View Full Version : Efficiency of rudder

01-24-2013, 07:28 AM
I am interested in calculating the force on a spade rudder taking into account its angle of deflection and heel angle of sailboat, knowing boat speed and and area of rudder. The basic question is: how fast does efficiency for steering degrade as heel angle increases?

01-24-2013, 01:59 PM
as a rough approximation I would say you lose rudder effectiveness with the cosine of the heel angle. As the heel increases the horizontal component of the rudder force will go down at about the rate of the cosine of the heel angle. Yet both the parasitic drag and the induced drag will stay the same for any given heel angle.

There may be some other effects from the shape of the hull and some details of the rudder design, but the majority effect I would suspect is simply a matter of the heel angle.

This is why BTW, any of the high performance monohull sailboats have two rudders at angles to the approximately match their heel angle. I suppose you could improve rudder efficiency if you can adjust its angle to match the heel angle while underway.

Dr. Peter
02-01-2013, 06:21 AM
I have a small 5.6m sailboat with a centreplate in the shoal keel. The boat weight 750kg and carries 360kg in ballast. It came with a fixed rudder which was too small and poorly mounted. As an experiment I fitted an ex-Hartley 18 all gal steel rudder. Its about 0.7m x 0.38m and about 3mm thick. Apart from rounding the front edge and squaring off the back it is a very non-technical rudder although I have ensured that, unlike the original it replaced, the leading edge is forward of the pintles. It is bigger then the original.

You can get lucky some times and the change in performance has been a revelation. Helm pressure is perfect and the boat no longer broaches like it used to. We can carry full mainsail and early reefing seems to be a thing of the past. Its handy to be able to pull the rudder into the up position.

You can also be a little unlucky and on a recent 9 day cruise, on launching the boat I found myself unable to drop the centreplate. Oh well, I'll just sail on the shoal keel. The shoal keel starts about 1/4 of the way back from the bow and finished just in front of the transom (about 1m). The boat has a draft of 0.55m in the shoal keel form while dropping the centreplate down makes the the draft 1.14m. A bit over half a metre more although it must be said that the plate would only be about 0.3m wide.

Thanks for sticking with me so far. I'll get to my question: I observed that with the 'new' rudder and just the shoal keel that the boat seemed to point well and we did not appear to be skidding to leeward. I say this because when I compensated for the expected skidding by sailing further before tacking, to pass a headland for example, I had so much sea room in the bank I was surprised.

What is going on? Do I need a centreplate or is an efficient rudder somehow compensating for its lack in some way?

02-01-2013, 06:32 AM
Dr. Peter,
Check this post:
What you have noticed on your boat s very similar to what is described in that post - just replace the word "chine" with the word "shoal keel". The mechanism of the generation of lift is essentially the same. If there's something that is not clear, do not hesitate to ask. :)

As about the question of the importance of the correct rudder shape for the overall performance of the boat, I would advice everyone to read the following paper:


Dr. Peter
02-01-2013, 05:32 PM
Thank you for the quick and helpful response. I checked out your post and it does seem that I have created a similar situation, albeit with a shoal keel rather than a chine. So I think my impression of my 'not' skidding to leeward, with the bigger rudder, may be valid.

Looking at those traditional fishing boats, I can't imagine professional fisherman of the day accepting a boat that won't work to windward. I read through the thread and an important, and a new concept for me (I'm not a naval designer) was that of total lift and total drag. In the past I have tended to think of the keel, rudder, hull as separate components. I think I have achieved a synergy here between my hull, shoal keel and the larger rudder. It certainly seems better able to support my sail plan. Soon I have to decide to either repair the tiny centreplate or fix the situation so that it is removed entirely from the equation. I think my total lift and drag, with respect to surface area only, is about the same as it used to be with the centreplate down and the old skinny fixed rudder. It has just moved these to more useful areas of this boat. I am actively considering removing this tiny centreplate and sealing up the keel - it would remove an ongoing maintenance problem and better leakproof the hull.

I fitted the Hartley rudder in the form of an experiment and like I have already said it is not particularly 'technical' but it seems to work very well. As a friend said to me, "If it works so well, why change it." My thoughts are that if a plate of galvanized steel makes such a difference what might be possible with a foil shape. So I was hoping for some guidance from the paper you suggested, but without an appropriate technical background, I struggled with it. Unfortunately, the conclusions, framed as they were with handicapping in mind, were unclear to me too. I think the article is saying a deeper rudder is best but I did not understand the effect of span or width so some further help would be appreciated.

02-01-2013, 06:42 PM
The article was oriented towards formulating handicap rules based on rudder depth in terms of drag vs. depth, not sure there was much useful information for designing a rudder.

