- Hi,I have done some more tests recently on the relations between camber, area and aspect ratio and for me the pieces of the puzzle are falling into place at last. I was a little surprised when I read Victors post saying that you don't need more than 6% camber as most western sails have 10% or more, but then I saw the light. Modern bermudan sails are the product of class rules and rating rules that impose a limit or penalty on sail area. That means the only option you have to increase performance is to go for maximum camber the conditions allow for. In Marchaj's book 'Sail performance' there is a graph that shows the relation between lift coefficient Cl and camber for a rectangular sail of AR=5 . Increasing camber from 5% to 10% gives an increase of Cl from 1.0 to 1.4 at 10 degrees incedence angle for about the same lift/drag ratio. This means that to get the same lift at 5% camber as at 10% camber you need 40% more sail area. So at 6% camber you need some 30% more area. The extra 30% area gives a better downwind performance so it may well be that 6% camber is the best choice for good performance upwind and downwind. Another good reason is that you don't need much camber in drifting conditions and strong winds and camber is not easily reduced once it is in, but sail area is.That leaves the question of aspect ratio. I have tested 4 rectangular models with AR=2.8 , 2.0 , 1.2 and 1.0 . When aspect ratio (height) goes down the center of effort goes down so area can go up. I used rectangular models because it is easier to apply uniform camber than in more complex shapes. A rectangle is not a bad shape for high AR ratio models but it is not so good for low AR ones as I will show later but to demonstrate the effects of aspect ratio they do just fine. I have uploaded a sketch of the models and a lift/drag graph to a subfolder 'aspect ratio at 6% camber' in the folder 'windtunnel' in the files section. From the graph it is clear that the high AR models generate more lift at low angles than the low AR models despite the smaller area. That's because air flowing from over the top and around the bottom from the high pressure windward side to the low pressure leeward side reduces the lift in the areas near the upper and lower edges of the model (I test the models in a horizontal position but let us assume they stand vertical like real sails) and it is obvious that a larger part of the total area is affected for low AR models. This overflow creates vortices that are responsible for the induced drag. At low angles and lift the induced drag is low but when the incedence angle and lift go up the induced drag increases rapidly (it is proportional to lift squared and inverse proportional to height squared) and the lift/drag ratio goes down.An incedence angle of 10 degrees is supposed to give the best combination of lift and lift/drag ratio for windward performance so I have drawn two lines in the graph through the point of 10 degrees incedence angle of the AR=2.8 model. A straight line for the lift/drag ratio and a curve for the lift-drag force vector. The lift/drag line shows that a low AR model can point as high at reduced angle and power. The force vector curve indicates you can have the same lift-drag vector by pointing some degrees lower. The difference in pointing angle between AR=2.0 and AR=1.2 is 3 degrees for the same forward drive and sideways force but AR=1.2 will have a lower heeling moment due to the lower center of effort.For AR=2.8 and 2.0 stall sets in at angles near 20 degrees and the performance drops but AR=1.2 and 1.0 continue to generate more power up to angles of 30 - 35 degrees. This is due to the fact that the vortices at the top and bottom (that are closer together on low AR models) grow so strong that their influence over the middle part of the model delays stall to high angles.So a high AR model gives the best windward performance and a low AR model gives the best reaching and running performance. The best overall performance has to be a compromise between the two with an AR between 2.0 and 1.2 .This brings me to the junksail model with AR=1.55 I tested earlier. This time I gave it 6% camber and I tested it against a rectangular model of AR=1.5 with the 6% camber and about the same area. I uploaded a sketch an lift/drag graph to the same subfolder I mentioned above. The junksail model is clearly superior at higher incedence angles. Its lift/drag curve is very similar to the one of the rectangle with AR=1.2 so aspect ratio (height/average chord) may not be such a good measure to compare models of different shapes. A better ratio is perhaps height/chord at 50% height. For a rectangle that changes nothing but for the junksail model that ratio is close to 1.2 so that explains the behaviour at high angles better.My conclusion is that a sail with about the same proportions as the junksail model will give the best overall performance for cruising (I am more and more convinced the Chinese knew their business). A low sail means a low mast that saves weight and drag. Also mast interference on the sail is reduced as it is proportional to mast diameter/sail chord.Last subject is the position of maximum camber. For sails the best position is at 50% chord, however varying the position between 1/3 and 2/3 of chord has little or no effect on lift and lift/drag ratio at incedence angles around 10 degrees used for windward sailing. There are some differences near the point of stall but as low AR sails have a high stall angle anyway these differences are negligible.I used to give the models maximum camber at around 40% of chord but this time I put it at 50% for the high AR models and at 60% for the low AR ones. The reason for this aft postion is that you can set the sail at a lower angle to the wind without luffing to get the best lift/drag ratio for a low AR sail if you want to point as high as possible (at reduced power of course).There are also more practical reasons. If you use cambered panels then having the camber further aft means the mast does not interfere much with camber when on the lee side of the sail and when your sail has angled battens so that the panels are wider aft than at the luff it is quite 'natural' to have the camber in a more aft position.Bernard
- Hi Victor,

Marchaj in his book 'Sail performance' says that the performance differences

when you vary the position of max. camber from 1/3 to 2/3 of chord do not

exceed 4%. This applies to a single sail. For a mainsail with a headsail in

front of it he says the positon of max. camber depends on many factors such

as overlap, camber distribution of the headsail etc. so he gives no specific

value. I do not think the (lack of) accuracy of my simple test equipment

allows me to detect such small differences with any level of significance.

Anyway the effect on performance of the amount of camber itself is much

greater.

Bernard

----- Original Message -----

From: Victor Winterthun <victor.winterthun@...>

To: <junkrig@yahoogroups.com>

Sent: Tuesday, July 23, 2002 9:18 PM

Subject: Re: [junkrig] Re: camber area and aspect ratio

> Hi Bernard.

>

> Long time ago, I read that a "cat-rig"(only one sail), shound have max.

camber at 50%, but when there were a foresail, the max. camber in the

mainsail should be ca. 30% from the luff. This refer to gaff. rig. May be

the same is the case for the junk rig?.

>

> Victor.