Hopped-Up Winnebago

Discussion in 'Hydrodynamics and Aerodynamics' started by Inquisitor, Sep 21, 2020.

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InquisitorBIG ENGINES: Silos today... Barn Door tomorrow!

I’m in the process of refurbishing my MacGregor 26M. I want to build a new daggerboard. They tend to be kind-of sacrificial. It appears on the Mac forum that replacing daggerboards is a popular thing to do. Being unwilling to leave well enough alone, and enjoy tinkering with the physics, I want to make a better daggerboard. Please help by throwing darts at the following logic.

Part A – Getting the Correct Wing Area

Does it seem reasonable to just make the lift created by the wing equal to the lift resisted by the daggerboard?

Doing all the algebra, we get a relative area of 0.68% for a proposed daggerboard area of 0.19m2.

As built, the stock MacGregor daggerboard has a full-down exposed length of 1.45m (57 in). With a chord of 0.3048m (12 in) gives 0.442m2. The proposed design would use the same chord (to fit the trunk). Therefore, the exposed length would only be 0.62m (25 in). This seems ridiculously small, but if correct this should improve speed and the higher center of force would result in less heeling.

Part B – Plan Shape

It is my understanding (from a 1930’s design capability) that the Supermarine Spitfire’s elliptical wing optimizes actual wing area. That a square wingtip (such as the MacGregor’s daggerboard) sheds a larger vortex and thus has decreased effective area. That an elliptical wing is more efficient because its wingtip chord goes to zero with a far smaller vortex. Is it reasonable to say that an elliptical wing has the same lift as the bounding rectangle wing has?

If so, I could make the exposed 25” daggerboard elliptical and have the same leeway prevention with less drag and thus improve speed. Noted: That I would give up some downwind speed because of the exposed trunk when the board is fully retracted.

Part C – Flap

Is it reasonable that if a flap was added to the daggerboard that could be deflected to leeward I could eliminate the 9° crabbing required to create the daggerboard’s CL of 1.0? I've several ideas on activation, but nothing I believe is real practical... yet. This would be a version 2 daggerboard.

Summary

In case all these ideas are moot, I’d still make the daggerboard the full height of the production version. I’d only make the bottom 25” elliptical and the rest the standard rectangle. That way, if it didn’t work, I still could drop it to the full 57”.

Last edited: Sep 21, 2020
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patzefranpatzefran

IMHO, dividing by 2 the area of the daggerboard and dividing the span by 2.3 you get a very high increase of the induced drag which will highly decrease your windward speed, just the opposite of your need !

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BlueBell. . . . .

I have modelled a centreboard after a Spitfire wing myself.
NACA 0012 profile.

I love the flap idea and have been dying to try it out.

Go for it!
Locking cable activation?

I like plan B & C.

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philSweetSenior Member

Your design targets are miles off. You want a steady-state cl in the neighborhood of 0.15 - 0.2 for the board. This gets your leeway down where it needs to be, and gives you a bit of headroom for the perturbation velocities in the water, and to still have some bite when tacking. You also need to match the hydrodynamic "stiffness" of the daggerboard and the rudder to have directional stability. If you were running 9 degrees of leeway, you would need nearly nine degrees of rudder trim to get it at the same cl as the board. This would be horrible. So design for about 4 degrees of board leeway at 3 knots boat speed with the sails at full draft and the jib sheeted in to the spreaders. This is probably an AWA of 25 degrees and maybe 5 knots AWS. This will put the rudder about 2 degrees to windward with things pretty well balanced. You can use a cl of 0.2 for this case. Sail cl might be 0.8 or so. So calculate the side force from the sail, and set it equal to the rudder+board. Calculate the total area needed, then subtract one half of the rudder area. That is your board area. If you have access to low wind speed polars for the boat, use real numbers.

Daggerboards are expensive and fussy. They are never sized big enough on production boats. Same with rudders.

srimes, fallguy, Erwan and 1 other person like this.
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patzefranpatzefran

Very good analyse of board's and rudder's area design, philSweet !

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InquisitorBIG ENGINES: Silos today... Barn Door tomorrow!

Thank you for analysis. I will try to find details so I can analyze as you suggest, but getting performance data for a "Winnebago" is a tough call. Which is why I was using the simplistic assumption that lateral load of sail must match lateral load of daggerboard. My best course of action seems to be trying to get righting moment for my boat. I might be able to estimate it from marketing literature and/or just pulling it over with the halyard to say 15°. Then back calculate the lateral force on the daggerboard to cause that same heel.

Back to my original post... in my defense, I felt pretty good about the result because the daggerboard area to upwind sail area ratio for:
1. 20' Tornado catamaran is 0.9% and it has a lousy aspect ratio of less than 2.
2. 40' Gunboat G4 (before they went to foiling) was around ~0.6%
Also, I did say I wasn't reducing the area that can be used... I'm still plan to make it the full length. I'm just asking if the above analysis held any merit: suggesting less extension might be more efficient: less drag and less heel.

I gather your answer is "miles off"... as-in leeway miles off of where I want to go.

