[Spaceships] simply fuel math...
 

RAW Super Fusion Torch, 50G 450mps but, if you allow use of an SM-4 section to get only 0.5G, how far will that tank of fuel take you - 45,000mps?

This is either one of those math things so simple you can't believe your own answer or it's Costello's rent arrears and I'm the landlord:/
I mean, I can't believe my own answer so, I need someone else to either say "Yup, it's really that simple." or swat me upside the head and show me the actual math that proves it's really all rocket science.

TQ in antici...

Re: [Spaceships] simply fuel math...
 

It's simple the other way around. It gets you 450 mps. No matter what size the engine is, the final velocity depends on the size of the fuel tank relative to the entire ship, not relative to the engine. A smaller engine just takes longer to get there - 40 hours instead of 24 minutes to burn your tank dry.

Re: [Spaceships] simply fuel math...
 

Looked at from a different angle, adding more engines doesn't get you any less delta-V from the single fuel tank, so removing fractions of an engine shouldn't get you any more.

Re: [Spaceships] simply fuel math...
 

Delta-V - the change in velocity - is a measure of engine efficiency and does not change with engine size (at least, not on the scale of engines mounted on spaceships). A larger engine uses fuel just as efficiently as a smaller engine does.

Re: [Spaceships] simply fuel math...
 

Thank you, all.
Brain off day. I think part of my scribbled notes were what if you "super" the rocket and scale from there and then I've wandered off into Lalaland:D

Re: [Spaceships] simply fuel math...
 

Ok, piggy backing on this thread...

Suppose you decide to design a spaceship with the following in mind:

You have a SM 9 ship. A single "reaction Engine" for this ship will produce 3G acceleration.

However, using the Swapping out rule from page 5 of Transhuman Space ships...

Suppose I decide to use one SM 8 rocket engine to produce 1G extra, allowing for a 4G acceleration?

Further suppose that I use the other two modules for Fuel. Those two fuel will be 2/3rds of a fuel tank for a SM 9 ship.

So what happens to the Delta-V increase (page 17 of the First GURPS SPACEBOOKS rules)?

It states that if you have 6 to 8 tanks, multiply your delta-V by 1.2. If you have 9 to 12, multiply by 1.4

Now, if we have 2/3rds of a tank, we have 2/3rds of the delta-V that a normal SM9 tank would have. No question there.

But what happens to the Delta-V multiplier when you're at the "threshold" level between the multiplier values? In other words...

if you have 5 and 2/3rds of a tank, does this get the full 1.2 modifier? If you have 8 and 2/3rds of a tank, do you get the full 1.4 multiplier?

How would you resolve that issue?

Re: [Spaceships] simply fuel math...
 

While the initial question is well answered, I'd add a thought - the smaller engine will take 100 times as long to burn through the reaction mass...but since it's producing 1/100 times as much acceleration, naturally the delta-V comes out the same.
So (A) there's no actual reason to involve the smaller rocket in this, it has no bearing on the question.

(B) Assuming I was using the by-the-book delta-V rule rather than using the rocket equation to smooth it, I'd use it by the book - 5 and 2/3s is not 6 to 8, it is less than 6, so you don't get that multiplier. 8 and 2/3s is slightly more of a problem, but for consistency I'd put it with the lower group rather than the upper group.

Re: [Spaceships] simply fuel math...
 

OK, if you want something more accurate, but more fiddly, then I think this is right. Take the natural logarithm of 20 divided by 20 minus the number of fuel tanks and divide by 0.05 (ln(20/(20-tanks))/0.05). This gives you the effective number of fuel tanks for that particular drive, so calculate your delta V from there.

Aside: The multipliers given in the book exist to approximate the rocket equation's effect on Delta V (i.e. higher proportion of propellant, higher delta V). However, they do seem to error on the low (but occasionally the high). For example, 19 tanks would have a multiplier of 3.15 according to my equations, but it gets a multiplier of three. On the other hand, 6 tanks should have a multiplier of 1.18 according to my equations, but it gets a multiplier of 1.2.

