

 

[Iplayfarmer]

...I was taught how to tie a bowline around my waist with one hand (by a grand mother in her 70's who had to learn it to go mountaineering with an Outward Bound group) and subsequently taught it in all marlinespike seamanship classes I taught. It can be a life saver in the outback as well as at sea...

Pat

I worked at a scout camp for a few years as a kid, and I met a guy who could throw a bowline... as in he'd give each end of the rope a little flip and twist and throw the one end up in the air, and it would come down as a bowline.

I still haven't seen the practical real-world application for this skill, but I was and still am thoroughly impressed by the feat.

 

[patrick_g]

Harry, The principle matter is not whether or not the friction goes down as ski speed increases. What matters is your conveyor's operating parameters.

1. If you move the snow or ice covered conveyor backwards at the same speed as the planes advance then clearly the plane takes off. At take off the skis will be going over the conveyor at twice the speed of the airplane. This result is analgous to the case with wheels.

2. If you use the ACME Super Conveyor (bought used from Wiley Coyote, movie co-star often on the bill with the Road Runner) the conveyor will speed up enough irrespective of the plane's thrust or dwindling coefficient of friction until the frictional force equals thrust and the plane will stand still. If you use a plane with a high thrust to weight ratio then the conveyor will have to run very very fast indeed but these are really good conveyors and can run fast enough such that the frictional force will be able to equal the thrust of the airplane.

Pat

 

[patrick_g]

Not to get too far afield...

Yeah, like I never done that before...

Sorry, except for the odd ref here and there I will not discuss theological issues here. In fact, I think the odd ref here and there is not discussing theological issues. If I were to have much to say about fundamentalism, creationism (creation science) and many other topics I would probably be in more jeopardy than Galileo Galilei (one of my heroes along with Martin Luther King) when he was brought before the Pope where he could either recant his heretical beliefs regarding the earth NOT being the center of the universe as was known to be a well established fact OR be killed as a heretic. I was given to believe in one of the books I read about him that he was heard to say as he left his audience with the Pope. "it moves!"

It isn't that I don't have opinions aplenty but this is NOT the venue in which to list or discuss them.

Thanks for the opportunity. I am flattered that you thought me to be someone worthy of commenting. I respectfully decline.

Pat

 

[SPYDERLK]

Harry, The principle matter is not whether or not the friction goes down as ski speed increases. What matters is your conveyor's operating parameters.

1. If you move the snow or ice covered conveyor backwards at the same speed as the planes advance then clearly the plane takes off. At take off the skis will be going over the conveyor at twice the speed of the airplane. This result is analgous to the case with wheels.

2. If you use the ACME Super Conveyor (bought used from Wiley Coyote, movie co-star often on the bill with the Road Runner) the conveyor will speed up enough irrespective of the plane's thrust or dwindling coefficient of friction until the frictional force equals thrust and the plane will stand still. If you use a plane with a high thrust to weight ratio then the conveyor will have to run very very fast indeed but these are really good conveyors and can run fast enough such that the frictional force will be able to equal the thrust of the airplane.

Pat

Pat, I must admit I am a bit baffled in some instances on how to deal with thrust. It seems that an engine that can produce constant thrust, such as a jet or rocket would effectively make more HP the faster it moved..[Force X Distance/T] ya know. I would really like to get a handle on it - and we need to in this case because it enters into the ski vs wheel comparison. ---------- To me these are not analogous. Wheels store energy both translationaly and rotationally. In the case of wheels, the conveyor manipulates the plane by thrusting the contact patch on the wheels. Acceleration of this contact patch is resisted by the mass of the wheels factored against their moment of inertia. In our case the acceleration is rearward in order to cancel the planes thrust via the connection at the axle. In a perfect sense, relying only on accelerating rotational mass for the counterthrust, the wheels are storing energy at the same rate as the engine is putting it out. The energy doesnt come from the engine - it comes from the conveyor resisting the thrust of the engine. The energy stored [HP x T] is available to be fed back to the plane if the conveyor is slowed at a rate that prevents a peel out.
With skis, as with wheels, the thrust of the plane can only be countered up to the point at which they slip. With skis on hardpack Im guessing that dynanic slip occurs at a force of about 0.01 to 0.02 of the weight the ski supports. With tires on pavement this value is static since the tire doesnt have to slip to move, and is usually high within the 0.5 to 1.0 range - enuf to counter the thrust of most planes. We are talking a multiple of 50 over the skis. It doesnt seem like ski drag would ever increase to the point of balancing a thrust-to-supported-weight ratio of anywhere near what even a normal plane has. While acceleration of the conveyor has no effect, since with skis there is nothing for the acceleration to work against because of slippage, the speed of the conveyor may. Thats where I have a problem. The quandary of low drag at high enuf speed being power, but having no apparent ability to cancel thrust in excess of said drag. I would really love to have this "click".
larry

 

[SFish]

OK here is the fundamental truth. C150 on the magic conveyer behind my little JD3320. A hawser between the rops and the landing gear is secured with bowline knots. Drop the box blade with the scarifier teeth down and rip the guts out of the conveyer, drag the plane off onto the ground, remove the rope, and the plane takes off. No problem.

