Prismatic coefficient discussion

Discussion in 'Sailboats' started by AdrienJousset, Dec 31, 2010.

  1. dougfrolich
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    dougfrolich Senior Member

    Just visualize stream lines passing over the fin and the hull when the fin canted to be in close proximity of the hull. It makes some sense when you have a beamy, nearly flat bottomed boat and a keel that cants to extream angles, and the piviot point is above the canoe fairbody. It does not have anyother advantage or application. Also keep in mind that daggerboards do the job of producing lift upwind and the keel strut is basically supporting the bulb way off centerline and should be acting at close to 0degrees angle of attack. It is not an elegant solution IMHO, but it does work in this narrow application.
  2. daiquiri
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    daiquiri Engineering and Design

    I see. And I agree, if it is limited to canting keels. I was having in mind the Farr's phrase cited by AdrianJusset:
    "Note in the profile how the hull flattens out right around the base of the keel fin. The Farr office does this in order to attenuate the “bump” in the longitudinal distribution of volume caused by the additional volume of the keel. Jet fighters do this too."
    It sounds like a nonsense to me, to use the supersonic jet fighter analogy to justify that design particular (of a sailboat). There is a mathematical justification of the aeronautical area rule, and it was derived by Richard T. Whitcomb, a great aeronautical engineer. It is aplicable to transonic flows (around the speed of sound), so it has nothing in common with sailboats...
  3. yipster
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    yipster designer

    and the next line is: "In aviation the section between wings and fuselages has been study'd"
    so as i read JuanK its essentially area rule (witch goes for steady keels as well)

    from cdf i've seen the nose of a bulb gives more drag than the hull attachment and keels leading edge even less
    seems logic considering again area rule but has little to do with prismatic coefficient
  4. Perm Stress
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    Perm Stress Senior Member

    I doubt if any commercial designer would reveal such data to the public, for free, or for any amount of money...
    To do so would mean loosing some part of personal know-how to sell, not to mention loosing all the time, money and effort, spent at gaining this know-how.

    By the way, some effects could be increased/decreased by synergy of many other details/solutions, used by particular designer...
    1 person likes this.
  5. yipster
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    yipster designer

    things you mentiont must be taken in account and balanced too but come to think of it water is, what was it..
    say 846 times thicker than air and imagine those almost incompressible water boundery layers merging at hull/keel
    and bulb/keel (going extremely weird) may be compensated for with a hollow if data shows enough reason testing further
    coming back on this arae rule thing here becouse i can be wrong and than set me straight and dont let me be an infidel

    have a look at this free cfd software no plane, no boat, yes its a car but with interesting foil flow particles
    and plz tell me how you download GNU, what files it takes, cant find it now, tomorrow i will
    going between the sheets now ;-)

    no figgers yet but one of my first cfd trials with tecplot as export66 below

    Attached Files:

  6. Joakim
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    Joakim Senior Member

    Air is just as incompressible as water when it comes to fluid flow phenomena at "slow" velocities (say below 0.3 Mach, ~100 m/s). Thus flow around a car is TOTALLY identical inside water and air, IF you keep the Reynolds number constant. You could replace the wind tunnel tests with water tunnel tests at about 1/18 speed for the same scale.

    There is very little you can learn from cars when it comes to hydrodynamic design of boats, since cars are quite bluff and their resistance is almost completely "form resistance" and only slightly friction resistance and there is no "wave making resistance" due to free surface.

    E.g. cars have Cd based on frontal area about 0.3 while boats and their fins (and planes and wings) are well below 0.1. Due to this Cd is typically based on side view area for wings and fins, since drag is much more related to surface area than frontal area.
  7. MikeJohns
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    MikeJohns Senior Member

    That's my view too. It's just not that applicable to boat hulls.

    I see I missed out a 'not' in my earlier post, now corrected, sorry to confuse anyone.

    Pierre De Saix's tests at the Davidson Labs showed that waisting in a boats hull to mimic the aircraft transonnic area rule increased drag overall and generated a small measurable secondary wave.
    Elvstrom and Kjaerulf also tested this but said but they claimed some 'satisfactory' results but never released their data.