Re: [Spaceships] simply fuel math...
 

It's probably simpler to describe "divide by 0.05" as "multiply by 20".

Re: [Spaceships] simply fuel math...
 

If you want to be really pedantic, divide by ln(20/19) instead of 0.05. Assuming the table is accurate for exactly one tank, that will give you 1 = 1. It's only about a 2.5% difference, though.

Re: [Spaceships] simply fuel math...
 

If you want
The formula in the second case is -20 * ln( 1 - 0.05* nTanks ).

Re: [Spaceships] simply fuel math...
 

As long as we're at it, I became idly curious about the RAW multipliers for tanks to e-tanks. So here's a table using Anthony's formula, with a column to convert that to a multiplier. Pick your own nTank ranges for 1.2, 1.5, or other rounded values that you like.

Re: [Spaceships] simply fuel math...
 

Just out of idle curiosity...

Would the formula for Realistic Delta-V from TRANSHUMAN SPACE apply here?

Presumably, each of the elements has a given weight (5% of the total mass) and consequently, the fuel mass would be equal to 5% per tank, and if using smaller SM tanks, each SM-1 tank relative to the overall SM of the ship, would add 1/3 of 5% or 1.67% per tank at the smaller size.

The only thing missing is the ISP for the fuel, but - I suspect that can be reverse engineered from the Delta-V values given with the original rules.

Just thinking aloud (so to speak).

Re: [Spaceships] simply fuel math...
 

I believe the realistic dV formula was the rocket equation presented above, and hidden behind the table in Spaceships, except Spaceships abstracts the choice of fuels to a somewhat generic representation and a limited set of mass ratios so it doesn't have to deal with individual Isp (shut up iPad, Isp is capitalized correctly).

Re: [Spaceships] simply fuel math...
 

Always good to know about the abstraction aspect. I find it mildly interesting that the Delta-V formulas do not give a value of 1 for 1 tank. But, if I work it out (which I'm doing to do now... <after a pause>

Unless I messed up?

Formula for Delta-V is .003 x Isp x Ln(Loaded Mass/Dry Mass)

Solving for ISP when you know Delta-V

Isp = Delta-V/.003/Ln(Loaded Mass/Dry Mass).

I got an Isp of 974.79 for Rocket Fuels that grant .15 MPS per single tank.

I used a SM:9 hull of 3,000 tons, with one fuel tank worth 5% of the mass for the hull. I probably could have gotten the same results using Ln(1/.95) as I did for using a mass of 3000 and a dry mass of .95*3000.

Seems kind of high to me that the Isp is that high.

I'm tired and maybe I didn't do the math right. Double check?

Re: [Spaceships] simply fuel math...
 

Formula for delta-V is ISp * ln( loaded/dry ). However, if ISp and delta-V are not in the same units, you need a conversion factor. ISp has historically been described in pound-seconds per pound (where the first pound is a lb force, the second pound is a lb mass), or just Seconds.

The conversion from Seconds to mps is ~0.0061 mps/Second, I don't know where you're getting 0.003 from.

Re: [Spaceships] simply fuel math...
 

From page 189 of TRANSHUMAN SPACE that reads under the heading of "Realistic Delta-V"

"For more realism, use this formula: Delta-V (in mps) = 0.003 ´ ISP ´ ln [Loaded Mass (in tons)/Dry Mass (in tons)]. The symbol “ln” means “natural logarithm”; a natural logarithm key, marked “ln,” can be found on most calculators."

My guess is that the .003 is a conversion factor required for translating the normal units Isp is given as, into mps values.

THS lists Oxygen/Kerosene as having an ISP of 514 - which is better than the other chemical rocket Isp values. I guess that's why I wondered at the calculated 974.79 value.

Granted, I only used ONE fuel tank for the calculations, but then again, one fuel tank's worth of Delta-V was given in GURPS SPACESHIPS, which seemed to me that I was talking Apples to Apples here. THS uses Delta-V in mps units, just like GURPS SPACESHIPS does.

