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

[rcgldr]

... various long descriptions of the physics ...

... keeps stating that cart speed is not greater than tread speed ...

Cart speed versus tread speed seems to be schroder's issue, until that gets resolved there's no point in discussing the physics.

Once again the claim for a DDWFTTW cart is cart speed greater than wind speed not cart speed greater than -1 x ground speed. There are no claims about the magnitude of cart speed versus the magnitude of ground speed. The claim is:

|v_cart - v_ground| > |v_wind - v_ground|

But you are right in that the cart must be doing some work at the drive wheels to generate the torque. But this cannot be the amount of work to cancel out the motion of the tread altogether.

The relative motion of the tread which is backwards, is increased as the carts forward speed increases. The only time cart speed == tread speed is at the initial start up. The tailwind then propels the cart forwards against the tread, and once there is motion, the cart speed is never equal to the tread speed. Put some signs on the numbers and this will make sense.

Using your floor based reference on a very long treadmill:

Startup states
treadmill speed -10 mph
cart speed -10 mph
wind speed 0 mph
cart speed - tread speed = 0 mph
cart speed - wind speed = -10 mph

cart at -5 mph
treadmill speed -10 mph
cart speed -5 mph
wind speed 0 mph
cart speed - tread speed = +5 mph
cart speed - wind speed = -5 mph

cart at 0 mph
treadmill speed -10 mph
cart speed 0 mph
wind speed 0 mph
cart speed - tread speed = +10 mph
cart speed - wind speed = 0 mph

cart at +2 mph
treadmill speed -10 mph
cart speed +2 mph
wind speed 0 mph
cart speed - tread speed = +12 mph
cart speed - wind speed = +2 mph (faster than the wind)

The tread as a power input. The backwards moving tread causes the driving wheels to rotate forwards. The forwards rotation of the wheels is used to turn the propeller which resists this rotation via an opposing torque. This opposing torque is transferred back to the wheels, and results in a forwards force against the tread. In compliance with Netwond 3rd law, the tread exerts an equal and opposing backwards force against the wheels. The power input from the tread equals the backward force at the tread times the relative speed of the tread (tread speed - cart speed). At start up, cart speed == tread speed and there is no power input from the tread, just power output at the prop acting as a bluff body.

The prop as power output. The torque at the prop is converted to a thrust and speed depending on the characteristics of the prop. For the DDWFTTW carts, the prop is configured to generate a high amount of thrust at a low amount of speed.

Comparason of forces: The thrust from the prop is greater than the opposing force from the tread unless the the relative headwind speed of the cart is too close to the thrust speed of the prop for the prop to be able to generate sufficient thrust. As long as the relative headwind is sufficiently below the prop thrust speed, the thrust from the prop is greater than the opposing force from the tread (or ground). The claim for the DDWFTTW carts is that this can occur even with some apparent headwind (cart speed greater than wind speed). In the case of a relative tailwind (cart speed < wind speed), the force at the prop is a combination of bluff body drag + prop thrust effects.

Comparson of power: The power output from the prop is less than the power input from the treads because of the much lower speed (thrust speed - cart speed) of prop's thrust versus the speed (tread speed - cart speed) at which the treadmill applies a force to the driving wheels. Even though the prop produces more force, it produce less power because of the lower speed.

 

[ThinAirDesign]

I have to disagree with you here JB. You already showed clearly for those with eyes to see that DDWFTTW works with your cart. The treadmill tests show that at speeds just below or at the wind the cart can accelerate to speeds faster than the wind. The starting from a stop test held outside showed that in a "real" wind the cart would start off from a speed of zero and at least approach the speed of the wind. It also showed it you watched it closely two different ways that the cart could start. With a gentler wind it ran just like it did on a treadmill. When the wind gusted it acted as a turbine at first and then once it got to a certain speed it acted like a proper prop cart (sorry couldn't help myself). People who would have a problem with the cart on a treadmill (like scrorder) would have a problem with any outdoor test, even if you had an anemometer that showed wind speed and a radar that showed cart speed.

Thanks Sub. I certainly agree that for those who already 'get it', those self start videos are an interesting demonstration. As you point out, they DO get into some of the subtleties of the device (like which way the prop spins and when) that tend to confuse a lot of people.

I got very, very tired of explaining the physics of those those starts on a second by second basis over and freakin' over. LOL This silly little thing can't just be "the wind blows and away it goes" ... no, it's "first it tries to do this and then it gets overpowered and tries to do that and then after a few seconds it goes into that mode and and and.

JB

 

[vanesch]

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.

Hahaha! We cut it in half ! The "correct" reference frame in which to compare the cart velocity to windspeed is in the frame midway between cart and treadmill !

I would actually prefer 1/3 versus 2/3, what do you think ?

In fact, no, you were right all along. We have to compare the velocity of the cart in the ground frame of course. The treadmill has nothing to do with it.
Wait, what was the velocity of the cart in the ground frame ? 2 m/s.
What was the velocity of the "wind" in the ground frame ? 0 m/s

Ha, my cart is going faster than the wind here: cart: 2 m/s, wind 0 m/s.

When we were looking at Hor/Ver comparisons, the answer was staring us in the face as it is an RMS solution. 10 m/sec x .707 = 7 m/sec
It all fits perfectly. The cart is running at 70% efficiency and will do 7 m/sec down wind in a 10 m/sec wind.

I will use your logic: you are forgetting that the wind is not doing 10 m/s, but only 5 m/s because we have to measure it half way (the propeller is only acting for half of the force in this setup, the other half comes from the treadmill), so here we have "true" wind velocity of 5 m/s, and an RMS corrected "true" cart velocity of 7 m/s, so it goes 2 m/s faster than the wind

Listen, if the trick is to just spout random mathematical operations until some numbers come up with a random inequality which suits you, I can play that game too !

You can do your more conventional analysis with wattage and velocities and I am sure you will find this is correct.
I am happy with this, maybe you will not be because it is definitely not DWWFTTW but it is the correct solution.

Ok, if you are happy, so am I. We have a many worlds solution to the problem here: we have generated enough meaningless quantities here so that you can pick two numbers from the lot and compare them, and find whatever you want to find, and so can I. This is post-modern mechanics! After all, numbers are relative. They are there to bring us happiness.

Seriously, you seem to suffer from a mental block on this issue. You seem to be able to do some elementary mechanics with cars and trains and so, but you have no trouble spouting any kind of incoherent nonsense reasoning when it touches upon DWFTTW. I give up. (vanesch hands in his black belt in Art of Zen - he failed the ultimate test of "bringing to reason the unreasonable")

EDIT: that said, I would like to ask you a favor. Next time I'm getting a speeding ticket, would you like to argue my case ? I'm sure you will be able to find a way to tell the judge I was not speeding. They simply measured my velocity in the wrong frame... as my wheels push on the road as much as the road is pushing on me, the correct speed of my car is half of what it is in the ground frame.
I never speed twice the speedlimit.

 

[vanesch]

Cart speed versus tread speed seems to be schroder's issue, until that gets resolved there's no point in discussing the physics.

I'm starting to realize that the issue is that for schroder, the starting axiom is that "DWFTTW is impossible" and from this, all else follows. "(a + b n)/n = x, donc Dieu existe".

( http://everything2.com/index.pl?node_id=105498 )

 

[vanesch]

Agreed. We do feel that we have a plan that will cover many of the concerns related to an outdoor test. It will take time, a fair amount of money and effort and a bit of luck related to timing the weather.

...

.

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

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.

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.

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

 

[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.