I had a try at answering it a few years ago on the 'Sail Twist' page, but have not been satisfied. Recently I returned with new enthusiasm and have created a revised spreadsheet TwistWash4.XLS (about 200 kb) which now gives rather more interesting results, this time for 'A' Class sails. As before, it exploits previous spreadsheets and combines them with new graphs and analysis. The spreadsheet has four worksheets: 'Summary', 'Analysis', 'PhotoData', and 'VPP'.
You'll need to refer to the wind gradient and apparent wind pages, the entry and exit page, the sail measurements (photo analysis) page, and the simple VPP page. It may be useful to also glance at the older 'Sail Twist' page for the diagrams it gives of what happens with entry and exit angles when you twist sails of different draft, and in particular for an explanation of the 'effective angle of attack' which is important in the calculations.
When you start up the TwistWash4 spreadsheet, you may get a warning dialogue about macros. The spreadsheet once had a macro, but I deleted it. Nevertheless, something (unremoveable!) has remained, and might cause this alert.
We will run through the spreadsheet, section by section.
We start on the 'Summary' worksheet. First up is the input section where you specify wind speed, heel angle, and so on as required. (You may also need to set a couple of input parameters on the 'Analysis' worksheet.)
Roughness is a parameter which makes the wind gradient 'flatter' or 'taller'. That is, if the water surface is very choppy with waves, then the surface air mixes at the boundary layer and yields wind speeds which are generally lower than if the water was mirror smooth. Think of the chop and waves as rough sandpaper on the earth's surface, and what it must be doing to the air that moves over it...
The input section reminds you to first enter your sail measurements (draft, max draft position, twist, etc) into the 'PhotoData' worksheet, on the assumption that you have a good set of sail photos and want to use that information. Review the sail measurements (photo analysis) page for more information on this worksheet.
The first major outputs are the estimated boat speed, from the 'VPP' worksheet, the calculations of the wind gradient and the apparent wind from the 'Analysis' worksheet, and the estimate of how much of a header the jib has given the main.
In this example, the jib has headed the main by around 4.3 degrees at the boom (AWA was 29.5 degrees, now 25.2), and around 3.7 degrees mid-main (AWA was 33.8 degrees, now 30.1 at #2 batten).
Elliptical lift distribution
The top graph on the 'Summary' worksheet shows the approximate lift distributions across the jib and main. What is interesting is that the first 'new' idea for setting twist and sheeting is that the lift distribution should be elliptical if you want maximum efficiency -- that is, maximum lift to drag ratios.
Note that the distribution we are talking about is the actual lift itself (in Newtons or lbf, for example), not the lift coefficient. The graph compares an 'ideal' elliptical distribution against the estimated actual. Lift is a function of angle of attack, the surface area, and the square of the apparent wind speed (AWS), amongst other things. In the 'Analysis' worksheet, the sail chord is used instead of area to represent how sail area decreases towards the head. Because AWS is squared, the estimated lift curves are very sensitive to the wind gradient (and hence to the roughness parameter) near the water surface. The example graph of lift distribution shows that the jib and main seem to be producing more lift in their middle than at their foot or head. The elliptical curves (dashed lines) indicate that the trends in these lift distributions seem to be reasonable and in right direction, no very large discrepancies, but that it would be 'good' to have both main and jib producing a little more lift at their heads.
Entry angle of luff to apparent wind
The second idea of the spreadsheet is to compare the actual entry angle of the sail luff with the direction of the apparent wind at that point.
One theory of sail shape is that the entry angle at a particular place on the sail luff should in some sense 'match' the angle of the apparent wind at that point. On the graph, the gap between the plot line for the entry angles and the line for the AWA for a sail is related to the sail's sheeting angle, and this is something that you change easily enough by changing the sheeting. More interesting is the extent to which the entry angle plot line runs in parallel with the AWA plot line. If the sail entry angle runs more or less parallel with the AWA it means that, moving along the luff, the sail is maintaining the same relationship to the apparent wind along its whole span or height. The theory is that this is 'good'. The example graph shows excellent parallelism for the jib with a suspicion that it could be sheeted in a little tighter, while the main sheeting looks a little better but the head might have too much of a mismatch between its entry angle and the oncoming apparent wind.
Entry angle of luff to apparent wind
The third idea of the spreadsheet is to compare actual sail twist with what is 'theoretically' ideal to accommodate the apparent wind.
The data for the graph comes from the 'Analysis' worksheet. This estimates the 'ideal' twist needed in jib and main by assuming that this twist should accommodate
In addition, for the main, the assumption is that the main 'ideal' twist should also accommodate
This analysis ignores any 'real world' twist you might need if you are sailing at the top of the rig's wind range, for example, or if you have really flukey wind and you want to cover all your bases by having a wide range of twist in your sails.
I'm not too sure about 'self-induction' of upwash, so have set it to zero (ie ignored it) in cells D49 and D70 of the 'Analysis' worksheet. This seems to give more realistic leech profile graphs (see below), and better matches between actual and ideal twists in the twist graph shown here. But set it to 0.623 and see what it does for you.
