center of flotation calculation and implications?

Discussion in 'Boat Design' started by capt vimes, Jan 7, 2010.

  1. Eric Sponberg
    Joined: Dec 2001
    Posts: 2,021
    Likes: 248, Points: 73, Legacy Rep: 2917
    Location: On board Corroboree

    Eric Sponberg Senior Member

    Certainly, you always have to consider the stability of the boat when deciding on sail area. GZ and sail area are two totally independent factors, but they both impact the stability of the boat. The more sail, the more the boat is going to heel in any given wind condition. You don't have to have all the sail area flying all the time. Maybe you want to give the boat a lot of sail area for light air sailing, and expect to reef at lower wind speeds. You can always reef a larger sail to a smaller size, but you can't make a small sail bigger.

    The SA/D ratios that I listed are not "required", only suggested ranges. You can design whatever you want, just make sure you know what you are doing and why. As Ancient Kayaker discussed in his post, the ability to carry sail increases with size. Review Chapter V in Skene's Elements of Yacht Design, (8th edition) which is a discussion on the law of mechanical similitude (scale factors):

    • Sail area varies with the square of boat length.
    • Displacement varies with the cube of boat length.
    • Heeling moment (from wind pressure on the sails) varies with the cube of length.
    • Stability varies with the fourth power of length.
    To quote Skene's: "So we realize from the figure of 'sixteen times the LWL for stability' why the power to carry sail increases much faster than the heeling moment (eight times the LWL) for a similar boat twice the water-line length. This is the reason that large sailing yachts are so much stiffer than small ones even with relatively much less draft and beam."

    Eric
     
  2. sailor54
    Joined: Nov 2005
    Posts: 3
    Likes: 0, Points: 1, Legacy Rep: 10
    Location: Nancy - France

    sailor54 New Member

    French S# data

    350+ crusing (classic keel) boats, LOA 6 to 12 m, excluding motorsailers and racing boats...
    Mid 60's to mid 90's

    (culled from E. van Deth Guide des voiliers d'occasion I & II Ed. Loisirs Nautiques, 2000)
     

    Attached Files:

  3. LyndonJ
    Joined: May 2008
    Posts: 295
    Likes: 20, Points: 0, Legacy Rep: 233
    Location: Australia

    LyndonJ Senior Member

    Thanks Eric

    So really the SAD is just a figure of possibly how well the boat will move in light air.
    It seems a lot of people use it as a performance prediction, across the board incorrectly and it needs to be tempered with the % of light air in the area you will sail in.

    Probably why higher lattitude or wind belt sailers always had much smaller ratios than the calmer lattitudes.

    For example in the south Pacific trades at 25 knots, sailing on anything higher than a broad reach there would be very little between a maximum SAD of 10 or 30 and other factors would come into play ?

    Cheers
     
  4. Paul Kotzebue

    Paul Kotzebue Previous Member

    So true ...

    Dimensionless ratios are best used for comparing similar boats sailing in similar conditions. For instance, back in the days before personal computers designers would plot dimensionless ratios of similar IOR boats from their rating certificates to optimize a new design.

    Eric is doing a good job of explaining things. People seem to be paying attention and are actually getting it.
     
  5. sorenfdk
    Joined: Feb 2002
    Posts: 511
    Likes: 27, Points: 28, Legacy Rep: 394
    Location: Denmark

    sorenfdk Yacht Designer

    No - the Sail Area/Displacement Ratio is a figure of how fast the boat will move in general.
    The Sail Area/Length Ratio is the figure that tells us how fast the boat will move in light air.

    But always remember that these ratios should be taken with a grain of salt - they are only indicators and they do not tell the entire truth!
     
  6. LyndonJ
    Joined: May 2008
    Posts: 295
    Likes: 20, Points: 0, Legacy Rep: 233
    Location: Australia

    LyndonJ Senior Member

    Soren, now I am getting confused again

    But you'd have to extract the power you got from the sail and equate that to the drag of the hull. The sail power will depend on the wind so the SAD will also depend on the wind since it determines the sails you actually hank on or unfurl.
    Presumably what you you saying the is thad the SA/D is variable and calculated for each wind speed?

