GZ GM Cb Cp and other

Discussion in 'Boat Design' started by yipster, May 6, 2003.

  1. yipster
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    yipster designer

    horizontal lever arm (GZ (but what does GZ mean?)) is probably made from CG (centre of gravety) and CB (centre of buoyancy) calculations and looks like its fairly easy to do. but what do those behind the comma decimals mean? whats a GM? yes its the distance from G (centre of mass) to M (metacentre) but whats a good initial stability? the more complicated Cb (block coefficient) is the ratio of displaced volume to the waterline lenghth, waterline beam and draught, but who can explain this and the froude numbers in a Cp (prismatic coefficient) in populair english? its more than worth giving it a populair quik study i think.
    maybe somebody can easely explain some terms and calcs or refere to a good book.

    yipster
     
  2. mmd
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    mmd Senior Member

    I have read quite a few books on the stability of ships in the twenty years that I have been doing vessel design, and I hold to my belief that the first one I read - my textbook in university - is the clearest and most approachable. It is called "Ship Stability for Masters and Mates" by D.R.Derrett (Stanford Maritime Limited, London, ISBN 0 540 01403 6, mine is 5th edition). It explains all the terms you refer to very well.
     
  3. SailDesign
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    SailDesign Old Phart! Stay upwind..

    Vessel stability and the terms associated with it are arcane sciences, and the secrets are carefully guarded lest the uninitiated gain access to this sacred knowledge.

    ;-)

    Steve Baker
     
  4. Tim Dunn
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    Tim Dunn Junior Member

    www.boatus.com/goodoldboat/stability.htm by Ted Brewer will answer your stability questions. More traditonal designers use the square root of the designed waterline length to compare speeds, rather than the scientific Froude number. Read www.boatus.com/goodoldboat/brewerformulas.htm by Ted Brewer will explain C.P. and other design numbers in plain English.
    Skene's Elements of Yacht design is a standard beginners' text.
     
  5. duluthboats
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    duluthboats Senior Dreamer

    Also this is related and worth reading

    Engineering the Sailboat—Safety in Numbers

    Tim Dunn, thanks for the link. Ted Brewer has always been able to write things so I can understand them.

    Steve, LOL :D the cloaks are slowly being lifted. ;)

    Gary :D
     
  6. SailDesign
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    SailDesign Old Phart! Stay upwind..

    Gary - about time, too, truth be told ;-)
     
  7. yipster
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    yipster designer

    0.5rhoV^2

    first of all thanks for the reply's guy's, have to go get THE BOOK...

    like to know how to calculate power needed on submerged pods. from the WSA? this seems the formula: cf = 0.075/(logRn - 2)**2 where rf = 0.5 rho v**2 S Cf but i aint understand it.
    from: >>how much power / hp is needed to proppel a torpedo?
    on a naval submarine board i got: >It depends. Need info. Cyl Diameter, Length >Drag Force = Cd.. * SomeArea * 0.5RhoV^2
    >Wetsurf + Form + Wave + Lift-induced(not here - planing only)

    other replys mention tanktesting and more. seems to me 0.5rhoV^2 is the basic sum but what the heck is rho? what i want to know is aproximate power for 3 x 100 liter pods, estimated for 22 squered ft wsa with only little form etc drag. also how much power for 3 x 2000 litre? i'll have to find all those terms and calcs explained in a good book soon!

    :confused: yipster
     
  8. BrettM
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    BrettM Senior Member

    rho (written to look like a "p") = density of fluid watch your units.
     
  9. Peter_T
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    Peter_T Junior Member

    The system failed to transfer Greek math symbols. rho from symbol now can transfer as "r". It is better to enter as Italics "p".
    Perhaps inserting Font feature may improve. (This goes to Jeff)

    The viscous resistance equation must be supplemented with a roughness coefficient. If you want to have quick runs with conservative margin, the Froude method base on L is not that bad for short lengths. For high speed functions, there will be significant errors.

    GM is the pendulum length of the floating vessel, as if the boat hangs on the point M. If you heel the boat a little, the B (buoyancy center) will move sideway and also go up a little due to the vertical wedge moment. The reaction of B' up to act in alignment with the initial M point. The M point also shift for greater angles. GZ is the horizontal moment lever from G to the active force lines from B' to M or M'. The GZ curve starts out in the form of GMsine(ang) but will follow a sine curve to the range ang. The shape is affected at the point of deck immersion and from there affected by the presence of intact deck house. Data can be generated by a computer model of the hull. The critical points are at the angle of the maxGZ and at the angle of downflooding. Rules on stability wrote a series of compliance criteria to meet.

