DDWFTTW Turntable Test: 5 Min Video - Is It Conclusive?

[vanesch]

If we use the numbers we were using in the example, 10 m/sec tread, 2 m/sec cart both wrt the floor. I was getting 2 m/sec too low! You were getting 12 m/sec too high!
At the wheel/tread interface, as you and Newton say and I agree, they are working on each other, it is not an all or nothing proposition as we were using (I was giving it nothing while you were giving it all)
So I need to add 5 m/sec to my 2 and the correct velocity is 7 m/sec
You need to subtract 5 m/sec from your 12 and the correct velocity is also 7 m/sec.

But now that I think of it, *even in these frames* you are wrong.

We agree that in the ground frame, the velocity of the cart (with the + sign in the sense opposite to the motion of the tread) is:
+ 2 m/s (it goes the other way)
and the velocity of the wind is 0 m/s

In the frame of the tread we have:
12 m/s for the cart
10 m/s for the wind

In your "half way" frame:

7 m/s for the cart
5 m/s for the wind

In your "vertical" frame (moving up 10 m/s):

the cart: sqrt (2^2 + 10^2) = 10.19 m/s
the wind: 10 m/s

In the "half way vertical" frame (moving up 5 m/s):

the cart: sqrt(2^2 + 5^2) = 5.38
the wind: 5 m/s

DARN. EVEN by picking just ANY of these frames, we STILL have the cart going faster than the wind...

 

[atyy]

Wow, still going for 6th dan? I'm sure you have 3rd dan by now.

 

[atyy]

Actually, I just noticed your last post was 666...

 

[vanesch]

Actually, I just noticed your last post was 666...

Mmm...

 

[zoobyshoe]

I'm actually amazed at how much debate this thing can generate. 2 weeks ago I never even gave this DWFTTW any thought, and as I said, if people would have asked me on the street if it were possible to make a device that does it, I would probably even have guessed "no" (as I've done some sailing and had courses on it and all that).

When I saw the issue raised here, it took a few minutes to understand that there's no principle prohibiting it (it took somewhat longer, with the help of Jeff, to get all the forces and so on right). But once the thing is understood, it is a simple application of classical mechanics - even to the point of getting bored about it.

I had the same experience the first time I heard the puzzle: can a plane on a backward moving conveyor belt take off? My off-the-top-of-my-head response was "no". Then they said "Well, where does a plane get it's thrust?" and I instantly saw my mistake: when imagining a plane at take off we instantly revert to thinking of it as a car whose tires are pushing against the road surface. (ThinAirDesign take note: I learned I was an idiot completely free of charge, here.)

Back when this thread first started (it's been years, right?) I was telling a friend about the DDWFTTW debate, and described it as another plane on a conveyer belt puzzle. Strangely, he'd never heard that one, so I asked him the question. He thought about it a moment and declared that the plane would not be able to take off. After I reminded him a plane gets it's thrust from pushing against the air, he repeated that the plane would not be able to take off. I must have reminded him the plane's tires are freewheeling a dozen times but it took an hour and a half of debate and gedankens to get him to free himself of the gut level feeling the plane could not generate the forward speed for lift without first accelerating itself by pushing against the road.

When first learning about planes people are directed to concentrate on how lift is created by forward speed because the perplexing problem being addressed is: how can something so heavy get into the air? How it gets it's forward thrust is a side issue, quickly explained and then usually forgotten. (The truly frightening thing about the Mythbuster's proof that a plane can take off in this situation was the post demonstration interview with the plane's pilot, who expressed surprise that it worked! He said he was pretty sure all along he wasn't going to be able to take off.)

 

[ThinAirDesign]

Seriously, why do you take all that trouble ? Is it a kind of hobby or so ?

I love to build stuff. Always have.

I'm actually amazed at how much debate this thing can generate.

I've said the same thing about POAT many times.

But once the thing is understood, it is a simple application of classical mechanics - even to the point of getting bored about it.

