sail aerodynamics

[brian eiland]

Perhaps I read it wrong, that there was no general rule about sheet angles, but certainly playing with the trim of our sails can have a BIG effect on the driving forces obtainable.

 

[Jamie Kennedy]

This is what happens when we let Republicans sail.

 

[markdrela]

So it would appear as though I have my sails trimmed (or designed) too tight to the centerline of the vessel in that diagram I posted HERE in #557

Not necessarily.

There's nothing fundamentally wrong with hauling in the mainsail so tight that the leech angle goes past the boat centerline. Yes, the airload on the leech area then appears to retard rather than propel the boat. But this "backwards" airload also has the side effect of making the airloads on the mainsail luff or on the whole jib point more forward. The overall lift is certainly increased, and overall drive may or may not be increased.

I'll say it again: Looking at the local sail angles or flow angles at any location away from the mainsail leech says nothing conclusive about the overall aero force on the whole rig, which is what really counts. Only the mainsail "leech return angle" by itself is a good approximate indicator of the overall CL of the entire rig. For the record, I define this as the angle between the aftmost ~15% of the mainsail and the relative wind.

The job of controlling the overall CL therefore falls on the mainsail trimmer alone. The jib trimmer has almost no influence on this CL, and should instead focus on suppressing separation indicated by telltales, especially those immediately behind the mast. If this is common knowledge then sorry for the spam.

 

[Petros]

all of this is true, but also keep in mind that too much aft camber, relative to the camber on the front third of the sail, can cause the flow to separate off the TE, loosing lift and created a lot of drag. this happens with old stretched out sails, badly designed sails or with improper trimming of the sail. This occurs because the curvature is larger than the flow can stay attached at the trailing edge, which is kind of twitchy area anyway because of a large boundary layer and the increasing pressure gradient going towards the TE of the sail. This is called the pressure recovery area, because the low pressure area at the forward part of the sail has to increase back up to the free stream pressure by the time it gets to the TE. If done with too much curvature on the surface, it will separate and lose lift and increase drag. you can see this when the TE of the sail is fluttering when using old stretched out sails.

This is a separate issue than the so-called leach return angle, but because there are those here that may confuse these issues I thought I would point out the difference.

 

[markdrela]

This is a separate issue than the so-called leach return angle, but because there are those here that may confuse these issues I thought I would point out the difference.

Yes. The boundary layers only care about pressure distributions, and certainly don't care about curvatures directly.

The curvatures affect BL behavior only via the curvatures' effects on the pressures. It seems the crucial pressure "middleman" is too often forgotten.

 

[markdrela]

The attached PDF gives the relation between an airfoil's lift coefficient and its local incidence angle distribution. This quantifies the stuff I've been saying about what does and does not affect the lift on a sail. The relation comes from thin airfoil theory, but it is still reasonably accurate if the camberline is broken up into a number of smaller pieces. It there's an overlap, then the local incidence of the overlapping sheets should be averaged.

The key part of the relation is the lift/incidence influence function f_a(x), which multiples the local incidence distribution. This f_a(x) is small on the front parts of the airfoil and grows over the rear parts, and becomes infinite (but integrable) at the trailing edge. Basically, any shape changes on the front of the airfoil get mostly quashed by the small f_a values there. Conversely, any shape changes towards the trailing edge get strongly magnified by the large f_a. So to control lift we need to modify the rear airfoil shape, and can mostly ignore the front airfoil shape.

The total area under the f_a function is 2 pi. So if the airfoil is flat so that alpha(x) is a constant, then we get cl = 2 pi alpha as expected.

Some area breakdowns under f_a are as follows:

From 0.0 to 0.5: 18%
From 0.5 to 1.0: 82%
This means that the shape of the rear half of the airfoil on average has 4.5 times more influence on the lift than the front half.

From 0.0 to 0.84: 50%
From 0.84 to 1.0: 50%
The means that the shape of the rearmost 1/6'th of the airfoil controls half of the total lift.

 

[philSweet]

<edit>> I cross posted with everything on this page above, sorry for the time lag and duplication.

<<edit #2>> I changed a term because I used a different def. than Mark did - swapped "hook" for "return angle"

<<edit #3>> In the end, it was mostly duplication, I decided to delete the whole thing.

 

[Jamie Kennedy]

Everything is a compromise when you are sailing 40 pounds overweight in a 26 year old boat.

Powered up:

 

[CT249]

Tell that to any sheet line trimmer (racing sailor), and see his/her reaction :!:

I think the best racing trimmers/sailmakers I've sailed with or raced closely against would agree that "There's no general rule that the various sheet angles must be such-and-such to get the best performance".

 

[Doug Halsey]

For those who might still be skeptical of what Mark is saying, the Gurney flap (conceived by famous race-car driver Dan Gurney) provides a real-life illustration of what a powerful effect a perturbation of the trailing-edge flow can have on the total lift of a wing. The following article credits the 2 vortices just downstream of the trailing edge for much of the benefit, but I'll bet that, even without the vortices, the change in the trailing-edge incidence would still provide a significant increase in lift. (Note - the wing is designed to lift down )

http://allamericanracers.com/the-gurney-flap/

 

[Jamie Kennedy]

Often in boats like Yngling, Soling, and even a laser, in flat water medium winds it can often pay to really go into ultra-point mode. So you use the main to really power up the jib even if it means hooking the leach to windward. In the Laser, no jib of course, in some rare conditions when the boat is going fast in flat water but the lighter side of medium, like say 5 knots, you can ease the traveler a bit and pull the boom in a bit on the traveller. The mainsheet is eased say 5-6 inches from block to block. The effect is you switch to an ultrahigh gear and climb up to windwards without losing too much speed or having too much leeway. You have to gear down to accelerate if you lose speed, but once moving you can pull the boom in and do it again.

