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Down wind faster than the wind

GregLondon said:
Can't you just change diameters of the gears so that you get the correct ratio?
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Sure. But I haven't been able to find any gears with negative diameters.


On another note, you asked about animation software. I started playing with Grapher that just happens to come free with Mac OS. If I can describe the cart mathematically, I can draw it, animate it and compute anything I want. But the documentation appears to be only in the form of examples so it takes some playing with to learn. The predecessor of this program was Graphing Calculator which has an interesting story.
 
Dan O. said:
Sure. But I haven't been able to find any gears with negative diameters.
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Simple. Make your counterweighted gear an annular gear on the rim of the wheel instead of at the hub.

ETA: Hmm. With the vane gears 2/3 the radius of the inner edge of the annular gear, the vanes make half a turn backward for each turn of the wheel. Which should be as good as half a turn forward.

However, it means the vane gears overlap and would get in the way of the struts connecting the vanes to the vane gears (and e.g. offsetting the struts from the vane gear centers doesn't appear to help).

Mender's more complete solution, planetary gears, is better and does not add to the moving part count, since one part (which can be either the hub or the annulus depending on what direction you want the vanes to turn in) is fixed to the main wheel.

Respectfully,
Myriad
 
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Dan O. said:
I just realized something. The fixed center gear will rotate the vanes 1.5 times per main wheel rotation. They should only rotate 0.5 times.
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Well I'll be darned! That's got me very intruiged. I even started to argue until I rolled a penny round another penny - I had thought that was 1:1, and of course it is if they're both rotating, but one going round the other doubles it. I haven't tried the double-size -> 1.5, but assume you're right.

I also see that as the ratio of these gears approaches infinity (the centre becoming a point that the other moves round), the vanes go to 1 x the wheel rotation! Obvious really now you point it out.
 
Who was it that said genius is the recognition of the obvious? I've been hoping this thread would become active again. If Dan is able to use Grapher to create an animated cart it would be of immense help to novices like myself. Good luck with that Dan O.
 
One of my designs for the non-prop cart had two moving parts if you didn't include the bearings. I tested part of the propulsion system with decent results and I'm quite sure it would work but I'm moving on to what I hope will be a better design. More parts but sometimes that's what it takes.
 
I got the equations mostly worked out...


T is the animation time, N is the number of vanes, K is orbit of the vanes and H is the width of the vanes. Everything else is just math so should be self explanatory.

ETA: I do have the animation produced by the above set of equations. Now I just need to figure out how to post it.
 
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Myriad said:
Simple. Make your counterweighted gear an annular gear on the rim of the wheel instead of at the hub.

ETA: Hmm. With the vane gears 2/3 the radius of the inner edge of the annular gear, the vanes make half a turn backward for each turn of the wheel. Which should be as good as half a turn forward.

However, it means the vane gears overlap and would get in the way of the struts connecting the vanes to the vane gears (and e.g. offsetting the struts from the vane gear centers doesn't appear to help).

Mender's more complete solution, planetary gears, is better and does not add to the moving part count, since one part (which can be either the hub or the annulus depending on what direction you want the vanes to turn in) is fixed to the main wheel.

Respectfully,
Myriad
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I can't understand how a planetary gear set will do it, unless it's something more complicated like a set for each vane. The planetary gear's output and input usually share the same axis. The planet gears are the ones we want to take output from, but then they seem to give no different ratios from the ones provided by a hub or annular gear, as far as I can tell, but I'm no expert.

I guess it could be done by rotating one (say the annulus) with the wheel, but also gearing the sun at a ratio from that via another train. This differential might then cause the planets to rotate at the correct speed.

There are two considerations here - the speed at which the vanes turn, which must be coordinated precisely (1/2) with the rotation of their axes around the wheel axle, and that rotation speed of the vanes (and planet carrier, if that's how it's done) round the wheel, which does not have to be the same as the wheel's rotation.

I think!:boggled:
 
Wouldn't it be easiest to post it somewhere that accommodates large gifs and then provide a link? I can't imagine shrinking the circus down to 48k, which is the limit for here. Sorry if this is a dumb suggestion, but I'd really like to see your annimation.
 
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So, you want the vanes to do half a revolution for every revolution the center gear does, don't you?

Every half revolution of the vane gear, the vane will be vertical and the wind can push on it.

Every full revolution of the center gear (weighted gear, what would you call that thing) the vane gear is at the bottom of the wheel. (or if you want, every full revolution of the ground wheel as the vanes go around the center gear)


So, if the circumference of the center gear is twice as big as the circumference of the vane gears, you should get what you want. I think.
 
GregLondon said:
So, if the circumference of the center gear is twice as big as the circumference of the vane gears, you should get what you want. I think.
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If I remember the diagram properly this is wrong. First of all, you'd want the center gear to be half the diameter - not twice the diameter. But even then you'd still be wrong, because even if the center gear were zero-diameter, the vanes would make a full revolution with one revolution of the wheel.

But admittedly, I may be thinking of a different diagram than you're refering to.
 
Greg, it might be easier to envision a wheel where the vanes stay vertical during the rotation of the wheel. To accomplish that, some method of countering the rotation is needed for the vanes to retain the vertical orientation. That would require a mechanism that turns the vane axles backward at the same rate as the wheel turns forward. Gearing that down to .5 would give you the vane movement that you're after.

That gearing can be achieved in a number of ways. I mentioned a planetary gear set because I'm quite familiar with its versatility.
 
Dan O. said:
I suppose you are one of those few people that don't instantly recognize e-2πit as the equation for a unit circle in the complex plane when evaluated from 0..1.
Click to expand...

I must confess that I read books that have pictures in them ...
 
Yes, that's what Dan realised a few posts ago. I've changed my diagram, being the only thing I can edit now, just to say it doesn't work, further up the page.

When you rotate same-size gears, one round the other stationary one, you have to add 1 to the ratio - in fact it looks to me like you add 1 whatever the value. Hence what most of us including Greg thought was 0.5:1 turns out to be 1.5:1.

I'd love to see how we could do a similar thing. The simple annular gear makes the centre gear too large, and I'm not convinced a planetary gear set does it either.
 
John Freestone said:
I'd love to see how we could do a similar thing. The simple annular gear makes the centre gear too large, and I'm not convinced a planetary gear set does it either.
Click to expand...

I would think you could simply add a pinion of any size between the vanes and the center gear. This would reverse the rotation of the vanes. Then I think you'd want the vanes to be on a gear of twice the diameter of the center gear. I suspect this is what mender is describing when he mentions a planetary gear setup.
 
John, it's easier to understand if you have a planetary gear set in your hands to play with. The essence is that the planet carrier is attached to the wheel, so it rotates at the same rate as the wheel when the wheel is moving along the ground. The axles of the planet gears are attached to the vanes, so the vanes move around with the planet carrier. The sun gear and the outer gear are geared to move in opposite directions, at a ratio that turns the planet gears backward half a turn every time the planet carrier moves forward one turn.

Changing the ratio between the sun and outer will allow quite a range of vane motion wrt the wheel motion.

This is one way to do it, but there are definitely others, one of which spork mentioned.

Dan O. was right about needing a gear with a "negative diameter", but I find it easier to call that "reverse rotation". :D
 
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