Question: Trapeze on Keelboat

I'm wondering if anyone can help me out with this problem.

I'm trying to figure out how heavy of a keelboat could you build and still have a 2 person (400lb total) trapeze system have a noticeable effect? Keelboat racers always sit the crew on the high side upwind to help balance the boat. Why not put them out further for more effect?

If you put a trapeze on say a 30 foot 7000lb keelboat could this correct heel more then the 1/2 degree I currently expect it would?

I'm not too confidant with the math on this sort of problem.

Details:
The weight (400lb) would be out 3 feet or so from the rail line.
Noticeable effect: A 5 degree difference from no trapeze would be acceptable.
Displacment :7000lb
Ballast: 2700lb
LOA: 30 feet.

Can anyone help me with this?

 

You probably already know but some handicap systems won't allow trapezes on ocean races....

 

It obviously depends on some figures you don't provide but around 2 or 3 deg

 

Some numbers and wild guesswork :
(I will go metric here)

let's assume your keelboat has fairly "standard" metacentric height GZ ~1.00m
let's assume max beam two guys will be trapezing from is ~3.00m
let's assume center of gravity of those guys is 0.9m from the ground when standing.

than heeling/righting moment those two guys on trapeze are creating will be:
(beam/2+height of CG of guys)*weight of guys=(3.0m/2+0.9m)*180kg=432kgm

Now, if we divide this moment to displacement of boat, we will get the heeling/righting arm for the same moment, created by the weight of boat, instead of weight of guys on trapeze:

432/3150=0.137m

no we could find a heel angle, necessary to generate a righting arm of 0.137m:

at small angles of heel, righting arm RA(a) is very directly related to GZ and heeling angle a:

RA(a)=GZ*sin(a);

In our case, we know RA(a), GZ, but do not know a; than, a will be:

a=arcsin(RA(a)/GZ)=arcsin(0.137/1)=arcsin(0.137)=7.88 degrees.

righting moment, equivalent to ~8 degrees of heel is HUGE!

of course, all this calculation is approximate, but I doubt if a real result will be more as 10-15% off.

Now, it is obvious, why most rules do not allow trapezing, (or hiking out, to that end) in races.

____________________________

after all, take two guys out on spinnaker halyard, with boat on the mooring (mooring ropes slack), and measure resultant heel angle .
I would be glad to hear about results of this inclining test .

 

X: with such a wide disparity in results I should also show my calculations so you can judge for yourself.

From this source http://www.boatcouncil.com/boat-categories/performance-sailboats.asp I took a value for a stiff boat of 1.7 for the ratio RM/B^3. RM is righting moment at 1 deg of heel, B is max beam. Theoretically that should be a dimensionless number but to be on the same side I will use imperial units since that source does the same.

For LOA/B = 3 or B = 10' that gives us RM = 1700 lb-ft. With 400 lb hanging 8' off center the heeling angle would be 8 x 400 / 1700 = 2 deg for a stiff boat, up to twice that for a comfort cruiser.

My calculations use figures averaged over a number of boats so it averages the effect of ballast and form factor.

 

trapeze on cruising boat

For what it's worth, I used to single-hand a PY-23 (similar pocket cruiser to an O'Day-23) with a trapeze. Might be similar geometry to your 30-footer with 2 men on trap. It made a terrific difference when wind got up to 12 knots or more. Sailed mostly Eastern Long Island Sound and Buzzards Bay. Got lots of attention from other, usually larger, sailboats. -- omegacubed