The rudder is a foil that creates a side force for both trim and steering the boat. The larger the overall surface the more steering force you can generate, but more surface area also means more drag. A high aspect ratio lifting surface (its width to length ratio) will have less drag for the same amount of lift force. So to minimize drag, you want a smaller surface with a high aspect ratio rudder. However, a high aspect ratio rudder stalls at a much lower angle of attack, so if you over control the steering you end up with little or no rudder control after it stalls. I think for recreational sailing a larger, low aspect ratio rudder is better because of it's stall resistance. A lower aspect ratio surface is more stall resistant, but suffers higher drag. Racing boats always have foil shaped very high aspect ratio rudders, but a skilled helmsman presumably knows the limitations of the rudder and can stay within its limited effective angle of attack.

If you were designing a new boat, the further aft you can put the rudder the smaller it can be since you have loner lever to rotate the boat. But the further aft it is the easier it is to damage when in the shallows or near a dock (or other boats!). But if you are stuck with what your current boat has now this is of little consequence. You have to work with what you got unless you are going to make major changes to the hull. I would advise you to get professional guidance if you do that.

You also have to consider balance at the helm if you have a very large rudder since tiller forces can be very large on a large boat. The location of the pivot line relative to the area of the rudder will affect the tiller forces.

Different foil shapes can also affect drag, and many have persued high tech laminar shapes to reduce their drag as well. Unless you are racing I would also not advise using a laminar flow foil, if the are not kept clean and shinny they will not have laminar flow, and they usually perform very poorly if they can not maintain laminar flow over most of the forward surface. I would advise just using a good old NACA 00XX series foil for recreational use. They behave predictably and perform good enough where most would never know the difference.

good luck.

Dr. Peter
02-01-2013, 07:45 PM
Thanks for your thoughts.

Based on what you say, what I have observed and what my friend said about it working so well then why change it, I think I should stick with what I have accidentally stumbled upon. I wouldn't want to overcapitalize my little boat with a 'super rudder'.

I have attached images of the two rudders and the centreplate which can go further down but this is its normal position (about 45 degrees).

02-01-2013, 08:34 PM
If it works, don't fix it.

02-03-2013, 08:16 PM
if it works you could improve it by making it with a foil shape this will greatly improve its performance even over what you have already :confused:

02-14-2013, 05:25 AM
I am interested in scenarios that might break a sailboat rudder, since this is known to happen. I would like to calculate the force on my 7 sq ft rudder and found the following in online Cruising World, by Jeremy McGeary:

While researching loads on rudders, I came across an online Cruising World article (July 5, 2005), "Rudder Loads on the Modern Cruiser." Under the heading, "Why Do Rudders Fail?" he presents a calculation for a worst case scenario, a wipeout at 16 knots and rudder deflection of 35 degrees:

"At 16 knots, with our 9-square-foot rudder, q = (16 x 1.69)2 x 9 x .57 = 3,751 lbs. The rudderstock has to be able to support the equivalent weight of a J/24 and its four crew."

However, multiplying the above numbers does not come close to his load calculation. Is there something missing from this piece?

02-14-2013, 06:22 AM
"At 16 knots, with our 9-square-foot rudder, q = (16 x 1.69)2 x 9 x .57 = 3,751 lbs. The rudderstock has to be able to support the equivalent weight of a J/24 and its four crew."

However, multiplying the above numbers does not come close to his load calculation. Is there something missing from this piece?

2 is square, then you get the correct number.

You can simply calculate the force using:

F = 0.5*rho*Cl*A*V^2

Cl depends on the angle of attack and the maximum is between 1 and 2 depending on many things.

9 ft2= 0.836 m2, 16 knots= 8.23 m/s, rho=1000 kg/m3, Cl=1 => 28 kN = 6400 lbs.

02-14-2013, 07:56 AM
Thanks. I did not see that '2' actually meant '^2'. I also did not mention that McGeary accounted for displacement of the rudder by 35 degrees (perhaps a hypothetical for a broach) by multiplying the rudder area by sin(35). His article in online Cruising World is at:


02-14-2013, 08:48 AM
Forgot to mention in my last note that the McGeary calculation does not say anything about the effect of heel angle on the entire rudder mechanism and its effect (if any) on the force exerted on the rudder. The actual area of rudder presented to the water would seem to be unchanged whether or not the boat is heeling.

02-14-2013, 09:03 AM
You have the worst case when the boat is navigating at zero heel. The heel angle actually decreases the intensity of forces acting on a rudder, because of several mechanisms related to the proximity of the water-air interface.

View Full Version : Efficiency of rudder