Re: [Spaceships] simply fuel math...
 

This is what you get for incorrectly using a unit of weight as a unit of mass.

(There is an American unit of mass, but even most Americans don't seem to know what it is. Technically it exists in Imperial measure too. https://en.wikipedia.org/wiki/Slug_%28mass%29 )

Re: [Spaceships] simply fuel math...
 

MrTim has the right of it gentlemen.

I went to the Wikipedia page to find what I could about Delta-V and they give an example for calculating it, which very nicely approximates what is in Transhuman Space (THS).

There, they use Exhaust Velocity x Ln(Loaded mass/empty mass). Elsewhere, I had to find the key element of how Isp is derived...

By definition, it is the Exhaust Velocity divided by Gravity. Whether you measure the Exhaust Velocity in Meters per second and divide by 9.8 meters per second per second, or you measure the velocity in feet per second and divide it by 32.174 feet per second per second, you should get the same value in seconds for Isp for that given fuel.

Consequently... (assuming I'm correct!!!)

Exhaust Velocity would equal 32.174 x 395 (for the Kerosene-Oxygen example in THS) x Ln(Loaded Mass/Empty Mass). Doing the math, I get a velocity of 651.8726292 feet per second. To convert that to Miles per second, divide by 5280, and the result becomes 0.123460725 miles per second (not too far off from .15 Miles per second!)


And this is where MrTim is right...

(32.174 * Isp)/5280 can be rewritten as Isp x 32.174/5280 (to get Miles per second instead of feet per second). Net result?

32.174/5280 = 0.006093561 per my Excel spreadsheet.

Since THS used the rule of 1/2 this total Delta-V to accelerate there, and decelerate, .003 becomes .006, which matches the value just above.

It appears that the THS formula is correct after all.

Now, to reverse Engineer what the ISP has to be to get a velocity that is .15 miles per second, and reverse the steps taken above... I get the final Isp as being 479.9097032 seconds, call it 480 rounded.

So, my initial use of the formula from THS didn't take into account the fact that it was HALF the total delta V. My initial 974.79 value using THS formula, should have been divided again by 2 due to the nature of the rules in describing Delta V for THS in the first place. 974.79/2 = 487.395. This is close enough to the 480 rounded above, probably due to rounding in the original rules formula and whether they used 32.174 for the gravity in feet per second per second, or 32.17, or even simply 32. I don't know.

But my confidence in the formula is restored. :)

Re: [Spaceships] simply fuel math...
 

As this would have bearing on the fuel issue, has there ever been a question about the mass of a GURPS SPACESHIPS craft where it wasn't exactly what the tables say it is?

For instance, can you have a spaceship whose loaded mass is say 260 tons?

If there are 20 "units" to a ship, each 5% of its mass, and you want a 260 loaded ton mass, 260/300 = .867 units of the 20 normally used in a ship, or roughly 17 units used, 3 left empty.

Can one build such a ship using that design philosophy? If so, then determining its Delta-V value could be based on 260 tons instead of 300 tons?

Re: [Spaceships] simply fuel math...
 

Its actually simpler to build the ship with 20 sections and multiply all costs and weights by the ratio of the two sizes. you also want to extrapolate DR, which is more complicated, because I can think of several valid ways of doing that. On the other hand, DR doesn't vary that much between sizes, so it doesn't matter nearly as much.

Re: [Spaceships] simply fuel math...
 

You'd multiply DR, hit points, and (if applicable) weapon damage by the cube root of the ratio.

Re: [Spaceships] simply fuel math...
 

Technically no. Spaceships is a simplified system and uniform masses are one of the simplifications.

Re: [Spaceships] simply fuel math...
 

That's the way DR scaling often works. You also have the logarithmic way, which is what the spaceships tables that generate the DR in the first place use. These are the two leading contenders. Then there is the lazy method of linear extrapolation, which probably won't give bad numbers, all things considered.

Re: [Spaceships] simply fuel math...
 

It's actually the same method. The DR tables in spaceships use the range/speed chart. The sizes also use the range/speed chart, and since the range/speed chart is 10^((SM-2)/6), we would expect masses to vary with the cube of length, or based on 10^((SM-2)/2). This is in fact the scale used for spaceships masses, once you include rounding errors.

Re: [Spaceships] simply fuel math...
 

Huh. And some quick comparisons verify that. Good to know.

Re: [Spaceships] simply fuel math...
 

So you can't simply state "Empty" for the slots in the hull? That sounds like a simplification from where I sit. Reduce mass by 5% for each hull section left empty/open. No cost, no mass, etc.

But, rules as written, the idea was never broached. Good to know.