Rudder Centre of pressure with PMB Foil ??

Discussion in 'Boat Design' started by MikeJohns, Aug 1, 2007.

  1. MikeJohns
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    MikeJohns Senior Member

    I have a large double hung rudder based on a 0012 section with Parallel Mid Body that is to be re-hung as a balanced rudder to give the hydraulics some reprieve. (Motor-sailing vessel)

    What happens to the centre of pressure ? Normally 25% aft the LE for a 0012 I presume the PMB will shift this further aft?.

    There's a princess fairing and a gap of 10mm. But I may just have to use the < 20% rule of thumb. Max deflection is 28 degrees.

    Any comments Anecdotes or observations very welcome.
     
  2. Guest625101138

    Guest625101138 Previous Member

    I have attached a screen dump from JavaFoil for a NACA0012 section. The Moment Coefficient is very low and slightly negative. This is based on 25% cord.

    If you have the shape of your rudder you could use JavaFoil to arrive at the correct value.

    You want to have some restoring moment so there is feel and a bit of self-centring.

    Here is a link to the applet:
    http://www.mh-aerotools.de/airfoils/jf_applet.htm

    I used an aspect ratio of 3:1. Just a guess.

    You can see that the rudder lift drops off dramarically after 10 degrees so really a waste of time being able to turn much beyond this angle for a 12% foil. I am a fan of short chord with fat section. You can reduce the area quite a lot. For a given depth you reduce the chord to about half so the aspect ratio goes up, the Cd on centre goes up a little but this is more than offset be the reduced area. I read somewhere that a 20% rudder is about the best and JavaFoil, as well as my experience, verifies this.

    Rick W.
     

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  3. MikeJohns
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    MikeJohns Senior Member

    Rick
    Thanks for your post.

    The Parallel Mid Body is inserted in the foil section at the widest point so you chop the 0012 at 30% and add a parallel sided section. My query was really whether it's possible to make a call on the movement of the COP aft from 25% when a PMB is inserted. But I'll see if I get some joy out of the app you linked to , thanks.

    The optimum foil shape of course depends on the flow field and the Re/Rn you are operating at. You will often see a stall at say 15 degrees sudden hard rudder but the flow alters as the vessel turns depending on the pivot point side-slip etc and then you can get effective lift at much greater rudder angles relative to the boats axis. Prop wash directing is another story too.

    For your pedal power applications you would want a narrow entry foil shape close to the surface with the max thickness well aft to reduce drag wouldn't you? Much lower Re/Rn s of course.

    cheers
     
  4. Guest625101138

    Guest625101138 Previous Member

    What are the dimensions of your rudder. How long is the parallel section. I can do the mock up for JavaFoil if you like.

    You are right about the change in flow when turning. Most of my recent experience has been with long thin hull shapes with little rocker and these are slow to turn. I like to place the rudder under the hull so it does not ventillate. I use the NACA0020 section for the entire depth these days.

    I have been surprised at how effective a fat rudder can be. It was not intuitive.

    Prop wash at slow speed is important as well.

    The rudder performance does not change much for Re# 200,000 to 2,000,000. What is your design speed?

    Rick W.
     
  5. tspeer
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    tspeer Senior Member

    The hydrodynamic center is hardly changed. But inserting the parallel midbody doesn't necessarily help the section at all.

    You haven't said how large your parallel midbody is, so let's assume it's 50% of the original chord, making the new section 1/3 forebody, 1/3 parallel midbody, and 1/3 aftbody, with a thickness of 8% compared to the original 12%. The shape of this PMB section and the original NACA 0012 are shown below.

    The effect of the PMB on the zero-angle-of-attack pressure distribution is shown in the next two figures. The NACA 0012 pressure distribution rises to a peak near the leading edge, then has a smooth, gradual deceleration to the trailing edge. The PMB has a similar peak (but smaller due to the smaller thickness), but then has an abrupt hollow in the pressure distribution followed by a smaller hump at the aft-body transition. This somewhat bumpy pressure distribution has a significant effect on the boundary layer transition. The transition tends to happen earlier on the suction side, and this negates most of the drag benefit you might expect by making the section thinner.

