Like a cotton reel that’s spinning
Against all logic spun.
We read to see who’s winning
An argument un – won.
By George, we think he’s got it,
But Louise must disagree:
A polite conjecture,
Against Terry’s decree.
Counter or anti, which way?
All must have their say.
And give personally
their own yeah or nay.
Like the circles that you find
In the windmills of your minds.

Then you’re welcome to explain how the friction of a cart slowing down can speed it up. So far we’ve covered ‘it just works, oh em gee’ and ‘it slows down the Earth,’ of which the former is useless and the latter is silly.

From my perspective, translational kinetic energy (cart motion) is transferred into rotational energy (shaft) and back to even more translational kinetic energy via the propeller. Despite those of you waving your arms and going “TA-DA!” like lovely assistants, where’s that energy coming from?

Propeller blades are effectively tacking as they spin. Thank you for pointing this out in #98, Twoshort.

The DWFTTW problem is in exactly the same class as tacking upwind, which is a more well-understood phenomenon. In either case, you are extracting energy to move against the motion of the air relative to the boat.

Of course, this raises another question:

UWFTTW?

Seriously though, please don’t post on that one.

Once a vehicle going downwind reaches the wind velocity, it “sees” *no* apparent wind. If a vehicle goes down wind faster than the wind velocity, it “sees” an apparent headwind.

The bottom line is *you cannot capture wind energy if your velocity is the same or greater than the wind*.

If you’re sitting in the boat, it seems like the faster you go the stronger the wind gets, and the more it’s direction shifts around toward the front of the boat. Which, in the reference frame of the boat, is actually true. What angle you set the sail at and what course you steer to get up or down wind fastest is actually a very complex, continuously changing equation, which is why some sailors are better than others.

You want to know how to make a wind powered vehicle that goes directly downwind faster than the wind? I explained one way that’s pretty darn hard to argue against. I offered links to an article showing that ice boats can maintain downwind VMG of 3X to 4X windspeed. This is supported by vector analysis, and by GPS data. It’s also proven by my own simple vector analysis here:

http://www.putfile.com/pic/8419299

I can also point you to ice-boating forums where this question has been put to them directly.

Moving on to directly downwind… just put two of these ice boats side by side and keep them on alternate tacks. Put a telescoping pole between them and sit on the middle of it. Done.

So instead of ignoring the answer to your request – how about responding that you either understand now, or telling us exactly where you see the problem.

Once you get this, it’s easy enough to explain exactly how it relates to the prop cart. But no point going into that when I’ve already explained this more basic approach twice without any traction.

Yeah it can get a little tricky. See if this helps:

Work done (energy) equals the force times the distance MOVED IN THE DIRECTION OF THE FORCE, or the distance moved times the component of the force in that distance.

In other words, if you have a force and it caused some movement, then the work done is “force times distance” along the SAME direction. If the force and the distance are not in the same direction, then one of the two has to be decomposed into the component that is parallel to the other (i.e. the whole thing has to be multiplied times the cosine of the angle between them, which is 1 if the angle is zero).

So if prop thrust is “forwards” (down-wind), then we care about the speed of the air in the horizontal direction (up-wind/down-wind). Either the air before the prop accelerates it, or the air after the prop accelerates it, either one.

What I call “wheel resistance” is the traction between the wheel and the ground, so yes, the static friction between the wheels and the ground. The ground pulls back (up-wind) on the wheels, and the cart pulls forward (down-wind) on the ground via the wheels. This is because the wheels power the prop (and some gears and axles and so on) so they see some resistance; that’s what powers the machinery on the cart.

Yes, if the axles and gears had more kinetic friction, and if the prop saw more drag as it spun, then you’d need more power into the wheels to make the machinery spin around, and the wheels would then experience a greater force pulling the cart back. (I.e. when you hit the brakes, things slow down).

I think there are probably way more than just two groups.

Unless, of course, this whole thing is still not being explained clearly.

Yeah, that’d be my take on the issue. I’m currently shuffling a bunch of stuff around on my document to try and explain it with as little jumping around as possible. I’ll put out another rev soon.

rat@212: Point being, what explanation fails to work for you is not therefor bad, and what works for you is not therefor good for others.

