Ship Math Problem

[Phaelen Bleux]

So, I was trying to figure the length and beam of a ship from known hull volume using the Builder's Old Measure. However, I could not solve the equation for L. The ship has Fine Lines, so Beam is 1/8 of Length:

Volume = (L - 0.6B) x (B)^2
so
Volume = (L - 0.6[0.125L]) x (0.125L)^2
so
Volume = (L - 0.075L) x 0.015L
so
Volume = 0.925L x 0.015L
so
Volume = 0.0144L

But not, and I don't know what I'm doing wrong. Any math whiz who can help??

I've already solved the problem by randomly plugging in Ls and Bs; Length = 150', B = 18'. But how should I have solved the equation for next time (i.e., if the ship doesn't have Fine Lines).

[SCAR]

(0.125L)^2 = 0.125 x L x 0.125 x L = 0.015625 x L^2

so
Volume = 0.925L x 0.015625 L^2
so
Volume = 0.0144L^3

You're multiplying the Numbers but not the L's !

[Phaelen Bleux]

Thank you!!

[thulben]

Originally Posted by SCAR

(0.125L)^2 = 0.125 x L x 0.125 x L = 0.015625 x L^2

so
Volume = 0.925L x 0.015625 L^2
so
Volume = 0.0144L^3

You're multiplying the Numbers but not the L's !

Yep. Also, always do a "unit check". Volume should be in units of cubic length (i.e. cubic inches or cubic centimeters). The original formula yielded units of length and thus could not represent a volume!

[Phaelen Bleux]

OK, now that I have this in hand:

To solve for the length and beam of a ship with known volume:

Fine Lines:
Beam = cube root [Vol/3.9362]
Length = 8 x Beam

Average Lines:
Beam = cube root [Vol/2.8723]
Length = 6 x Beam

Mediocre Lines:
Beam = cube root [Vol/1.8085]
Length = 4 x Beam

I assume 100 cf per ton of displacement and use the BOM formula of
Volume = [(L- 0.6 x B) x (B^2)]/188 x 100

Technically, this only works for Age of Sail ships, and is probably the most accurate for ships with Mediocre Lines. I do not use the 35 cf/ton displacement of Vehicles as I feel this is too low. If you like a different figure for cf, you could simply multiple the divisor by the ratio of 100 to your figure (e.g., 100/35 = 2.8571 for Vehicles Standard).

[vierasmarius]

Originally Posted by Phaelen Bleux

Technically, this only works for Age of Sail ships, and is probably the most accurate for ships with Mediocre Lines. I do not use the 35 cf/ton displacement of Vehicles as I feel this is too low.

Isn't that 35cf/ton based on the density of water, and thus not really open to much variation? Water is approximately 62lb/cf, or around 32cf/ton, so that 35cf/ton is already a bit high.

[Phaelen Bleux]

Originally Posted by vierasmarius

Isn't that 35cf/ton based on the density of water, and thus not really open to much variation? Water is approximately 62lb/cf, or around 32cf/ton, so that 35cf/ton is already a bit high.

Yes, 35 cf is the density of salt water. But what we are really after is the approximate density of the ship. This is where I think Vehicles went awry. If you look at the solved equation (#4) you are back to a factor of about 100.

http://en.wikipedia.org/wiki/Builder's_Old_Measurement

And, anecdotally, it has been working for most of the TL4/TL5 wooden ships I have designed (i.e., I get about the right tonnage from the length and beam).

[Lord Carnifex]

Originally Posted by Phaelen Bleux

Yes, 35 cf is the density of salt water. But what we are really after is the approximate density of the ship.

Right. But if the ship is denser than water, then it sinks. So 35 cf/ton is the maximum density of any seagoing ship other than a submarine.

[Peter Knutsen]

Originally Posted by thulben

Yep. Also, always do a "unit check". Volume should be in units of cubic length (i.e. cubic inches or cubic centimeters). The original formula yielded units of length and thus could not represent a volume!

Quoted for truth. Always do unit checks.

[Phaelen Bleux]

Originally Posted by Lord Carnifex

Right. But if the ship is denser than water, then it sinks. So 35 cf/ton is the maximum density of any seagoing ship other than a submarine.

True enough. I would only say that Vehicles makes it sound like all ships are 35 cf/ton for the design rules, which throws a wrench in things when trying to model a real-world vessel. I suspect most are of far less density, since engineers wouldn't want to ride the line of My Floatation Device Is Exactly As Dense As The Water.

So, I use 100 cf/ton. . .seems to work, historical precedent, nice round number, and much less dense than saltwater, so my designs float!