Rudder Design

Discussion in 'Sailboats' started by tspeer, Mar 24, 2004.

  1. tspeer
    Joined: Feb 2002
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    tspeer Senior Member

  2. Lester
    Joined: Sep 2003
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    Lester New Member

    Scratching my head a little here...

    The three rudders have different planform (profile) areas, but the drag and lift results are plotted against something called "drag area" and "lift area" rather than against drag and lift coefficients. The drag and lift areas do not seem to have the planform area differences between the rudders removed, so it isn't clear that the deep rudder, for example, "really" gives lower drag at higher rudder sweep (angle of attack). It seems to, but its planform area is around 1.2 m^2, while the shallow rudder has 1.6 m^2.

    The three rudders are said to have identical lift slopes, but table 2 seems to show dCl/dA around 5.3 for the deep rudder, and 4.1 for the shallow (this is dCl per radian; in degrees, around 0.09 for deep and 0.07 for shallow). What seems to be identical is the lift area at (presumably) 4 degrees angle of attack instead.

    The rudder section isn't mentioned, but the t/c varies quite dramatically between the rudders. The deep rudder sports a root t/c of 18%, while the shallow has 12%. Would I be wrong to expect a 12% section rudder to show lower drag at low angles of attack (it is thinner) but higher drag when it enters its stall region which it would presumably do well before an 18% section?

    The paper is all about deep, medium, and shallow span rudders, yet as far as I can see aspect ratio isn't mentioned anywhere. The IMS rule doesn't seem to use AR, but it would have been useful to cross-check the results against known AR effects on drag. Hmmm...
     
  3. tspeer
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    tspeer Senior Member

    Lift area is the coefficient of lift times the area. Or the lift divided by dynamic pressure. Drag area, likewise, is the drag divided by dynamic pressure. So they are not quite nondimensional, but can be used much like nondimensional coefficients.

    The 12% thick rudder isn't necessarily thinner than the 18% thick rudder. They probably have the same thickness to accommodate the same rudder stock. But the low aspect rudder has a longer chord and thus a lower thickness ratio.

    And from Fig. 11 on, they've subtracted out the parasite drag and are only working with the induced drag of the rudder.

    It turns out drag doesn't depend at all on aspect ratio. Drag depends on area and span (squared). Aspect ratio only shows up in the nondimensional coefficients - it's really the nondimensional version of span (squared). Two rudders producing the same lift (or lift area) will have comparable induced drag if they have the same span, even if they have different planform areas, chord lengths, and aspect ratios.

    The lift area is dictated by the demands of the hull and rig, not the rudder design per se, because the rudder will be trimmed to null out the net yawing moment. You can get the same lift area with a small rudder operating at a large deflection, or a large rudder operating with a small deflection.

    So the question is, for the required amount of lift area, how much drag area is incurred? That's what the paper is about.

    The rudders can have the same lift area/radian because the shallow rudder has more area than the deep rudder. The shallow rudder will have more profile drag because of the area and more induced drag because of the shorter span. The table shows the change in lift coefficient/radian (dCL/dA), and if you multiply that by the planform area, you get the same lift area slope for each rudder (d[L/Q]/dA = S*dCL/dA).

    When I look at the minimum drag numbers of Fig. 11, I get effective span ratios of 0.75 for the deep rudder, 0.90 for the mid rudder, and 1.14 for the short rudder. At the high drag end, the effective spans ratios are 0.47, 0.57, 0.74. So evidently the shorter rudder gains more from the presence of the hull than the deep rudder, which isn't surprising. This helps to cushion the variation one might expect between the rudders.

    The difference in drag with speed and heel of Fig. 11 is probably due to free surface effects. Higher Froude numbers should increase the induced drag and greater heel brings the rudder closer to the surface, also increasing drag.
     

  4. Lester
    Joined: Sep 2003
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    Lester New Member

    I guess I am worried (perhaps unnecessarily!) about the apparent "outcome" of the paper being already decided by the input... The deep rudder has been given the same lift area (around 0.456 m^2) as the shallow rudder, based upon performance at a sweep (angle of attack) of 4 degrees as far as I can see. Because the deep rudder they have in mind is a better lift producer (for whatever reason), it pulls a coeff of lift of around 0.37 at this angle of attack, and so its planform area is about 1.23 m^2. The shallow rudder doesn't work quite as well, and only manages to pull CL=0.285 with alpha=4, to yield a planform area of about 1.60 m^2. My concern is that this early decision about the characteristics of the rudders they test more or less determines the results they go on to find.

    For example, another approach to sizing a rudder would be to ask that its lift area equals "X" (0.456 m^2 or whatever other value you think reasonable) at the point that the rudder stalls, rather than when set at alpha=4. I don't think it is clear what the result would be in this case. A higher aspect ratio rudder (sorry, still gotta think in these terms!) will presumably stall earlier than a low aspect one (other things being equal), but the necessity to carry the same rudder stock (or even a thicker stock since the deep rudder has a higher moment acting on it) presumably gives the deep rudder a higher t/c and hence a later stall than the t/c of the shallow rudder...

    As you note, Fig 11 shows induced drag only. Taking the highest induced drag area shown, for the shallow rudder we can read off a value around .0178, which yields CDi = 0.111 when the shallow rudder's profile area is taken into account. For the deep rudder, we read an induced drag area around .0145, yielding CDi = .0118 when its area is taken into account. Alpha = approx 2.2 for the lift area of 0.25 quoted for Fig 11, so the deep rudder is pulling CL = approx 0.2 and the shallow is pulling CL = about 0.16. It seems that the deep rudder shows only a very modest (negligible) 0.6% improvement in CDi over the shallow one, but it is running at 25% higher CL. Given that CDi is in proportion to CL squared, if the shallow rudder was pulling CL = 0.2 or so, its CDi should be expected to be around 56% higher, not 0.6%. So I'm wondering if (in theory) their suggested IMS modifications penalize a deep rudder enough... (Not that I would know, I just sail toy boats!)


    Yes. However, in the paper they say, "... all three rudders have the same lift slope", and this simply isn't true as far as I can see. Not a big deal 'cos I can see where they are headed, but it rather puts me in a skeptical mood when reading the rest of their paper...
     
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