Reconciling Formulas

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

1. Joined: Jan 2005
Posts: 2,233
Likes: 290, Points: 83, Legacy Rep: 1110
Location: Philippines

rxcompositeSenior 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.

1 person likes this.
2. Joined: Jan 2005
Posts: 2,233
Likes: 290, Points: 83, Legacy Rep: 1110
Location: Philippines

rxcompositeSenior 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:

• Formulas.xls
File size:
196 KB
Views:
236
3. Joined: May 2008
Posts: 2,402
Likes: 229, Points: 63, Legacy Rep: 1082
Location: Beaufort, SC and H'ville, NC

philSweetSenior Member

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