    The drag polars for the NACA 0012 at Reynolds numbers ranging from 250,000 to 2,000,000 are shown in the fourth figure. I've assumed a fairly turbulent oncoming flow (ncrit=3) due to operating near the surface and in the propwash. At zero angle of attack, transition occurs earlier as the Reynolds number increases (third plot on the right), but varies smoothly as angle of attack increases.

    The PMB polars are shown in the fifth figure. Transition at zero angle of attack occurs earlier than for the NACA 0012. With a modest increase in angle of attack transition on the pressure side jumps from near the forebody to the aftbody.

    The final figure shows a comparison between the NACA 0012 and the PMB. Despite being 2/3 the thickness, the PMB actually has more drag at zero angle of attack. Once transition jumps to the aftbody on the pressure side, the PMB has comparable drag to the NACA 0012.

    The hydrodynamic center of the PMB foil is very near 25% chord for both sections. For moderate angles of attack, the PMB hydrodynamic center is slightly aft of where it is on the NACA 0012, but I don't think you'd see the difference in practice.

    The last figure shows the PMB section has a higher minimum pressure coefficient than the NACA 0012 over the entire lift range. This means the PMB will cavitate at a lower speed than the NACA 0012.

    Bottom line is, the PMB section has no hydrodynamic advantages over the NACA 0012. It is thinner and structrually weaker. It might, however, be easier to make. You could start with a plate of the desired thickness, and then carve away at the leading and trailing edges to make the PMB. The longer the midbody, the more it's going to act like a flat plate instead of a NACA section.
     

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  6. MikeJohns
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    MikeJohns Senior Member

    Tom

    I'm re-positioning the pivot on an existing installation.

    The foil is a bit more complex than I said ;longer at the bottom than the top by around 30%, NACA 0012 900mm long foil at top and NACA 0012 with 30% PMB at bottom

    Sheet metal fabrication was by constant rolled section, consequently there's a triangular shape of PMB

    Dims: Top foil 900mm Bottom foil 1200mm, h 1.7 m, Area 1.8 m^2


    I was trying to fathom where I should put the bearings for an easing of the helm without undue effects, seems from what you say its pretty much the same, I'll put 18% of area ahead of the pivot line.

    Thanks
     

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  7. MikeJohns
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    MikeJohns Senior Member

    Tom, Rick

    As a matter of future reference what ideal 00xx would you recommend for the pictured keel-rudder configuration full foil shape no PMB ?

    I always thought 0012 was about the best all-rounder. But would you get a better re-attachment with a thicker foil ?
     

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  8. Guest625101138

    Guest625101138 Previous Member

    Mike
    As I said earlier I have found that the fat section works better than the thinner one for a rudder.

    Looking at the rudder in the drawing I am estimating it has an aspect ratio of 2. JavaFoil tells me that a NACA0012 foil will have a maximum lift coefficient around 0.5. The inline drag coefficient is .0047.

    If the rudder is halved in length so the aspect ratio goes up to 4, using a NACA0020 section and Re# is halved. The maximum Cl becomes 1.13 and the inline Cd becomes .0078.

    So allowing for the reduced area, the fatter section (it is actually thinner because it is only half the chord length) will generate 13% more steering force for 17% less inline drag.

    I tried to find the paper that did an analysis on optimum rudders but cannot find it right now. I am sure it arrived at a NACA0020 section. I looked at a NACA0025 for this application and I think it ends up worse than the NACA0020.

    I considers rudders as a necessary evil and only have one large enough to do the specified job. Any more power is a waste and it is always costing you. I have tried to develop a temporary rudder but can never get any of my boats to track true without a tiny amount of steering.

    Rick W.
     