Re: [Spaceships] simply fuel math...
 

Huh. That looks like errata territory.
Or there could be multiple competing errors. LOx/Kerosene has an Isp of 304. This may be an artifact of GURPS Vehicles attempting to simplify math by giving fuel consumption based on some theoretical average use rather than operating at 100% of design power.

Re: [Spaceships] simply fuel math...
 

...Which amounts to g-seconds, but who's bothering with actually communicating well? Apparently not historical American-units rocket scientists.

Re: [Spaceships] simply fuel math...
 

Just above that box on p. 189 of Transhuman Space, we have:

That "half" is why it's 0.003 and not 0.006.

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.

Re: [Spaceships] simply fuel math...
 

Cal them "Cargo" rather than empty. It comes to the same thing if you never fill your holds but it screws with the damage charts less.

Spaceships isn't really written as a campaign/world-building aid as much as people want to use it for one. It's meant to do double duty as an rpg supplement _and_ a stand-alone space combat game. That's where some of the gamist elements come from.

Re: [Spaceships] simply fuel math...
 

But that would largely be a "house rule" kind of thing. Not that I mind it!!! On the contrary, If someone were the layout the entire formula for me to follow (or I take the time to figure it out) - then it is a good house rule to utilize.

:)

Re: [Spaceships] simply fuel math...
 

So, if the ratio were to be .86666667 that of the next largest hull mass, the ratio would be the cube root of .86667 times what? The next smaller hull?

Re: [Spaceships] simply fuel math...
 

The hull it's a 0.86667 times multiplier of. You should probably use the next smaller hull size, though, so it would be the cube root of 2.6 x the stats of a 100 ton hull.

Re: [Spaceships] simply fuel math...
 

That would be full of problems.

Reducing mass should increase the acceleration of drives and the delta-V of fuel tanks, and lower HP. Having slots on the ship that correspond to nothing makes a hash of the damage system.

Re: [Spaceships] simply fuel math...
 

I'll give that a shot and see how it works.

Right now, I started working on how to calculate the values for hulls as given in the table. As best as I could figure...

It works out to:

if SM is odd, value = 3
if SM is even, Value = 10

Then, multiple the "Value" times 10^(round(SM/2,0)+2).

Where possible, I'm trying to reduce things to formulas that are a function of SM values. Otherwise, I need a table lookup to find out what values go where relative to the SM involved.

I know there is an Excel spreadsheet out there that does this, but I like to see what I can sleuth out on my own. :)

Re: [Spaceships] simply fuel math...
 

If you really want to make intermediate size vessels, start with the stats for a vessel the size of the next smaller official hull.

• For any stat that progresses x10 for +6 SM, multiply the stat by the cube root of the ratio of mass to that of the next smaller official hull.
• For any stat that progresses x10 for +3 SM, multiply the stat by the square of the cube root of the ratio of mass to that of the next smaller official hull.
• For any stat that progresses x10 for +2 SM, multiply the stat by the ratio of mass to that of the next smaller official hull.
• For any stat that has a linear progression, use the stat of the smaller official hull if the mass ratio is less than 1.8, and that of the larger official hull if the ratio is 1.8 or larger.
• Be careful that many stats have substantial rounding or minima at the low end. It may be necessary to figure out the progression and calculate a theoretical value for your base hull, the reapply the rounding and/or minima after modifying for your actual hull. For example, SM+6 habitat should have 0.6 cabins.

So a 260 ton vessel would have 1.37 times the DR, 1.89 times the open spaces areas, and 2.6 times the cargo capacity per component of a 100 ton ship, and would have the handling and computer complexity (and SM) of a 300 ton ship. There are a few odd progressions, like hangar bay launch rate (though if you look carefully, you may note that if you express launch rate as seconds per hangar, you get a neat x10/+6 progression).

Re: [Spaceships] simply fuel math...
 

works for me. :)