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Down wind faster than the wind

Thabiguy said:
Now, if there is wind on every red herring that is not a fan, but no wind on iceboats, which of the following is true, which is false, and which cannot be determined?

a) Some treadmills are not iceboats.
b) Some fans are red herrings.
c) All iceboats are fans.
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The OP says that a cart can go downwind faster that the wind.

The cart is not an iceboat nor is it on a treadmill.
 
mender said:
So what would the 1.2 to 1.4 equal in proper-advance-ratio-speak?
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.71 - .83 (it's just 1/1.4 and 1/1.2)


tsig said:
The OP says that a cart can go downwind faster that the wind.

The cart is not an iceboat nor is it on a treadmill.
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I have two hermit crabs. They are named Bob and Bob.

(I assumed this is the part where we just post random facts)
 
spork said:
This part is simply the prop pitch. You can imagine the prop moving through jello without anything holding it back. The distance it would advance in one rotation would be the prop's pitch (which in my description is the numerator of the advance ratio). If you want to think of it analytically... the prop's pitch is given by:

pitch/circumference = tan(tip_angle)

pitch = circumference * tan(tip_angle)

pitch = 2*PI*prop_radius * tan(tip_angle)

Where tip_angle is the angle the tip of the blade makes relative to the "disk" of the blade.

Effectively, the pitch of a propeller is the same thing as the thread-pitch of a screw.

So, in my definition you'd define advance_ratio as the prop-pitch divided by the distance the wheels would roll given a single prop rotation. This of course is determined by the gearing and wheel diameter.

wheel_advance = gearing * 2*PI*wheel_radius

So...
advance_ratio = prop_pitch / wheel_advance

advance_ratio = 2*PI*prop_radius * tan(tip_angle) / (gearing * 2*PI*wheel_radius)


Finally:
advance_ratio = prop_radius * tan(tip_angle) / (gearing * wheel_radius)

Where gearing is defined to be greater than 1.0 if the axle spins faster than the prop-shaft.



Yeah - that's just because we invented this term to define a key parameter of the cart, and didn't actually agree on whether prop_pitch should be the numerator or denominator. I'll see JB at the office tomorrow and administer the appropriate beating.
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Does the jello power the cart?
The idea of ground power that supports the above notion, is pre-Newtonian. All of the energy comes from the wind. That is what Newton says, and will be so for all velocities that the cart will encounter. The argument for "equivalent frames" is a sophism.

Sophism:
"Sophism can mean two very different things: In the modern definition, a sophism is a confusing or illogical argument used for deceiving someone. In Ancient Greece, the sophists were a group of teachers of philosophy and rhetoric."

Both abundant in this thread.

The gearing is not a source of power or energy, but a governing mechanism. In fact, it is simple positive-feedback controller. If the ratio is greater than one, an incremental increase in one, will cause a larger incremental increase of N:1 in the other.
So, prop drives cart (increased velocity) drives wheels (further increase) and so forth. Is is the rather like the 'opposite' of the governors found on early stationary steam engines.

If there is sufficient energy available, this simple positive-feedback will drive the propeller at an ever increasing rate, and that may increase the rate of acceleration, but the terminal velocity will be limited by the available power, and the forces of friction and drag that impede it, in the usual way.

Also, this gearing allows the cart to be driven by kinetic energy from the propeller's rotating mass. The energy stored in this mass can drive the cart, even if the blades of the propeller are incapable of providing any thrust. This is useful. When the opportunity arises, the gearing comes into play, driving the propeller ever faster by the wind but augmented by the stored energy, meaning that a higher average velocity may be achieved.

Straight forward engineering can be used to optimize this system, so claims for performance over and above this would require very careful measurement, and not the finger in the air measurements of the street.

The treadmill does nothing to support the cart in this respect, so there is no need to think too much about that gimmick.
 
spork said:
.71 - .83 (it's just 1/1.4 and 1/1.2)




I have two hermit crabs. They are named Bob and Bob.

(I assumed this is the part where we just post random facts)
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You are the one who brought up iceboats.
 
Christian Klippel said:
Could you please answer my question, tsig? have you read http://home.san.rr.com/tadhurst/DWFTTW.htm?
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The calculations do not include any real or plausible figures for the system efficiency, or how that may vary with prevailing conditions. So?

Propellers have v/f curves. They are not simply a linear function of say, V, but complex profiles. The tangent of that profile can be regarded as the V/F or "gearing ratio" for any given rpm. However, the total power available, varies and is always less than 100%. If in the calculations the total energy budget is ignored or fitted, then there will be no surprise that a positive result is achieved. Also, sailing boats are not wind carts!!

If external gearing is added to effectively modify the propeller's 'normal' profile, you can perhaps mimic the behavior of a variable pitch propeller.
So, as I have said, the gearing tends to drive the system to maximum V for any level of available power. That may result in an overall gain in efficient extraction, but nothing more than could not be achieved by other means. So what?