    If it's blowing 25 knots and you have a reefed main and a small jib then the SAD will be low and yet the boat will still perform well. So surely this is a light air number only.
    What's the SAD of a laden clipper ship displacing several thousand tons running downwind flying topsails alone and otherwise bare rig in 50 knots of wind and travelling at 20 knots ?? Around 5 ?

    Don't you mean [Sail area/ Wetted surface area] rather than length?

    Also I see 'upwind' and 'downwind' figures for some boats. When they are apparently including a spinnaker. I wonder what the advertisers count for production boats

    Cheers
     
  7. Eric Sponberg
    Joined: Dec 2001
    Posts: 2,021
    Likes: 248, Points: 73, Legacy Rep: 2917
    Location: On board Corroboree

    Eric Sponberg Senior Member

    Lyndon,

    I think you are trying to read too much into these ratios. As I explained in my post on SA/D and SA/WS, SA/D is a measure of the power a sailboat has in moderate air. You have full sail up, the boat is cruising along near hull speed and wave making drag is a significant amount. Drag due to displacement is comprised of friction, form, and wave-making drag. The higher the ratio, the more powerful the boat is in these conditions, and therefore you can expect higher speeds. But you cannot predict any certain speeds in these conditions.

    SA/WS is very similar, but it really applies only to very light air sailing where friction drag, due to the wetted surface of the hull, is paramount over the other types of drag (form and wave-making, which are very small when the wind is light, say below 8-10 knots). A boat with a higher SA/WS ratio will be faster than one with a smaller ratio when sailing in light air, all other things being equal (which they rarely are).

    These ratios are not calculated for any specific wind speed--they always utilize the overall design numbers--upwind sail area (usually main and fore triangle area), the volume of displacement at the design waterline, and the upright wetted surface at the design waterline. The numbers don't change, even though the weather conditions might.

    You don't use these numbers to predict absolute speeds. You use them only to compare one boat against another, to see which boat might be faster than the other.

    Eric
     
  8. ancient kayaker
    Joined: Aug 2006
    Posts: 3,497
    Likes: 147, Points: 0, Legacy Rep: 2291
    Location: Alliston, Ontario, Canada

    ancient kayaker aka Terry Haines

    I think of a boat moving close to hull speed as climbing up a hill, so it seems intuitive that the wave drag would increase in proportion to the displacement if hull dimensions and speed were all scaled linearly. For the same case, skin friction would be proportional to wetted area, but would also vary as the square of the speed.

    is that correct? If so then skin friction follows a fourth power and is going to assume a greater share of total drag for the larger boat than the smaller one. That I find counter-intuitive, but I am probably confusing skin friction with surface tension.
     
  9. Eric Sponberg
    Joined: Dec 2001
    Posts: 2,021
    Likes: 248, Points: 73, Legacy Rep: 2917
    Location: On board Corroboree

    Eric Sponberg Senior Member

    No, not correct. Total resistance is made up of three primary components--friction drag, form drag, and wave-making drag.

    Friction drag is proportional primarily to wetted surface area and is related to Reynolds number. It varies with the cube of the speed.

    Form drag has three components. The first component is due to the hull curvature and is affected by the Length/Draft or Length/Beam ratio. Short stubby shapes have higher form drag than long slender shapes. The second component is due to viscous pressure drag--that is, the boundary layer--the bigger the boundary layer, the higher the resistance. The third component is due to flow separation at the aft end of the hull and it is related to the viscous pressure drag. As such, all these forms are pretty much proportional to the displacement/length ratio (DLR as we have noted it). No one has actually been able to predict form resistance (or form factor coefficients) for any type of hull form, and this is one reason why we have to do model testing.

