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Old 10-04-2017, 03:44 AM   #11
Anthony
 
Join Date: Feb 2005
Location: Berkeley, CA
Default Re: [Spaceships] simply fuel math...

If you want
Code:
Tanks	eTanks
1	1.03
2	2.11
3	3.25
4	4.46
5	5.75
6	7.13
7	8.62
8	10.22
9	11.96
10	13.86
11	15.97
12	18.33
13	21.00
14	24.08
15	27.73
16	32.19
17	37.94
18	46.05
19	59.91
The formula in the second case is -20 * ln( 1 - 0.05* nTanks ).
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Old 10-04-2017, 07:16 AM   #12
Anaraxes
 
Join Date: Sep 2007
Default 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.

Code:
Tanks	eTanks	Multiplier
1	1.03	1.03
2	2.11	1.05
3	3.25	1.08
4	4.46	1.12
5	5.75	1.15
6	7.13	1.19
7	8.62	1.23
8	10.22	1.28
9	11.96	1.33
10	13.86	1.39
11	15.97	1.45
12	18.33	1.53
13	21.00	1.62
14	24.08	1.72
15	27.73	1.85
16	32.19	2.01
17	37.94	2.23
18	46.05	2.56
19	59.91	3.15
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Old 10-04-2017, 09:10 AM   #13
hal
 
Join Date: Aug 2004
Location: Buffalo, New York
Default 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).
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Old 10-04-2017, 10:17 AM   #14
RyanW
 
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Default Re: [Spaceships] simply fuel math...

Quote:
Originally Posted by hal View Post
Just out of idle curiosity...

Would the formula for Realistic Delta-V from TRANSHUMAN SPACE apply here?
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).
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Old 10-04-2017, 04:14 PM   #15
hal
 
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Default Re: [Spaceships] simply fuel math...

Quote:
Originally Posted by RyanW View Post
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).
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?
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Old 10-04-2017, 04:26 PM   #16
Anthony
 
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Default Re: [Spaceships] simply fuel math...

Quote:
Originally Posted by hal View Post
Formula for Delta-V is .003 x Isp x Ln(Loaded Mass/Dry Mass)
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.
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Old 10-04-2017, 04:39 PM   #17
hal
 
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Default Re: [Spaceships] simply fuel math...

Quote:
Originally Posted by Anthony View Post
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.
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.
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Old 10-04-2017, 04:44 PM   #18
Anthony
 
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Location: Berkeley, CA
Default Re: [Spaceships] simply fuel math...

Quote:
Originally Posted by hal View Post
From page 189 of TRANSHUMAN SPACE that reads under the heading of "Realistic Delta-V"
Huh. That looks like errata territory.
Quote:
Originally Posted by hal View Post
THS lists Oxygen/Kerosene as having an ISP of 514 - which is better than the other chemical rocket Isp values.
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.
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Old 10-04-2017, 07:08 PM   #19
Ulzgoroth
 
Join Date: Jul 2008
Default Re: [Spaceships] simply fuel math...

Quote:
Originally Posted by Anthony View Post
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.
...Which amounts to g-seconds, but who's bothering with actually communicating well? Apparently not historical American-units rocket scientists.
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Old 10-05-2017, 12:58 AM   #20
MrTim
 
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Default Re: [Spaceships] simply fuel math...

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

Quote:
Delta-V
This is the approximate maximum speed to which the vessel can accelerate using half its reaction mass, retaining the other half to decelerate.
That "half" is why it's 0.003 and not 0.006.
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