    But its tied up with keel root flow separation, Cp and the Froude number as well as the curve of areas. In reality the pressure field and flow around a hull is anything but constant outside of a smooth water tank. Many innovations that look good in a testing facility fall well short in the real world or are even detrimental most of the time for most of the sea states and most of the real conditions experienced.
  8. tspeer
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    tspeer Senior Member

    Certainly transonic flow doesn't apply to sailboats. But the area rule is really based on linearized equations for supersonic wave drag. In the limit of very weak shock waves (linearized equations), the minimum drag is provided by the Sears-Haack body, and the area rule simply seeks to maintain the same cross-sectional area distribution as that axisymmetric shape.

    It's well known that the wave drag of a sailboat depends mostly on its cross-sectional area distribution and much less on the details of the cross sectional shape. So including the keel in the cross-sectional area distribution would make sense, and the result would be area-ruling of the hull.

    As for the proper area distribution to start with, I've found one paper that did tank tests of tanker hull configurations, varying the forebody and afterbody shapes to find the optimum area distribution, and the area distribution of their models was the same as the Sears-Haack body! The cosine wherry is a small boat that also uses essentially the same area distribution. So there is a connection with the transonic area ruling used in aviation.

    However, I suspect Juan K's local modification of the hull shape has more to do with the boundary layer than with wave drag. There are a couple of things going on at the junction of the keel and hull that would be relevant. The first is that the superposition of the flow velocities around the keel and the hull result in an increase in the local velocity near the junction. When there's higher velocity in one location, that means a more adverse pressure gradient and more susceptibility to separation as the flow moves away from the region of local acceleration and has to slow down again. So what you'd like to do is to shape the hull so it has a local region of lower velocity that will cancel out the increased velocity from the keel.

    Instead of a keel, one could conceive of a bump that would produce similar velocities, and that leads to a hollow that would have the opposite effect. Put the two together, and you end up with mounting the keel in a local hollow on the hull. The tricky bit is if you don't get the superposition right so the added velocities cancel, you could make things worse. I suspect that is what Juan K was referring to in is comments.

    The other thing that is going on at the keel/hull junction is the hull boundary layer meeting the leading edge of the keel. The stagnation pressure is high along the keel leading edge, but drops off in the hull boundary layer because of the reduced speed of the fluid in the boundary layer as it hits the keel leading edge. This means there is higher pressure on the keel stagnation line outside of the boundary layer than inside the boundary layer, resulting in vertical flow along the keel leading edge. When this vertical flow hits the hull, it has no place to go but to spread out along the hull and push forward against the oncoming boundary layer. It slows as it spreads out, and at some point the outflow from the keel leading edge is the same speed as the incoming boundary layer flow, and the two flows have nowhere to go but out away from the hull surface. This separated then gets swept up by the faster flow outside the boundary layer and the result is a necklace vortex that drapes around the keel/hull junction.

    The necklace vortex can be countered by a faired ramp-like leading edge extension from the keel called a dillet. The dillet lets the outer flow ride up and counter the vertical secondary flow before it has a chance to penetrate the hull boundary layer and form the necklace vortex. I can't see the photo as I write this, but I think there may have been a small dillet built into the keel junction as well.
  9. David Cockey
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    David Cockey Junior Member

    The aerodynamic drag of automobiles is much closer to aircraft than is generally thought. This is due to comparing the Cd numbers without accounting for the differences between frontal area and planview area. Aircraft can have Cd's similar to those of automobiles or even larger IF the Cd is calculated using the frontal area rather than the planview area.

    If the Cd of an automobile was calculated based on planview area as is generally used for aircraft, the Cd of the automobile would be lower than the value based on frontal area by the ratio of the frontal area to the planview area.