  9. tspeer
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    tspeer Senior Member

    It's not necessarily true that thicker is better. The NACA is a very good all-round section. If you have a need to go much thicker, say to 20%, there are better sections than the NACA 0020. A roof-top section like the one described in Gabriel Elkhaim's dissertation, is better if the thickness is large.

    The best section, of course, is one that is specifically designed for your application. Then you can trade thickness for structural strength, low minimum drag for efficiency in a straight-line, and high-lift for maneuvering.

    Here's a blast from the past. Back in the 1980's I designed a section (S25e4042508) using a similar design philosphy to Dr. Elkhaim's. I used a von Mises transform coupled to an optimization routine, programmed in Microsoft FORTRAN on an 8-bit Z80 card running the CP/M operating system! Other than the thickness, it doesn't have much more to offer than the NACA 0012. Of course, that thickness could be a major design consideration.

    Today, with XFOIL, I can take that section and improve it quite a bit. The rooftop can be made truly flat and the wiggles taken out of the pressure distribution. The entrance to the pressure recovery made more rounded so there's not such a large laminar separation bubble there.
     

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  10. tspeer
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    tspeer Senior Member

    Here's an example of the kinds of trades you can do. Let's say you really wanted a 20% thick section. S25e4mod1 is S25e4042508 cleaned up a bit. The change in the contour is hardly noticeable, and the drag is nearly the same, but there's a little improvement in stall. Compared to the NACA 0012, this section trades minimum drag for thickness.

    S25e4mod2 is optimized to trade maximum lift for a lower minimum drag. The rooftop is designed for a lower angle of attack (5 degrees vs 8 degrees for the S25e4mod1) and it extends farther back to get more laminar flow. This section's minimum drag is predicted to be the same as the NACA 0012's even though it's 20% thick vs 12% for the NACA foil, and it has an exceptionally wide drag bucket - all the way out to Cl=0.5. This would be a good choice if high speed drag was more important than low-speed maneuvering. A smaller chord could be used with the same thickness of the rudder post for strength.

    Compared to the NACA 0020, the S25e4mod1 has about the same minimum drag, but less drag at high lift, out to Cl=1.1. The S25e4mod2 is better than the NACA 0020 out to Cl=0.8

    With a bit more work, one could come up with a more balanced design. The specification might include raising the stall break to Cl=1.0, trying to maintain minimum drag comparable to the NACA 0012, but sacrificing some of the width of the drag bucket.
     

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  11. jehardiman
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    jehardiman Senior Member

    Tom's posts point out something that I have found. NACA AEROdynamic sections are too thin/too long tapered aft for optimum HYDROdynamics. TMB EPH shapes are much bluffer, carry their area further aft, and generally perform better in higher Rn conditions. A fair amout of this preformance is based upon the hyperbolic afterbody. However many all moveable rudders of satisfactory performance are still designed with a NACA 0018 root, a 0012 or 0015 tip, 50% taper, and significant sweep
     
    Last edited: Aug 4, 2007
  12. tspeer
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    tspeer Senior Member

    I think the notion of using conic sections for large portions of a section's shape is a pretty out-dated approach. There's nothing about conic sections that are particularly relevant in themselves to the aero/hydrodynamics of foil sections. I'm sure that for any conclusion you would make about the bluffness of their shape or the location of their maximum thickness one could find a counter-example.

    For example, if you compare the NACA 0020 to the E25e4mod1 of my previous post, the NACA 0020 does everything you mention - the leading edge is blunter, the maximum thickness is further aft, and the trailing edge is fuller (first figure). But at high Reynolds numbers (2 million), the E25e4mod1 is superior to the NACA 0020 up to a lift coefficient of about 1.1, while at low Reynolds numbers, the NACA section has lower minimum drag and higher maximum lift (second figure, below). This is exactly the opposite of what you propose.

    So how to account for this discrepancy? For that, you have to look at the boundary layer characteristics. The transition points on the polar plots (right-most plot in the second figure) have some important clues. The transition point on the NACA 0020 starts off reasonably far aft (almost 40% chord), and then moves smoothly forward with angle of attack on the suction surface and smoothly aft on the pressure surface. But the transition point of the E25e4mod1 hardly moves at all by comparison.