The example graph shows the reverse of what the earlier graph of wind angle suggested! Here, it seems that the main twist is reasonably well set, and it runs in parallel with the 'ideal' twist it needs to accommodate the jib's downwash. By contrast, according to the 'ideal', the jib seems excessively twisted at the head... So perhaps the 'ideal theory' for the jib hasn't yet reached an acceptable level of practical use, though the 'ideal' analysis for the main looks promising.
If you want to go into the details, the 'Analysis' worksheet is the place to look. At the top are the calculations for the wind gradient and the apparent wind, taken from the wind gradient and apparent wind pages, and an estimate of the boat's speed, taken from the simple VPP page. Note that the simple VPP has been modified to suit an 'A' Class boat in the spreadsheet and included as the worksheet labelled 'VPP'.
You may need to tune the worksheet to your particular boat. In particular, you might have different heights for your booms and battens. If they are very different, change them on the PhotoData worksheet, not here. The heights are adjusted here from the Photo Data according to the heel angle you set in the 'Summary' worksheet.
Then the 'Analysis' worksheet calculates the sail parameters, using techniques discussed on the older 'Sail Twist' page. The result of the analysis is to yield an estimate of the angle of attack of the sail.
The 'Analysis' worksheet then analyses the sails, first the jib, and then the main. The purpose of the analysis is to estimate the downwash from the jib, and hence the change in the apparent wind angle seen by the main.
It is assumed that the downwash of the sail is directly proportional to its angle of attack -- that is, directly proportional to its coefficient of lift. Based on a relevant NACA paper referenced in the spreadsheet, roughly an angle of attack of 10 degrees is assumed to yield 10 degrees of downwash.
We need to note that there is another factor to consider, one which I have decided to set to zero generally, but which another NACA paper says should be around 0.623. It is the 'self induction factor', and describes the upwash at the luff, to which the sail needs to be adjusted if its angle of attack is not to be excessive. In theory, yes, if there is significant upwash then the sail should be twisted somewhat to prevent stalling. In practice, I'm not too sure.
There is a line labelled 'Parallelism with boom', and this indicates the angle between the top batten and the boom. Many rough guides to twist set-up suggest you should start by having the top batten parallel with the boom, and then working from there to get the boat speed and handling that you want. In this example, the top batten is twisted off 10 degrees relative to the boom.
Now that we have an estimate of the jib downwash, the next section of the 'Analysis' worksheet calculates how this affects the apparent wind at the main.
The major problem we have is that the downwash estimates from the jib analysis are in the wrong place. The jib boom and batten heights do not match the main boom and batten heights, yet that is where we now want to know the main's apparent wind. So the worksheet plots the jib downwash on a graph, calculates a quadratic trend line of best fit, and uses the equation of that line of best fit to predict downwash at the required heights to suit the main.
This isn't an ideal solution to the problem, mainly because the quadratic line of best fit is unduly affected by the end points -- the estimated downwash at jib boom and jib head. While poorly estimated wash at the jib boom isn't too much of a problem, that at the head is. As you can see from the example graph and quadratic estimate shown here, it will more than likely underestimate the downwash that the main sees in the region of the jib head.
The calculated jib downwash that is now seen by the main is adjusted depending upon whether the boat is beating (all factored downwash hits the main) or reaching (half the factored downwash hits the main, since the slot is much wider), and this is called the adjustment for 'biplane gap'. The result is given in the line 'AW angle (deflected) at main'. On the 'Summary' worksheet, this line is reproduced so you can see how it is different from the apparent wind angle on the main if the jib was not present.
From here, the analysis is similar to that of the jib.
Finally, the 'Analysis' worksheet calculates some data used in the earlier graphs of the 'Summary' worksheet, specifically the amount of lift and its ideal elliptical distribution, and the entry angles at the luff. The lift is estimated and then normalised so it always totals 1.0 in the spreadsheet. In the example shown below, the worksheet estimates that around 74% of the lift is generated by the main, and 26% by the jib (seen in the 'sum' columns).
The spreadsheet has a new graph, showing the estimated leech profiles that you might see if you looked back at the sails from aft of the mast. As you can see, the graph claims I have too much twist in both jib and main!
Having gone through all of this analysis, the spreadsheet allows you to do it all again as a 'what if', so you can compare against your sail photo data. In this case, go to the 'Summary' worksheet, and enter into columns T to AD and rows 14 to 16 the sail shape parameters you want to play with -- draft, position of maximum draft, and twist. Is that cool, or what?
Using the 'what if', you can change the way you want to cut your sails. See what happens if you increase draft towards the head of the main, or decrease draft towards the head of the jib. Model a 'shelf foot' jib which has no draft on the boom, but maximum draft at the lowest batten. See what happens if you set the outhaul of the main to give no belly. And so on... Good luck!
The spreadsheet handles heel angle by the simple expedient of reducing all heights in proportion to the angle of heel. Not many things change as a result, but some things do. Because the effect is to take the foot of the main and jib closer down the wind gradient, its effect is exaggerated in that region. If you compare graphs of lift at heel of 0 and heel of, say, 45, you will notice a larger discrepancy from the ideal elliptical distribution when heeled at the foot of the main.
©2011 Lester Gilbert