Question: Trapeze on Keelboat

[Xirroh]

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?

[Doug Lord]

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

[ancient kayaker]

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

[Perm Stress]

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 .

[ancient kayaker]

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-cate...-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.

[omegacubed]

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