One reason it hasn't bored me is that in explaining it I keep gaining a better understanding of other related areas. For example: I learned there are very big misconceptions among even experienced sailors regarding how sails work. I learned this because in demonstrating that our prop is simple a sail on one continuous broad reach, sailors would come back and say "not so ... a sail always has work done on it by the air and a prop does work on the air". I've learned that this simply isn't true and that a sail properly arranged for downwind use it actually functioning the same as a prop on a Cessna. I keep learning and that makes it fun.

In fact, the treadmill test is, on the mechanics level, more interesting than an outdoor test. It is a very good exercise in classical mechanics, and I would even suggest that it is taken up in a regular curriculum of first year mechanics, because it illustrates many aspects without being intuitively obvious.

I'm surprised this sort of a problem isn't used more.

But once it is understood, what's the use of spending a lot of effort doing a controlled outdoor test ?

Well, we aren't doing it because we have any doubts regarding DDWFTTW, that's for sure -- the challenge for me is in attempting to document a test in a way that would address the concerns I would have if I were not in the camp that understands how it works. I have a lot of friends who won't call me a liar or a fraud and the know me well enough to not just say "you're a fool", but that's what they would call anyone else. This test is really for them and others in that camp.

It's really hard to produce good test footage and before I move on I want to put just one good outdoor test in the can.

JB

 

[ThinAirDesign]

Just to show that even with the best demonstration available (a plane actually taking off from a treadmill), many folks still can't accept it:

http://community.discovery.com/eve/forums/a/tpc/f/9401967776/m/4441931059

Close to 300 pages and close to six thousand posts of people arguing about it SINCE the episode aired in which MythBusters busted the myth.

JB

I had the same experience the first time I heard the puzzle: can a plane on a backward moving conveyor belt take off? My off-the-top-of-my-head response was "no". Then they said "Well, where does a plane get it's thrust?" and I instantly saw my mistake: when imagining a plane at take off we instantly revert to thinking of it as a car whose tires are pushing against the road surface. (ThinAirDesign take note: I learned I was an idiot completely free of charge, here.)

Back when this thread first started (it's been years, right?) I was telling a friend about the DDWFTTW debate, and described it as another plane on a conveyer belt puzzle. Strangely, he'd never heard that one, so I asked him the question. He thought about it a moment and declared that the plane would not be able to take off. After I reminded him a plane gets it's thrust from pushing against the air, he repeated that the plane would not be able to take off. I must have reminded him the plane's tires are freewheeling a dozen times but it took an hour and a half of debate and gedankens to get him to free himself of the gut level feeling the plane could not generate the forward speed for lift without first accelerating itself by pushing against the road.

When first learning about planes people are directed to concentrate on how lift is created by forward speed because the perplexing problem being addressed is: how can something so heavy get into the air? How it gets it's forward thrust is a side issue, quickly explained and then usually forgotten. (The truly frightening thing about the Mythbuster's proof that a plane can take off in this situation was the post demonstration interview with the plane's pilot, who expressed surprise that it worked! He said he was pretty sure all along he wasn't going to be able to take off.)

 

[atyy]

Just to show that even with the best demonstration available (a plane actually taking off from a treadmill), many folks still can't accept it

Yeah, I haven't understood why Mythbusters's solution was right.

Consider a plane on a rigid surface with only static friction (Fr) that increases with applied force up to a maximum (Frmax).

In the case of a plane without wheels, the plane cannot accelerate unless the jet force (Fj) is greater than Frmax. In this case, the plane will take off, since the puzzle doesn't even make sense unless Fj>Frmax.

But a plane with rigid wheels can accelerate if Fj is less than Frmax, which is reasonable if we assume the wheels always roll without slipping.

Assume Fj is applied through the center of mass of the wheel of mass M, radius R and moment of inertia about its axis I.

Let Ap be the translational acceleration of the wheel relative to the ground.
Let alpha be the rotational acceleration of the wheel about its axis.
Let Ab be the translational acceleration of the belt relative to the ground.

