Displacement Tonnage

[daltoncalford]

I am very confused - not a state that I am unfamiliar with, but, in this case, one that is truely bothersome.

In Traveller, displacement tonnage has been listed as 13.5 or 14 cubic metres.

That is supposed to represent one displacement ton of Hydrogen.

So, being the fool I am, I started to look up a few things.

1.) The molar weight of Hydrogen is 1.0079 grams per mole.
2.) The displacement volume of a gas at Standard temperature and pressure is 22.414 cubic litres
3.) A cubic Litre is 10cm*10cm*10cm.
4.) A cubic Metre would hold 1000 litres of volume.
5.) There are 1000 grams in a kilogram, and 1000 kilograms in a metric ton, so, you divide 1,000,000 by 1.0079 to find out the number of moles in a metric ton of hydrogen.
6.) A metric ton of hydrogen would contain 992,161.92 moles of hydrogen.
7.) 992,161.92 moles of hydrogen would encompase the volume of 22,238,317.29 cubic litres of volume or 22,238.31 cubic metres of volume
8.) Taking the cube root of 22,238.31 gives us a cube that is 160metres to a side.

So at STP, one ton of hydrogen is VERY big.
Now, Liquid Hydrogen, can occur at different temperatures and pressures, depending upon the combination of the two, and the expansion/compression of the volume has certain ratios

Liquid (-252.9oC) to gas (-252.9oC) 1:53
Gas (from –252.9oC to 20oC) 1:16
Liquid (-252.9oC) to gas (20oC) 1:848

So, liquid hydrogen, at it's preferred temperature, is 848 times smaller in displaced volume than it is at STP. (roughly as I am grabing this information from a document http://policy.lanl.gov/pods/policies.nsf/LookupDocNum/LIG402-1200-03/$File/lig402120003.pdf and I have not gone through all the extended bits of math)

If we divide the 22,238.31cubic metres of volume by 848, we get a displacement of 26,224.43 cubic metres. A bit smaller, but still not 13.5 or 14 cubic metres as what has been the standard for traveller. This would state that a ton of hydrogen, would fill a cube 21.16 metres to a side.

If we say that a deck square is 3 metres high, that would mean that a ton of liquid hydrogen would take up an area 62 1.5m deck squares to a side.

Notice I used the maximum compression ratio.

So, I have screwed up somewhere.

Could one of you math/chemistry wizards show me where I have gone wrong.

Thanks

Dalton

 

[Scott Martin]

Erm... start by dividing by 2: you're looking at monatomic hydrogen in your equation (H1, not H2) which is ermm... unstable.

Liters to cubic meters is 1/1,000,000 not 1/1,000

I could continue, but that already gives you a number in the 11 cubic meter range (demonstrating that lHyd in Traveller is not cryogenic)

You are also taking the very long route around to get the calculation (more steps = more chances to screw up)

look here:
http://www-formal.stanford.edu/jmc/progress/hydrogen.html
point number 2 is that HydroGen has a density of 0.07 grams/cc AKA 0.07 T/M3
(Remember that a cc is 1/1,000,000 of a cubic meter, a gram is 1/1,000,000 of a ton so dividing these gets you "1")

1 T / 0.07 T/m3 = 14.3 m3 (the actual density is a hair over 0.0708 at standard temperature giving a hair over 14 m3 for a ton, and less if you refrigerate)
http://en.wikipedia.org/wiki/Liquid_hydrogen
I prefer to check my facts at academic institutions before wikipedia-ing: sometimes Wiki is *waaaay8 off.

I'm pretty sure that the "13.5" was to make deck plan conventions work out to a nice round number.

I could use Rybergs equation and compression ratios, but I prefer to get directly to a workable solution

Scott Martin

 

[daltoncalford]

Thanks Scott,

That is what I needed - I knew I had a major mistake somewhere.

Best regards

Dalton

 

[Fritz_Brown]

Spot on for both of Scott's points: 13.5 makes for a nice 1.5m x 1.5m square (3m high) on a deckplan, but 14 works better for the actual numbers.

 

[Straybow]

LH2 specific gravity is 0.071 = 14.08m³/ton. Look it up.

What is confusing is... why the hell would anyone use such a "standard" for starship design? Maybe the Vilani would be so crazy, but the OTU history is that sensible Earthers took over at the first opportunity. That foolishness would've been the first thing out tossed out.

