Foil Design 1970's Keel Boat

Tim B.

Excellent summary!

Eric

 

Still searching for that paper. It is here somewhere...

 

So here it is!
Published in "Katera I yachty" 1984/1

Some explanations for those not fluent in Russian.

Drawing on page 24:
*T -driving force of the sails,
*R- longitudinal part of all hydrodynamic forces
*C -transversal force on rudder, which act to compensate luffing moment
*a -luffing moment lever arm
*b -compensating moment lever arm


Graph on page 25:
*horizontal axis: R(IOR) or LWL (normally they are numerically similar), m
*vertical axis: coefficient of rudder efficiency
*curves:
*"1": yachts with higher course-keeping ability
*"2": yachts with normal course-keeping ability
*"3": yachts with satisfactory course-keeping ability
*"4": yachts with poor course-keeping ability and poor maneuverability

Table on page 25:
* 1st column -type of yacht
*2d column -IOR group
*3d column -length on waterline, m
*4th column -measured sail area, m^2
*5th column -height of sails above waterline, m
*6th column -rudder area (together with skeg if any), m^2
*7th column -distance from rudder center of area to keel center of area, m
*8th column -rudder area/measured sail area ratio, %
*9th column -rudder area/keel area ratio
*10th column -rudder system efficiency coefficient
*11th column -evaluation of maneuverability in following terms:
5-very good
4-good: wind ~10m/s, rudder angle beam reaching with spinnaker ~15 degrees
3-satisfactory: wind ~10m/s, rudder angle beam/broad reaching 10...15 degrees
2-bad: wind ~10m/s, rudder angle close hauled 8...12 degrees

Some of the Yachts mentioned in table:

"флайер" Flyer, famous winner of Whitbread, the only one both handicap and outright winner of this race ever.
"конрад -54" 16.5m offshore racing yacht made in Poland in Soviet times; drawing in page 24 is hers, article author was her captain at the time.
"картер -30" Carter -30 30feet/9m Carter design, mass produced in Poland under license mainly for use within Soviet camp.


Main formula in left column, and formula in middle column, page 26:
*Kэpк - rudder efficiency coefficient
*Sp - rudder area, m^2
*lp - rudder arm, m (distance between keel and rudder centers of area)
*Sп - measured sail area, m^2
*Hп - Height of sails above waterline, m

____________________________________

Some (my personal, to be distinct from article) considerations on usage:
*Measured sail area could be roughly substituted by fore triangle + main triangle area; if someone more familiar with IOR know better, please correct this.
*My personal feeling is that with fractional rig, Hп should be the height of spinnaker halyard above WL, not that of "bare" head of the mainsail.

 

What you found is rubbish!

Underwater fluid mechanics at 4-7 knots are fundamentally different than flow at Mach 1.0 to 1.2. At Mach 1.0 an object is traveling at the speed of sound. The speed of sound in water is around 2,900 knots. Boats do not go that fast. Shock waves form on an airfoil starts to approach Mach 1. At Mach 1 the shock waves extend to infinity, and above Mach 1 they sweep back with the anble becoming more acute as the speed increases.

For the record, the NACA 4 digit series including 00XX are not a particularly good choice at transonic speeds (speed close to Mach 1). Modified 64-xxx and 65-xxx are better choices among the NACA series though anyone designing for transonic speeds these days should be using more modern sections.

A NACA 0012 section does not have a "narrow elliptical shape", which a cursory look at a NACA 0012 section profile will confirm.

I wouldn't trust anything about aerodynamics or hydrodynamics on the site the quote first appeared on.

 

"Originally Posted by alex_sailor View Post
Interesting because, here is what I found since Perm Stress' response:

An underwater AirFoil

The foil shape I decided on is the NACA 0012 foil. It''s a narrow elliptical shape and has undergone thousands of hours of testing by the aero industry. Turns out that its the best foil shape for both lift and the absence of drag for air speeds in the range of MACH 1.0 to 1.2. Also turns out that the fluid dynamics of air speeds in that range are very similar if not identical to underwater fluid dynamics at 4-7 knots. Lucky for us sailors. Its the foil design going into almost all new production boats out there (Hunter, Catalina, Beneteau, etc.)..."


NACA 00XX foils were created long ago, when subsonic aircraft was still a remote dream...

 

Perm, I see you a bit distracted in this thread... You meant to say "supersonic" I guess?

 

This formula is strikingly similar to the so-called Tail Volume Coefficient used in aircraft design, explained in my post #8 of this thread: http://www.boatdesign.net/forums/boat-design/rudder-size-26163.html#post258297

Applied to rudder design, it could be called Rudder volume coefficient, and would be:

Vr = (Sr x Lr) / (SA x Cs)​

where:
Vr = rudder volume coefficient
Sr = rudder area
Lr = longitudinal distance from the rudder hydrodynamic center to the boat CG
SA = sail area
Cs = mean chord length of sails.

The term "volume" refers to the fact that by multiplying an area by a length you get a volume.

