Rudder Plan Form

[Bill Roberts]

I'm having a hard time holding my tongue on some aspects of these AC boats.
On the cover of the April/May Catamaran Sailor Magazine is an AC45. Standing out in the picture is a nice, white, shiney rudder. Look at the planform. It has a straight trailing edge. The leading edge starts out straight up near the hull but as the leading edge approaches the ridder tip, the leading edge curves back to the trailing edge.
Have you ever seen an airplane wing that did that??? I think I did years ago when I was looking at a Batman comic book and it was Batman's airplane or maybe it was Wonder Woman's airplane. I don't remember which for sure.
The leading edge curving aft into the trailing edge at the tip will cause spanwise flow near the tip and this will increase the size of the tip vortex and reduce the effective area of the rudder.
The boat, the AC45, has a nice airfoil going up in the air above the deck and this airfoil terminates in a 'squared off tip' like any high performance low speed airfoil ends. The squared off tip for a low speed airfoil is the most effective and lowest loss way to end an airfoil. Check out and see how the airfoils are terminated on World Class Gliders. They all end in square tips. So should the rudders and centerboards of sailboats end in square tips.
And by the way, not be swept aft either. This also causes "spanwise flow".

Hey Guys, Did you know that SC and ARC were the first sailboats, beach cats, to come out with "squared off tip" mainsails.
And BTW, how about squared off tip jibs???

[Kevin Keller]

It's been a long time since I read High Performance Sailing by Braithewaite but if I remember correctly he said that using the rounded tip sails or foils gave a longer effective length. Having read that though, I wondered why the trend had gone to square top sails.

The square tips do look better and as everyone knows, as long as you look good that is what counts.

I always wondered why they didn't put a small winglet on the top of the mast/sail to prevent flow over the top of the sail, sort of like an MD11 jet. You could do the same to the rudders and dagger boards but you would probably damage it pretty good if you hit something and also trying to steer with a raised rudder would be much harder.

[Bill Roberts]

I don't know what Braithewaite's training background is. In Aeronautical Engineering, text book Aerodynamics 101, there is discussion about how to end an airfoil in free stream airflow. Many different end of airfoil shapes are shown and discussed. The parameter for judging the quality of the airfoil termination is called "span effectiveness". The end of the airfoil shape that produces the highest span effectiveness is a clean, straight, cut off at the end of the foil parallel to the free stream airflow. The worst end of foil shape is to bring the foil to a point, like a pinhead sail.

Winglets are needed on commercial airliners because the wings are swept back to minimize aerodynamic drag at their cruise speeds and the sweepback leading edge produces spanwise flow. The winglets are aerodynamic dams to reduce the spanwise flow at the wingtip and minimize the wing tip vortex. The wingtip vortex is a loss in "span effectiveness".
Our little beach cats don't sail along smoothly like like an airplane at cruise. Our mast tips and CB and rudder tips move through their flow fields in a very choppy motion due to the bows of the boats moving up and down sailing across rough water. Winglets would not work for us. Sometimes in rough seas our wingtips are instantaneously moving backwards in a forward and backward chopping motion while the boat is moving ahead.

Years ago there was an Australian AC monohull boat designed by a guy named Bob Miller. The keel on the boat had a slight swept forward leading edge angle to it,(no spanwise flow), and then there was a large tip plate on the bottom of the keel. This boat was significantly faster than Conners and won the Americas Cup easily. There never was a correct technical discussion about that keel shape in any US sailing magazine that I read.

[havliii]

Bill, does the square top sail also help to twist off the top of the sail in a strong gust?

[Bill Roberts]

Yes, it helps twist off in puffs. Twist also helps to adjust the relative wind angle of attack on the mainsail. As we go up in height above the water for about 50 ft the wind velocity is ever increasing, the wind velocity gradient. This means that as we go up in height above the water and we are sailing to windward for example, , the relative wind angle is swinging to a more abeam position as we go up in height. Therefore for the sail to have a constant relative wind angle, the best angle, on it from boom to mast head, the sail must twist to match the ever changing relative wind angle. Relative wind angle and velocity is what we sail on, not true wind.