I think the reason this works is there is enough wind to get the boat close to hull speed where you start getting some diminishing returns on going faster, but there is not so much wind that you can point high due to the velocity shift from true wind speed. You still need a powerful sail so you don't want to overflatten, but you also want to point high so you don't mind hooking a bit. It seems to work, but you really need other boats around to guage yourself against so you don't strangle yourself stalling the sail or keel/centreboard. I think I will call this the Gurney Flap next time I try it.

 

[Remmlinger]

The means that the shape of the rearmost 1/6'th of the airfoil controls half of the total lift.

This lecture on sail aerodynamics at boatdesign.net by Prof. Drela is extremely helpful for me, since it teaches the facts that really matter. I also admire that he takes the time to answer individual questions and to guide the laymen to the right conclusions. Thanks a lot to this awesome teacher!
Uli

 

[brian eiland]

For those who might still be skeptical of what Mark is saying, the Gurney flap (conceived by famous race-car driver Dan Gurney) provides a real-life illustration of what a powerful effect a perturbation of the trailing-edge flow can have on the total lift of a wing. The following article credits the 2 vortices just downstream of the trailing edge for much of the benefit, but I'll bet that, even without the vortices, the change in the trailing-edge incidence would still provide a significant increase in lift. (Note - the wing is designed to lift down )

http://allamericanracers.com/the-gurney-flap/

Here is the problem I have with that 'analogue'. I have no problem seeing that this sort of treatment to the trailing edge of the foil will increase its 'lift'. But remember this is on a foil that is being powered into the wind, NOT on a foil that is deriving its lift from the airflow over itself.

Think of the drag consequences of the two. With the race car there is excess power available to overcome that extra drag created. In fact that rear foil is really called upon during braking/cornering to create that extra downforce for traction. Dang the extra drag,..who cares at that point. You can likely bet they don't run down the straight-aways with that rear foil fully deployed.

On a sailboat we don't have the luxury of an engine to power us into the wind (at least that is not how it is suppose to work). We rely on the wind to develop the lift in our sails, and I image there is only a certain amount of tail-end configuring that we want to do just to increase lift?

If we added a 'hook' like that Gurney foil I would image we might slow down quite a bit. I also question how much 'lift' we need from our sails considering that the very large percentage of the lift force on on our sails is directed athwartships rather than in a forward driving direction (sailing foils rather than flying foils).

So it becomes a lift-drag trade off in our sailing vessels, not how much total lift we can generate. And that is where I thought the shape of the sails (along their whole length/camber), and the interaction of different sails on any particular rig design that became important to keep the flow as laminar as possible to help reduce drag. In other words it was not just primarily the leech return angle?

 

[Jamie Kennedy]

Such drastic measures are usually not called for in sailing, but there are exceptions such as when the boat is underpowered in say 5 knots of wind, and has excess righting moment, and can handle a little extra induced drag in order to get greater thrust to overcome non-aerodynamic drag forces. In such instances you bring the traveller of a two sail boat up to weather more than you normally would, even to the point of the top battens hooking somewhat, and the boat goes a little slower but a lot higher. It is difficult to point well in 5 knots because the boat speed can be a greater fraction of the wind speed in this amount of wind.

 

[Doug Halsey]

Originally Posted by brian eiland :
If we added a 'hook' like that Gurney foil I would image we might slow down quite a bit.

I agree totally. Gurney flaps might slow you down (if it would even be possible to mount them on a sail). The reason for my post was simply to illustrate the importance of the trailing-edge area, not to suggest that you would want to use them.

I also question how much 'lift' we need from our sails considering that the very large percentage of the lift force on our sails is directed athwartships rather than in a forward driving direction

That's an interesting subject in its own right. It's important to know what we're trying to achieve.

If you were writing a VPP code (which balances the aerodynamic & hydrodynamic forces), it would be important to know that the maximum speed on a given point of sail would be when you trimmed the sails in such a way as to minimize the sum of the aerodynamic & the hydrodynamic drag angles. Each drag angle is defined as the arc cotangent of the lift/drag ratio. While that nails it down for the code, it doesn't give a practical sailor much to sink his teeth into.

Looking at some special cases can help though.

The simplest special case is the idealized iceboat, which assumes that the runners can provide whatever sideforce is necessary, but with zero drag. In that case, the maximum speed in any wind direction is obtained by trimming the sail for maximum lift/drag ratio. (where it should be emphasized that the lift & drag from all sources need to be included, & limitations on heeling moment would of course need to be considered). This might be a practical result for iceboats, but usually not for softwater sailors.

Another special case which is much more commonly applicable is the case where the hydrodynamic drag due to sideforce is a small part of the total hydrodynamic drag. This is the situation much of the time, especially for heavy keelboats where the drag is dominated by wavemaking drag, but also in many circumstances for light-displacement boats. In this case, the sails should be trimmed in order to maximize the thrust in the forward direction (again, subject to heeling moment limitations).

To get the thrust & heeling force, a straightforward rotation of coordinates is applied :

T = L * sin(beta) - D * cos(beta)

S = L * cos(beta) + D * sin(beta)

where L & D are the aerodynamic lift & drag components (including the sail + everything else in the air), T & S are the components in the forward & side directions, and beta is the apparent wind angle.

From these relationships, you can see that maximum lift is the optimum at beta=90Deg (~beam reach) & maximum drag is optimum at beta=180Deg
(~dead run). At values of beta smaller than 90Deg., the optimum lift is somewhat less than maximum, but also larger than the point with max L/D.

This is illustrated by the attached figure from Marchaj's 1st book (Sailing Theory & Practice, which I recommend highly to anyone interested in this subject.