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A puzzle for Engineers

Downwind faster than the wind (DWFTTW) – can that be done, even if only in theory?

Before we go any further let me clarify the question.  The question is whether it is possible to  design a sailing boat which, in theory at least, is capable of sailing directly down wind at more than the wind speed.  Yes, that does mean that if you stand on the deck you will feel a direct headwind!    What do I mean by ‘in theory at least’?  By that I mean that we want to know whether it could be done given the availability of a hull(s) having very low (but still finite) drag and hydrofoils and aerofoils having high (but not infinite) ratio of lift to drag.  We also assume the availability of mechanical components such as shaft bearings and gear wheels which have low (but not zero) friction. 

This question certainly generated some vociferous argument among members of the Amateur Yacht Research Society (AYRS).  The AYRS had an email forum which has been defunct for the last few years but perhaps it will be started again sometime.  I recall that this question generated the longest running series of email, including a few ‘flame mails' ever seen on this email forum.  I was one of a minority who argued that it should be possible in theory although in practice it may not actually be possible, primarily because the drag of practical boat hulls is too great.

In the Catalyst (Journal of the Amateur Yacht Research Society), Volume 1 No 3 page 26, Peter Sharp reviewed practical experiments by Andrew B Bauer in the 1950s and also introduced a concept which he terms ‘Power Alternating Sailing’.  In the 1950s Bauer built a wheeled vehicle carrying a large airscrew  having a fore and aft oriented horizontal axis of rotation.  This airscrew was coupled to the wheels of the vehicle by a mechanical system of shafts and gears.  There was no engine involved.  It was claimed that this vehicle was capable of travelling downwind on level ground faster than the speed of the wind, a claim that has certainly been disputed.  Indeed there is probably some scope for doubt with any such claim due to the variable and non uniform nature of the wind close to the land surface.  To substantiate such a claim you presumably do need to average the wind speed over a reasonable period of time and you need to ensure that your wind speed sensor(s) are mounted at a representative height above ground level.  After all, the wind speed very close to the ground is almost zero even on a windy day.

Peter Sharp’s concept of power alternating sailing is something rather different to the Bauer vehicle.  Peter described in his article a number of possible forms of this concept applicable to land and water borne vehicles.  As a typical example of these possibilities consider two boats linked together by a (very) long flexible electrical cable.  Peter argues that two boats linked in this way can be considered to be a single vessel.  Lets call the boats A and B.  Each boat carries a large windmill driving an electricity generator and an electric propulsion motor driving a propeller.  Boat A rides to a sea anchor, remaining effectively stationary and using its windmill to generate power which is transferred to the propulsion motor of boat B via the electric cable.  When the limit of the length of the cable is reached boat B rides to a sea anchor and boat A feathers its windmill blades and catches up and overhauls it using its propulsion motor.  If this cycle is repeated continuously I think that it is obvious that, in theory at least, this is a feasible approach to sailing DWFTTW.  After all, if very low hull drag is assumed and there is plenty of electrical power almost any boat speed could be possible.  But to my mind this proposal is a bit of a cheat, it seems just too far removed  from what could be achieved in practice.  Any sailor will tell you that towing a mile or so of high voltage cable (presumably it would be a high voltage to reduce resistive losses) through the sea is not very sensible and also of course the cable would in practice cause horrendous water drag. 

I find the Bauer vehicle much more interesting than the ‘power alternating sailing’ idea.  It is a self contained single vehicle and it has actually been built and tested and, unless there were some problems with the speed measurements, we have to take it that it did actually work.  The Bauer vehicle was a land vehicle but we can easily imagine a waterborne version in which a hull supports the weight of the vehicle and a water screw rather than a land wheel is mechanically connected to the airscrew.  Perhaps the simplest embodiment of this concept is as shown below – just a hull and a slightly inclined shaft linking air and water screws. 

screwboat01

Below is a slight variation in which two angle gear boxes allow a more convenient positioning of the screws and also give the possibility of fine tuning the system by adjustment of gear ratios.  I have drawn both these diagrams with quite modestly proportioned air and water screws, I suspect that a practical version would need huge diameter screws, espeicially the airscrew.  The weight of the airscrew and the mast needed to support it is likely to be one of the practical difficulties in constructing such a craft.

screwboat02

So are the designs shown in the two figures above even theoretically capable of sailing DWFTTW?  I say that they are but to give you a chance to think about it I have not included my reasoning on this web page, for that you can CLICK HERE 

John Perry - 2002