# Flat plate rudder vs naca drag

Discussion in 'Hydrodynamics and Aerodynamics' started by 23feet, Mar 20, 2016.

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### 23feetJunior Member

I'm reading "Marine Rudders and Control Surfaces" by Molland and Turnock (on Google Books) trying to get up the courage to pull the trigger on fabricating rudder cassettes and NACA 0012 foils for my Wharram Tiki 21.

The current stock Wharram rudders are 0.625 (5/8") plywood with minimal fairing and are >1 aspect ratio. This translates to an thickness to chord ratio of about 0.035. Figure 5.5 (pp. 97) of Molland and Turnock gives drag values (CDo) at 0.0 angle of attack of 0.033 for a similar flat plate rudder vs 0.020 for a NACA 0015 foil. At 20 degrees angle of attack, the drag increases to 0.290 and 0.135 for the flat plate and NACA 0015, respectively.

In other words, for these measures the NACA 15 has about a third less drag at 0.0%, and a half less drag at 20% angle of attack.

OK, here's the question. I'm not a math person and so don't have a good grasp for what these measures are. Does this mean that the NACA 15 actually has 1/3 less drag then the flat plate, or some smaller proportion of a variable that I don't get?

Many thanks for any thoughts...

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### upchurchmrSenior Member

Actual drag is 1.3 less, as I remember.

The Cl (lift) should be better for the NACA at the same time

This is the whole reason NACA foils get suggested.

The NACA foil will need to be turned less for the same lift (turning force) and will have even lower drag at the same lift.

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### PARYacht Designer/Builder

For this boat, going to a NACA 00 section will make modest improvements, but hardly noticeable, unless sailing with an identically built and skippered Wharram Tiki 21. The helm will be more responsive, turning will be slightly crisper, drag will be slightly less, possibly less noise or vibration and maybe a fraction of a bit better sailing ability, but again only really noticeable, against another identical Wharram Tiki 21. Personally, I like to make good foil shapes, because they give you a wider range of operational efficiency, but you'll have to decide if the bother of making a new set of blades and related gear (cassettes, etc.) can be justified.

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### 23feetJunior Member

Hi PAR,

Thanks very much for the feedback. This must mean that the drag numbers from the book are smaller in "real life" than they appear on paper. You have addressed my question as to how such a difference would actually feel.

What brought me to considering such a big change in the rudders is that the boat is quite slow at the top end, that is, on a howling reach it can only manage 14 knots. I have owned several cats and know that this is slow for 21" multi. It seemed logical that the flat plate rudder design could be causing a lot of drag as the boat exceeds its displacement waterline speed.

I can see that the improvement from a NACA rudder foil would be modest up to displacement speed, but is it possible that the benefits would be larger at 2X or 3X displacement speed?

Thanks again

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### jehardimanSenior Member

PAR is correct that the performance limit may be Tiki 21 itself. Its SA/D ratio is much lower than many comparable daysailer cats. I would look more towards minimizing weight and moving CG to improve performance.

FWIW, 15% thickness is getting into the range where shaping will give some benefit, especially in increased stall angle. However, changing to a faired shape will reduce the allowable bending moment at the root. This may have significant impact on the actual material selected to use for the rudder.

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### 23feetJunior Member

Hi jehardiman,

Thanks for the input. Yes, the SA/D of the Tiki is modest compared to a performance cat. Nonetheless, when pushed to the max in high winds (25-30 knots windspeed on a beam reach), the limitations in sail area disappear, and something else must be limiting the speed. I don't think that the hull shape is the limiting factor as wetted surface in the vee hull become less important as speed increases (I think I read this on these forums elsewhere), which leaves rudder drag as the potential dynamic limiting speed?

BTW the Tiki rudder plate thickness is 3.5%, not 15%. The NACA 15 is what I was looking at as a comparison.

Thanks

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### jehardimanSenior Member

Ah, now I see where we were getting confused....Go look and see how the area for CDo is defined. CDo (or CD"dot") is usually written when the reference area based upon frontal area (thickness * span), so for a similar span and cord the "effective" CD based upon plan area (i.e. CDs or CD"square") would be 0.033 for the 3.5% flat plate and 0.085 (i.e. 0.0.20*15/3.5) for the naca 0015. This agrees quite well with Figure 2, Chapter 6 of Fluid Dynamic Drag by Hoerner, and my confusion over why a thin flat plate would have a larger CDo than a fairly thick airfoil.

Now, from this starting point, we can see that in order to make the NACA 0015 have the same drag as the existing rudder, you have to reduce the area by 62%. Then you can compare the lift to see if that loss of area is acceptable.

