Reconciling Formulas

Discussion in 'Boat Design' started by rxcomposite, Feb 7, 2012.

  1. rxcomposite
    Joined: Jan 2005
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    Location: Philippines

    rxcomposite Senior Member

    I have trouble reconciling these formulas from several sources. Any sharp eyed NA’s out there who could give me the correct one?

    1.Wetted Surface Area
    a. WSA=L(2T+B)Cm^0.5 (0.4530+0.4425Cb-0.2862Cm + 0.003467(B/T)+0.3696Cwp)+19.65Abt/Cb
    b. WSA=L(2T+B)Cm^0.5 (0.4530+0.4425Cb-0.2862Cm - 0.003467(B/T)+0.3696Cwp)+ 2.38Abt/Cb

    "a" was posted by the late Mike D and appears also in Design of Naval Ships, b. as it appears in Principles of Naval Architecture. Notice the difference in the two. The (+) sign in 0.003467 in “a” and the (–) minus sign in “b”. Notice also the 19.65Abt in “a” and 2.38Abt in “b”. I have no problem when Abt (area of bulbous bow) is set to 0 (zero) as the result comes out the same, but when I input a number for the Abt, the results are not the same. Obviously, one set is wrong. So which one is the correct formula?

    2.Frictional Resistance
    Basic formula (Froude’s son) Rf= fSV^1.825

    In PNA, Rf = ((0.000418+0.00254)/(8.8+3.281L))S Vk^1.825
    Where:
    f= values in parenthesis
    L=length in meters
    S= Wetted Surface Area in square meters
    Vk= Speed in knots
    Rf= Resistance in kNewtons

    In Naval Architecture by Tupper-
    f=0.00871+(0,053/8.8+L)- English System
    Rf= lbf
    L= feet
    S=feet squared
    V= Knots

    f=1.365+(2.530/2.68+L)- Metric System
    Where:
    Rf=Newtons
    L=meters
    S= meter squared
    V=meter/second

    The problem seems to be the f values in PNA as it is very small. I get better results with Tupper.
     
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  2. rxcomposite
    Joined: Jan 2005
    Posts: 2,114
    Likes: 229, Points: 63, Legacy Rep: 1110
    Location: Philippines

    rxcomposite Senior Member

    The sharp eye of Philsweet noticed something wrong in the PNA's Rf formula. I had the book's typo error corrected. Still having problem with the Metric system. I am attaching the spreadsheet as it is more comprehensive.

    Thanks Phil.
     

    Attached Files:

  3. philSweet
    Joined: May 2008
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    philSweet Senior Member

    I suggested a term was missing assuming the () were ok. It now looks like there is an unwanted pair.

    Perhaps should read:
    In PNA, Rf = [0.000418+0.00254/(8.8+3.281L)]S Vk^1.825 for metric meters

    In PNA, Rf = [(0.00871+0.053)/(8.8+L)]S Vk^1.825 for English feet

    (edit: deleted last para. logic error.)
     
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