The point being that I was kidding. Once you understand the prop-cart, the shortest explanation is “ta-da!”, cause you hear the explanation and you understand the prop cart after you hear it.

course, you understood it before you heard the explanation too, but that’s what’s so funny about it.

You’re math is off just a bit. You’ll get 1.25X wind speed. But I don’t think there’s any theoretical reason it won’t work.

The energy comes from the motion of the air relative to the ground. You can take energy out of that differential and use it to move relative to the ground, even upwind. You can also take energy out of that and use it to move relative to the air, even downwind.

Unfortunately, you are mistaken. Moreover, your counterargument has been made and addressed many times.

The bottom line is *one should understand what they are talking about before attempting to instruct others*.

the energy is coming from the speed differential of the two conveyer belts: the wind and the earth, moving at different speeds.

you cannot doubt our little ruler cart above, right? it makes sense that you can set gears that would harness the differential of the upper belt (ruler) and lower belt (table top). and if there was no relative motion, the cart would not move. it only moves when one of the belt moves. yet there is no functional difference between moving the upper belt (ruler, actual conveyer belt, or wind) and moving the lower belt (table, treadmill, or earth). ANY differential works.

the key is this: a propeller is a special gear for connecting to the wind. here’s how i think it works:

the propeller has props. these props are set at an angle. let’s say you spin that propeller at 5 mph at the center of the props. because the props are set an an angle (say 45°), this means the *blades of the prop are effectively moving backwards 2.5mph from the cart!*

from the point of view of a vector of wind approaching from the rear of the cart, they are encountering an object that is moving slower than the cart itself. so, the wind pushes the slow object, which in turns pushes the cart, which spin the wheels, which then turn the propeller even faster.

in this way, a propeller really is a kind of gear for engaging the wind.

Still, I’ll concede that it is possible, at least when using a tacking strategy.

It’s probably way more than just two models.

Unless, of course, this whole thing is still not being explained clearly. But that could NEVER happen.

Yeah, I’m in that camp. I’m in the process of shuffling my document around quite a bit, trying to put things in an order that requires the least amount of intuitive jumping. Oh, and I put in a table of contents at teh beginning. I hope to have a new rev soon.

rat@212: Point being, what explanation fails to work for you is not therefor bad, and what works for you is not therefor good for others.

Point being, I was kidding.

The shortest explanation for someone who already understands the prop-cart is “ta-da!”. because they hear the explanation and they understand the cart after hearing it.

The fact that they already understood it before hearing the explanation just makes me chuckle.

I could go around the web and find two dozen different generic sites and say “This explains it perfectly”. ANd if you understand how the cart works, sure, it’ll explain it.

And in working on my document that tries to explain the prop-cart, I ran into that website fo simple machines, realized everything in the cart is explained on that generic page, and I had to chuckle.

The prop has “blades”. These blades are really just airfoils that create lift (in this case thrust) exactly as a wing does. The blades have twist to them so that any point on the blade is trying to move forward a specified distance over one full rotation. This is the “pitch” of the prop.

To say the blades present a “backward moving surface” to the air has a definite intuitive attraction, but tends to lead to an incorrect explanation of lift (namely that air molecules bounce off the lower surface of the wing or back surface of the prop blades). Nevertheless, this backward moving surface theory does correctly describe the theoretical max speed of the cart in terms that are almost identical to the ruler cart of the above video.

“Except there is no gound/wind interface that can be exploited. There is only the interplay between wind/device/ground. Throwing the device in there creates drag against the ground and the best you can do is simply get very close to the wind speed.”

Of course there is such an interface to exploit. Or perhaps our cart doesn’t understand physics, because it DOES go faster than the wind – directly downwind.

As a good friend said to me yesterday – “sure it works in practice – but can you prove it in theory?”

#167: “Spork, have you thought about a long plexiglass wind tunnel?”

I’d LOVE to do this in a long plexiglass wind tunnel. If someone has one I’ll send them the cart.

#168: “I read this entire thread to see if there was a single person who, after claiming it was impossible (precisely my initial intuition) then followed up to say “Sorry, I was wrong.”

