Foil balance point changes with aspect ratio?

It has come to my attention that as the aspect ratio of a foil is reduced the center of pressure moves forward relative to the 25% chord for a high aspect foil. Here is one of the papers that led me to this conclusion: https://eprints.soton.ac.uk/43260/1/001-78new.pdf

I'm really not sure what exactly is considered a low aspect ratio. My planned single element wing sails will have an ar of 2.5, rudders and keels an ar 0f 2; all will be naca 0018. The plan was to have the pivot point at 18% of chord, but after reading up more my decision on balance point is being called into question. I'd like to achieve as close to fully balanced as possible with zero risk of overbalancing in any circumstance(high speed, various angles of attack), and maintain a self-feathering characteristic.

Am I safe sticking to the 18% pivot point?

 

Richard Woods says this on another thread:

"Up to about 20% balance is usually OK. The CofE moves at speed so it can overbalance suddenly if you go fast, not usually a problem under 10 knots though. So if you are close to 20% then actual balance depends on many variables, including AR and chord shape."

 

Yes, but.....
Not really the AR, but the effective Cl. Remember that CP for a "lifting" section is a 2D finding, not 3D. Just as important as Richards AR and cord are Reynolds Number (really a function of cord and speed), sweep, and taper. The paper you list has several flaws (typical of a student paper which is artificially temporially and financially limited) in that they didn't explore the whole variable field (even though the paper listed some other factors). Additionally, the "effective" AR of lifting surface is doubled by an end plate...such as a sail to a deck, or a keel to a hull....the "ancient interface". I feel/know that a different answer would have been found if all variables where examined to produce a workable 3D maxima. Focusing on a single factor of a 3D foil leads to strange results that are not reflected in a survey of "good" real life results. FWIW, not even an effective AR of 5 is "high aspect".

That said, a well chosen sweep and taper will keep ~approximately~ the same line of CP and the true CP is generally along this line. I would suggest going back and consulting Hoerner and Marchaj.

 

"It has come to my attention that as the aspect ratio of a foil is reduced the center of pressure moves forward relative to the 25% chord for a high aspect foil."

Yes

"I'm really not sure what exactly is considered a low aspect ratio"

Aeronautical Low AR < 4 AR
Nautical Low AR < 3 AR

It is an imprecise term, it is a way of speaking, but this is more or less the way the expression is used in the two communities.

The practical issue is that the Center of Pressure is about 20% of the chord.

Now I am looking for the book to put a drawing

 

Aspect Ratio (AR) = A

 

"I'd like to achieve as close to fully balanced as possible with zero risk of overbalancing"

Good question

18% is a good bet, I don't know what to say exactly because there are various nuances of taste, desires and risk perception. 20% i think is the limit of the prudent. 18% is a good figure.

 

So the rudders and keels on my design are surface piercing, for both simplicity and so they can kick up, as I will be doing much of my sailing in very shallow water. They will be rectangular, no sweep or taper.

The more I look into this the more complicated it seems. Here is what I have learned from further research since I posted this thread and read your replies. Amazing how much of a difference search terms can make in finding relevant material.

The aspect ratio has a profound effect on the angle at which a given amount of lift is developed. I knew this before but did not know just how great the difference was. It seems that above ar 4 the difference is minimal as ar increases, 3 is modest but below that the angles get pretty extreme. I imagine this plays a big role in how much drag is created for a given amount of lift. But is more gradual development of lift with rudder angle a good thing? Would a high ar rudder be twitchy? Is lower susceptibility to stall with low ar that important?

One paper states: Naca oo12-0015 cp location; ar 1-2 = 12%, ar 2-3 = 18%, ar 3+ = 22%. Recommends balance points of 11%, 17%, 21% respectively. I imagine this is more of a spectrum in reality.

Effective aspect ratio for surface piercing rudders? A couple papers indicate that the free surface acts to "mirror" thus double the effective aspect ratio at low speeds, but at higher speeds it acts as true to its geometric aspect ratio. I believe the froude numbers referenced were .3 and .8. Because of this it seems prudent to plan for using the geometric aspect ratio as the design criteria for choosing the balance point to avoid loss of control at high speeds, such as when surfing down the face of a wave.

It seems that higher ar foil would be less susceptible to ventilation. This begs the question: How much of a problem is ventilation with surface piercing foils?

Am I interpreting all this correctly? What else should i be considering?

 

Yes, generally. With a well balanced vessel you don't need large forces or extreme rudder inputs. Because the effect of a rudder varies greatly with speed, it can be a problem to steer vessels with high AR rudders at low speed. Comments to follow...

Somewhat, but the propensity to precipitously stall is a greater issue.

IMHO, yes it should be selected for.

The attractiveness of a high AR rudder is the seeming increase in turning moment for a reduction in drag. A rectangular planform high AR rudder generates more lift per area than a lower AR rectangular planform rudder of the same area. However, this only occurs at high speed in calm waters (i.e. low variable angles of attack). It must be remembered that vessel operates in a dynamic seaway. You are never guaranteed to get the seaway and winds you want (c.f. Alinghi in the 2010 33rd America's Cup). Because negative sweep increases lift per area and tip taper reduces area outright even a low AR, most modern rudders or lifting planes are not designed with high AR in order to increase the viable operational envelope.

 

"Effective aspect ratio for surface piercing rudders?"

ARe = 0.9 x geometric AR

The formula to make a good calculation is a bit complicated; but for this thread (ARg about 3) it is a reasonable simplification.

"How much of a problem is ventilation with surface piercing foils?"

At more than 20 knots it can be. A simple solution is a fence starting at the leading edge and up to say half the rudder and about 5 centimeters underwater.

Fence:

 

Anti Ventilation Fence

PS Advisor: Cure for the Ventilating Rudder - Practical Sailor https://www.practical-sailor.com/mailport-ps-advisor/ps-advisor-cure-for-the-ventilating-rudder

In this case they have put the Fence quite deep because the sailboat is going to have a bow down attitude.

On small sailboats where the crew moves aft it is normal to be about 5 cm below the water.

 

A sailboat rudder

Taper ratio = 1
Sweep = 0

A rectangle

A rectangle 3.3 -3 ARg, 3-2.7 ARe
Area = 0.5 x Keel

 

It should be noted that the rudder of a sailboat is similar to that of an aircraft and just the opposite of a large ship.

In a big ship the tiny rudder is just the alarm clock or the fuse that wakes up Mr. Max Michael Munk, and once awake Mr. Munk is in charge of turning the ship.

In a Sailboat the big rudder is in charge of putting Mr. Munk to sleep, deactivating and calming his nerves.

I mean that on a sailboat it is worth a good rudder (3 AR, 0.5 x Keel) or a pair of good rudders; but in most cases, outside the racing world, it is not worth playing with the shape beyond a rectangle or overdoing it with AR.

 

Thank you CarlosK2 and jehardiman for your input.

It seems that my original plan is tenable and prudent based on the information and opinions you have provided, and other research. I think I'll stick with the plan for the 2 ar, 18%. I think adding the fences would be a good idea, would only be a minor increase in drag.

Yes, in all my research it seems that the rectangular foils are not far off in efficiency from other forms, and have better stall characteristics.

 

I just had a realization while browsing through various threads. I need to also consider the change in cp when reefed since that will change the aspect ratio. That could have been an unfortunate oversight.

Edit: I meant as applied to the sails.