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philSweetSenior Member

The trouble with your logic is that a M 26 and a gunboat have very different speed ratios at the critical design point for your daggerboard. The speed ratio is how fast the hull is going through the water divided by True Wind Speed (TWS). Lets say the M26 @ 45 degrees True Wind Angle (TWA) has a speed ratio of 0.5, and the Gunboat @ 50 degrees TWA has a speed ratio of 1.2

The M26 has a Boat Speed/Apparent Wind Speed (AWS) of 0.357 at an Apparent Wind Angle (AWA) of 30.4 degrees.
The Gunboat has a Boat Speed/AWS of 0.601 at an AWA of 22.6 degrees.

Since lift on the board is a function of speed squared, the Gunboat's board only needs to be 35% as big relative to sail area. And realistically, it's even worse than that, because there are scaling factors related to size that favor the bigger boat. Catamarans hulls with high L/B ratios can develop more sideforce than a chubby monohull. The large separation between board and rudder allows the big boat to load the rudder more. The tighter AWA of the gunboat suggests a smaller optimum lift coefficient of the sail. You should be around 3.5% area ratio in M26. Compare your boat to other little tubby monohulls, not performance boats. What is the area of a Seaward 26RK's drop keel?

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philSweetSenior Member

Okay, so you are talking about a set of board polars analogous to sail polars. Yes, under very favorable conditions you can raise the board some. The thing to keep in mind here is that induced drag is purely a function of span in this scenario. Puling the board up is going to increase induced drag no matter what the heading and sea conditions. The question is, can you reduce the other drag components by more than you increase induced drag. This is harder to do than you may think. But dagger boards have a better chance than pivoting centerboards. The primary issue is the speed ratio. If you are running a beam reach, have a glass-smooth sea, and are below hull speed, you will have a higher speed ratio; and the daggerboard's coefficient of lift will be lower. I normally would kick the rudder up first under these conditions. But you can raise the daggerboard some because the friction is greater than the induced drag.

But you also mentioned raising the board to reduce heel. That won't improve sailing. To reduce heel, you change the load and moment from the sail. You reef, twist, and sheet out the sail, you don't raise the daggerboard. You need more board, not less, under these conditions because, again, the speed ratio drops once you get to hull speed or are in heavy seas. When you can't add board, you reduce sail. Which is why I say boards are never big enough. I'm always reefing too soon on small boats. I don't mind heeling if the board is still hooked up.

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srimesSenior Member

You're optimizing for sailing at 8 knots? Planning to motor-sail most of the time?

Seems like better performance would be had by making the daggerboard longer, and possibly with ballast at the end.

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InquisitorBIG ENGINES: Silos today... Barn Door tomorrow!

I can fantasize about sailing at 8 knots in my Mac… can’t I?
I explain why I picked 8 knots below.

First off, thank you philSweet. I appreciate you taking the time trying to explain this to me. When it comes to fluid dynamics, I'm rather cookbook. Just using, "Theory of Wing Sections" (ToWS) and JavaFoil type stuff. I don't want to even try to wrap my head around boundary layer theory and burp bubbles . I'll stick to beer for that. I am certainly willing to concede that my opening thread is invalid. Since I'm keeping the daggerboard the same length, I'm obviously not committing my theory to failure that would force me to make a third board. I can simply slide it up or down to validate. Please understand, I'm not trying to argue to convince you I'm right, but allow you to use terms that I can logically say. OH s#i+! I get it now.

I am still trying to wrap my head around the concepts you're describing and how boat speed, AWS and AWA enter into the equation... except in being another way of describing Reynolds Number and foil AOA. I might dream about sailing up against a G4, but only for the moments I could stair dumb struck at it as it passed me by. But according to ToWS sizes of foils and speed of foil comparisons are completely accounted for by Reynolds number. Otherwise wind tunnels and tow tanks would be worthless. My analysis above used proper Reynolds numbers and fluid densities for the foils (sail and board respectively), proper speeds that are entered into the equation at V squared. I also used calculated aspect ratios in the JavaFoil numbers to arrive at realistic Cl values. IOW, I'm not quite seeing the error in my logic... YET.

Now, engineering statics is something I am completely familiar with and tried to apply it to this problem... sum of lateral forces must balance. Force on sails MUST be reacted by force on daggerboard. Sum of the moments due to the relative centroids of the sail and board is balanced by the boat righting moment. Real, trivial algebra. The fact that I ignore the lateral force generated by the hull only causes the daggerboard to take the entire load and thus will come out of the analysis actually oversized.

I am going to use your suggestions, however I did have a method to my madness at why I used the higher Cl and speeds. As srimes so eloquently put it, I will never exceed 8 knots unless the boat is on the trailer. At peak speeds now, the boat runs up against hull speed. But I have noted it falling off as if the daggerboard stalled. That is why I picked 9 degrees on the JavaFoil plot as the MAX lift at a speed slightly above one I can ever achieve.

I'll post that analysis here for shits and grins.

P.S. As I'll probably be testing in the Neuse, I hope to see your gorgeous schooner... as it flies by.

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InquisitorBIG ENGINES: Silos today... Barn Door tomorrow!

First printing of daggerboard. These are the first sections that make up the elliptical portion in front of the spar.

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InquisitorBIG ENGINES: Silos today... Barn Door tomorrow!

Fresh off the printer.

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