When does the low aspect foil shine?

I know that a high aspect foil is the most efficient for fast boats, but what about slow boats? I am tinkering with a design for a dagger board for my Tiki 21. It needs the most help to windward in light conditions, say a couple of knots of boat speed. The speed to windward maxes out at about 7 knots fully powered up. Is a low aspect ratio foil going to work better in the low speed range (< 5 knots)?

 

Your question makes me think about the venerable Mirror dinghy.
Mirror (dinghy) - Wikipedia https://en.wikipedia.org/wiki/Mirror_(dinghy)
We had one when I was a wee lad, and our sail number in the 60's was already 20,628 - I think that they eventually got up to 50 - 60,000 in number?
And they just have a flat plywood board as a daggerboard - nothing 'aerofoil shaped' (in the conventional sense) here.
Yet they could / do sail very effectively to windward - a flat plate will still generate lift when subjected to an angle of attack in a fluid.
But if you make it foil shaped, then all else being equal, it should perform better than a flat plate, although the difference is probably not going to be significant if you are pootling along at less than 5 knots.

 

No.
For the same surface area, a high aspect ratio will perform better.

 

A low aspect keel allows for shoal drafting.. At the expense of windward performance.

 

I personally don't think the issue is about the actual performance of the keel, the more important question is which would make a better boat given the operational requirements.

 

I assume by "aspect ratio" you mean the ratio of the span (distance from the bottom of the boat to the tip of the foil) to the average chord (width in side view).
Aspect ratio is also equal to span^2 / side view area

There is also the thickness ratio and the section shape of the foil to consider.

Same surface area and higher aspect ratio implies a deeper draft / longer span.

If the draft/span is fixed the situation is more complicated. Drag due creating vortices while creating lift (side force) is known as "induced drag" and depends only on span and is independent of aspect ratio. Reducing the area of the board to increase the aspect ratio does not reduce induced drag for a fixed lift as the angle of attack will need to increase to keep the lift the same.

Drag also occurs do to viscous skin friction. This is a function of area, foil section shape and angle of attack. For a given foil section shape, span and lift there will be an area and corresponding aspect ratio which results in minimum drag. However there can be reasons why a larger area / smaller aspect ratio is better for the boat than the minimum drag area / aspect ratio. For instance the minimum drag area foil may be too close to stalling.

My experience sailing several boats with a flat plate centerboards is below a certain speed the centerboard stalls when trying to sail upwind due to the combination of the slow speed and angle of attack. I believe a a centerboard with suitable airfoil section would be much less prone to stalling at slow speeds. For flat plates to efficiently develop lift the Reynolds Number, in other words speed, needs to be sufficiently high. Also flat plates tend to stall at lower angle of attack than an airfoil section.

Replacing a flat plate board with a board with airfoil sections is likely to have a considerably larger impact on slow speed performance than changing the aspect ratio.

 

To expand on my question. I am assuming that the board will be a NACA 00 profile. My reading of posts on this site is that a low aspect foil is less inclined to stall, therefore for low speed performance a low aspect foil may be superior to a high aspect foil despite increased drag, because it maintains an attached flow when the high aspect narrow chord board has stalled?

 

For arguments sake, let's compare two boards with the same surface area:
1' chord and 6' span - 1.44" thick at 30% chord (NACA 0012)
2' chord and 3' span - 2.88" thick at 30% chord (NACA 0012)
The first board would be expected to produce more lift and less drag when at speed.
But does the shorter board work better at low speeds or in rougher (pitching) conditions despite having higher drag?

 

If low speed is low enough, yes. But above 2 knots is definitely not enough. 0.5 knots probably is.
In conditions where the latter foil is better, 2' chord and 6' span foil would be superior compared to it, while having double area.

Keep in mind the target is not to optimize drag of just the keel/board, its to minimize drag of the boat.
Larger area foil with less leeway increases drag of the board, but reduces drag of the hull in most cases. Up to a certain size the reduction of hull drag is larger, thus reducing drag overall despite increasing board drag. Above such size any increase of foil area will increase drag overall. This is the main cause why optimum size exists for any boat speed, but it is not the same size for all speeds.