It’s VERY rare. Typically people either dissappear, or they explain that they actually knew it all along, or when they finally agree, they explain that the whole problem is how poorly we explained it, but now that they understand, they’ll explain it properly (followed by a horribly faulty explanation). That’s the typical script.

On the other hand we have had two world-class apologies from people that started out insulting us and later came around. The most amazing part – they were both Mark C. (two different guys).

“Anyhow, I just wanted to say wow – I kinda get it now! Thanks for showing how my initial theories were wrong, and filling me in. I really appreciate the patience and detail people, especially Spork and Airshow, have put into explaining this in a whole bunch of different ways.”

Thanks for having an open mind and a great attitude. As you’ve observed, both are relatively rare.

#171 “I called the plane on a treadmill instantly. And this one I see no issue about either… I call it impossible.”

Then you’re batting 500. That would be pretty darn good in the majors.

#174: “MichaelC’s videos are meant to answer but one of many mistaken objections and does so with elegance, wit and charm. A device of transparent simplicity is shown to outrun its power source.”

Very well put. I consider Michael’s videos as excellent companions to our own. Ours are not terribly illustrative (and aren’t intended to be). Michaels are.

#175: “Ok I’ve sketched a wind based version of the ruler example above, don’t see why it wouldn’t work.”

I buy it. It would be challenging to build a working model, but I don’t think that’s your point.

#176: “My sailor friends are laughing hysterically at the idea that the wind “pushes” a sailboat”

“pushes” is a very broad verb. If you want to get extraordinarily technical, lift is strictly about air pressure pushing on a wing (which is what a sail is).

It definitely took me a while to see it, but it’s exactly the same. The iceboat uses it’s motion over the ground to moves its airfoil (the sail) side ways through the air by moving the whole boat. The cart uses it’s motion over the ground to move its airfoils (the prop blades) sideways through the air by spinning the prop.

I apologize if you’ve taken offense, I was merely responding in kind to ratwerks. I tend to counter snark with snark, as I find it an enjoyable way to argue on the internet and those who dish it out can generally take it.

As far as my disbelief goes, you’ve yet to put forth a convincing argument as to why it works. Specifically, how this is not defying the second law of thermodynamics. I haven’t looked over the boingboing guidelines lately, but I think we still believe in that here. Your cart loses momentum through the wheels, then transfers it to the propeller through which it gains even more? I don’t buy it, Jim.

you cannot doubt our little ruler cart above, right? it makes sense that you can set gears that would harness the differential of the upper belt (ruler) and lower belt (table top).Actually, I can. Please note my comment above, describing the equivalent force differential and how it’d cancel out any gains you get from distance.

The first thing to understand is that “energy” or “work” (sort of interchangable) is a force x a distance. But not any force times any distance. Work done = the force applied times the distance that force moves through – in the same direction of the force. Now you have to bear with me because energy and work are weird (seriously).

I can push on a wall all day and do no work if I don’t manage to move that wall. Remember, it’s the force I apply on the wall times the distance the wall moves in the direction I’m pusing it.

I can also lift a suitcase and carry it for a mile, and the only “work” I’ve done is lifting the suitcase a foot off the ground. That’s because I lift it upward and it moves upward. The suitcase may weigh 300 lbs, but walking for a mile with it moves it horizontally, while the 300 lbs acts vertically. Remember the work is the force times the distance that force acts *in the direction of the force*.

So, getting back to the cart…

The work on done on the wheels is equal to the force the road applies horizontally to the wheels times the distance the wheels roll. The vertical force does no work because the cart doesn’t move vertically. Now this horizontal force on the wheels will be partly due to rolling friction and other real-world losses, but the most “important” component of that force is that which is required to turn our prop shaft.

Now, for the purposes of analysing the cart, we’ll treat the prop as a prop-disk for now. That disk produces an aft thrust, and it moves through a distance relative to the medium in which it’s operating (the air). Because there’s a tailwind, it moves through a smaller distance in its medium than the wheels move on their medium (the road). So… the wheels can “take in” more energy than the prop needs to “output”.