    To see why, look at the pressure distributions for the two sections (third figure). The E25e4mod1 has a roof-top type of pressure distribution, consisting of a comparatively flat (near-constant) pressure from the leading edge back to near the maximum thickness point, then a steep pressure increase that flattens as it runs out to the trailing edge. The transition point doesn't move much because at angles of attack lower than the design angle, there is a favorable pressure gradient over the roof-top region and the start of the pressure recovery region is so steep that laminar separation or transition is bound to occur there. It turns out this is a high-Reynolds number design approach. The steep initial gradient of the pressure recovery makes it difficult for the flow to reattach until the pressure starts to flatten out, causing a long laminar separation bubble. There's also the risk that the flow won't reattach at all after laminar separation, causing sudden stall at low Reynolds numbers.

    You can see this better in the final figure, which shows the pressure distribution for the S25e4mod1 at an angle of attack of 8 degrees for low and high Reynolds numbers. I've also change the transition criteria to represent a very smooth oncoming flow to accent the impact of the laminar portion of the boundary layer. At a Reynolds number of 250,000, laminar separation occurs around 20% chord and doesn't reattach until approximately 35% chord. There's a very large and pronounced constant pressure "shelf" sticking out of the backside of the pressure distribution. This is due to the separated flow. The very steep increase in pressure signals the transition from laminar to turbulent flow in the boundary layer. The losses in the large separation bubble result in a thick boundary layer at the trailing edge, and this in turn reduces the lift - the height of the rooftop is much lower for the low-Reynolds number case than the high-Reynolds number case. by contrast, at a Reynolds number of 2,000,000, the laminar separation hardly gets decently established before the flow transitions to turbulent and reattaches. The conditions at the trailing edge really dictate the lift over the entire section, and the thinner boundary layer at high Reynolds number means the rooftop is closer to what it theoretically would be if there were no boundary layer losses at all (dashed black line).

    The NACA 0020 has a high pressure peak at this angle of attack, but it has a much more gradual adverse pressure gradient over the forward half of the section. This adverse gradient is reduced at lower angles of attack and increased at higher angles of attack. So at low angles of attack, the flow can make it further along the chord until the adverse gradient leads to laminar separation, but laminar separation occurs earlier at higher angles of attack. Once laminar separation occurs, the pressure becomes flat for a short distance due to the distortion of the shape by the separated flow, but transition quickly occurs. Once the flow transitions to turbulent, the pressure increases rapidly and soon intersects the pressure profile that would exist had the flow not separated at all. This forms a short laminar separation bubble that produces less drag than a long bubble. So the more gradual adverse pressure gradient produces a short laminar separation bubble that moves smoothly toward the leading edge as the angle of attack increases. This is a classic low-Reynolds number design philosophy.

    So it's really hard to generalize what a section's characteristics are going to be just from geometric measures like thickness, position of maximum thickness, and leading edge radius. Within a given family of sections, these may correlate with trends in the section characteristics, but they're not a reliable indicator across different families. What's absolutely crucial is the boundary layer development, and the main way of affecting boundary layer development is through shaping of the pressure distribution.

    The shape of the section will tend to mimic the pressure distribution somewhat. A concave pressure recovery will tend to produce flat or hollow aft contours and a convex pressure recovery will produce full aft contours. The pressure recovery region will tend to begin near the position of maximum thickness. A longer rooftop will tend to produce a finer leading edge. So it is possible to look at a section and make an intelligent guess as to what the overall design approach is and possibly even some key operating conditions.