    Wave making drag is the real bugger, and up to about speed/length ratio of 1.5 or so, it is actually proportional to the sixth power of vessel speed. There are many parts to wave-making drag related to the formation of waves along the hull. These waves have interference effects, depending on speed, and wave-making drag can increase dramatically (the hump, for example) before dropping down again and leveling off by the time the hull starts to plane.

    So, in no way is overall resistance linear with speed. Resistance is exponential with speed to varying degrees. And this is why we have so much trouble trying to predict what speed a boat may actually have, and why we have model testing. It is also why we cannot hope to definitively state what a speed of a certain boat may be based on SA/D or SA/WS ratios; they are too simplistic. These ratios only give us a sense of what could be, but not definitive proof.

    Eric
     
  10. Paul Kotzebue

    Paul Kotzebue Previous Member

    Residual resistance, including wave making resistance, is proportional to displacement for a given Froude number (speed/length ratio). If the hull dimensions are scaled linearly by a scale factor, the speed is scaled by the square root of the scale factor. Intuitively it would seem that skin friction is proportional to wetted area x speed squared, but it is dependent on wetted area and Reynolds number as Eric said.

    Because skin friction and residual resistance scale differently, you can't scale total resistance from a model test. The basic procedure is (roughly):

    1. Measure total resistance of the model.
    2. Calculate skin friction of the model.
    3. Subtract calculated model skin friction from model resistance to obtain model residual resistance.
    4. Scale model residual resistance by the scale factor cubed to obtain full size residual resistance.
    5. Calculate full size skin friction.
    6. Add calculated full size skin friction to full size residual resistance to obtain full size total resistance.

    Full size speed = model speed x square root of the scale factor.

    See also the Skin Friction Formulas thread in the Software forum.
     
  11. mcollins07
    Joined: Jan 2006
    Posts: 220
    Likes: 11, Points: 0, Legacy Rep: 166
    Location: Texas

    mcollins07 Senior Member

    Form Drag


    In regards to Form drag, I noticed that the first cause is attributed to the hull geometry while, while the second two causes are attributed to characteristics of the fluid model.

    1st – due to hull curvature
    2nd – due to boundary layer thickness
    3rd – due to flow separation point

    Seems a better model would trace causes to Froude number, Reynolds number, and hull geometry (including curvature).

    I’m interested in reading more about these models of Form Drag if anyone has Internet references.

    ~ Michael
     
  12. DCockey
    Joined: Oct 2009
    Posts: 5,229
    Likes: 634, Points: 113, Legacy Rep: 1485
    Location: Midcoast Maine

    DCockey Senior Member

    What is "viscous pressure drag" due to the boundary layer, and how is it different than "friction drag" which is related to Reynolds number?

    The hydronamic forces acting on a hull are the vector summation of the the stresses (forces acting over a very small area) on the surface of a hull. These stresses can be divided into shear stresses which are tangential to the surface of the hull, and the stress normal to the surface which the pressure (definition of pressure). The effects of both over the wetted surface of the hull produce drag.

    Are the shear stresses which result from viscous effects in the boundary layer being divided between "friction drag" and "viscous pressure drag"? If so, how? Without viscosity and viscous flow in the boundary layer there would not be any shear stress and therefore zero "skin drag" as it's sometimes refered to.

    Perhaps "friction drag" is the drag resulting from a simple model or curve which does not fully consider the shape of the hull. Then "viscous pressure drag" could be the difference between the "friction drag" from the simple model or curve, and the total drag due to shear stresses?

    Or is "viscous pressure drag" intended to be an expression of the difference in the pressure distribution and therefore drag increment which results from the presence of the boundary layer altering the flow around the hull compared to a "ideal", inviscid flow?

    Moving on, flow separation will affect both the pressure distribution on the surface of the hull and the viscous shear stresses including the regions of the hull where the flow is not separated.

    The waves generated by the hull moving through the water affect the pressure distribution and the flow around thehull. In theory at least the energy lost throught he waves can be analyzed by evaluting the waves at a suitably large distance from the hull, though this may not capture the secondary effects due to the waves altering the flow and thus shear stresses.

