Mizzen madness

Imagine the sail layout of a cat yawl. The mizzen is generally thought of as a trim or balance sail rather than one that generates meaningful drive. I am told the the mizzen is usually cut as flat as a bedsheet. The mizzen is small with respect to the main. Make it really small and we'll call it a jigger.

Here is the question. Would we calculate center of effort in the usual way or would we ignore, or partially ignore, the jigger.

Use a hypothetical boat of 20 feet LOA and 16 feet LWL. The main is 120 sq. ft. and the mizzen is 15 sq. ft. The two masts are 13 feet apart. The theoretic CE of the main is 40 inches aft of the mast, the CE of the mizzen is 16 inches aft of its' mast. That makes the relative CEs 132 inches apart. Using the mainmast as a reference point we do the arithmetic....3.333' x 120 =400 and 11' x 15 = 165.......165+400/15+120 = 565/135 = 4.185 feet or 50.2 inches aft of the main mast. (Now I make a wild assed guess at the appropriate lead) If we ignore the jigger then the CE is at 40 inches +\- whatever the lead might be. Big difference for such a small boat.

Intuitively, I would include the jigger in the calculations because it will surely create a turning moment whether or not it provides any drive. I have, in the past , made too many intuitive mistakes. Thus I can not bet the farm on such stuff.

Comments please.

 

Balance

I can't quote my source, but I believe that only half the sail area of the mizzen is used in balance calculations.

 

For the calculations of the total centre of effort of the sail plan, full area of the mizzen have to be included, as for any other sail.

Using partially reduced area for the mizzen could make sense (depends which formula is used), only in the performance prediction, not in the calculating the balance of the sail plan. Actually, real position of the lift for the flat shape is further aft then for the efficient aero foil. So, if you would really want to calculate it perfectly using traditional methods, you should probably need to use a bit bigger number, rather then smaller. But in practice there is no need to make it overly complex. Approximate empirical formulas with a geometrical centres work well enough.

 

Thanks for the feed back LP and Milan. My question was for academic purposes as I do not own a yawl. I might just want to try that rig however. I became interested a while back when I chartered a Bolger Black Skimmer in the Florida keys. That boat is yawl rigged in the Bolger fashion with sprit boomed main etc. That was among the easiest boats to sail that I have skippered. I reckon there is something to be said for old fashioned stuff.