    Cd (frontal area based) * Frontal Area = Cd (planview area based) * Planview Area = CdA

    Drag = CdA * 0.5 * density of air * Velocity^2

    Cd (planview area based) = Frontal Area / Planview Area * Cd (frontal area based)

    Hypothetical example for an automobile:
    Length: = 4.8 m
    Width: = 1.9 m
    Height: = 1.5 m
    Frontal Area: = 2.34 m2
    Cd (frontal area based) = 0.30
    CdA = 0.701 m2
    Planview Area = 7.75 m2
    Cd (planview area based) = 0.0904

    I don't know what a typical ratio of planview area to frontal area for an aircraft is, but a value of more than 10 wouldn't surprise me. I do recall seeing an example where the Cd of a jet fighter based on frontal area was considerably higher than most automobiles.
  10. David Cockey
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    David Cockey Junior Member

    Confusion between wave drag of aircraft and wave drag of boats is not uncommon. Wave drag of aircraft is due to shock waves while that of boats is due to water waves. The physics are entirely different. Shock waves are non-dispersive and propogate at the speed of sound, INDEPENDENT of the frequency or wave length. Water waves (other water of depth much less than the wave length) are dispersive and the speed of propogation is directly linked to the frequency or wave length.
  11. daiquiri
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    daiquiri Engineering and Design

    It could be that the numerical values of drag are similar or comparable, but the airflow type is generally not. I believe Joakim was comparing the airflow and drag types, not the numerical values.

    A well-streamlined aircraft (take the Piaggio P180 aircraft as an example of aerodynamically streamlined body: ) will have most of it's drag made of friction (shear stress) and induced (drag due to lift) components.
    On the other hand, a bluff-body, which commercial cars generally are, will have a major contribution from pressure drag.
    They are qualitatively different forms of drag, with different associated airflow types, though their numerical value can be similar.

    I'm sure you already know that, just wanted to add my smart stuff to the discussion... ;) :p

  12. Joakim
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    Joakim Senior Member

    I did say frontal area based Cd. Aircrafts have planview area based Cd around 0.02. And that planview has only wing area, thus Cd would be even lower for full planview area. For wings only the frontal area based Cd are about 0.05.

    The fuselage drag based on frontal area is well below 0.1 (CdA in this paper):

    Jet fighters may have much higher Cd, but that's because they are optimized for supersonic and maneuvering, not at all for minimum drag at subsonic speed.

    As Daiquiri and I have already said, the drag is totally different, since aircraft drag is mainly friction based and car drag mainly form based. Try reducing flat plate friction drag from a car and an aircarft see what is left.
  13. DCockey
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    DCockey Senior Member

    The reference you provided is for bodies of revolution, not aircraft fuselages. No wings, tails, rudders, engine cooling flow, etc. Add those and the drag would be considerably higher.

    A significant portion of the drag of automobiles, particularly those with Cd of 0.3 or below, is due to:
    - wheels and tires in open wheel wells
    - cooling flow through the heat exchangers (radiator, etc) and engine compartment
    - underbody roughness
    - windshield wipers, cowl air inlets for passenger HVAC
    - outside review mirrors
    An idealized shape which looks like a reasonably low drag auto body but with a sealed front end, no wheels and tires and wheel wells closed and faired, and a smooth underbody can have a Cd well below 0.20 and likely below 0.10.

    I'm not claiming automobiles have as low drag as aircraft on a frontal area comparison basis, but it's much closer than generally thought.

    I do believe there is something, though perhaps not too much, to be learned from automobile aerodynamics, particularly for boats with aft chines or small radius bilges at displacment speeds. Considerable drag can result from trailing vortices shed by chines, etc which are crossed by the flow at the "wrong" angle. But that's a topic for another thread, and I don't have my references at hand.

  14. Joakim
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    Joakim Senior Member

    Wings and rudders etc. do not add Cd, since they have at least as low Cd. Of course there are other things that do add to Cd, but the total frontal area based Cd is still well under 0.1.

    Even if a car would have Cd ~0.1, it would still have a considerable amount of form drag, since it doesn't have that much surface area compared to frontal area.

    Yes you can have "bad" hulls for displacement speeds that do have considerable amount of form drag and maybe for those there is something to learn about car aerodynamics.
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