CentralCoaster wrote:
Dammit Jim, I'm an engineer, not a sailor.

-----Original Message-----
To: multihull_boatbuilder@yahoogroups.com
Sent: Mon, Jul 12, 2010 6:44 pm
Subject: [multihull_boatbuilder] Re: Answered: Can you go downwind faster than the wind?


Ok, we'll move forward on the assumption that a traditional modern sailing rig can propel a sailing craft to a speed such that it's downwind VMG is greater than the speed of the wind.

(The above assumption is easy to support in real life btw).

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NOTE: below I have used some easy to work with numbers (like 45 degrees) simply for convenience. Actual numbers in real life may vary from these.
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Imagine for a moment a world that rather than being shaped as a sphere is shaped as a cylinder. The cylinder 'world' is laying on it's side in our view and we are standing at the south "end" of the world on top of the cylinder. The entire surface of this world consists of one enormous uninterrupted dry lake bed with one wind blowing from the south to the north.

Let's send a land-yacht on a 45 degree reach running to the NW. Without making a single gybe, this craft will 'corkscrew' it's way around the world as many times as needed to reach the far end of the cylinder. We know that if we release a neutral bouyancy floating balloon into the wind at the same time as the land-yacht, by the time the land-yacht has made one circumnavigation of the cylinder world and reappears to us on top it will be significantly farther downwind and 'downcylinder' than the balloon. This of course is just a simple matter of the craft having a downwind VMG greater than 1.0 wind speed.

Now, imagine that when the initial craft we sent on it's 45 degree path is halfway around the world (and now on the 'bottom' of the cylinder), we set another identical craft off on an identical 45 degree downwind reaching path. We start this craft off at the same 'longitude' as our craft already in motion. What we now have are two land-yachts on opposite sides of the world, going the exact same speed and carving the same helical path -- all the while remaining exactly opposite of each other on the cylinder. Every rotation they make they cross the DDW path of the drifting balloon and each rotation they get farther and farther ahead of it.

Imagine now in this thought experiment that we begin to shrink our cylinder world a bit at a time. We have not changed the speed of the wind nor the speed of the land-yachts. As this 'world' shrinks, all that changes is the diameter of the helical path shrinks and the number of revolutions that the yacht makes in any given period of time increases. Keep shrinking this imaginary world until the wheels of the land-yachts are on such a small cylinder that they are essentially touching each other as they spin dizzyingly around and around -- their sails protruding in opposite directions.

If you are with me so far, you'll see that our two land-yachts are still achieving a downwind VMG of greater than 1.0 -- every time they rotate they increase their advantage over the floating balloon. Also, those sails spinning in a perfect circle are sure looking familiar (propeller anyone?)

Going a step further in this 'morphing' process, let's replace the chassis of both land-yachts with something more simple without making any changes to the spinning sails.

We know that both the sails and the chassis are carving a 45 degree helical path so let's dump the frames and wheels of the land-yachts and replace both of those with a single, oversized threaded rod. This rod is equipped with grooves that match the sails 45 degree path and is aligned with the wind, taking the place of the 'pole' of our cylindrical earth. Let's spin on a matching oversized nut and drop the masts into holes in that nut.

Now, without ever interrupting the spinning sails nor their downwind VMG >1.0 paths we have created the simplest DDWFTTW vehicle of all -- two spinning airfoils on a nut traversing a threaded rod. At the center of these rotating airfoils, we now have a nut that is going DDW and continuing to press it's advantage over the balloon with every rotation.

(Before taking the last step to our vehicle, it's interesting to note that the sole purpose of the keel mechanism on a traditional sailing rig is to force the airfoil to take an advantageous path through the air. In the case of a 45 degree reach, it's purpose is to ensure that for every foot that the airfoil moves downwind, it also moves one foot to the right (or left). It's this forced diagonal path through the air that creates the apparent wind needed to generate thrust. Of course the purpose of the non-articulated skates of an ice-boat, the wheels on a land-yacht and the threaded rod and nut in our above example serve the same purpose as the keel of the sailboat -- forcing the airfoil to maintain it's path diagonal to the wind.)

Last step: Once we reach the point that we have a pair of spinning airfoils happily pushing the nut DDWFTTW down a threaded rod, we need someway to translate this into a vehicle that can traverse any dry lake bed DDW. Realizing that to do this we only must find a way to force our airfoils to continue on their 45 degree helical path -- a path from which they have yet strayed, we arrange gearing between the wheel axle and the prop axle to ensure that for every foot the wheels roll across the dry lake bed DDW, the airfoil is forced through the air one foot to the side just as before -- and there you have it, DDWPDV -- a DDWFTTW vehicle.

As you can see, through this entire process the wind never changed directions, the angle of the apparent wind to the airfoils never changed, the speed of the airfoils through the air never changed, the downwind VMG of the airfoils never changed, the lift and drag vectors of any given airfoil section never changed -- in short, other than a slow change in the diameter of the helical path of the airfoil, all remained the same from "sail" to "prop".

Turns out that the airfoils of a traditional sailing rig on a faster than the wind reach and those of the DDWPDV are acting in the same manner -- one can *call* it sailing or not, but it's a distinction without out a difference from an aerodynamic standpoint.

Here is the 'Cliff-Notes' version of the above: The airfoils of the propeller are one loooong and continuous downwind helical reach while the chassis travels DDW. Adjusting the gear ratio between the wheels and the prop is the equivalent of adjusting your ground track on the land-yacht (and thus altering your sails path through the air) and changing the pitch of the propeller is the equivalent of adjusting the angle of the sail on the land-yacht.

Here is a link to an animation which illustrates the above:

http://www.youtube.com/watch?v=UGRFb8yNtBo

Hope this helps.
JB