About the author of this item …
Sandy Day is a professor of hydrodynamics in the Department of Naval Architecture, Ocean and Marine Engineering at Strathclyde University in Glasgow, where he teaches a range of subjects including yacht design and performance prediction. He is currently learning to sail MUSTO GBR111.
Some thoughts on the aerodynamics of alternative designs
There’s been some discussion on the forum recently regarding the possibility of a new-look sail for the MUSTO, and a “square top” sail has been suggested as one possibility. This seems to have been driven by a number of factors, including the desire to make the boat more modern looking, but also to make the sail more efficient. One important question is whether there could be any obvious aerodynamic benefit which might result from a re-design if the spars and the sail area stay the same.
One of the key parameters affecting the upwind performance of the sail is the Aspect Ratio (strictly speaking the Geometric Aspect Ratio) – this is the span of the sail divided by the average chord, or span^2/area. If the mast and the sail area are fixed for the re-design, then this won’t change, so any benefits must come from changes in the planform shape. These effects are typically quite small.
In upwind sailing, when the sail is fully powered up with the mainsheet trimmed in and the twist set correctly (i.e. before any depowering is needed) the fastest speed will be obtained by maximising the drive – the force in the direction the boat is moving. This is a function of both the lift and the drag of the sail. The lift will be relatively insensitive to the planform shape if the area and aspect ratio are fixed, so the main scope for benefit in these conditions lies in reducing the drag. When the boat is sailing upwind, the main elements of drag are skin friction drag of the air flowing over the sail, and induced (or vortex) drag, which is related to the generation of lift on a 3D sail and the vortices shed from the leech of the sail. At a given speed, the friction drag is essentially dominated by the area, so again, there is no real opportunity for improvement. This leaves the induced drag.
For a given lift force and fixed sail area the induced drag will reduce as the aspect ratio increases, but this isn’t possible without increasing the mast length. With mast height fixed, any benefit must come from changing the distribution of lift along the mast. Classical aerodynamic theory suggests for a high aspect ratio lifting surface (like the MUSTO sail, with AR about 4.1) that minimum induced drag for a given aspect ratio and lift force is generated by a surface with an elliptical distribution of lift. This can be achieved in a variety of ways. With the correct twist distribution this could be achieved by having an elliptical distribution of chord. A very similar alternative which would be subtly different, due to the mast curve, would be to have an elliptical leech profile.
To examine what these “ideal” sails would look like compared to the current design, I measured up my sail (as well as I could on my living room floor), made a CAD model, and then generated two alternative elliptical planforms, one with elliptical leech (“ellipse 1”) and one with elliptical chord (“ellipse 2”). In each case I kept the batten ends in the same vertical locations, and adjusted the areas to be the same as the original sail.
Results in both cases are very similar to the current sail (no doubt the sail designers were thinking the same way!) and the sails all look similar, so it seems there would seem to be no real benefit to be gained by changing the design in this way.
Once wind strengthens so that the sail starts to need to be depowered the elliptical planform will not be optimal, due to the high CE. Depowering will often increase twist, which will reduce lift, and lower the CE (both of which contribute to reducing heeling) but leads to a penalty of increased induced drag (which reduces drive). At this point a smaller sail on the same mast (for example a sail with less roach) could well be quicker; it will have a higher aspect ratio, so good for induced drag, and lower CE, so less heeling lever, but it would also require less depowering, so would have less induced drag penalty for non-optimum twist.
A second alternative would be to go for a “square top” or trapezoidal sail. The key question then is to pick the best Taper Ratio, (the ratio of the chord at the head to the chord at the base). For the MUSTO, I used the chord at the clew as the reference value for the base. For aircraft wings it is well known that at an aspect ratio of around 4, a trapezoidal lifting surface with taper ratio of around 0.35-0.4 and optimum twist gives induced drag almost indistinguishable from an elliptical lift distribution.
I calculated two geometries, one with a trapezoidal distribution of chord (“Square-top 1”), which leads to a hollow leech shape (due to the mast curve) and one with a straight leech (“Square-top 2”), which gives a slightly non-trapezoidal chord distribution. Again the sizes were adjusted to give equal area. The lower limit on the taper ratio is driven by the length of the boom – with a taper ratio of 0.35, and a straight leech, matching the current area requires a longer boom. Even with a taper ratio of 0.4, the hollow leech version still requires a longer clew than the current sail. The straight-leech version has a clew length very similar to the current sail. It would be possible to achieve a slightly lower value of taper ratio with the same clew length by adding a small roach to the sail.
The centre of effort for the square top is about 2.5% higher than the current sail, and the heeling moment will be correspondingly higher; the bow-down moment on the bear away will also increase, as will potentially the weight of water on the sail when capsized.
It is interesting to note that current Moth sails typically have a planform shape not unlike this, with a taper ratio of around 0.4, although the aspect ratio of a moth sail is slightly less than the MUSTO at about 3.3 (see for example http://www.lennonsails.com/moth-sails.html). The RS600ff switched from an elliptical-style sail to a square top of a similar form, though also lower aspect ratio.
In theory then, the aerodynamic performance upwind in steady winds would probably be affected very little by a change to a square top sail like this when fully-powered up (but not depowering),. Sailmakers can comment on the cost and weight implications, and the ease of twist control (though the moths seem to manage well enough).
Going for a sail with a higher taper ratio (i.e. a more rectangular sail, with more area at the top and a shorter clew) would most likely increase induced drag compared to the current sail as well as presenting challenges in twist control. Boats which have been designed with more extreme square top sails are often trying to increase sail area on a given mast height. This might work in principle for a larger light-wind sail for the MUSTO, assuming that the spars can take the loads, and that the twist could be controlled, but it would be hard to add a substantial sail area without lengthening the boom.
Leaving aside the question of styling, it seems that the most likely benefits of the square top sail might be the ease of depowering in stronger winds and/or the dynamic response of the sail – perhaps the square top sail might depower more controllably than the current design, which could make the boat easier to sail in strong and/or gusty winds. Maybe some of the moth sailors in the MUSTO fleet can comment on that
Sandy Day (GBR111)
