{"id":42,"date":"2008-11-24T23:31:58","date_gmt":"2008-11-25T07:31:58","guid":{"rendered":"http:\/\/projects.m-qp-m.us\/donkeypuss\/?p=42"},"modified":"2008-11-25T13:29:33","modified_gmt":"2008-11-25T21:29:33","slug":"directly-down-wind-faster-than-the-wind-ddwfttw","status":"publish","type":"post","link":"https:\/\/projects.m-qp-m.us\/donkeypuss\/directly-down-wind-faster-than-the-wind-ddwfttw_2008-11-24","title":{"rendered":"Directly Down Wind Faster Than The Wind (DDWFTTW)"},"content":{"rendered":"

Over a year ago there was an article in Make magazine by Charles Platt<\/a> inspired by a YouTube video of a propeller-driven cart<\/a> that allegedly could go down wind faster than the wind that was pushing it…. Everyone’s first instinct is to think “free energy”, or “perpetual motion machine”.<\/p>\n

I was convinced that this was not the case, and that the cart could work. I had seen a similar cart presented by Paul MacReady, founder of Aerovironment. I remember him saying “this is the kind of innovative thinking we need to take the world forward”. The cart<\/a> he showed was built by Andrew Bauer. There is a paper on it apparently, but I have no been able to find it. As described by MacReady, this cart would be operated in windmill mode, that is, the wind would be used to turn the “impeller” and drive the wheels until sufficient speed was achieved, then the pitch on the propeller suddenly reversed so that it is producing thrust, which would increase the cart’s speed beyond that of the wind speed pushing it.<\/p>\n

The cart in the YouTube video, built by Jack Goodman, was a simpler design. Its drag alone would propel it forward, the wheels driving the propeller. At some point the cart would reach a speed at which the thrust would exceed the friction and it would accelerate to a speed faster than the wind that was pushing it. This is not a perpetual motion machine, since once the cart accelerates past wind speed, there is a relative wind vector acting against it (that is, there is drag going the other way) and it would achieve a terminal velocity which is greater than the wind speed.<\/p>\n

At the time I was very frustrated by Platt’s treatment of the subject. I did not think his primitive construction methods were nearly enough to prove or disprove anything (although since then a very simple design<\/a> has emerged). I wrote as such in the magazine’s forum<\/a> and was challenged by Platt himself to build a cart. With the help of some friends, and guidance from Jack Goodman, I did just that.
\n<\/a><\/p>\n

\"cart-back.jpg\"<\/a>
\nBack of the cart, showing twisted belt. <\/a><\/em><\/p>\n

<\/a><\/em><\/p>\n

\"cart-front.jpg\"
\nFront of the cart. The battery pack and servo are for the steering.<\/a><\/em><\/p>\n

The first test with my version of the cart (shamelessly copied with permission from Jack Goodman) was tested on the treadmill in June of 2008. But the steering was not good enough for it to easily stay on the treadmill for long periods of time. After some modifications and arduous waiting it still wasn’t good enough for several minutes of continuous testing, so we had to retort to some guide plates.<\/p>\n

The treadmill test is scientifically sufficient to prove that, once at wind speed, the cart can exceed it. If a cart is going down a road at x<\/em> miles an hour in x<\/em> mile-per-hour winds, then the wind speed relative to the cart is zero and the ground speed relative to the cart is x<\/em>. Thus the cart on the treadmill at x<\/em> miles per hour is exactly the same situation. If the cart can move up the treadmill, or add tension to an anchor rope, as is the case in our tests, then that means that there is positive net thrust, that is, the thrust exceeds the friction and thus the cart can accelerate. The treadmill cannot simulate what happens after that (the relative wind goes from zero to against the cart) or before (when the wind is going faster than the cart). However, the first point is inconsequential, because we are not looking for the terminal velocity, just knowing that it is greater than wind speed. As for the second point, there are numerous ways to get the cart to wind speed if its own drag is not enough: imagine, for example, a set of hinged sales that open flat like a book when the wind blows from the aft and close into a “double flag” when the wind blows from the front.<\/p>\n

One way to analyze this from an energy point of view goes as follows: imagine the cart has just reached wind speed; let’s call this state 1. At some short time later, the cart is at state 2. Between the two states 1 and 2, the cart’s kinetic energy change is
\n[tex]1\/2m(v_2^2-v_1^2)[\/tex]
\nand this energy change must come from the work done by the cart by any external forces over some distance [tex]l[\/tex] covered in this time. The two forces acting on the cart are the thrust of the propeller [tex]T[\/tex] and the overall resistance (friction, propeller turning drag, other losses) [tex]F_r[\/tex]. So our equation reads
\n[tex]1\/2m(v_2^2-v_1^2) = Tl – F_rl[\/tex]
\nIf the speed at station 2 is larger than that at station 1 (meaning the cart has accelerated past wind speed), then the quantity on the right side must be positive. That is,
\n[tex]T \\geq F_r[\/tex]
\nPart of the resistance comes from the propeller itself. It is essentially a rotating wing, so it has lift and drag, and the two can be related by the lift to drag ratio, which depends on a number of factors, but to some extent can be considered a design choice. If we call the ratio [tex]a[\/tex] then our expression becomes
\n[tex]aD \\geq D + F_l[\/tex]
\nwhere [tex]D[\/tex] is the propeller drag force, and [tex]F_l[\/tex] are all the other losses combined. This inequality can be simplified to yield
\n[tex]a \\geq \\frac{F_l}{D} + 1 [\/tex]
\nNote that if our losses are small relative to our drag, the lift to drag ratio need only be greater than 1\u00e2\u20ac\u201dan easy task. Either the losses must be minimized (good bearings, low rolling friction, etc.) or the drag on the propeller must be increased. As bad as that sounds, what this really<\/em> says is “or the propeller must be made bigger”, or “the propeller must be made to generate more thrust”, keeping a constant lift to drag ratio, of course.<\/p>\n

There is another equally superficial analysis which shows that, if taken to wind speed, the cart immediately decelerates. However, initial short-time treadmill tests showed that the cart definitely moved up the treadmill at some speeds; it just wasn’t obvious whether it would do so continuously, or if it was only releasing stored energy or momentum from being held in place on the treadmill.<\/p>\n

So it was essential that, in these tests, the cart be allowed to run on the treadmill “indefinitely”, to show beyond any doubt whether or not the net thrust it produced at certain speeds was constant or not. The answer seems to be a most definite yes.<\/p>\n

The videos below are divided into two parts. The first probably shows enough for most people; if you’re a real skeptic, you can watch the second one which shows us changing the treadmill speed several times back and forth.<\/p>\n

Part 1 of the test:
\n