While the precise answer depneds on the geometry of the boom vang, 3:1 sounds a little on the light side. It would be cheap and easy to add a wire cascade which would bring the vang up to 6:1 which should proove more than adequate. To make a wire cascade, you would buy a small bullet block made for wire and a length of 1/8" 7x19 wire with thimbles in each end. One end gets shackled to the vang bale and the other end to the upper block of your existing 3:1 vang. You are then pulling with a 3:1 mechanical advantage on a 2:1 tackle resulting in a very low friction 6:1 system.
Ahoy,Jimq Yes, better to snap a rope than a boom or a mast or you might even flip oh no! But relly now have you tryed it or are ya just yanking our sheets? Hey I know where you can get a hydrulic winch that ought to do the job. Let me make you a little bet, go to the local harware store buy a couple of galvanized blocks and some 1/2 inch sisal rope. If it breaks let me know. I send you a book with the technical info you need. Big Red 56
The only problem using galvanized blocks is that pretty quickly you end up with rust stains on your deck and frozen blocks when the typical steel pivot rusts. While 1/2 inch sisal rope is cheap, it rots out in a couple years or less, is very stretchy and is quite incomfortable on the hands. I sail on boats with these kind of "welcome to yesterday" type details in traditional boat regattas and have no nostalia for this kind of backward in time setups.
Ahoy Jeff my point was it is not necessary to over engineer a rig just because you can. Not every sailor has buckets of money to throw overboard on the best rig, or repair. The original question was purley a math question and in my opinion the solution I offered explained two distinct points, 1. If you want to make a performance upgrade you can rig almost anything to work for the purpose of trials. 2. The math required to compute the load requirements isn''t woth the effort in this case except possibly to the original author. The information given is insufficent in any event and without condensendingly trying to explain it all I offered a practical way to work out the problem. Not everything in sailing has to be so complicated. Just do it.