    But this is a lot like looking at a mirror and making a judgement on it's image quality by characterizing it as being deep or shallow. You know a deep mirror will have a shorter focal length than a shallow one. But a circular arc mirror will have a distorted image while a parabolic mirror will have a finely focused image. In this case, the parabola is something that falls out from calculating how to focus parallel rays striking the mirror. If the rays were from a point source, the same calculations would produce an elliptical mirror. The two mirrors may be fairly close in shape, but one will focus well in one situation but not in the other, and vice versa. And a given elliptical mirror won't focus well if the point source is closer or farther than the design point, so you can't make a blanket statement that mirrors should be elliptical or parabolic to focus well. The same thing holds for foil sections. Like a circular arc mirror that is a simple shape and pretty good at producing a general concentration of light, a geometrically designed section may have adequate performance over a wide range of conditions. But one can do better than that by calculating the shape from a specification that more precisely describes the design requirements.
     

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  13. tspeer
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    tspeer Senior Member

    Somehow the couple of attachments to the previous post didn't make it. Here is the comparison of the S25e4mod1 and NACA 0020 shape, and their respective drag polars.
     

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  14. jehardiman
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    jehardiman Senior Member

    Tom, I need to check the software that you are using (Xfoil?) to plot your sections, but it seems that your data actually fully supports my methods of design and comments about bluff trailing sections.

    Look at the plot of the two foils S25e4mod1 and NACA 0020. There is a term there called "delta theta TE". This term is the included angle symetrical on CL that touches tangent to the afterbody, without being "in" the section. I have found that this is the single most important factor for good hydro performance of a section. If you notice, the S25e4 angle is 37.7 degrees and the NACA is 26.3. As far as flow effects are concerned, the S25e4 section is bluffer than the NACA section, and very close to the optimum for foil sections that my studies lead me to; ~38 degrees or 19 degrees half angle. There is a reason for this and it has to do with energy propagation in the viscous properties of water, and yes it is very closely related to the 19 degree angle of the wake pressure distrubance. Try to get a look at the data in Blevins (I don't have it in front of me now) where they show the drag of a cylinder with a thin plate tail attached, there is a optimum length for the tail, and yes it is very close to 38 degrees. Also try to get your hands on some "flagged" cable drag data such as Pode's, again it shows that there is an optimum length for the tail. In actual practice, from a drag point of view it wouldn't matter if the afterbody was ridgid or not, but it would for a rudder.
     
    Last edited: Aug 8, 2007

  15. tspeer
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    tspeer Senior Member

    Here's a blow-up of the trailing edge of the S25e4mod1 section (green) and the NACA 0020 (red). The S25e4mod1 has a larger trailing edge angle, but it's all in the last two ordinates as it closes to a sharp trailing edge. The NACA 0020 has a squared-off blunt trailing edge, which is why the final slope of its contour is smaller than the other section.

    I've opened the trailing edge the S25e4mod1 to give it a trailing edge angle of 14 degrees to make the S25e4mod3 section (black) - away from the trailing edge the differences become indistinguishable. The S25e4mod1 section is right at your optimum 38 deg trailing edge angle, while the S25e4mod3 is way off. But there's no change in the section data for the low to medium angles of attack that are the operating range for most sections. The differences in performance of the S25e4 family due to trailing edge angle are all at high angles of attack, where the trailing edge angle affects the onset of separation. And the section that has the "optimum" 38 degree angle is clearly inferior to the one that has the 14 degree angle.

    The trailing edge angle didn't change the ranking of which section is better at low Reynolds numbers vs high - the NACA 0020 is still better for low Reynolds numbers and the S25e4 family is better at high Reynolds numbers. The rooftop and its effect on the boundary layer didn't change. But there is a definite improvement at high angles of attack because the onset of separation is delayed. It also brought the hydrodynamic center back to 25% chord.

    Trailing edge angle has an effect, but I don't think you can call it the most important factor. And I'd be inclined to go for small trailing edge angles over large ones.

    :) You're messin' with me, ain't cha? Like I'm going to seriously take the separated flow behind a bluff body like a circular cylinder with a splitter plate to be relevant to the attached flow at the trailing edge of well-designed section. Good one!
     

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