These AC boats can go out in 10 knots of true wind and reach 25 knots of boatspeed. This sounds like black magic doesn't it. The boat can not go faster than the relative wind speed. The relative wind speed is greater than even the 25 knot boatspeed. So, the boat can make more windspeed due to its own boatspeed than the absolute value of the true windspeed. You know what, boats that can do things like this sound to me like the ideal boats for places where there is not much wind, like inland lakes. Our beach cats can't generate numbers like the AC boats but we can sail equal to the true wind speed on almost any point of sail and faster than true windspeed on some points of sail. There is a choice: We can sail cats and go out in a 5 mph breeze and sail around at 5 to 10mph. Or we can sail a small keel boat in the same breeze and sail around at 2 to 4 mph at best. Which type of sailing is going to be the most fun? Which type of sailing/boat is going to teach us to be better sailors? Which type of boat is going to be more attractive to young people and help the sport of sailing grow and help our sailing clubs grow?
PS: Hobie cats, 14s and 16s, won't do this. They won't work; they won't tack: they are very frustrating to sail in light winds. It takes a well designed beach cat to perform well in light winds and be fun to sail and they are out there.

[Kevin Keller]

Hi Bill,

I figured you must have read Bethwaite's book in the past. His book taught me more about how a sailboat works than any other source I have come across. It even gave me some good theory on airplane wings too. I think you would find his book very good reading, not that you have anything else to learn. If others have not read it I highly recommend it. His first book is the one I am talking about, High Performance Sailing. There is SO much information in there I have never been able to digest it all.

Anyway here is his bio from Wikipedia:

Bethwaite built his first boat (a 16 ft sailing canoe) as a teenager. He joined the Royal New Zealand Air Force at the outbreak of the Second World War, becoming a flight instructor and test pilot before flying bombing missions over the Pacific during 1944 and 1945. He rose to the rank of Squadron Leader and was awarded the Distinguished Flying Cross. After the war he became a commercial airline pilot for Tasman Airways (later Air New Zealand).[3]

Bethwaite had four children with his wife Nel: Christine, Mark (an Olympic and World Championship competitor), Nicola (also an Olympic and World Championship competitor) and Julian (World Championship Competitor and boat designer). After settling in Sydney, Bethwaite designed a small boat suitable for his youngest children to use to learn how to sail. This became known as the Northbridge Junior (now known as the 9er). Bethwaite is most well known for designing the Tasar [4] and Laser 2 Dinghy Classes.

He was awarded the Medal of the Order of Australia in 2000 for his services to sport. In 2006 he won an Innovation Hero lifetime achievement award from the Warren Centre for Advanced Engineering at the University of Sydney for the design and commercialisation of innovative high-performance sailing craft.[5] He died in 2012.

[SC15Av8or]

Look at the planform. It has a straight trailing edge. The leading edge starts out straight up near the hull but as the leading edge approaches the ridder tip, the leading edge curves back to the trailing edge.
Have you ever seen an airplane wing that did that??? I think I did years ago when I was looking at a Batman comic book and it was Batman's airplane or maybe it was Wonder Woman's airplane. I don't remember which for sure.
The leading edge curving aft into the trailing edge at the tip will cause spanwise flow near the tip and this will increase the size of the tip vortex and reduce the effective area of the rudder.

ac45nz1d6_3729[2].jpg

Bill .....

As an average aviator I have to say your observation of the AC45 rudder to that of an airplanes wing is a bit off. I think they are on to some thing with curving the leading edge back to the trailing edge. So much so that both Boeing and Airbus are now shaping and retro fitting their wingtips in the same fashion. The 747-400, 767-400, 777, 787, A350 all have this feature/look/appearance. Even the Hoerner tip on a glider is curved back and then bends down to move the vortex away from the upper surface of the wing. Also there are several propeller driven aircraft that have Scimitar propellers. Bae J41, C-130J, A400-atlas, Antonov An-70. In fact you would be hard pressed to find a propeller driven plane that does not use a Scimitar propeller or that can not be converted to one these days. Even helicopters are using this feature on the main rotor blades. These are more efficient and less noisy foils. The increase in efficiency comes from a decrease in drag as these propellers/rotors are airfoils too. I know we are not dealing with wave drag with the AC45 rudders but there must be some increase in efficiency/reduction in drag that makes this worth their time.