 

Fascinating thanks. Is there a rule of thumb for this board area drag vs hull drag (I'm not good at math)?

 

Aspect ratio is often misunderstood. Aspect ratio is most often presented as how skinny is the board - the ratio of its length to its width. But I think it helps to consider the length and the width separately.

The first thing is the side force (lift) from the board is not determined by the board design. The side force from the board has to equal the applied side force from the rig if the boat is to travel in a straight line. What changes is the leeway angle required to generate that side force. The board design is primarily concerned with how much drag is associated with that side force. You want to go upwind at 2 kt, which is a fairly low speed, so the board needs to be big enough that the flow isn't separated as it tries to generate that side force at low speed.

Assuming the board has adequate size and the flow is attached, the two principal sources of drag come from skin friction and the induced drag from the lift on the board. The skin friction is proportional to the wetted area of the board, so while the board needs to be of adequate size to perform well at low speed, it shouldn't be grossly oversized as that will add to the skin friction drag. But since the drag due to skin friction is small compared to the drag from separated flow, it's better to err on the side of an oversized board than an undersized board.

The induced drag does not depend on the area of the board. It depends on the span (depth) of the board. Actually the square of the span. So adding 40% to the depth of the board will cut the induced drag in half. If you do that while keeping the area of the board the same, it will have to be more narrow. Hence higher in aspect ratio. But you can get the same induced drag reduction by simply making the board longer and keeping the same width. In that case there will be some additional drag due to skin friction. Or you could scale the board up, keeping the same aspect ratio, and increasing both the span and the chord. In that case, the area will be doubled, doubling the skin friction, but the induced drag will be halved with no change in aspect ratio.

While the skin friction goes up with the square of the speed, the induced drag actually drops with the square of the speed when producing the same lift. So a long board is especially valuable when trying to optimize the performance at low speed.

Since your Tiki 21 has a daggerboard, which allows the area to be varied, I'd say make the board as wide as will fit in the trunk, and as long as you can stand it to be when it is raised all the way. Then you can have the board all the way down for good performance in light winds. If that proves to be too much drag in higher winds, then raise the board. When you raise the board, the induced drag will go up, but the skin friction will drop. However just going fast will reduce the induced drag and increase the skin friction, so the best size for the board will be smaller at high speed.

If you find that you never really need to use the full depth of the board in light winds, chop it off.

 

You are assuming that all the side force is created by the board, while in reality, some of it comes from the hull or hulls.
In order to minimize drag of both hulls and the board will always lead to less leeway than minimizing drag from the board while producing all the side force on its own. And that means a larger and/or deeper board than it would otherwise be.

Sure, then all that is still missing is your analyses of the planform shape. The part of board intended to be at the height of the hull bottom at any condition need to be close to the same chord as the trunk, otherwise there will be extra junction drag. But considering the condition when board is in the most lifted position, the remaining lower part still in the water does not have to have the same chord, it can be shorter and deeper for the same area if it's not. How should it be shaped from the perspective of minimizing drag?
Is there a practical minimum chord, that is needed to keep Re number high enough at low operating speeds to avoid early separation?
Obviously dependent on 2D section as well.

 

I had in mind a rectangular planform (constant chord), but if you wanted to add some taper to the lower part of the board that would work, too. There's no reason to go with such a small tip chord that you'd have to worry about very low Reynolds number. A taper ratio of 35% to 50% would work fine and get you quite close to the ideal curved planform. The taper could start at roughly half of the span of the exposed board when it was at the highest sailing position.

 

If you are looking for a rule of thumb, you are plenty good enough at math.


A low aspect ratio wing will never out perform a high aspect ratio wing, as a wing. It can outperform as a 'not a wing'.
Structurally low aspect wing is better than higher aspect ratio wings.
For example, generally, a span constrained low aspect ratio wing will be out performed by taking the given materials and making 2 higher aspect ratio wings to replace it.
However these skinny wings will probably not work well as rock colliders.

If you add to the wings duties the job of tolerating rock collisions, then a low aspect ratio wing will be better at this one job. So, structurally, a low aspect wing is better than higher aspect ratio wings.

Be careful, if you begin to worry about the structure of wings, you will start down the path of bell shaped wings, and everyone will think you mad.