ETA:
It is common to see this in power conversion. The author lays claim to a highly efficient converter, while avoiding the now discredited, and so unpopular, idea of over-energy. There may be 20 pages of detailed calculation, yet the authors seem to ignore the fundamental fact that( P = I^2*R) always applies no matter how fancy the "math". It is then a matter of looking for where the author has included some resistance to stop his equations 'exploding' to infinite current, but not included them elsewhere. The values are arbitrarily assigned, ( usually justified by some simple "assumption") and then inconsistently applied. When these sophims are removed, you get back to a standard device, as in the cart.
 
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Thanks for the clarification, spork, that's the trend that I was thinking would be the best as well. After my last mental hiccup when I forgot that the propeller was changing the momentum of the air around it, NOT "pushing" back against the wind, I wanted to make sure I was back on track.

The .7 to .8 advance ratio that you have tested and confirmed as the best performing would be close to the limit of the advance ratio for downwind. Makes sense, extracts the most energy from the ground - air interface.
 
mender said:
Thanks for the clarification, spork, that's the trend that I was thinking would be the best as well. After my last mental hiccup when I forgot that the propeller was changing the momentum of the air around it, NOT "pushing" back against the wind, I wanted to make sure I was back on track.

The .7 to .8 advance ratio that you have tested and confirmed as the best performing would be close to the limit of the advance ratio for downwind. Makes sense, extracts the most energy from the ground - air interface.
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So how is that different from building an efficient machine, Mender?
Could it be even better done?
Is a new explanation of "relative frames" at all necessary?
How does the treadmill support this?

You mentioned Occam's Razor to me in an earlier post. Yes, indeed.
 
Clive said:
How about a "Spork cart" that can be shown to self-start, and can also be shown accelerate from wind speed. Can we be 100% sure that this is enough to guarantee it can do the whole thing?
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Yes. If the cart gets off to a correct start, with wheels rolling along the ground and not skidding, it will continue to accelerate past the speed of the wind until it reaches a point where the forces are in equilibrium. At this point, given a steady wind speed, the cart will maintain a steady speed above that speed.

Spork already explained the theoretical speed of the propeller through the air. Think of a propeller as a screw, worming its way though the air like a screw through wood. The pitch of the screw, or propeller, is the distance it moves forward in one rotation. The pitch of the propeller, together with its speed of rotation, will give its theoretical speed through the air.

The prop is geared to the wheels, so it is forced to turn as the cart advances. If the prop is turning at a theoretical speed through the air of x mph, and the actual speed of the cart is less than x mph, the prop generates a force that accelerates the cart forwards.

The prop on Spork's cart is geared to the wheels so that its theoretical speed through the air is about half that of the cart along the ground. If you do some calculations, you'll see that just after the cart has started, the theoretical speed of the prop through the air will be greater than the actual speed of the cart though the air (at the start the actual speed of the prop through the air is negative: putting the prop in a downwind is equivalent to dragging it back through still air). The cart goes on accelerating until theoretical speed through the air is equal to actual speed through the air, at which point the machine is in equilibrium.
 
spork said:
Finally:
advance_ratio = prop_radius * tan(tip_angle) / (gearing * wheel_radius)

Where gearing is defined to be greater than 1.0 if the axle spins faster than the prop-shaft.
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Thanks - that's very clear now and also lines up pretty closely with what I was trying to say earlier (although almost incomprehensibly I fear).

spork said:
I'll see JB at the office tomorrow and administer the appropriate beating.
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My sympathies go out to him... and perhaps an apology is in order also!

spork said:
There are a number of ways to approach the math without getting overly complex. I think the most obvious approaches involve energy balance, or force-vector diagram. I find the force vector diagram more compelling, but both certainly have their place. In the case of the force vector diagram it's far easier if we unwind the path of the prop tips and look at this path in two dimensions. From there we can easily show how it winds up to produce the DDWFTTW cart.
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Thanks for the offer to go further into the mathematics. I am interested, but it seems that there are already a number of quite detailed analyses floating around, so I'll try to get my head around those first and then perhaps ask for more help if I need it. The page linked to in #2166 looks like a reasonably detailed analysis so I think I'll start there.

The difficulty is trying to find the useful information in amongst everything else in this and the other threads I've looked at. Isn't there a master index out there somewhere by now? :)
 
spork:
I'll see JB at the office tomorrow and administer the appropriate beating.
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Clive:
My sympathies go out to him... and perhaps an apology is in order also!
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Not so fast Clive -- spork is the one using the term wrong. You know how we know this? --- because I use it the other (and proper) way. :-)

JB
 
tsig, enough playing around. You still haven't told us your definition of "wind", so I'll give you one here:

Wind is relative motion between air and ground, in a direction parallel to the ground. It doesn't matter if we consider the ground to be staying still and the air to be moving, or the air to be staying still and the ground to be moving: in both cases there's a wind.

If you agree, please say so. If you don't, please say why. If you just want to answer with another nonsensical one-liner, you might consider the fact that it only makes you look stupid.
 
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