Hey, "techheads"...volume/mass question...

[SicOne]

The real question here is what happens if you know the volume of a starship but learn that it's a little longer or shorter than you previously thought. If the old length is 120 meters, how do you calculate volume for a new length of 140 meters, for example?

First, imagine it's made of soft clay, and roll it into a ball. Then calculate its radius, knowing nothing but the original stated volume.

r3 = .75*v/pi

Find r and increase/decrease it by the percentage difference from old length to new length.

Then simply use the formula for the volume of a sphere (a new ball containing exactly enough clay to resculpt your ship in the new size):

v = 4/3*pi*r3


Now, the short form of all that is to find the cube root of your known volume, change it by the percentage difference, then cube that.

My brain just imploded.

 

[SicOne]

Uh oh. Discussions on this topic always end up bathed in blood...

Well, we do have this reference:

Starship Volumetrics

And when citing mass, even though it's an estimate, don't forget to slip in a 47, if possilble:

MASS: 647,000 M.T.

Hey, Masao, welcome back (if you're the Masao Okasaki I'm thinking of...)!

Guys, challenge for you...if any of you are good at 3d modeling and crunching numbers, I am wondering if we can complete and enhance that Starships Volumetrics chart with the following length, cubic meter volume, and estimated tonnage figures for...

(1) Constitution (original and refit) saucer section and secondary hull

(2) Constellation saucer and nacelles

(3) Oberth saucer and lab pod

(4) Excelsior (original and B-type) secondary hull

(5) Ambassador saucer and nacelles

(6) Akira nacelles

(7) Nebula secondary hull and both triangular and AWACS pods

(8) Nova secondary hull and nacelles

(9) Sovereign secondary hull and nacelles

(10) Prometheus secondary hull and nacelles, as well as overall figures for the separated mode

(11) overall figures for Olympic, including separate nacelle/secondary hull/"ball" stats

(12) overall figures for Klingon Negh'Var-class

(13) K'Tinga nacelles

(14) overall figures for Cardassian Hedeki-class

Are there any ships we missed?

A few months back, I was working on crunching numbers and deriving length/width/beam figures for saucers/secondary hulls/nacelles, etc, based upon known ship lengths, but real-life intervened and sidetracked me. This thread seems to me a good time to dust that stuff off and see what we can come up with.

Also, I seem to recall in threads past various discussions concerning ship length. It looks like the "correct" lengths are referenced in that Volumetrics chart, though I was of the understanding that the following ships could also be interpreted to the following lengths (sources given as well), and if anyone can also recalculate the cubic meter volume and estimated tonnage based on the revised lengths...

(a) Nebula of 465m length (Starship Spotter)

(b) Akira of 464m (Starship Spotter)

(c) Ambassador of 478m (Trek BBS discussion on Ambassador-class)

(d) K'Tinga of 214m (Starship Spotter)

(e) B'Rel of 88m (Starship Spotter)

(f) D'Deridex of 1,041m (Starship Spotter)

(g) Galor of 371m (DS9 Tech Manual...seems a good compromise between the 228m figure from Starship Spotter and the identical-to-Vor'Cha-length 480m from the Volumetrics chart)

(h) Jem'Hadar fighter of 68m (Starship Spotter)

Good luck if you should decide to accept this challenge!

 

[Bill Morris]

My brain just imploded.

I'll make it even easier. Starship Voyager: 344 m overall length, 700,000 M.T. mass. Suppose new evidence reveals overall length of 350 m. That makes the new mass 736,983. That was easy. How?

350/344 = 1.01744 (relative change of length)

700,000^(1/3) = 88.77904 (cube root of mass!)

(88.77904*1.1744)^3 = 736.983 (pure evil)

That's working directly with a known length and a known mass, which we now believe to be wrong. Things like furniture wouldn't really change size, and that creates a little inaccuracy. So adjust for that, if you like.

 

[John O.]

If you have absolutely zero information about the volume of the nacelles, but you know all the dimensions, you could always just superimpose a 3D coordinate system, figure out the f(x,y,z) function of the curvature (that's probably the hardest part... might have to just do some trial and error with different quadratic forms or if you wanna get fancy you could bust out a TI-83/89, plot the data points and fit a quadratic curve... or if you wanted to get REALLY fancy you could use an exponential regression) and triple integrate over the whole solid.

Technically you could do this for an entire starship, assuming you know all the external dimensions... you'd just have to find geometrically convenient places to cut it up into segments.

This actually sounds really fun (to a math major!), if I had the dimensions, I might try it!

I would imagine the nacelles and whatever the pylons connecting the saucer sections to the engineering section would be the toughest because they are not conventional geometric solids and volume/area formulas do not exist for them. By the way... the above described is exactly how the well known formulas for the volume of spheres, area of rectanges, perimeter of circle, etc... were originally derived.

 

[SicOne]

If I can get you guys the various dimensions of the nacelles, secondary hulls, etc, given the lengths posted in the Volumetrics site...could you figure out volume in cubic meters from that, with the resources at your disposal?