I am surprised however they have not incorporated this efficiency into the wing sail. I would guess that is to come, along with dagger and center boards. I would guess the foil boards do have some component of this as well. An object that creates a high pressure on one side and a low on the other is a foil (basic and in simple terms). That said why are not ALL the foils on the boats shape as such if it is more efficient?? The wing sail has to create this hi/low like an aircraft wing/foil. I would guess the rudders work more off Newton's law of lift then the Bernuullie's principle of lift.

799px-Boeing_787-8_Dreamliner_N787FT_KBFI[1].jpg

Mother nature has some sense of the same AC45 hydrodynamics as well.

Dolphin011507_001[1].jpg

great_white_shark_fin-350x234[1].jpg

Either that or it just looks cool as hell when you are flying a hull and folks can see your curved shaped rudder. So maybe Batman and Wonder Woman knew some thing we are just now finding out.

By no stretch of anyones imagination am I claiming to be some kind of aero/hydro dynamic engineer by any means just my 2 cents respectfully into Bills post.

[Bill Roberts]

Professional,
The reason modern commercial aircraft have swept back wings is that they fly the majority of their mission time in the edge of the transonic drag rise, just a little below Mach 1.0. We are not there. Dorsal fins on fish are not wings and they do not generate lift. I do not know exactly what these fins do; they probably have something to do with stability, but they do not generate lift that holds the fish up. They are not a lifting device. Wing shapes that are related to the way we fly are the wings of gliders. These are long and skinney wings, high aspect ratio, with squared off tips. The glider wing shapes are backed up by millions of dollars of wind tunnel testing.
Bill

PS Propeller tips and rotor tips also like to stay away from the sonic drag rise. Mach 1.0 at SLS is 1116ft /sec or 761mph on a standard day. There have been some special efforts to delay or push back the sonic drag rise as Mach 1.0 is approached but WE ARE NOT THERE!
Professional, try sailing with a swept back rudder. Put the ruder down about 90% or 95% of the full down position and put a knot in the pull down line, the green one, to keep it there. Go sailing especially on a windy day and watch the rudder malfunction as you try to go fast. Listen to the spanwise waterflow suck air down the leading edge. It makes a swooosh sound and the rudder becomes ineffective at steering. It takes a boat speed of around 18 to 20 mph to make this happen on a grand scale. The sweepback angle that lets this happen can be very small.

[SC15Av8or]

Bill again I am not sure of all the hydro dynamic forces at play under a catamaran and if they are different for a monohull or an airplane and how much hull shape plays into all this. That said if you look at the new NACRA F20 they have a curved dagger board that ends in a scimitar shape and then the rudder plan is, what we call in aviation, an elliptical wing. This was a very efficient wing due to a greater Oswald efficiency number in the induced drag equation. This was due to the lift being almost zero at the tips by shortening of the chord near the tips, that minimizes induced drag. Could this be true of the rudders on the AC45 in that the induced drag is reduced, so be it at a much slower speed then that of an airplane, but is reduced non the less the same way?? If so then why not follow the same plan form to the AC72 which clearly they have not.

DISCLAIMER......AGAIN I am no engineer in this stuff.

nacra F20.jpg

[Bill Roberts]

Pro,
The more I look at and think about and try to be positive about the AC72 rudder plan form and the tip especially, here's what I can come to. The curved back tip is a winglet. Since it has to work with load from one side and then the other, the compromise position is to put it, the winglet, in the same plane as the wing or rudder itself. Remember that the winglet makes drag also. My information, "Horners Lift and Horners Drag" say the cleanest way to end an airfoil is to end it clean, cut it off parallel to the flow. Add no additional area because area makes drag. The scimitar shape is added area. The elliptical wing area distribution or tapered wing plan forms are a structural advantage also. It moves the center of lift on the wing closer to the fuselage therefore reducing the wing bending moment so the main wing spars can be lighter in weight. The way airplane wings are unloaded at the tip is to put a little twist in the wing to reduce the angle of attack near the tip therefore reducing the tip vortex and tip losses.
Pro keep in mind here that what we are talking here are very very small changes in drag. You would be very hard pressed to ever see a speed change on a speedometer. Another very very small improvement in glider wing performance, less drag, is to angle the wing forward slightly a few degrees. This way you pick up a very small air velocity component tending to stop the wing tip leakage. It creates a small free stream air velocity component that opposes the tip leakage.

[Kevin Keller]

What about the Supermarine Spitfire with the elliptical tips? They were very successful but more complicated to manufacture than a square tip wing. I think that is why you find most gliders have a square tip because it is cheaper.

