# A Puzzle for Engineers

## Downwind faster than the wind – One way it can be done, even if only in theory

An airscrew, for example an aircraft propellor, moves through the air in a rather similar manner to a metal screw moving through a nut. An obvious difference is that with a screw operating in a fluid medium there is some 'slip', with a metal screw and nut there is no slip. So if we take 10 turns with a metal screw having 10mm pitch the screw will move 100mm through the nut. If this were an air screw of the same pitch the movement of the screw through the air would only be 100mm if there is absolutely zero axial load on the screw, any axial load will cause some slip and hence less than 100mm movement. As an example consider the paper toys we used to make as school children, at least we did in our primary school. By simple origami it is possible to make a light fine pitched airscrew which can be dropped down a stairwell. Since this toy is light it can have a small ratio of axial load to airscrew disc area and slip can be quite small. I have not done any measurements but I guess that the actual rate of descent can be not much less than that predicted assuming zero slip.

If we assume small slip (and the implication of that is large diameter screws) the airscrew and water screw combination shown in the diagram above behaves very much like the two joined metal screws shown in the figure below. We have replaced both the air and water fluids by metal nuts. Note that we have chosen to use a coarse pitch for the thread representing the water screw and a considerably finer pitch for the thread representing the air screw.

Now think what happens if we hold the nut representing the water still and we move the nut representing the air away from it in the direction shown by the arrow. The length of shaft between the two nuts now has to increase. Assuming that nothing breaks or stretches, the shaft has to rotate clockwise as viewed in the direction of the arrow, so that more length of screw is wound through the coarse pitch nut than through the fine pitch one, thus accounting for the increase in distance between the two nuts. This direction of rotation causes the shaft and screws to moves relative to the air nut in the direction of the arrow, that is in the same direction as the 'wind'. By suitable choice of screw pitches and use of low friction threads (ballscrews would be ideal) we can actually make the double screw move much faster than the wind nut, say twice as fast.

Turning from the analogy to the figure at the top of the page, the boat is attached to the double screw and shaft assembly so the boat will move in the direction of the wind but faster than the wind. The alternative mechanical arrangement with two gear boxes allows us to freely choose the screw pitches, the gearing changing the effective pitch difference between the two screws.

Some small slip at the air and water screws will of course reduce the speed advantage of the boat over the wind but will not necessarily negate it. We can envisage a situation where the slip is just sufficient to reduce the speed of the boat from that possible with no slip down to exactly wind speed. In this case we have a boat sailing down wind with no wind discernable to an observer on deck. You will never do that just by setting a larger spinnaker! What more can I say? Sorry for such a long winded explanation, I just wanted to try to make it as clear as I can.

The obvious question is could it be made to work in practice? My guess is that it probably would not work in practice, mainly because of the drag associated with real hulls. The Bauer vehicle discussed in the previous page was reported to have exceeded wind speed but it had no hull drag, its weight being carried on low friction wheels. Hull drag would result in increased axial loading on the screws and hence increased slip at the screws. As discussed above, slip may well negate the excess of boat speed over wind speed. Keeping the slip low requires the screws to be of large diameter, in the case of the airscrew perhaps very large diameter! That means a big heavy airscrew supported on a tall mast, which in turn means a heavy boat, more hull drag and so on in a vicious circle.

I think it was Dave Culp, an AYRS member living in California, who suggested a way round the hull drag problem by using a hull floating in the air rather than one floating in the water, ie an airship. The diagram below shows the idea. The advantage is that the hull is now moving much more slowly relative to the fluid in which it is floating. Say, for the sake of argument, that the wind is 20 knots and the craft is sailing downwind at 21 knots. (we only specified that it had to be faster than the wind, it does not necessarlily have to be an awful lot faster than the wind). So if we use a hull floating in air this hull will be traveling through the air at 1knot. Had the hull been floating in water it would have been travelling through the water at 21 knots. Remembering that the drag of an object in a fluid is roughly proportional to the square of the speed through the fluid (in the case of a boat hull this is indeed a rough approximation) one can guess that the airship idea could greatly reduce the effect of hull drag. It is not of course quite as simple as a square law though, the relative sizes of airship and water ship hulls and the differing fluid properties comes into it as well.

For the purposes of demonstration to some doubters at an AYRS get-together I did actually make the mechanical model with two threads on a shaft and two nuts and I can assure you that it did work as expected, why shouldn't it? For the fine pitch thread I used just a length of threaded steel rod, I think it was an M6 thread having 1mm pitch. To avoid friction jamming the whole thing up I wanted a really big diffenence between the pitches but my metal turning lath will only turn threads up to 5mm pitch and in any case I could not be bothered to try cutting coarse pitch (hence multi start) internal threads on the lath. So I made the coarse pitch screw by taking a strip of soft aluminium about 3mm thick and 15mm wide, holding one end in the vice and twisting the other end round with a wrench, the edges of the strip then forming a double helix of something like 50mm pitch. For a nut on this screw I used just a piece of plastic with a slot in it. That gave me a 50:1 ratio between the two screw  pitches which is more than necessary but it proved my point (to my own satisfaction at least!) whilst ensuring that the screws would not jam up with friction. Unfortunately, even after I had made this demonstration, not one member of the audience was convinced, am I just bad at explaining things or what?

If you have read this you probably have some interest in innovative sailing boat technology in which case you might be interested in the Amateur Yacht Research Society, website at:- CLICK HERE for their website.

Since writing this article in 2002 I have recieved emails from several people telling me either that it is a lot of nonsense or giving me alternative explanations for how or why DWFTTW is possible. I felt that it was time to do some calculations to justify my initial guess that DWFTTW is possible in theory but probably not possible in practice so I wrote a computer program to analyse the situation of a windmill boat sailing downwind at exactly wind speed. If the propulsive thrust available when the boat speed is exactly wind speed exceeds the hull drag that might be expected at this boat speed then we can conclude that DWFTTW is feasible in practice as well as in theory.

The results from my computer program suggest that DWFTTW might just be achievable in reality but it would not be an easy task to build a boat to demonstrate this. Such a craft would require highly efficient water screw and air screws and probably a hydrofoil system to carry the weight of the craft rather than hulls floating in the water.

The calculations within my computer program are quite simplified and based on assumptions which may or may not be justifiable. For example, one of the main assumptions is that the airflow is of uniform velocity across the area swept by the air and water screws, an assumption commonly made in simple propeller and windmill analysis.

This program runs on my Windows computer and I am told it is also OK with Linux under WINE. If you would like to run it you can click on the download link below then choose the option to save the file on your computer then use WinZip to unzip the folder which contains a .exe file that you can run plus a text file. The text file is a C++ listing of the part of the program which does the calculations, this being fairly short and simple. I have put in copious comment statements so that you can see how it works and tell me where I have gone wrong!