Effective Aspect Ratio of Surface Piercing Rudders?

The effective aspect ratio of under-hull rudders is usually assumed to be twice the geometric aspect ratio due to the presence of the hull as a large end plate.

Does this also apply to transom hung rudders due to the presence of the water surface as a boundary?

In a number of places I've found a comments to say that a transom hung rudder will have only half the effective aspect ratio of a spade rudder. but without any discussion of why.

I can see that a surface piecing foil is prone to ventilation, and will add some additional wavemaking drag, but it can't have a "tip vortex" at the top, surely?

So what is the effective AR of a surface piercing foil?

Cheers,
George

 

No end plate effect, so aspect ratio is as measured, no doubling required.

 

says who?...it is dictated by the amount of turn/lift required for the hull.

What is the purpose of the rudder?...to steer the boat.

If the rudder is dropped from the transom, is the rudder in free flowing water, or still behind the transom?

Answer that, and you've answered your question

 

I've read this before, but it never seems to come with a theoretical or experimental basis, which is what I was hoping for here.

The air/water boundary must have some effect, right?

 

Ad hoc,
I think you've missed my point.

Simplifying hugely, the drag created to produced the required lift increases as the AR decreases. If I change from a spade rudder to transom hung rudder or, for that matter, daggerboards to leeboards, I want to know how much drag I have added, give I still require (as you point out) the same lift.
Clear?

 

Its a function of the rudders WSA.

But you also have to be careful. Since increasing the AR..you're increasing the bending moment and torque on the rudder stock. Which means you inevitably end up increasing the stocks diameter, which means thicker rudder which means more WSA and thicker suction more form drag too.

Nothing is free

 

Good points.

What I'm digging at is that a rudder underneath a hull acts like it's twice as long as it actually is (in terms of Cdi, Cl vs AoA etc.), and I'm unclear how this changes if it becomes a surface piercing foil.

The thread title could be clearer:
I want to find the "Effective AR" of a foil of a fixed shape, not find the most effective AR for a foil.

George

 

Willis, C.J., Crapper, G.D. and Millward,
"A numerical study of the hydrodynamic forces developed by a marine
rudder", Journal of Ship Research, Vol. 38, No. 2, pp. 182-194, 1994.

From memory, they used the same similar lifting surface technique
I used in my "Lifting Surface Program". See:
http://www.boatdesign.net/forums/design-software/lifting-surface-program-lsp-36973.html

Willis et al also accounted for the effect of the free surface and the
the variation in flow along the span of the wing.
At low Froude numbers, the free-surface can be assumed to be rigid, so the
effective AR is doubled, as you suggested. At very high Fr (based on chord
length) the situation is more complicated because the free-surface acts
as a plane of anti-symmetry. However, it is not really so simple because
of the variation in flow along the span and the flow from the hull and
other messy stern bits, as AdHoc mentioned.

Good luck,
Leo.

 

Great stuff, thanks Leo.

I wasn't expecting a simple answer, but I couldn't see how the water surface would have no effect.

 

Nice clear answer Leo!

It is also important to note that you cannot apply lifting line theory in the same way for rudders under the hull vs. one that is exposed to the free surface. Rudders that pierce the free surface will start ventilating as soon as the rudder is turned. The amount of ventilation will depend on the profile geometry, aspect ratio and whether the rudder is fitted with "fences" to prevent ventilation. A numerical or experimental analysis is probably the only way to determine the forces accurately for such rudders.

Another good general reference:

Blount, D. L., & Dawson, D. (2003). Rudder Design fог High-Performance Boats. Professional Boatbuilder, (August/September), 72–85.

It does not say much about behind transom rudders though.

 

Thanks. I never use lifting line theory because it is not a consistent low-aspect
ratio formulation.
I appreciate what you are saying about surface-piercing lifting surfaces and I
hope one day to find time to finalise some work on them. (There is a hydraulic
jump behind the rudder that makes things messy numerically in my current
approach.)

 

In propeller design, we use the term "image" for the "mirror" effect that you are describing. We have an "image" at the hub, of course, but also sometimes at the tip for tip fin or ducted propellers. (However, we do not have the luxury of 2D symmetry. Our "mirror" is about a cylinder, so the image function is no longer 2D.) The tip image in a ducted propeller also is complicated due to the tip gap, which means a full image correction is not correct.

How this relates to rudders is that we typically are able to use corrections in the circulation distribution near the tip to account for the tip gap. Would this be suitable here to account for the free surface? I have to think that papers could be found that comment on the span-wise circulation distribution in various settings (under hull, surface-piercing). As Leo points out, this distribution may have a speed-dependency, but I suspect that there would be a way to estimate a circulation distribution correction based on non-dimensional parameters.

Also, as a personal observation, don't sell lifting line short. It can still be very useful, especially with empirical "anchors" for viscous, scale, and blockage. And it has the benefit of pretty consistent behavior. I'm a big fan of "simple models"...

Don MacPherson
HydroComp

 

The effect of Froude number on sideforce and drag coefficient are discussed in:

Ba and Guilbaud, "A simple method of investigation of the Froude number effect on lifting flows about ships", J. Ship Research, Dec. 1998

Kuhn and Scragg, "Analysis of lift and drag on a surface-piercing foil", 11th Chesapeake Sailing Yacht Symposium, 1993

Uli

 

My two cents worth: http://www.boatdesign.net/forums/boat-design/rudder-configuration-33622.html#post380246

 

Sure, lifting line theory can be very useful, as long as it is used where
appropriate, e.g. at moderate to high AR.
I am just saying that at low AR it is quite poor compared to some other models,
as shown in the attached graph of lift slope versus AR for rectangular wings.