Mast rake

I was doing some research online and came across an article that indicated that the leading edge of a keel should have a rake of 15 degrees to generate the greatest amount of lift and least drag. Got me to thinking that might also hold true for a mast. It would probably only work on a catboat or cat ketch with a free standing mast. I did a sketch comparing a vertical mast to a mast raked 15 degrees and the masthead of the raked mast was approximately 10% lower than the vertical mast with the same amount of sail area. The center of effort was also about 5% lower. Haven't found any studies yet on this but also haven't looked very hard either. Anybody have any thoughts on this?
Chuck

 

A sharply raked mast causes some auxiliary problems that may not be what you need. The clew end of the boom will be lower if the sail is not re-cut at the foot. In light to moderate airs, off wind, the weight of the boom will tend to bring it amidships. That's a pain that means that you might have to pole the boom out.

Some of the imagined ( or actual) advantage is that a raked mast will generate some lift in the vertical direction. That essentially lightens the boat with respect to the water. Depends on the boat and its all up weight, whether this is a worth while adjustment. Sailboards use this to some advantage.

You must consider that the center of effort of the sail will move in accordance with the degree of rake. That can give you excessive weather helm which may very well defeat the advantages, if any advantage actually exists, in the aerodynamic realm. It seems to me that increasing tip vortexes may be counter productive. We'll have to let our aero experts, like........ Tom Speer, comment about that.

 

DO NOT compare keel leading edge angle and mast rake... two different things.

Leading Edge rake of a keel is dictated by sweep (generally slightly negative) and taper for the desired aspect ratio and plan form. It has only slight connections to things like sheading kelp and lines.

In a modern Bermuda rig, sweep is always negative, but the mast is raked for more practical reasons...like keeping the boom out of the water (EDIT) and as messabout says, placing the center of effort.

 

Not sure if this is entirely helpful, but here is a good example of mast rake in use.

On a Hobie Cat(16), the mast is very adjustable, and is typically raked back, rather extremely.
For one, in racing, it moves the center of effort aft, and because the boat has no daggerboards, it puts it over the rudders more, allowing them to act as daggerboards.

It also moves the sails aft relative to the hulls, so I've heard it reduces the tendency to pitchpole, something these cats often have trouble with.

 

J24's benefited from more mast rake than was legal under class rules. Young 88's and Farr 1020's went better with more rake. My seawind 24 is better with alot more rake than standard. I am sure it depends on the boat, get a big long shackle or two and experiment. Ian Brown (sail maker) used to run a bit more rake than designed in all his boats that I saw, he is not too slow around the track.

 

Block to block was the goal. They say it generated lift which the low buoyancy Hobies greatly benefited from. All the quick guys did it from my memory.

 

From a sail design point of view, the least induced drag is created with a sail that has an elliptical cross section when viewed from the side. Designers approximate this by raking the mast back and curving the leach of the sail forward (nicely shown in the Hobie Cat photos). This is mainly a factor when going to weather. Most gliders approximate an ellipse by having several wing sections with different tapers.

 

Induced drag is only one consideration and not as important, as it's been impressed into many mind sets. Simply put, yeah, you can save some tip vortice generation with an elliptical plan form, but you also lose a good amount of lift across the tapered portions of the span. It's been found that using a square(ish) tip is more beneficial, though you do have more tip vortice generation, the additional area and lift offered offsets these loses.

The famous example in elliptical wings is the WWII SpitFire, yet it too had it's tip clipped square in the MK 12's and other special service variants, as early as 1941, suggesting even the mighty SpitFire was figuring out the real importance of tip vortice/versus lift generation. As far as gliders using sectional differences to make plan form changes, this is difficult to grasp, but you'll note these long aspect foils typically have square tips, much like the fastest of the latest speed demons in sail design.

Back to the initial OP question, rake can be beneficial, though to a degree and shouldn't be compared to water flow over a foil. Too much rake on a mast will make sheet and halyards load exponentially higher, plus the lose of aspect for it's length. A sailboat fin's leading edge can have it's entry angle and root entry optimized, for it's plan form and aspect ratio, though you may lock yourself (the design) into a specific speed range where it's efficiency is ideal, instead of a broader range of effectiveness a different set of choices might bring.

 

That's not really true. The planform for minimum induced drag actually looks more like a sailboard rig, and is more egg-shaped than elliptical.

The reason Hobie 16s rake their rig back doesn't have much to do with the sail rig. It's because they don't have daggerboards. The induced drag of the hull is inversely proportional to the square of the span (depth), and the boardless hulls have a very small span, and create a lot of induced drag. The rudders are much deeper, so if you generate the side force with the rudders instead of the hulls, the drag is a lot less.

The force on the rudder depends on the directional balance of the boat. Raking the rig aft results in weather helm. The rudder has to be trimmed to oppose the helm, generating the side force. Since the total hydrodynamic side force has to equal the total aerodynamic side force, this unloads the hull - it's a zero sum game. The rake shifts the load from the hull to the rudders, and hydrodynamic induced drag is reduced.

You don't want to do this with most boats, because they usually have a board or keel that is deeper than the rudder. So they are best sailed with a light load on the rudder and the side force produced by the deepest appendage.

This is why it takes a VPP to figure out how to optimize the sail trim for best performance. You have to trim for what's best for the whole boat, not just the best from an aerodynamic perspective.

 

Good article

Thanks for the link - good article. Interesting that essentially any gap changes things dramatically. I don't see much change in the pressure profile on the mainsail near the gap compared with above it, although the flow is obviously strongly affected.

 

I believe simple theory over-estimates the effect of small gaps. You can see that in this figure:


The Hoerner curve is empircal data, while the line with diamonds is from the lifting line. In practice, the drag may not shoot up quite so fast for small gaps. But a gap of 5% span is not unusual in sail rigs, depending on how much credit you want to give to the hull and sealing of the foot of the jib.

The lift has to go to zero at a gap. That typically means the spanwise lift distribution drops off rapidly approaching the gap. The vorticity shed into the wake is proportional to the slope of the spanwise lift distribution, and there will be a sizable increase in the induced drag due to the gap. It may be that in a viscous flow, the lift doesn't quite go all the way to zero at the end, and that's why the empirical results look better than simple theory would suggest.

I think Artemis discovered this effect in the last America's Cup campaign. They started with a wing that had discrete changes in flap deflection along the span. There would have been a vortex shed at each step between flaps, because of the sudden change in spanwise lift distribution. with an attendant increase in induced drag. They eventually went to a continuous spanwise variation in their flap deflection.

 

In real life a boat that gripes a bit to weather is fast than one that doesn't in the hands of most helmsmen, all other things being equal. This is one reason that a bit of rake is faster upwind in reality even though it may not be in theory. The helmsman is not always "on it" where as a a bit of weather helm is.

 

Seeing as almost all modern go-fast boats have no or almost no keel rake I would be dubious about the real world application of that article.