Keel design issues

Foil shape evaluation

In evaluating various keel foil shapes, how much weight do you give to the Lift/Drag ratio at target leeway angles versus the widest possible Low Drag Bucket & Lowest Profile Drag?

RW

 

Remember, the lift to drag ratio for leeway includes the hull drag also. The drag bucket really only applies to the 2D (i.e. very high aspect) foil and it's effect is moderated by 3D flow and the hull.

As for how much much design effort to give to selecting a foil L/D depends upon the application. A lot for a one-way speed course reaching cat...not much for a dead down-wind raft like Kon Tiki . As you know,one does not design the foil section, or any part of a vessel, in a vacuum. I tend to balance L/D with stall angle/behaviour to give predictable performance vice riding the knife edge or giving the boat bad habits.

 

"I tend to balance L/D with stall angle/behaviour to give predictable performance vice riding the knife edge or giving the boat bad habits."

Roger that! So considering windward performance only, the higher the L/D for your target leeway range (with acceptable stall) the better?

RW

 

Yes, generally speaking.....to a point. Remember, what we are after here is VMG to weather. The "lift" of a keel is not to weather or athwartships, but is rather perpendicular to the course made good and is a function of leeway and speed. In order to balance the sails the keel lift must resist the sail heeling force (perpendicular to the vessels heading, not course made good) therefor sufficent speed is required at a given leeway angle to generate the this force Leeway angle in turn is the angle of attack of the foil and hull and therefore changes the "drag angle" (the angle between the lift and the resulant force) of the hull. Asuming a fixed "drag angle" for the sail (the angle between the driving force and the resulant sail force), the "pointing angle" becomes the sum of the two "drag angles". Therefor a keel with too high an L/D at a low leeway angle may require too high a driving force while on the wind and therefor is a poorer performer.

This is becoming too complicated without a picture and better discussion than I can give, so see the first 25 pages of Marchaj Aero-hydrodynamics of Sailing and note the discussion of "The ten degree yacht".

 

[the first 25 pages of Marchaj Aero-hydrodynamics of Sailing and note the discussion of the “ten degree yacht".]

Great, I have that, though it's been a while since I read it. I'll dig it out again tonight.

Thanks, RW

 

Keel design question

I would like to ask a couple of questions on this “keel design” thread. Keeping a keel’s root cord short and having an appropriate fillet at the keel/hull intersection appears to be the accepted design for current performance/cruisers with bulb keels. This past weekend when looking at a 37’ bulb keel boat with what I estimated to be a root cord greater than twice the cord at a distance less than one quarter of the span below the hull, I was told by a person, whom I consider knowledgeable about such things, that the long root cord minimizes structural problems, especially in groundings, and reduces drag despite the added surface area. Are there major structural issues associated with bulb keels and short root cords on current performance/cruisers? Does or can an extended root cord of this type actually improve performance?

 

I agree with the first statement, but the second statement makes no sense to me at all. The fact that the keel's lift is perpendicular to the course is simply the definition of lift. The total force is at an angle of 90 degrees + hydrodynamic drag angle from the course through the water. Likewise, the lift on the rig is defined as the component that is perpendicular to the apparent wind. And the total force on the rig is at 90 degrees + aerodynamic drag angle from the apparent wind. The total hydrodynamic force will line up to be equal and opposite to the total aerodynamic force.

As you point out, the lift on the keel has to match the load from the rig (the component of the total aerodynamic force that's perpendicular to the course). So the higher the keel's L/D, the lower will be the drag to produce that same lift at a given speed. The boat speed will increase so the hydrodynamic drag increases to match the driving aerodynamic component. You can't have too high an L/D.

But you can go too far in a misguided effort to raise the L/D. For example, cutting down the keel's chord will cut wetted area and raise the L/D. But if the keel stalls because the area's too small to produce the required lift at the speed the boat can attain, that's bad.

I think the problem with laminar flow sections for keels is the section is constrained to be symmetrical. But the classic NACA 6-series symmetrical sections have a drag bucket that is too narrow - the upwind operating point for the keel is outside the drag bucket. If you enlarge the keel to bring the leeway angle within the drag bucket, you've still lost - it does no good to cut the drag coefficient in half if you have to double the area to do it. A NACA 4-digit section can actually have less drag at the medium lift coefficients used for upwind sailing. And the NACA 6-series sections have a nasty leading edge stall, especially at low Reynolds numbers.

So the way to design an efficient keel is #1 to make it as deep as possible, #2 size the area to provide an adequate reserve of leeway angle to handle down-speed conditions like tacks but still keep the upwind leeway angle high enough that you haven't added excessive wetted area, and #3 pick a section that's consistent with your operating condition. But #3 is way down in importance to #1 and #2.

 

Tom, what I was trying to say, and did poorly, was two points that I pull out of the aero-hydro drag equlibrium.