 

[Anthony]

My impression is that they had maps (with two 5' squares per 'ton', 5' being a standard scale for maps at the time) and at some point had to retcon an explanation.

 

[mike wightman]

Since jump ships require a huge quantity of liquid hydrogen it kind of makes sense to rate them this way.

 

[BillDowns]

Originally posted by Sigg Oddra:
Since jump ships require a huge quantity of liquid hydrogen it kind of makes sense to rate them this way.

Totally agree, Sigg

for what that's worth.

 

[BillDowns]

Let me approach this from a different point of view.

Question: what's the #1 or #2 requirement for spaceships in an RPG?

Answer: Deckplans for playing the game. Almost everything else is window-dressing.

Therefore: Ship design must be based on volume, not mass. This is an RPG, not a simulation.

Under that criteria, any arbitrary selection of a volumetric standard will do. Since the chosen standard was based on the ship's largest volume requirement - LH fuel - this makes more sense than basing it on, say, the U.S. DOT per axle weight limits - the freight ton; or the charging standard for the Panama Canal in 1914 - the register ton.

 

[aramis]

Scott:
you said: "Liters to cubic meters is 1/1,000,000 not 1/1,000"

from Rowlett's online dictionary of units:

Throughout this dictionary, the liter is used as a name for exactly 1 cubic decimeter, 1000 cubic centimeters, or 0.001 cubic meter. In its renewed guise as the cubic decimeter, the liter is approximately 61.023 744 cubic inches.

1000L=1m^3 since 1L=0.001m^3

10cm on a side to 100cm on a side is 10x the linear; linear uniform change is cubed to find volumetric change. 10^3=1000.

I think you were thinking of mL aka CC's...

 

[Straybow]

Originally posted by BillDowns:
Let me approach this from a different point of view.

Question: what's the #1 or #2 requirement for spaceships in an RPG?

Answer: Deckplans for playing the game. Almost everything else is window-dressing.

Therefore: Ship design must be based on volume, not mass. This is an RPG, not a simulation.

As I recall, the original LBB set never mentions any volume, just "tons." Apparently it isn't as important as you suppose.

We had to guess the size of the mysterious Trav "ton" based on the crew requirements and such, and overestimated at 10 times the wet displacement instead of 5. We never needed deckplans except for the fact that I liked to draw them. Never had a boarding action.

Even given your "requirement" to base ship design on volume for deck plans is not justification for calling 14m³ a "ton" and thereby throwing all standards and measures into confusion and disarray.

Under that criteria, any arbitrary selection of a volumetric standard will do. Since the chosen standard was based on the ship's largest volume requirement - LH fuel - this makes more sense than basing it on, say, the U.S. DOT per axle weight limits - the freight ton; or the charging standard for the Panama Canal in 1914 - the register ton.

The largest single requirement on any conventionally fueled oceanic vessel is fuel capacity. That does not make extrapolating fuel tankage to fill the ship a good standard for indicating ship size.

DOT gross weight and axle weight limits are in place for entirely practical reasons: the roadway must be able to bear the traffic, expecially bridges. However, a trucking company doesn't charge a client based on much diesel fuel would fill the space occupied by the shipment. Unless, of course, the truck is a tanker.

The Panama Canal charged by the register ton because people use the Canal to move cargo. The Canal didn't charge by how much fuel could have filled the cargo space because it is a stupid way to calculate things. Unless, of course, the ship happens to be transporting fuel.

The register ton came about as a standard because long experience showed that a ton of average goods was roughly equal to 100 ft³, including dead space due to stacking limits, access, and load balancing. Of course, the fact that 100 ft³ made the math easy helped a whole bunch as well.

Even today, a standard 53' trailer is roughly 3300 ft³, and the normal load limit based on gross axle weight is about 30 tons. The register ton works, the LH2 displacement ton doesn't work. That's why the questions keep coming up.

 

[mike wightman]

So basing a system of measurement off the number of barrels a wooden ship could carry makes more sense in the far future than basing it off the fuel volume that is critically important for moving the ship through jump space?

IMTU the displacement ton is a Vilani thing, the Terrans prior the RoM measured their ships either in tonnes or m^3 - usually both.
But since the volume of fuel used to jump x10 is a measure of ship size, and since the mass of the ship doesn't matter for jump purposes, only its volume, then it made sense to the Terrans to adapt to the Vilani standard.