Question about sail performance and weight

Is there a general rule for approximating sailing performance loss with weight gain? For example, every 10% weight increase cause "x" decrease in speed.

An example, the MOD cats weigh 6.3 tons and can go 40 knots. How fast could one go if you doubled the weight. Of course assume the hull is modded to take the additional weight.

I expect it is a complex problem that would require analysis but I am only looking for a ball park answer.

Is this line of reasoning all messed up? It seems the doubling of weight would require double the submerged volume. But volume is a cube relationship and surface area is a squared relationship so the skin friction would not be doubled. Lets assume wave drag stays close enough to the same for this example. Then we have the same sail power but more skin friction.

 

There is no general rule like that and no ball park answers applies.

 

Sail boats speeds are limited by stability to drag, not weight. While you might double the submerged volume by adding lead to double the stability in a monohull, you may not increase the drag significantly. Whereas on a multi-hull you may keep the same weight and double the stability, but also double the drag. Additionally, there is a real limit to maximum speed in the physics of the sails themselves, so decreasing weight or increasing stability does you no good in terms of absolute speed. No conventinal sail or wing can go dead upwind and designing for maximum speed on a single heading has limited usefulness.

 

I was just looking for a general approximation of the speed penalty associated with weight. For an airplane it is simple to calculate exactly how speed, range etc are affected by weight. But, I guess boats are still too much of an art.

Searching I found a thread on Hp and equivalent sail area.

PAR said in force 4 winds 50 ft^2 is about 1 Hp.

Another poster gave different values.
0.015 hp/sqr ft of sail @ 7-10 kts wind speed
0.020 hp/sqr ft of sail @ 11-16 kts ''
0.040 hp/sqr ft of sail @ 17-21 kts "
0.070 hp/sqr ft of sail @ 22-27 kts "

So at 20 knots a 4000 ft^2 sail is 160 Hp, or in force 4 wind it is 80Hp? Edit - Oops I just noticed force 4 is 11-15 so both posters gave the same Hp value.

If you have Hp and newtons of drag are you able to calculate speed?

Edit - using those conversion values a 70 ft MOD cat at 40 knots uses 444 Hp!

 

I would think that if you can calculate the change in wetted area of the hull, with each additional pound of displacement, you could determine the drag increase. Of course the drag is a function of the square of the speed, so it would not be a direct relationship.

That would assume the extra weight has little/no affect on righting moment. And it would only be valid for displacement hulls. On a planing hull extra weight would delay coming up on plane.

Also, this ignores other issues, like comfort in rough conditions. That would be more important in cruising boat.

 

At the risk of oversimplification, or displaying my ignorance, I will posit; for every extra pound of displacement the boat must push another pound of water out of the way. If one added another ton, then another ton of water to push out of the way.

Yes I know. That is too simplistic but it must be so.

 

I'm affraid the wetted area is just a smaller part of the game when considering the maximum speed. Adding displacement influences much more the wave drag, and hence the relationship will not be simply speed-squared...
Then there is the influence of the stability (heel angle) on the drag of a sailboat. The added weight might increase or decrease the heel angle, depending on the point where it is added. The underwater parts will react differently to the modified heel angle, some might produce an increase in drag while some might decrease it.
Same thing about the change in longitudinal trim, whose effects can sometimes be drammatic.
Aerodynamic drag - is the additional weight being accompanied by a rig modification? In that case, how does the aero drag change? Etc.
As PAR has put it - too many variables in play to give a general answer valid for each and every case.

 

Mod 70

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You've mentioned the MOD 70 a couple of times-but not the most important part( which makes your proposed calculation even more difficult in some respects) : when the MOD 70 is going its fastest it is flying the main hull with about 70% of the boats weight supported by the lee ama foil......

 

Amazing how I missed that. Duh. I totally overlooked the flying hull part of performance, thanks.

I am asking these questions because I am just trying weigh performance vs comfort. I consider the 70 ft MOD at the no f'n way end of comfort and a lagoon 620 at the too heavy and slow end of performance. A gunboat 66 is a pretty good compromise and and moves 20t at 20 knots without flying a hull.

If you haven't seen my other posts I am working on laying out a small version of the Planet Solar boat but with sails. I really like the large center hull small cat hulls concept. I have decided 70 ft LWL hits the sweet spot of efficiency, ride and comfort. So I am working on a 70ft version of the Solar Planet. The cat hulls are very small at just 6ft tall and 4 ft wide. The big decision if how large to make the central hull. If I go 70 ft long it ends up cavernous, no way I need that kind of room.

I want to efficiently sail at 15+ knots and the occasional motor to 20+ knots. Performance like that would be double of any sailboat I have experienced and really help shorten trips. I think that is the basic philosophy behind Gunboat but I don't have a few million dollars to drop on a Gunboat.

Malcolm Tennents 72 ft long motor sailer Carillion claims 24 knot performance but I don't thing one has been built.