Calculating Sail Area to Achieve Heeling Angle

Discussion in 'Stability' started by tbracken, Oct 3, 2016.

  1. tbracken
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    tbracken New Member

    Is there a formula available to calculate the sail area needed to achieve a particular healing angle for a given wind velocity?

    I sail a C&C 27, Mk IV. I believe the ideal heeling angle is 22 degrees (How do I calculate the ideal heeling angle to be sure?). I would like to verify that.

    Moreover, is there a formula that will project a particular sail plan (total sail square footage) to maintain the ideal heeling angle for a variety of wind velocities? For example, if the wind velocity is 15 knots, how much sail area is needed to produce 22 degrees of heeling? 25 knots? 35 knots? etc.
     
  2. TANSL
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    TANSL Senior Member

    Once known the boat's GZ curve for the loading condition under study, you can determine the righting arm to 22 °, for example. That righting arm, multiplied by the displacement, allows you to calculate the total righting moment at 22 °, which must equal the heeling moment of the attachement formula. With that you can deduct the sail area in each case, for a given wind speed.
    The same can be done for any other heeling.
     

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  3. tbracken
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    tbracken New Member

    Do you have an MSExcel spreadsheet with the necessary formula you could send me?
     
  4. TANSL
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    TANSL Senior Member

    If what you need is calculate GZ values, see attached figure.
    If procedure is not enough clear for you, you'll need help from a professional.
     

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  5. daiquiri
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    daiquiri Engineering and Design

    Why 22°, and not 21° or 23°? Where does such precise number come from? :)
     
  6. Petros
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    Petros Senior Member

    seems to me there are so many variables about your particular boat, that it is not easy to determine without a lot more information about your boat.

    if you install a simple heel angle gauge in your cock pit you can just sail to your perceived "ideal" heel angle. With the addition of a knot meter you can also verify which heel angle produces the best speed at each point of sail.

    The size of the sail is not really relevant unless you always sail in the same force wind at the same angle relative to the wind direction. Sail size is only one of many other factors: the type of sail, apparent wind angle, height and weight of rigging, beam of boat, depth of keel, weight of keel, weight distribution of crew and cargo (the smaller the boat the more relative that becomes), even how well you have adjusted and trimmed the sail will all affect heel angle. The age of the sail as well, old stretched out sails tend to cause more heal with less forward drive than new sails.
     
  7. jehardiman
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    jehardiman Senior Member

    That's what we used to do, record the wind speed, wind direction, knot log/ GPS, charted current, and "fun meter". Pretty soon trends tend to drop out (like taking the high side or low side of Alcatraz Island depending on the current)
     
  8. gonzo
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    gonzo Senior Member

    The set and trim of the sail will change the heeling angle and speed too.
     
  9. TANSL
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    TANSL Senior Member

    Yes it is clear, great find, but to answer what really questions the OP, what is the procedure that you think he should follow?
     
  10. MikeDrummond
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    MikeDrummond Junior Member

    All of the following is approximate!!

    I can't vouch for the Selden RM calculator.

    1. Righting Moment at 30deg
    http://www.seldenmast.com/en/services/calculators/rm_calculator.html
    Be careful with your input units!

    2. RM at 22deg
    RM22 = RM30 x sin(22)/sin(30), close enough

    3. Heeling Arm - vertical distance between centre of sails and centre of keel

    HA = 0.4 x mast height + Freeboard + hull depth + (Keel Length)/2

    If reefed, then "0.4 x reefed height"

    4. Sideforce at 22deg
    SF = RM22 / Heel Arm

    to be clear about units,
    SF in kg = (RM22 in kNm) * 1000 / Heel Arm in metres / 9.81

    5. Now check if this seems reasonable. Eg even more roughly, the mainsail leech load ~~ 3x the sideforce.

    6. Aero forces
    Sideforce in kg = 0.61 * Sail area * CL / 9.81 * AWS^2

    a. CL is lift coefficient and varies with shape and angle and trim. Roughly, use CL=1.2
    b. AWS is Apparent Wind Speed in metres per second
    c. rearrange above to get
    AWS = sqrt( SF in kg * 9.81 / .61/Sail Area / 1.2)
    AWS in knots = AWS m/s * 1.852

    7. Compare with boat performance
    Estimate BS, TWS, TWA to calc AWA and AWS.

    There are many approximations in the above, but I guess the answer will be within +-3kn TWS. Not close enough to be useful for performance, but enough to be surprised by simple physics yet again!