1: Fj-Fr = M*Ap (used 'F=ma')

2: Fr*R=I*alpha (used 'torque=I*alpha')

The plane is moving forwards, the belt is moving backwards, so the translational acceleration of the plane relative to the belt is (Ap+Ab), so for rolling without slipping:

3: (Ap+Ab)=alpha*R

Solving for the friction gives:

Fr=I*(Fj+Ab*M*R^2)/(I+M*R^2)

Thus if Ab=0, then Fr<Fj, and the plane can accelerate.
But for sufficiently great but finite Ab, then Fr=Fj, and the plane cannot accelerate by rolling. It also cannot accelerate by sliding since Fj<Frmax.

 

[Subductionzon]

JB after watching swerdna's bubble test I think I would go with some sort of smoke bomb to indicate wind speed for your next outdoor test. The bubbles seem to drop too quickly and by the time your cart is up to speed they would have either hit the ground and popped or they would be spread out too much to be of much use. Smoke can be fairly diffuse and still be of use.

 

[ThinAirDesign]

Yeah, I haven't understood why Mythbusters's solution was right.

Before addressing your nitty gritty, I'd like to understand your above statement.

Is your overall position:

A: The POAT brainteaser is semantics based and worded such as there is no possible solution?

B: The intent of the brainteaser is to determine if a real world runway treadmill could keep a normal airplane from taking off?

C: Other.


The above questions matters because depending on the interpretation of the wording, any of the above can be derived. I just don't want to argue on thing while you're arguing another.

JB

 

[ThinAirDesign]

JB after watching swerdna's bubble test I think I would go with some sort of smoke bomb to indicate wind speed for your next outdoor test. The bubbles seem to drop too quickly and by the time your cart is up to speed they would have either hit the ground and popped or they would be spread out too much to be of much use. Smoke can be fairly diffuse and still be of use.

I agree Sub -- I have a hard time getting information from something that vanishes just as I need to see it.

JB

 

[atyy]

Before addressing your nitty gritty, I'd like to understand your above statement.

Is your overall position:

A: The POAT brainteaser is semantics based and worded such as there is no possible solution?

B: The intent of the brainteaser is to determine if a real world runway treadmill could keep a normal airplane from taking off?

C: Other.


The above questions matters because depending on the interpretation of the wording, any of the above can be derived. I just don't want to argue on thing while you're arguing another.

JB

Option C. My understanding is that the answer is yes or no depending on the exact wording of the teaser, and the interpretation of the wording. I sketched my reasoning for both no and yes answers in #673. Essentially I think an accelerating treadmill can apply a force to the aircraft. Discussing POAT here would probably be very off topic from DDWFTTW, but I'd certainly be glad to hear vigourous rebuttals, even if I don't reply to them!

 

[zoobyshoe]

I should never have mentioned that plane.

 

[swerdna]

The plane killed the thread!

Using a variation of the Brennan Torpedo principle, I have designed this as a possible directly down river faster than the river device.

It is a one-piece construction with no moving parts other than the cable. As the floating paddlewheel is taken downstream with the flow of the river it rotates off the stationary cable and “paddles” against the flow of the river, thereby traveling directly down river faster than the river. Anyone think it would it work or not?

http://www.accommodationz.co.nz/images/roller.bmp

 

[vanesch]

It is a one-piece construction with no moving parts other than the cable. As the floating paddlewheel is taken downstream with the flow of the river it rotates off the stationary cable and “paddles” against the flow of the river, thereby traveling directly down river faster than the river. Anyone think it would it work or not?

Mmm, this should be worked out in more detail, but I would guess it would travel up the river. This looks so much like the yoyo on a table. With a force balance, there will be a net torque on the thing which will wind up the wire, no ?

(unless I misunderstood your drawing: the water is flowing from the right to the left in your picture, right ?)

 

[swerdna]

Mmm, this should be worked out in more detail, but I would guess it would travel up the river. This looks so much like the yoyo on a table. With a force balance, there will be a net torque on the thing which will wind up the wire, no ?

(unless I misunderstood your drawing: the water is flowing from the right to the left in your picture, right ?)

If the cable spool had a small diameter compared to the paddlewheel diameter then I have no doubt that the paddlewheel would wind up the cable against the flow of the river as the yoyo does on a solid surface. If the spool diameter was close to the size of the paddlewheel diameter however what would happen then? It wouldn't roll up the cable against the river if they were the same size.

