The key idea is that the winch produces half its torque at half its speed. The spreadsheet estimates the sail forces, multiplies by the lever arm for main and jib booms, and matches that against the winch max torque. It then reads off the resulting winch speed, or says the winch is stalled if it is under-powered.
Along the way, the spreadsheet attempts to account for friction losses in the jib sheeting run, the mainsail sheeting run, and the control line run. To do this, you count how many blocks and fairleads these lines pass through. On my Italiko with an arm winch, there are two blocks for the control line, one on the arm itself, and one at the stern, and there is a through-deck "S" fairlead. Then, the main sheet passes through a block and the mainsheet post, while the jib passes through a fairlead on the side of the hull, and through a jib sheet post. No wonder the poor winch can't sheet in at the top of A rig wind speeds!
The input parameters are shown in the screen shots above. The left-hand side data relates, more or less, to an RMG 280D winch with a 26 mm drum pulling an IOM A rig with my Italiko sheeting arrangements. Worth noting that a 26 mm drum has a 13 mm radius... (smile). The right-hand side data relates to a Hitec 5745 set up as an arm winch with a 80 mm radius. (Note that, in version 3, you enter the rig number, and the spreadsheet looks up the correct IOM values for the sail parameters. Of course, if you want to look at a different class, just enter all the data manually as above.)
The above screen shots show the results. For the RMG, around 3.8 turns to set the jib boom at 90 degrees, and about 1.3 seconds from full in to full out. You can see that the torque required is much less than the winch can deliver, which is good. For the Hitec, about .31 turns, ie about 112 degrees of swing, taking 1.4 seconds. This slow speed is because I am close to the max torque of the Hitec, and is the reason I have to assist it with an elasticated Constant torque pre-tensioner cam.
The following graphs illustrate how a winch gets overpowered only in a very narrow range of wind speed which is just below its maximum. In this example, an 18 kg-cm arm winch (80 mm arm, entered into the spreadsheet as 160 mm because of the block on the arm) stalls with the apparent wind at around 4.5 m/s (actual breeze around 3.5 m/sec) in IOM No.1 rig (and all the friction from the blocks and fairleads mentioned earlier), but handles the range 0 to 4 m/sec apparent reasonably cheerfully.
In No.2 suit, notice that the winch runs out of steam with the wind over 5.2 m/s apparent (perhaps 4 m/s actual). Not good -- you would want to sail in No.2 suit up to around 8 m/s actual.
And in No.3 suit, the winch runs out of steam with the wind over 7 m/s apparent (perhaps 5.5 m/s actual).
There are some details which might be interesting to note.
1. The coefficient of friction suggested for the block yields about a 7% friction loss with a 180 degree turn of the line, and the coefficient suggested for the fairlead yields about a 17% loss with a 90 degree turn of the line. You can do a little editing of the formulae if necessary, noting that the estimated friction loss is an exponential function of the friction coefficient and of the angle of the turn:
2. The jib and mainsail are crudely approximated by simple right-angle triangles, in order to estimate their centres of effort. This is at 25% of luff for the mainsail, and at 75% of luff for the jib. Then, in order to get the torque right for each sail, their pivot points must be taken into account and related to their CEs. No problem for the mainsail, but for the jib this needs an estimate of the pivot point offset as a percentage of the jib foot.
3. At first, I though that the spreadsheet would not need to analyse the actual sheeting arrangement or the run of line or what the size of the winch drum is or what kind of action there is on the winch arm. But this turned out to be wrong, it does need to know the drum or arm radius of action. It can then figure out the rest. Note that, if an arm carries a block in order to double its purchase, you must double the arm radius to reflect this. For the Hitec example, the "effective" arm radius is therefore 160 mm. See a picture of the arm with a block on the Arm Winch Geometry page.
©2011 Lester Gilbert