Help quick please

[kms]

Sailboat stability. To be considered safe for ocean sailing, the capsize screening value C should be less than 2 (www.sailing.com). For a boat with a beam (or width) bin feet and displacement d in pounds, C is determined by the function

​

How do i come up with the formula for the following ?'s

?

a)	Find the capsize screening value for the Tartan 4100, which has a displacement of 23,245 pounds and a beam of 13.5 feet.
b)	Solve this formula for d.
c)	The accompanying graph shows C in terms of d for the Tartan 4100 (b = 13.5). For what displacement is the Tartan 4100 safe for ocean sailing?

 

[HallsofIvy]

To be considered safe for ocen sailing, the capsize screening value C should be less than 2. For a boat with a beam or width (b) in feet and displacement (d) in pounds, C is determined by the function C=4d^-1/3b. In the graph provided it shows the capsize screening value with b=13.5 ft on the left and the displacement in pounds on the bottom. Their formula is C=54d^-1/3b.
How do i come up with the formula for the following ?'s

?

A) find the capsize screening value for the Tartan which has a displacement of 23,245 pounds and a beam of 13.5ft.

Set d= 23245, b= 13.5 in your formula! \(\displaystyle C= 4(23245)^{-1/3}(13.5)= \frac{4(13.5)}{\sqrt[3]{23245}}\)

B) solve this formula for d

Your formula is \(\displaystyle C= \frac{4b}{\sqrt[3]{d}}\). Multiply both side by \(\displaystyle \sqrt[3]{d}\) then divide both sides by C to get \(\displaystyle \sqrt[3]{d}= \frac{4b}{C}\). Finally take the third power of both sides.

C) The accompanying graph shows C in terms of d for the Tartan (b=13.5). For what displacement is the Tartan safe for ocean sailing?

You say that "the capsize screening value C should be less than 2" but your graph only goes down to about 17 before going "off the page"! If you mean "20" rather than "2" then you would follow the horizontal line marked "20" across to where it crosses the graph. What vertical line is that?

 

[Ishuda]

There are two C's in your question so let us distinguish: For b in feet and displacement d in pounds, let C_a = 4 b d^-1/3 for the actual capsize screening value and Cg = 54 b (d/1000)^-1/3 for the values on the graph.

Now convert C_g to C_a with a simple multiplication factor and work out the problem.

EDIT: BTW: With a quick look, I'm not sure the graph is what it purported to be.

 

[stapel]

Note: There have been questions about the assignment's graph in other instances of this exercise, such as this one.