Yes from right to left as indicated by the arrows.

 

[rcgldr]

If the cable spool had a small diameter compared to the paddlewheel diameter then I have no doubt that the paddlewheel would wind up the cable against the flow of the river as the yoyo does on a solid surface. If the spool diameter was close to the size of the paddlewheel diameter however what would happen then?

If the advance ratio (paddle wheel diameter / cable spool diameter) is > 1, the device goes up water (or it doesn't move at all). You need the cable spool to be larger than the paddle wheels (advance ratio < 1) in order for the paddle wheel to go down stream, so that the wire "unwinds" as the device goes downstream. The advance ratio need to be > 0 but < 1 in order to go DDSFTTS (S = stream).

 

[swerdna]

If the advance ratio (paddle wheel diameter / cable spool diameter) is > 1, the device goes up water (or it doesn't move at all). You need the cable spool to be larger than the paddle wheels (advance ratio < 1) in order for the paddle wheel to go down stream, so that the wire "unwinds" as the device goes downstream. The advance ratio need to be > 0 but < 1 in order to go DDSFTTS (S = stream).

Are you taking into account that water is fluid?

ETA - Would a larger than paddlewheel spool cause the paddlewheel to travel directly down river faster than the river?

ETA (again) - Would the true diameter of the paddlewheel be the tip of the paddles?

 

[rcgldr]

Would a larger than paddlewheel spool cause the paddlewheel to travel directly down river faster than the river?

If it's effcient enough, for a given advance ratio (paddlewheel diameter / wire spool diameter), the theoretical limit for the device with stationary wires and moving water is:

(device speed) = (water speed) / (1 - advance_ratio)

A small advance ratio has a lower theoretical limit, but requires less efficiency, however in this case, a small advance ratio meants a large spool diameter, which increases drag in the water. You'd want a narrow spool and wide paddles. I don't know how "aggresive" (advance ratio close to 1, paddle wheel diameter close to spool diamter), a setup would work.

Although not part of the experiement, to continue with the advace ratio concept:

If paddlewheel diameter = 0, advance ratio = 0, and max device speed = water speed

If the wire unwinds from the top of the spool, regardless of size, then the advance ratio is < 0 and the device goes downstream at slower than water speed.

If this advance ratio stuff gets confusing, go back to the yo-yo running on rails example (so the yo-yo "axis" can be larger than the "wheels") where nothing slips.

 

[swerdna]

I think an important thing to consider is that the flowing water is exerting force on more surface area of the paddlewheel than just the very tips of the paddles. In other words it’s not exactly comparable to what happens to the yoyo on a firm surface.

ETA - In other words, I think the amount of the paddlewheel that is submerged is also important.

 

[rcgldr]

I think an important thing to consider is that the flowing water is exerting force on more surface area of the paddlewheel than just the very tips of the paddles. In other words it’s not exactly comparable to what happens to the yoyo on a firm surface. In other words, I think the amount of the paddlewheel that is submerged is also important.

True, you'd need to figure out the "effective" advance ratio to make a good prediction, but assuming that the device doesn't have to be optimized, then paddle wheel diameter = 1/2 to 2/3 of spool diameter would probably work. In addition, you'd probably want some large thin disks on either side of the spool to keep the wire from sliding off the spool and to act as rudders.

 

[swerdna]

True, you'd need to figure out the "effective" advance ratio to make a good prediction, but assuming that the device doesn't have to be optimized, then paddle wheel diameter = 1/2 to 2/3 of spool diameter would probably work. In addition, you'd probably want some large thin disks on either side of the spool to keep the wire from sliding off the spool and to act as rudders.

I think a central long paddlewheel with a spool on either end would be a better design than what I’ve drawn.

ETA - Like this . . .

http://www.accommodationz.co.nz/images/paddlewheel.bmp

 

[rcgldr]

I think a central long paddlewheel with a spool on either end would be a better design than what I’ve drawn.

With two wires sufficiently far apart, it would be more stable (less prone to turn), as long as the wires unwind relatively evenly.