The only difference between this formula and the one in that russian article is that the latter uses rig height instead of the rig mean sail chord. On this regard, also take note of the formula Tcubed has shown in the other thread, with Displacement at the denominator.

It basically means that it considers mast height more important than rig chord length in creating the yaw moment. Which is correct in strong winds, imho, when the boat is very heeled and the aerodynamic forces act at a lateral point far away from the hull centerline. In lighter winds, at smaller heel angles, the yaw moment is more related to the sail chord - as it is proportional to the lever arm length through which the sail's aerodynamic force produces a yawing moment around the mast.

Using the boat displacement in the denominator part of the formula, like Tcubed did, probably has the least physical meaning of the three, at least for sailboats. However, it could make sense for powerboats - though it is still preferabe to have in denominator something physically related to the source of yawing moment (like Lateral plane area multiplied by it's distance from the CG, for example).

You might say "why is Lr refered to boat's CG instead of CLR or COE?". I believe it would be more significant to use CG as a reference point when defining a design coefficient, since it doesn't move around with varying heel and yaw angles, with changing angles of attack of both sails and keel, or with other on-the-run rig modifications.

Cheers

 

I meant aircraft flying close to speed of sound, just below it including .

 

Transonic then.

 

"The only difference between this formula and the one in that russian article is that the latter uses rig height instead of the rig mean sail chord. On this regard, also take note of the formula Tcubed has shown in the other thread, with Displacement at the denominator. ..."

As pointed out in this article, main concern was indeed strong wind sailing in races, including spinnaker reaching (including in high and steep waves, so characteristic for Baltic Sea) in marginal conditions, when rudder efficiency could mean difference between being able to fly a spinnaker and not being able to do it.



Personally I did skipper for a while a 50ft/15m sailboat with 3/4 rig, converted for masthead spinnaker. For fractional spinnaker, ruder area (and efficiency as described in Russian article) was perfectly enough. With masthead spinnaker, beam reaching at ~30 degrees of heel, the boat was "locked", i.e. rudder had only marginal control over the direction and it was pretty clear for me at the helm, that very first broaching will mean "douse the spinnaker". Thankfully, water was flat and only a couple of miles had to be sailed this way... .



In light winds, sails not so often overpower the rudder, and this is probably the cause why author of this article do not consider light wind qualities as critical factor for rudder size selection. In light winds you can "paddle" with quite an effect with your rudder.
It is my feeling that in light winds the rudder area is not so important, as inability so set enough sail far enough aft, to develop right balance and weather helm at close to 0 heel. From the other side, as speed trough the water is so low, rudder area again became the dominant factor for effective control...

 

The greater coefficients for smaller boats author do relate to surface flow of breaking wave crest influence to rudder. As this surface flow has some finite depth, smaller boats (hence their shallower rudders) are affected more as big boats (with deeper rudders).

 

I agree with you about strong winds being the critical factor in rudder design.

However, I believe that the two coefficients (based, respectively, on the mean sail chord and on the rig height) are both valid indicators of rudder effectiveness, since the SA depends on both mean chord length and on rig height, and hence accounts for the missing one, when the other is explicited. So, though the two calculation methods are numerically different, I think they would give a comparable rating scale of various designs.

Could also be related to stability scaling factors. Have to check it out.

Cheers!

P.S.
Damn, can't give you reps for bringing out this theme - tells me that I have to spread it around first...

 

It was the author of article who find strong winds critical, not me.
My experience so far confirm it more or less.
Light winds however, can present very own set of design issues.

 

Measure 2x Cut Once

So, after all your informative messages.which re-ignited my fascination with the art and science of aero-hydrodynamics, I decided to re-measure the old balanced spade rudder and found it to approximate a NACA 0018 NOT NACA 0012! If I understand correctly the "18" refers to the percentage of thickness to the chord, so at the upper surface I measured 3.875" and the chord at the same point measured 21", ergo 18% > NACA 0018.

Now, from the contributions I understand this will have more drag than a 0012 but more lift and a higher stalling angle as well. Looking at the hull under which the rudder is slung, there is a matching molding with the same profile, so the designers meant it to be what it is.

MY new question is should I go for the "fat" profile to match the boat, or go slimmer? Eric Sponberg's response was the foil no. was not as important as the planform.

More ruminations for a blustery February day....

 

Sufficient strength and stiffness should be your first and major concern. If the rudder bends then it doesn't matter one bit what section it has or what the planform shape is. And failure of the rudder can jepordize your safety as well as the boat. The thickness of the rudder may have been determined by the diameter of the rudder post, not to "optimize" the section. What is the diameter of the original post? If you are tempted to re-engineer the rudder post have a look at Eric's article on keel and rudder construction which he provided a link to.

How do you plan to fabricate the rudder? Will you be doing it at home or will it be done by a shop with a CNC mill? That should be a major consideration in the planform shape selected.

Will you be racing the boat in very competitive races? If not then I doubt you will notice the very small increment in speed due to the difference in drag of a 0012 vs 0018 section.