If you really think that the rudders are the cause of major drag, check the rudder toe-in.

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### 23feetJunior Member

Hi jehardiman,

that's quite confusing given that my reading of the data is that the NACA 15 would have less drag than the flat plate, even though it is much thicker.

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### jehardimanSenior Member

That is only true for a c/t less than ~10. Once you get below 10% thickness real drag has more to do plan form, environment, and vessel response than with sectional shape. And once you get below ~5% thickness there is really no difference in lift and drag in a real fluid. Even less if you just round the LE and 4:1 taper the TE.

Stall, however is a slightly different matter. High speed vessels use proportionally thicker sections to delay stall at low speed where the small plan form of the rudders is less effective.

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### 23feetJunior Member

OK. So what you are saying (as did PAR) is that total drag is going to change very little by switching from the thin plate section to a NACA profile, especially at zero degrees angle of attack.

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### upchurchmrSenior Member

Perhaps what it really means is that the overall drag of the boat is primarily driven by the boat hull shape and weight.

The major effect was never the rudder, so you cannot improved much overall with just a rudder change.

Typically these boats are underpowered sail wise, so you also just don't have the power to drive it as fast as a daysailer.

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### DCockeySenior Member

"Flat plate" to airfoil comparisons need to include how thick the flat plate is and the shape of the leading edge and trailing edge of the flat plate. A sufficiently thick flat plate with a square leading edge will have higher drag than an airfoil section.

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### PARYacht Designer/Builder

It's probably a 5/8" plywood blade Dave.

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### 23feetJunior Member

Yes, as noted in my first post the, the blade (plate) is 5/8 plywood.

This is all good, but the one thing that has left me confused is jehardimen's comment that the flat plate section will cause less drag (for the same plan area) compared to a NACA foil (because it is thicker). The data in Molland and Turnoch clearly shows less drag on a NACA 15% (0.02 CDo) than a 3.5% plate (0.03 CDo) at zero degrees angle of attack. This seems to show that the NACA foil has less drag even though it is thicker.

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### jehardimanSenior Member

23feet, as I pointed out in post #7 it's not the same thing.

So as an example, let us say I have a flat plate foil made out of 5/8 ply with a thickness of 3.5% and a span of 1.2 feet (similar to the Tiki 21's rudder immersed span). A physical thickness of 0.625" (0.052 feet) and a thickness ratio of 3.5% means that the cord is 17.85" (0.625/0.035) or ~ 1.5 feet. So the straight line drag at 14 knots (1.689*14= 23.64 ft/sec) would be 1.14 lbs (0.033*0.5*1.99*0.052*1.2*23.6^2). Drag at 20 degrees would be 10.0 lbs (1.14*0.290/0.033).

So now lets replace the same sized foil with a NACA 0015 section. Span and cord remain the same (1.2' and 1.5') but thickness changes to 0.225' (1.5 feet *0.15 = 0.225' = 2.7"). I don't think you intend to have a 2.7" thick foil but we will complete the exercise. So now drag at 14 knots will be 0.020*0.5*1.99*0.225*1.2*23.6^2=2.99 lbs. Likewise drag a 20 degrees will be 20.1 lbs (2.99*0.135/0.020).

So you can see that the NACA 0015 will have more drag than the thin plate foil due to its thickness. If we wanted to decrease the drag of the NACA shape to that of the flat plate, the thickness, and therefore the cord of the foil, must decrease. So for this example we will reduce the thickness to match the flat plate drag; 0.225*(1.14/2.99)=0.0857' or ~1.029". Likewise the cord decreases to 0.571' (0.0857/.15) or ~6.8". This is plan form area reduction of 62% (again see post #7 above). So now drag is 1.14 lbs at 0 degrees and 7.7 lbs at 20 degrees.

While this looks better, we would need to check the CL of the two foils to determine is this is an improvement because the rudder force must be matched also. However, since the CL per degree of a flat plate and a NACA foil at these low aspect ratio (span/cord so ~1 for the flat plate and 3 for the NACA foil) are not that different (~ 0.0305 for the flat plate and 0.033 for the NACA based on plan form area) the loss of more than 60% of the rudder area will make the rudders less effective. (see 1989 PNA Vol III, Section 14)

Anyway, that is the story for a simple foil. However it looks like the Tiki 21 has a skeg to protect the rudders. In that case the whole above discussion is moot as this is now a flap, see Hoerner & Borst, Fluid Dynamic Lift, Chapter IX, Control Surfaces.

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