    While the hydrodynamic forces acting on a hull can be divided up any number of ways, only some directly relate to the fundamental physics. That doesn't mean the other ways don't have their uses, particularly when trying to correlate data from different boats and from scale model testing.

    (For the record, I have a reasonable background in hydrodynamics and aerodynamics, and spent several years researching low speed, bluff body (automotive) aerodynamics.)
     
  13. Eric Sponberg
    Joined: Dec 2001
    Posts: 2,021
    Likes: 248, Points: 73, Legacy Rep: 2917
    Location: On board Corroboree

    Eric Sponberg Senior Member

    Friction drag is the drag due solely to wetted area. It does not take into account any flow effects around the body whatsoever. So anything NOT related to wetted area or to wave-making necessarily is defined as the form drag. And this includes hull shape and viscuous fluid effects. There is an equation for the coefficient of friction drag which is the 1957 ITTC friction line, established by the International Towing Tank Conference. This equation is a function of the inverse of the logarithm of Reynolds number. There is no equation for form drag. You have to measure it in the model tank. Likewise, there is no equation for wave-making drag either; that is also measured in the towing tank.

    Remember we said that the total drag was made up of three components: Friction, Form, and Wave-making. In the towing tank, we measure the dimensionless coefficients of these types of drag:

    Total drag = Ct = Cf + Cform + Cwave

    Cf comes handed to us on a sheet of paper from 1957 ITTC

    Ct is measured in the model tank, and when brought together in a plot of the ITTC friction line, we can discern which parts of the resistance curve that are Cform and Cwave.

    The total resistance for the ship then = Rt = Ct x 0.5p x A x V^2

    Where p = density of water
    A = wetted area
    V = vessel speed
    All in consistent units.

    The different coefficients must be measured at corresponding speeds, that is, and the same Froude number (speed/length ratio). Using coefficients is just a convenient way of expressing the forces we are trying to discern. The equation above for total resistance is simply the classic way of expressing any force due to motion in a fluid. Once we know Ct from the model testing, we project that to the Ct for the ship on the ITTC plot, and then we convert it to force units (pounds of force) for the ship by the above equation.

    This is an exceedingly complex topic and getting beyond the scope of this thread. This information is covered in third year college courses in naval architecture at universities around the world. If you would like to read up on the development of the resistance of ships and model testing, I suggest you get a copy of "Principles of Naval Architecture", Volume 2, from the Society of Naval Architecture and Marine Engineers (SNAME) which covers Resistance, Propulsion, and Vibration in depth.

    Eric
     
  14. fredschmidt
    Joined: Jan 2010
    Posts: 155
    Likes: 4, Points: 18, Legacy Rep: 73
    Location: Natal - Brasil

    fredschmidt Naval Architect

    Sa/d

    SA/D is only a parameter to compare boats.

    Like car that can be compared with his HP/Weight, SA is the motor of the sailboat. More sail, more HP.

    Only this. A parameter to compare boats and to the designer, where he want go.

    Only this, not more than this. If I want design a speed hull I have a notion that I need do a boat with a certain SA/D zone.
     

  15. Paul Kotzebue

    Paul Kotzebue Previous Member

    Well put Eric. Even though subjects like resistance and model testing are beyond the scope of this forum, your clarifications of these subjects are just what this forum needs.

    I think it is helpful to those who have an interest in boat design to know that methods of predicting and quantifying resistance (model tests) have been around for decades and they can be applied to small craft design. It is also helpful to know that non dimensional ratios such as D/L, SA/D, and SA/WS are not predictors of performance, but simply a basis for comparison.

    I appreciate a trained naval architect shedding some light on subjects that are frequently misunderstood by practicing yacht designers, much less those with a more casual interest in boat design.
     
Loading...
Forum posts represent the experience, opinion, and view of individual users. Boat Design Net does not necessarily endorse nor share the view of each individual post.
When making potentially dangerous or financial decisions, always employ and consult appropriate professionals. Your circumstances or experience may be different.