 

[zoobyshoe]

If the advance ratio (paddle wheel diameter / cable spool diameter) is > 1, the device goes up water (or it doesn't move at all). You need the cable spool to be larger than the paddle wheels (advance ratio < 1) in order for the paddle wheel to go down stream, so that the wire "unwinds" as the device goes downstream. The advance ratio need to be > 0 but < 1 in order to go DDSFTTS (S = stream).

Changing the " "advance ratio" " will not change the direction of the force on the paddle wheels. A larger central spool will just cause the device to wind itself up stream faster.

 

[rcgldr]

A larger central spool will just cause the device to wind itself up stream faster.

No, as the device goes down stream, the wire applies a forwards torque on the spool greater than the opposing torque from the paddles, and unwinds from the bottom, allowing the device to advance relative to the water. This is an advance ratio > 0 and < 1.

If the spool is smaller, then the backwards torque from the paddle wheels is greater than the forward torque from the wire, and the device goes upstream as it winds in the wire.

Think of the advance ratio as a lever, the interface with the most leverage (force) wins.

 

[zoobyshoe]

No, as the device goes down stream...

What force moves the device down stream to begin with? The force of the stream is being turned around to wind it upstream.

 

[vanesch]

In fact, it is easy to see what way the thing will turn: you take the effective point of attachment of the force with the water, and the effective point of attachment of the force on the rope (which is easy: it is along the rope itself). This couple of (balanced) forces will make up a torque, and the direction of the torque will give you the direction in which the system will rotate.

So if the effective interaction point of the water with the wheel is BELOW the rope, then obviously, the torque will work in the sense of the hands of the clock and the rope will wind up, while if the interaction point is ABOVE the rope, it will unwind.

 

[zoobyshoe]

In fact, it is easy to see what way the thing will turn: you take the effective point of attachment of the force with the water, and the effective point of attachment of the force on the rope (which is easy: it is along the rope itself). This couple of (balanced) forces will make up a torque, and the direction of the torque will give you the direction in which the system will rotate.

So if the effective interaction point of the water with the wheel is BELOW the rope, then obviously, the torque will work in the sense of the hands of the clock and the rope will wind up, while if the interaction point is ABOVE the rope, it will unwind.

I have sketched this out for myself for the case of a spool which is larger in diameter than the paddle wheel. (In this case the rope must be all underwater.) If we consider the paddles alone, the force of the water on the paddles still acts to rotate the device such that it will wind itself upstream. The force of the river on the thing as a whole, however, is surely enough to counteract this and will push it downstream, unwinding as it goes. When this happens, the paddles are moot, and do not give it any thrust in excess of the speed of the water. It will be pushed down stream at some speed less than the river speed, unwinding as it goes, paddles contributing nothing to forward speed.

 

[vanesch]

I have sketched this out for myself for the case of a spool which is larger in diameter than the paddle wheel. (In this case the rope must be all underwater.) If we consider the paddles alone, the force of the water on the paddles still acts to rotate the device such that it will wind itself upstream.

You mustn't consider a torque wrt to the center of the wheel, but between the two forces. (well, you can consider the torque wrt the center of the wheel, this will add and then subtract an extra contribution).

The force of the river on the thing as a whole, however, is surely enough to counteract this and will push it downstream, unwinding as it goes.

Well, we make abstraction of "the rest" and consider that only the paddles are in contact with the water, can we ?

 

[zoobyshoe]

Well, we make abstraction of "the rest" and consider that only the paddles are in contact with the water, can we ?

Consider then:
A table whose surface can slide. The x-axis of a milling machine is a good example. We put the wheel assembly on the table with the large diameter spool sticking down into one of the bolt slots. We then affix the "cable" to the wall. The smaller diameter wheels rest on the table surface on either side of the slot. Then we crank the table. Contact between the "water" and the "paddle wheels" will be the only "effective point of attachment."

Sound right?

 

[rcgldr]

Assume the paddlewheel diameter is smaller than the spool diameter and the wire unwinds from under the spool (0 < advance ratio < 1).