1) That as the L/D increases, the hydrodynamic drag angle decreases as you point out. What is not apparent is that conversely for equlibrium (for a fixed aerodynamic drag angle), the driving force is reduced and the heeling force is increased. As the drag of the keel is a small part of the total drag of the hull but the lift of the keel a large part of the total side force, having too much lift in the keel increases heeling force faster than it reduces driving force. This is most likely to be detremental to the performance of the boat.

2) In a low leeway situation with a fixed aerodynamic drag angle, decreasing the leeway angle, means that you must increase the pointing angle to perserve the aero drag angle. This may mean that you go to weather slower, depending on the reduction in hydrodynamic drag angle to the reduction in driving force. Otherwise in the real world if you try to preserve the pointing angle, the aero drag angle must decrease which greatly reduces driving force.

As for laminar flow sections, I just offer the following. The kinematic viscosity, nu, of 70 F seawater is 1.11x10^-5. Nominal speed of a moderate sized modern sailing yacht is ~7 knots = V= 11.82 ft/sec. Now given a real world velocity fluctuation of ~0.5% of V we can expect transition to begin on a smooth surface at a Rn ~1.2x10^6 (Hoerner, FDD, p 2-6, he also says that it is very rare to have laminar flow at Rn > 1.0x10^6 even in experiments but I can't find the quote on short notice) so the maximum distance we expect to have laminar flow is: x=Rn*nu/V = 1.13 feet This is as good as it gets. If we give ourselves a 1 ft, 4 sec chop, then the laminar length drops to 0.12 ft. And we haven't even begun to consider roll, pitch, and yaw effects

 

I think this is totally wrong. The lift on the keel will adjust itself to the required value because the boat will be accelerated sideways until it does. For example, what is the L/D of the keel when sailing dead downwind? Zero. But it's the same keel! Nothing you do with the keel will directly affect the driving force - that is set by the rig.

The right way to look at it is, with a higher L/D the boat can achieve the same performance with less driving force required from the rig.

I don't think this is right, either. The locus of points on a performance polar, which have the same combination of aerodynamic drag angle and hydrodynamic drag angle, is a circle. The center of the circle is at (Vmg=VT/2, VT/(2*tan(beta)) on the polar chart, and its radius is VT/(2*sin(beta)); where beta = sum of aero- and hydro-drag angles, VT is the true wind speed, and Vmg is the velocity made good to leeward. Or, in polar coordinates, the center is at (90+beta, Vt/(2*sin(beta)). All these "constant-beta circles" all meet a the origin of the polar plot, and at (Vmg=1, 0).

One does not have to point higher just because the hydrodynamic drag angle is reduced - one can simply go faster. And this works in the real world, too. I've experienced it every time I took my landyacht out to a dry lake. When the yacht is hooked up, the apparent wind angle is virtually the same on all points of sail.

I don't think the orbital velocity of the chop affects the boundary layer in the same way as turbulence in the oncoming flow does. The frequency is so low that it's more like a change in steady speed rather than a turbulent fluctuation. I think one foot of laminar flow sounds reasonable, but I'm quite sure more than 0.12 ft can be maintained on a keel, even in a seaway.

Now I can believe the majority of keels are fully turbulent because of their surface roughness - it's hard to maintain a really smooth surface unless you dry sail the boat.

 

Here we disagree, and I need to run up a vector example.

Crossflow velocities and thier associated pressure gradients can trip laminar flow to turbulent above the critical Rn (for water and laminar about 2x10^5 see Hoerner FDD p 10-1, and 2-11) and wave orbitals are not a steady change as anyone who has "tripped" down the face of a wave with no steerage or been brought up standing and slipped to leeward by a wave slap will tell you. It is major concern in ship/boat control at low (i.e. small sailboat) speeds.

 

TS & Jehardiman-

Have we adequately resoloved the correctness of the above statement?

RW

 

Sorry to jump in here but going back to wing body fairings, would there be an advantage to such a fairing on the root of a windsurfer fin or the daggerboard of a planing dinghy? Or do you not get the vortex forming at high speeds?

 

Sorry, But I got told soon last week i had to go TDY for 2 weeks starting Monday, so I havn't had time to complete the analysis. Maybe i'll work it up at night while I'm TDY.

Yes, there is both a foil root and tip vortices, and speed actually increases the strength. But vortex strength is also function of foil thickness but not cord length. So in terms of drag, the vortex is more important to thick foils than to thin ones. In terms of total wetted surface to foil thickness, vortex drag in windsurfers and dinghies is down in the weeds and ignorable because such vessels tend to be overpowered anyway. The only thing is if the foil vortex begins to interfer with the rudder/skeg, then you may wish to address it.

 

Looking forward to it.

RW

 

This document may help to size your keel: http://hem.bredband.net/b262106/Boat/Boardsize.pdf

Notice the importance of depth in reducing the drag.