Pros and Cons of Transom Hung Rudders

Here's a different way of looking at the drag of foils. Induced drag depends on the span and the lift, but doesn't depend on the area. The lift from a big rudder and the lift from a small rudder is the same, because that's what's needed to balance or maneuver the boat. The pilot controls the lift on the rudder as required, and will use as much, or as little, deflection as needed to get it. So the intentional loads are nearly independent of rudder size.

If you know the maximum load you want to apply to the rudder, and you set the depth to minimize the induced drag that results from it, that pretty much sizes the rudder stock. What's left is to size the chord so you can achieve that maximum load.

If you look at the profile drag normalized by the thickness instead of the chord, you get a completely different picture. You can easily do this with published section data just by dividing the drag by the thickness ratio. What you'll find is thin sections and thick sections are closer together when compared on the basis of the same physical thickness.

For example, at a Reynolds number of 1,000,000, XFOIL predicts the following minimum drag coefficients, with the last column using the NACA 0012 as a reference for comparison:

Foil Cd_min
NACA 0006: 0.00334 62%
NACA 0009: 0.00428 79%
NACA 0012: 0.00539 100%
NACA 0015: 0.00634 118%
NACA 0018: 0.00712 132%
NACA 0021: 0.00791 147%

it looks like there's a big difference in drag between the thick and thin sections. But when you divide through by the thickness ratio, you get:

Foil Cd_min/t
NACA 0006: 0.0557 124%
NACA 0009: 0.0475 106%
NACA 0012: 0.0449 100%
NACA 0015: 0.0409 91%
NACA 0018: 0.0396 88%
NACA 0021: 0.0377 84%

This is equivalent to basing the minimum drag on the frontal area of the faired rudder. Now the difference is not all that dramatic, and the thin sections fare worse than the thick sections.

If you keep the physical thickness of the rudder stock the same and the depth of the rudder the same, a narrow high aspect rudder will have less drag than a rudder with larger chord. As you might expect because of the reduced wetted area. But the difference is not all that great. A rudder with a NACA 0009 will be twice the chord of a rudder using a NACA 0018, but the large rudder will only have 20% more profile drag when they share the same stock. A NACA 0009 rudder will have 50% more wetted area than a NACA 0012 rudder, but only have 6% more profile drag.

The wide rudder will have a greater maximum lift by virtue of its larger size, even though it has a somewhat smaller maximum lift coefficient because of its smaller thickness ratio. Here's the maximum lift coefficient from XFOIL at a Reynolds number of 1,000,000 (which probably over-predicts the max lift somewhat):

Foil Cl_max
NACA 0006: 0.765 56%
NACA 0009: 1.218 89%
NACA 0012: 1.373 100%
NACA 0015: 1.425 104%
NACA 0018: 1.421 103%
NACA 0021: 1.387 101%

Scaling by thickness again to get the maximum lift for their physical thickness:

Foil Cl_max/t
NACA 0006: 12.75 111%
NACA 0009: 13.53 118%
NACA 0012: 11.44 100%
NACA 0015: 9.50 83%
NACA 0018: 7.89 69%
NACA 0021: 6.60 58%

So the 9% thick foil will stress its rudder stock the most. If the rudder is wider, the larger area does not make up for stalling at a lower angle of attack. And the converse is true for the thicker foils - their larger stall angle of attack doesn't make up for the reduction in area when the foils are compared on the basis of equal physical thickness.

Probably the best metric is to divide the maximum lift by the minimum drag. This means the rudder is sized by the maximum lift and you want to have the minimum drag rudder that will do the job. Again, the span and planform shape are kept fixed, and just the chord is varied.

Foil Cl_max/Cd_min
NACA 0006: 229.0 90%
NACA 0009: 284.6 112%
NACA 0012: 254.7 100%
NACA 0015: 224.8 88%
NACA 0018: 199.6 78%
NACA 0021: 175.3 69%

9% to 10% thick is again the optimum size when optimized on a purely hydrodynamic basis. But there's not a dramatic difference between 6% thickness and 15% thickness when the foils are designed to the same requirements. The minimum drag for the same maximum steering power is within +- 12% of the 12% thick section I've used as a baseline.

Finally, the maximum stress in the rudder stock scales inversely as thickness cubed for the same load. The required chord is inversely proportional to the maximum lift: Cl_design*chord_baseline = Cl_max*chord; chord = Cl_design/Cl_max * chord_baseline. The load acting on the foil is also proportional Cl_max*chord. The minimum drag is proportional to Cd_min*chord. When you multiply the stress by the minimum drag, you get a metric that looks like the minimum drag coefficient times the maximum lift coefficient-squared divided by the thickness ratio-cubed. Here's what the same three foils look like using this metric (lower is better):

Foil Cd_min*Cl_max^2/t^3
NACA 0006: 9.05 154%
NACA 0009: 8.71 148%
NACA 0012: 5.88 100%
NACA 0015: 3.81 65%
NACA 0018: 2.47 42%
NACA 0021: 1.64 28%

So what does all this mean? For the cantilevered spade rudder, thin sections pose a difficult challenge. They produce almost as much lift as thicker sections and there's no room to put in strong stock.

There's not much reason to go any thinner than 9%, even with a transom hung rudder that uses the whole section for strength instead of just a post in the middle. The drag you save is offset by the loss in maximum lift, forcing you to use a slightly bigger rudder.

For spade rudders, it is worth it to go with a thick section to reduce the maximum stress in the stock. The drag due to the extra thickness is not prohibitive, and it can be reduced further by designing sections specifically for the purpose instead of using off-the-shelf NACA sections. Hence the typical practice in spade rudders of using a very thick section at the root and tapering the stock to get down to around 9% -10% thickness to get the hydrodynamic optimum.

What you save in induced drag in a spade rudder by going deeper is well worth the added profile drag due to using thicker sections for strength.

 

I think this is a big advantage of transom hung rudders - you can see and remove it if necessary. But it's also easier to damage a transom hung rudder because it's exposed. It's also harder to make pintles and gougeons as strong as the rudder shaft bearings supported all around by the bottom skin and cockpit sole.

I often wonder about the performance advantages of spades. As others have pointed out, a small gap between the hull and rudder can spoil much of the end-plate effect.

 

That is fully correct. The gap between rudder and hull should be as minimal as possible.

 

tspeer: a small gap between the hull and rudder can spoil much of the end-plate effect.
D'ARTOIS: The gap between rudder and hull should be as minimal as possible.

That's an interesting argument for the keel-hung rudder, at least for cruising. In order for a spade rudder to get a full end-cap effect, the hull around the rudder post must be "conically symmetric" within the rudder's range of motion. First of all, that means the upper edge of the rudder has to curve upward from the post, which is structurally not great but maybe not a huge problem. More importantly, the conical shape is not ideal for that part of the hull, which needs to be angled upward toward the transom but horizontal athwartship. The hull is more horizontal just aft of the keel, so fitting the rudder to the hull will be much easier there. It just won't work very well in tight racing or similar situations.

 

Personally, I'm not sure that the transom-hung rudder is any stronger either, the bending load is still concentrated in the small section that is thickest anyway. When you use one on a boat much larger than a dinghy you usually have to notch out the leading edge so there isn't too much weather helm, and that's an obviously unfortunate place to put a substantial stress-riser.

Further problems can ensue when plywood is used for a core, if the rudder deflects too much under load, the lignin holding the chord-wise wood-fibers together can break down and allow them to turn into "rollers".

My preference is for rectangular or slightly trapezoidal section carbon shafts, that way the load is shared between the fibers a lot less unevenly, and the primary load-bearing fibers are just below the skin of the blade.

Yoke.