    8. Also check out WB Sails calculator
    https://cdn2.hubspot.net/hub/209338/news/SailPowerCalc/SailPowerCalc.htm
     
  11. MikeDrummond
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    MikeDrummond Junior Member

  12. TANSL
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    TANSL Senior Member

    It would be interesting to know if anything of what has been said here has been of interest to tbracken.
    Should we congratulate because he has solved his problem or should we expand our explanations?
     
  13. tbracken
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    tbracken New Member

    Thank you all for the very valuable information. It is of significant interest to me and has been helpful. I must admit the math involved has been a bit of a stretch for me, but I'm trying to wrap my mind around it because I want to understand the principals involved.

    I'm wanting to establish a reefing regimen for my C&C 27, MkIV sloop. I have one mainsail (Quantum, with two reefing points) and two genoa sails, a 151%(#1) & a 136%(#2, reefing genoa) (on a Schaefer Furler/Reefer).

    We don't get a lot of high wind in central Indiana, typically 5-15 knots, so it's difficult to aquire practical experience with what sail configuration works best in higher wind velocities, thus my interest in establishing a theoretical reefing regimen.

    Why 22°? It's my understanding - I have no idea where I got it from - that 22° is the point where the LWL reaches its longest point (based on hull design) without excessive heel and wasted power.

    I've already created a reefing regimen based on the total sq. ft. of sail area. It is my understanding that with masthead sloops (opposed to fractional rigging), the genoa is the primary "driver" sail. Thus my reefing regimen reefs the main first once the 151% genoa is replaced with the 136% genoa.

    Reefing Mainsail Headsail Main Headsail Total
    Regimen Config. Config. sq. ft. sq. ft. sq. ft.
    A Full Main #1 (151%) 170 257 427
    B Full Main #2 (136%) 170 238 408
    C Main Reef 1 #2 (136%) 135 238 372
    D Main Reef 1 #2 Reef 1 (115%) 135 171 305
    E Main Reef 2 #2 Reef 1 (115%) 103 171 273
    F Main Reef 2 #2 Reef 2 (95%) 103 116 219
    G Main Reef 2 #2 Reef 3 (75%) 103 73 175
    H Main Reef 2 #2 Reef 4 (55%) 103 39 142
    I Main Reef 2 #2 Reef 5 (35%) 103 16 119

    Known sailboat characteristics of the C&C27, Mk.IV:
    LOA=27'-10.5"
    LWL=22'-10.5"
    Beam=9'-2"
    Draft=4'-6"
    Ballast=2116 lb.
    Disp.=5500 lb.
    Rig Height=37' 0"
    Displacement to LWL=204
    LWL to Beam=2.5
    Hull Speed=6.42
    Motion Comfort=18.06
    Sail Area to Displacement=19.1
    Capsize Ratio=2.08
    Pounds Per Inch=751
    I=37.0'
    J=11.17'
    P=31.0'
    E=10.0'

    Assuming a close-hulled point of sail (TWA 44°) with no crew on the rail, what wind velocity (TWS, kn) would produce a heeling angle of 22° for each of the above nine reefing regimens (A-I)?
     
  14. TANSL
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    TANSL Senior Member

    Although I'm afraid I have not enough knowledge of sailing to help you, I think it will be necessary to consider the following points:
    - It will probably be necessary to have a ship lines plan to carry out some naval architecture calculations with which to determine the effects of wind on the boat.
    - Needless to say that, anyone who has minimal technical knowledge knows, in a theoretical study, as you intend to do, you can not say that the absolute results are accurate, nor how close to reality they are. What one can do are comparative studies to see what rig makes tilt the boat more or less for a given wind.
     

  15. Petros
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    Petros Senior Member

    if you have identical hull/keel, the rig with the best L/D ratio (lift over drag) will have less heel. The drag tends to heel the boat over, the lift or in this case the drive, moves it forward. so for the same amount of drive, the lower the rig drag the less heel.

    This is not just sail shape, aspect ratio, camber and size, it also means less rigging and cleaner mast shape.
     
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