I imagine the dorsal fin on a shark or other fish acts somewhat like a rudder and does create lift albeit in a different plane. It looks like most of them come pretty much to a small tip.

I think a lot of people read your posts Bill. I know I enjoy reading them and usually learn something. I know your knowledge far surpasses mine and most people probably feel the same. I don't want to look or say something stupid. I like my boat going fast but usually it's used for enjoying the day out on the bay with friends. I race it when I can but it's laid back racing. I want to make my boat faster but I've got too many more important irons in the fire to concentrate too much more time on that right now. There are a lot of things I would like to do to it. I do like experimenting if I have the time.

Kevin

[Bill Roberts]

Pro,
On those world championship all carbon gliders "money is no problem". The wings are tapered. They are about three ft wide at the root chord, the fuselage, and taper down to about one ft chord at the tip. The top surface rolls down to the lower surface at the tip and extends down about another inch or two below the bottom surface. This lip or aerodynamic fence that extends below the bottom surface is parallel to the free stream airflow. Therefore a squared off tip apperance. Again Money is no problem on these gliders.
The shark top fin acts more like a centerboard. Watching a shark swim, the tail moves side to side and so does the head in concert. The center part of the body doesn't move sideways and seems to be the center axis, vertical axis, for movement sideways between the head and tail.
Bill
PS If you are thinking of an experiment or something new to you to try on your boat, Check with Tom and I. We have tried a whoooooole
lot of stuff that is not on the boats. What's on the boats is the best of our testing and experiments.

[SC15Av8or]

Bill ....

Yes Dr. Hoerner did say that "The very worst wingtip is a rounded wingtip with a round cross section. (Tip "B" in the lower image.) The very best wingtips are ones which have a sharp cross section."

Vortice Illustration[2].jpg

But he also went on to to say "it is favorable to keep the tip vortices apart from each other as far downstream as possible. Thus designed what is now known as the Hoener wing tip (Tip "A" in the lower image.). This is better due to the delay in joining of the vortices (other wise known as induced drag) down stream of the tip. Thus there was a improvement due to reduction in drag, induced drag. He also said that "a longer wing is a better thing -- and if you get that length 'for free' (by using better wingtips), that is a really good thing." That said in the next image tip A would be the best way to end any foil. So then why did you not employ this on the rudders and dagger boards of the SCs' and ARCs' ??

Hoerner vortices[1].jpg

The sail would be different however as it has to create equal amount of lift on both sides of the sail depend upon sailing to port or starboard tacks.

[Kevin Keller]

Bill ....

He also said that "a longer wing is a better thing -- and if you get that length 'for free' (by using better wingtips), that is a really good thing." That said in the next image tip A would be the best way to end any foil. So then why did you not employ this on the rudders and dagger boards of the SCs' and ARCs' ??

Hoerner vortices[1].jpg

The sail would be different however as it has to create equal amount of lift on both sides of the sail depend upon sailing to port or starboard tacks.

I guess the foils have to create lift both ways also.

[Bill Roberts]

Pro,
Just so you understand: Induced drag of the CB and Rudder are functions of lift coefficient squared. It is a big number. This tip leakage and tip vortex thing that we are talking about here is a very small thing relative to Cl**2. The lengthwise tapering of a daggerboard's thickness approaching the bottom end and tip would make that tapered length of the board ineffective as far as generating lift. That in itself is a loss in span effectiveness. That lower end of the board that has a tapered thickness vertically near the tip has water flow across it and is making drag. Because it is thin, it is making little or no lift. It would also leave the tip of the board fragile for running aground . Also the reason boards are untapered in thickness is so that they plug the bottom of the CB trunk when the board is in the up position. The pumping and churning of water in the trunk is another parasitic drag. The vertical tapered thickness board would allow much pumping and churning of water in the CB trunk. The way SC and ARC and RC board and rudders ends are finished is the lowest drag and the toughest tip to put on the end of CBs and rudders.

Also Pro if you look further into Dr. Horners book, you will find a study of foil tip plan forms. Many different shape foils in the plan form of the tip were evaluated. Half round tips were considered, elliptical tips were considered, parabolic tips were considered, squared off tips were evaluated and others. The plan form that resulted in the smallest loss in span effectiveness from perfect, zero loss, was the squared off tip.