## September 21, 2016

A recent comment gave me reason to read back over my post on using sails on an airship and realize I didn't include any pictures of how the vectors I was talking about were oriented.  In that post I was so much more concerned with finishing and organizing my own thoughts I didn't do a very good job of expressing what I was talking about at all.
This picture shows the two most important vectors when talking about either a triangular sail or a wing.  Blue here represents the prevailing wind, or possibly the current direction of motion for the vehicle.  Green represents the lift, or the direction that the sail causes the vehicle to move in.  Wings convert forward motion into an upward force, while sails convert wind into a forward force.
On a ship the collected forces cause a net motion as shown below:
Here the wind exerts a net pressure (in orange) on the hull which pushes the vehicle in that direction.  This force should be fairly weak, but on an airship can't be compensated for by the keel as on a waterborne sailing ship.  Between the lift and pressure forces a net force creates some velocity (in yellow) which in turn creates a drag force (in red) on the ship.  This is what I calculated in the previous post, merely to demonstrate that such a vehicle could indeed generate a meaningful velocity.

There is a concern in this image that I didn't raise in the previous post.  What happens when the breeze is coming from the fore, rather than the aft, of the ship?  So long as the sail can be angled properly and the wind is coming from at least a little behind, or even directly to the side, of the desired direction then this image is roughly accurate.  When it comes from ahead, though, that pressure force that normally would be compensated for by the keel becomes a serious problem:
Here the pressure and lift create a net velocity not ahead, but to the side.  Obviously a sufficiently well sized sail and a properly sleek ship can somewhat mitigate this issue, but never eliminate it.  By beating to windward, however, this problem is significantly reduced.  Doing so causes the pressure and drag forces to be almost in line, meaning velocity is reduced but the direction is controlled:

This is a pretty complex maneuver used in real sailing, one that I can't possibly do justice to here. In short, it involved keeping the desired momentum more or less opposite the direction of the prevailing wind.  The ship constantly moves back and forth about that vector, so the wind is always coming slightly to either side.  In this case so long as the forward component of Lift is greater than the backwards components of Drag and Pressure then the ship will continue moving forwards.  Since the sideways components of the two orientations are opposite each other they cancel out over time and the drift is minimal.  Unfortunately the effect of pressure here will make this a much less effective maneuver than it is for a ship at sea, but it ensures the ship can maintain forward velocity regardless of the direction of wind.

I haven't bothered here with the particulars of design or calculation, the majority of which was done in the first post.  While the new issues raised here would impact any real attempt to construct such a vehicle we've also seen that such issues could be overcome by a sufficiently dedicated designer.  There is a combination of hull and sail design that would make this work.  That is enough for now, unless we want to start really building one.

1. Thanks! I'm gonna build a model. Everyone else talking about airships that I could find on the net doesn't think its possible, or they have wild ideas about sending kites up into the jet stream. Which might be cool for a fiction story but def not FAA approved.

as for the keel action found on a maritime vessel would there be anyway to recreate it using another wing or ballast or would I simply need to overcome the problem with proper aerodynamics in ship hull design? There was a fellow who built his airship to be the sail and he had a really nifty keel he tossed in the ocean to produce the effect, but then this limits the ship to sea and I might as well go sailing.

My last question is this, and might I add that I'm very appreciative of your input, will miniaturizing the concept produce difficulties in achieving accurate test results. The main concern being weight of the smaller version and it getting pushed around too easily where a larger version would not.

Cheers!

1. The issue with miniaturizing airships is the cube-square law. It says that the surface area goes up much slower than the volume does, so the bigger a gas-bag gets the more gas it can carry when compared to its weight. Airships get more efficient the bigger they get. At a small scale you need to use very lightweight materials and reduce structure to a minimum in order to make up for how little gas you can fit into the bags. In a model the gas bags will be much larger relative to the hull than they would for the 30' airship described in the previous post.
Sails will still work at small scale, but the actual scale relative to the overall hull length will change. Sail effectiveness increases with the area of the sail.

Mostly what the keel does is provide stability. In the previous post I suggested that making the gas bags outriggers would do the same job, they would prevent the vehicle from tending to flip over. You'll notice that outrigger sailing canoes don't need keels at all. Imagine this as the same kind of vehicle, except that the pontoon outriggers are replaced with large bags of hydrogen. Or helium to be safer.

The other job the water does is prevent the ship from being pushed off course by the wind. Water produces so much friction on the hull that the wind can't overcome it and the ship keeps going the way it is. It would be equivalent to totally ignoring the orange "pressure" arrows above. That's the main problem. As wind pushes on the hull it pushes the whole vehicle in that direction. Aerodynamics can reduce this, but no additional sails or wings can reverse it. You can't make a sail that moves you directly opposite the prevailing wind. Hence the maneuver described above, where you move just slightly off the direction of the wind back and forth so the lateral components cancel out.

Note: I inappropriately used the phrase "tacking into the wind" above, when I should have said "beating to windward." I'll fix that mistake.