This is good, because in the real world there are frictional losses, aero losses, etc. Also, the prop isn’t really a disk – it’s a prop. So the prop does swing through the air doing work on the air that’s not in the direction of the cart. Some of this work is related to “induced drag” which is effectively the minimum the prop needs to do its job, but there’s also “parasite” drag on the prop. This is just another real-world loss that gets lumped in with the frictional losses.

So… if we simplify a bit – the prop pushes aft on the air and it pushes that air a certain distance (over a given period of time) and the wheels are pushed on by the road, and they are pushed a certain (horizontal) distance in that same period of time. But since the road is going by faster than the wind, there’s extra energy available to take care of all the frictional losses.

Excellent. Then we’re just a few short steps away from the prop cart.

If you consider an ice boat on a downwind tack, you’ll realize it’s actually tracing out a giant circle – because it’ll eventually go around the earth (let’s assume the earth is frozen over with ice).

Now let’s pretend the earth is a cylinder rather than a sphere. If the wind is blowing along the cylinder, our ice boat will just make one long spiralling downwind tack around and around that cylinder. And it will be moving along our cylindrical earth faster than the wind itself is (as evidenced by the downwind performance of ice boats).

Now let’s imagine we have two ice boats – on opposite sides of our cylindrical earth. They both spiral their way downwind – along the cylinder – faster than the wind.

Now it’s just a matter of changing scale. These two ice-boats might as well be prop blades making their way down a big cylinder that isn’t actually the earth. As long as they maintain a 45 degree downwind course at all times, they can outpace the wind along the cylinder.

Finally, we replace the cylinder they ride on with a simple structure that enforces the same kinematic constraint. This structure is a simple cart that gears the prop to the wheels. The gearing is such that the prop tips must move 1 foot around the circle when they push the cart 1 foot forward. So now we have two sails that are constrained to follow spiralling 45 degree downwind paths, just like our ice boats that circled the cylindrical earth.

Looking at it this way, you can see that the prop doesn’t exactly power the wheels any more than the wheels power the prop. The prop does push the cart forward, and the wheels do provide the torque to turn the prop – in exactly the same way that the sail pushes the ice-boat downwind, while the skates make it follow the 45 degree downwind course.

Side-note for technical accuracy: energy and work are bizarre quantities that have more to do with mathematical bookkeeping than they do intrinsic measurable quantities that an object has. As a result we can conclude that the air does all the work, the ground does all the work, or anything in between. This just depends on the frame you choose to do the analysis in – but really doesn’t have much to do with how or why the cart works.

Imagine a tube in which sits a propeller in a housing that completely blocks all air flowing around its sides, and which has wheels which press against the sides of the tube – the one in my head looks like a Tunnel Boring Machine crossed with a turbine. Now push it from behind: The wheels drive the propeller and it sucks air from in front of it and moves that air to behind it.

Now replace the “pushing it” with the wind coming from behind it in the tube.

If you remove the seal from around the outside of the propeller, it doesn’t change the fact that the propeller still sucks air from in front it.

I totally grok this now. Or I could be wrong. No, I think I’m right. The wind effectively pushes the craft as a whole up to wind-speed and the propeller sucks on the air in front of it..

Where I had problems initially was realizing that the wind doesn’t turn the propeller in the direction I expected, so the argument that the spinning propeller will eventually meet the velocity of the wind is moot.The wind moving against the prop tries to push it like a spinwheel, but meets resistance and instead pushes the craft forwards, which turns the wheels and thus the propeller in the _opposite_ direction, which increases the resistance of the craft as a whole, and pushes the wheels faster. Effectively, at top speed, the work done by the wind passing through the area of the cross-section of the prop pushes the vehicle forward relative to the ground, at a ratio dependent on the gearing between the wheels and the prop.

Sorry to all those who find this post redundant.

Show me the cart in a well calibrated wind tunnel.

Sailboats and iceboats can sail across the wind faster than the wind, but neither can sail faster than the wind if going directly downwind.

That’s not the same at all. Iceboats would work best if the surface were totally frictionless and only used as a guide to keep the boat pointed in the same direction. Propeller carts wouldn’t work at all in a frictionless environment – they depend on friction to drive the propeller to overcome the loss due to friction. Aside from both involving touching the ground, they seem pretty different to me.