    The displacement coefficients commonly used are Cb as shaping from a block of wood or Cp as shaping from a prismatic block of the midhsip section. For ships the Cm, midship shape factor is as high as 0.98 from 0.95. For small craft Cm can be from 0.5 to 0.9.

    Cp is used in determining flow resistance of the wave generation form, in conjuctin with the displacement function of displacement distribution over length.

    Peter
     
  10. tspeer
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    tspeer Senior Member

    Cb and Cp are simply measures of how blunt the boat is. Cb is how much of a rectangular block of wood is left after you carve it into the shape of a hull. Cp is much the same thing but starting with the block routed to the shape of the maximum cross section before you start carving. The blunter the ends, the less you are whittling away and the higher the Cb and Cp will be.

    Since nearly every boat has a different shape, these measures are a way of coming up with some common basis of comparison. They work well for correlating resistance measurements because the resistance is not overly sensitive to the specific details of the shape.

    The same goes for other parameters like displacement/length ratio, beam/depth ratio, etc. Without these measures of gross shape and size, all you'd have is a massive number of special cases and no way to make sense of it all.

    Froude number is a measure of speed, but referenced to the speed of the waves created by the boat. Water waves are quite different from, say sound waves or electromagnetic waves, because longer waves travel at faster speeds than shorter waves. When a boat travels through the water, the waves you see are the ones that have the same wave speed as the boat - the other ones are rapidly left behind or spread out and dissipate, but the ones traveling at the same speed as the boat get reinforced.

    As a result, wave drag is highly correlated with how how long the waves are compared to the length of the boat at a given speed. The Froude number is a measure of this ratio. At the same Froude number, you'll see the same number of wavelengths along the hull, whether you're looking at a ship moving at high speed or a model moving at low speed, as long as their respective Froude numbers are the same. So the physical mechanisms creating the wave drag are similar, and it's possible to scale the wave drag up and down for similar boats of different size.
     
  11. SuperPiper
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    SuperPiper Men With Little Boats . .

    Tom:

    Great explanation! Even I can understand that. In the next edition, please expand on the Froude number. I get a little overwhelmed by numbers with more than 1 trailing zero.
     
  12. tspeer
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    tspeer Senior Member

    I explained some of the physics behind the Froude number in my previous post. The Froude number (as used for boats) is

    Fn = V/sqrt(gL)
    Fn : Froude number
    V : boat speed
    g : gravitational acceleration (32.2 ft/sec^2 in English units)
    L : reference length

    The speed of water waves is sqrt(g*lambda), so the Froude number is simply the ratio of the boat speed to the speed of a wave whose wavelength is the same as the reference length. Note also that since g is a constant, the speed/length ratio and Froude number only differ by a constant - they may have different units but are fundamentally the same.

    There are actually many different Froude numbers, depending on what you choose for the reference length. The most common definition uses waterline length. You'll also see a "volumetric Froude number" in which the reference length is cube root of the submerged hull volume. There's even a version based on beam rather than length. Hydrofoil designers use Froude numbers based on the chord, span, or depth of submergence.

    The idea is still the same no matter how you define the Froude number - two similarly shaped hulls will produce the same wave pattern if they are traveling at the same speed relative to the square root of their size. So if you were tank testing a quarter scale model, you'd want to run it at half the full-scale speed to get the same Froude number. Since the wave patterns are the same, you can scale the wave drag in a meaningful way.
     
  13. yipster
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    yipster designer

    Had to read three times, comprehend, let it sink in, calculate, but think I got those. Is there a book(s) that popular explains this whole spectrum of boat formulas, or is greek math really a must?

    Skene's Elements of Yacht design seems at first glance for wooden boats and not really handling the terms? stange is that there also is a book with the same name by Francis Kinney. Other books on (the formulas behind) yacht design I looked at often have reviews that call them confusing or plain difficult to read.

    Ship Stability for Masters and Mates looks like a good readable book but deals only on stability.

    Here again some links that make good reading from the hydrostatics tread with thanks to Dionysis: http://web.nps.navy.mil/~me/tsse/NavArchWeb/1/toc.htm
    and another link that explains stability:http://persweb.direct.ca/tbolt/stabilit.htm
    and a couple for kayaks especially:
    http://www.oneoceankayaks.com/smhydro/hydro.htm
    http://www.guillemot-kayaks.com/Design/
     
  14. Dim
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    Dim Senior Member


  15. Dim
    Joined: May 2003
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    Dim Senior Member

    Part I

    Same stability info.
     

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