Assume the device is not moving and take the simplified case where the initial downstream force on the paddles is equal to the downstream force on the wire. The spool has a larger diameter, resulting in more torque, so the net torque rotates the paddlewheel in the downstream direction, and the paddles themselves upstream. At this point, the downstream force on the paddles is greater than the downstream force on the wire (during acceleration), but the ratio of the the spool diameter to paddle wheel diameter is greater still, so the net torque still results in a downstream rotation of the paddle wheel. As long as the paddlewheel diameter is sufficiently smaller than the spool diameter (advance ratio << 1), the device should work. Slippage of the paddles through the water could be an issue, but it should be less than slippage of a prop through air, so I don't see an issue here.

To compare this with the DDWFTTW cart, the wires are the equivalent of the treadmill or ground, the paddle wheels are the equivalent of the prop, and the paddlewheels interact with relatively dense water, while most of the vehicle travels to relatively thin air. It should be more efficient depending on paddlewheel versus water efficiency.

As previously mentioned, the advance ratio (paddle wheel diameter / spool diameter) puts an upper limit on the theoretical maximum speed, with stationary wires and moving water:

maximum speed = water speed / (1 - advance ratio).

At this maximum speed, the paddle speed equals the downstream speed, so no thrust is generated by the paddle wheels. The actual limit will be less. For example, assume advance ratio is 1/3, then max speed = water speed / (1 - 1/3) = 1.5 x water speed. With respect to the device, at 1.5 times the water speed, the wires move 1.5 times the water speed upstream, the relative water speed is an upstream flow at .5 times the water speed, and the upstream paddle speed = 1/3 of the wire speed = .5 times the water speed, the same speed as the apparent upstream speed at the device so no thrust is generated.

 

[swerdna]

In fact, it is easy to see what way the thing will turn: you take the effective point of attachment of the force with the water, and the effective point of attachment of the force on the rope (which is easy: it is along the rope itself). This couple of (balanced) forces will make up a torque, and the direction of the torque will give you the direction in which the system will rotate.

So if the effective interaction point of the water with the wheel is BELOW the rope, then obviously, the torque will work in the sense of the hands of the clock and the rope will wind up, while if the interaction point is ABOVE the rope, it will unwind.

I think you’re spot on. Whether the paddlewheel rolls up (Fig1) or down (Fig3) the cable or neither (Fig2) depends if the force of the water is above or bellow the point where the cable leaves the spool. So will this design ever be able to travel DDSFTTS? (S = Stream)

http://www.accommodationz.co.nz/images/ratios.bmp

 

[rcgldr]

paddlewheel rolls down (Fig3) the cable. So will this design ever be able to travel DDSFTTS?

Yes. If the cable unwinds from the bottom of the spool, below the paddles, the device is advancing against the water (0 < advance ratio < 1). If the spool were reversed so the cable unwound from the top of the spool it would move downstream, but slower than the water, regardless of the relative diameters (advance ratio < 0).

 

[zoobyshoe]

My curiosity got the better of me and I made a model using a spool of thread with a dowel pushed through the hole. For the water I cut a slot in a cardboard box. The spool goes in the slot and the dowel's ends ride on the box. With the thread tied down, I pushed on the box. This gives the spool a thrust according to the ""advance ratio"", but too much. It gets so much momentum that it rolls faster than the water can keep up, unrolling more thread than it should so that the thread tension is lost. It comes to rest and sits there at water speed doing nothing till it's carried far enough downstream to restore the tension. Then it gets another impulse. Then it loses tension. And so on. It sort of works. In spurts. It's much like my prediction about the cart, which was that it might be able to temporarily go faster than the wind on momentum, but then it would slow back down to wind speed.

 

[rcgldr]

It sort of works. In spurts.

In the case of the spool on the box, there's nothing significant to dampen out the motion caused by jerks on the thread. For the DDWFTTW carts, the momentum of the components, and the drag related factors provide enough damping that the cart doesn't oscillate noticably on a treadmill. In a real outdoor test with a wind that varied, the carts momentum would tend to smooth the motion due to momenum, alternating between powered mode and coast mode.

The water based device should have plenty of damping from the water. It apparently wasn't an issue with the Brennan torpedo which relied on wire tenstion to both propel and steer it.