(Don't tell me not to tow with the rops, it's magic) Steve

 

[David Cockey]

You obviously want to prove that the plane can't take off, rather than analyze the problem as given. The original statement of the problem has the conveyor/runway traveling at the same speed of the plane but in the opposite direction. Hence the speed of the conveyor never exceeds the airspeed of the plane, it's just in the other direction.

The wheels only store energy when accelerating, not when moving at constant speed. At constant speed the wheels have constant kinetic energy.

The force acting against the motion of the plane is NOT the coefficient of friction of rubber against the pavement multiplied by the weight on the wheel. Rather it is the force required to accelerate the rotational speed of the wheel at the rate corresponding to the linear acceleration of the plane, plus the rolling resistance of the tire. Both will be small compared to the force require to overcome the aerodynamic drag of the plane plus accelerate the plane. Since the plane is capable of flying the thrust of the engines will exceed the minimum force required to "unstick" the plane by a considerable amount.

A refresher of basic dynamics might be in order.

Now I assume the problem will be re-defined again to discuss another possibility of the plane not flying, in order to keep the discussion going.

 

[SPYDERLK]

You obviously want to prove that the plane can't take off, rather than analyze the problem as given. The original statement of the problem has the conveyor/runway traveling at the same speed of the plane but in the opposite direction. Hence the speed of the conveyor never exceeds the airspeed of the plane, it's just in the other direction.

[[[The wheels only store energy when accelerating, not when moving at constant speed. At constant speed the wheels have constant kinetic energy.

The force acting against the motion of the plane is NOT the coefficient of friction of rubber against the pavement multiplied by the weight on the wheel. Rather it is the force required to accelerate the rotational speed of the wheel at the rate corresponding to the linear acceleration of the plane, plus the rolling resistance of the tire. Both will be small compared to the force require to overcome the aerodynamic drag of the plane plus accelerate the plane. Since the plane is capable of flying the thrust of the engines will exceed the minimum force required to "unstick" the plane by a considerable amount.]]]

A refresher of basic dynamics might be in order.

Now I assume the problem will be re-defined again to discuss another possibility of the plane not flying, in order to keep the discussion going.

Good description of parameters governing the conventional interpretation of the problem statement.

Many here dont have basic dynamics to 'refresh' hence their initial inability to instantly see the points you have made.

Others are making the point that a conveyor can be designed to counter a wheeled planes thrust for some time period, holding it stationary for that period. The mechanism by which it can do this can be deduced from your description.
larry

 

[David Cockey]

Others are making the point that a conveyor can be designed to counter a wheeled planes thrust for some time period, holding it stationary for that period. The mechanism by which it can do this can be deduced from your description.

Original statement of the problem was (message #1 in this thread):

a plane is standing on a movable runway( something like a conveyor).as the plane moves the conveyor moves but in the opposite direction.the conveyor has a system that tracks the speed of the plane and matches it exactly in the opposite direction.

the question is
will the plane take off or not?

Where did the question about whether a conveyor could be designed to hold the plane stationary come from? The velocity of the conveyor is defined in the original problem statement - same speed as the plane but in the opposite direction. It's clear that an ordinary airplane could take off under the conditions defined in message #1.

It is possible to change the definition of the problem to make it such that the plane can't take off. Lot's of possibilities:
1) Conveyor is covered with magical glue in one section. When the plane rolls over the glue the tires stick to the glue and the plane stops rolling.
2) Conveyor has grapples which grab the plane as it rolls past.
3) Conveyor is covered with super-viscous liquid to a sufficient depth that it increases the rolling resistance of the tires to a great enough extent that the plane can't achieve sufficient speed to lift off.
4) Pilot applies brakes for unknown reasons.
5) Tires blow out.
6) And so on ad infinitum
But these are all changing the the definition of the problem to result in the desired answer.

 

[David Cockey]

The inertia of the wheels affects the acceleration effectively as an "added mass". In a real plane (other than a small plane with giant tires designed for tundra operations) it is very small compared to the mass of the plane. The conveyor doubles the rotational speed of the wheels relative to the forward motion of the plane, which doubles the "added mass" but it's still very small compared to the mass of the plane.

The ratio of the rotational speed of the tires relative to the ground speed of the aircraft is constant, and determined by the effective rolling circumfrence of the tire.

In reality planes are designed with more power than what's needed to achieve sufficient speed to "unstick". A real plane needs to be able to climb and fly at higher speeds than take-off speed. So the added mass effect of the tire spinning twice as fast won't be enough to keep the plane from taking off.