What is the unit of measure for rocket fuel? It does NOT appear to be liters!

[-Velocity-]

OK. Sorry if this has been asked before, but I seem to have found an inconsistency in the units of measure for rocket fuel, if it is assumed to be liters. I found this while I was playing around with creating my first mods (very large xenon tanks), and was trying to figure out how much xenon I should put in them.

First of all, by comparing dry mass and empty mass of the stock xenon tank and its fuel capacity, I saw that one unit of xenon fuel is actually 0.1 kg. A little odd, but whatever.

OK, fine. So now I wanted to figure out how much xenon fuel I should put in a modified Jumbo 64 tank. The Jumbo 64 supposedly, by my understanding, holds 6400 liters of rocket fuel. The number of liquid fuel units and oxidizer units certainly add up to 6400.

However, rocket fuel is like, maybe on average (if using kerosine and liquid O2), *roughly* around the density of water, about 1000 kg/m^3, which is the same as 1 kg/L. I noticed that the difference between the dry weight and the full weight of the Jumbo 64 is in fact 32 metric tons, or 32000 kg. Thus, the Jumbo 64 actually should hold about 32000 liters of fuel (using the 1 liter = 1 kg approximation), NOT 6400 liters.

The final nail in the coffin against liters being the unit of rocket fuel was when I measured the dimensions of the Jumbo 64- they are 2.5 meters by 7.5 meters. That is a volume of pi*1.25^2*7.5 = 36.8 m^3. 36.8 m^3 is 36800 liters. This agrees VERY CLOSELY with my predicted volume of 32000 liters based on the density of rocket fuel and the mass difference between a full and empty tank, especially if you allow for a bit of dead space inside the tank.

So using two completely different approaches, one based on density and weight and one based on volume, we arrive at the conclusion that the unit of measure for rocket fuel is NOT, in fact, liters. It is something else. It would appear that the volume of rocket fuel in game is actually around 5 liters per unit (32000 L / 6400 units = 5 L/unit).

So what in the heck is going on? Anybody know? Am I just doing something incredibly stupid? Or are the units of rocket fuel actually GALLONS?!?! If so, it would agree closely with the numbers then (1 gallon = 4.5 liters).

Edited September 8, 2013 by |Velocity|

[Johnno]

This has indeed been asked about and discussed before. It stems entirely from the faulty assumption of 1 unit = 1 Liter.

[-Velocity-]

This has indeed been asked about and discussed before. It stems entirely from the faulty assumption of 1 unit = 1 Liter.

Thanks... that makes me feel a lot better.

I did do a forum a search (multiple forum searches) and couldn't find the discussion. Also, the KSP wiki backed up the 1 unit = 1 L assumption, so I found it of no use.

Maybe instead of liters, the unit of fuel should be called "Kerbal gallons" or "kerballons"?

Anyway, it actually looks like I could realistically fill a Jumbo 64 up with almost 1 MILLION units of xenon , xenon is a very heavy gas and liquid xenon is over three times denser than water.

Edited September 7, 2013 by |Velocity|

[Dispatcher]

Kallons? Kiters? I was aware of the Wiki 'liter' designation, but I've always felt uncomfortable with it, since the tanks seem to be able to hold more in terms of volume, even if they were splash-baffled. Thanks for the clarification on this.

Edit: from KSP Wiki, it looks like the liquid fuel density is 5000 kg/ m^3.

Edited September 7, 2013 by Dispatcher
More detail.

[-Velocity-]

Kallons? Kiters? I was aware of the Wiki 'liter' designation, but I've always felt uncomfortable with it, since the tanks seem to be able to hold more in terms of volume, even if they were splash-baffled. Thanks for the clarification on this.

Edit: from KSP Wiki, it looks like the liquid fuel density is 5000 kg/ m^3.

Fuel density is 5000 kg/m^3? I know the wiki SAYS that, but that's ridiculous and makes no sense considering the entirety of the facts. It would imply that only a small amount of a fuel tank is actually used to store fuel, and the rest is just empty, wasted space.

As I said in my initial post, a Jumbo 64 is 1.25m in radius, and 7.5m long. This gives it a volume of 36.8 m^3. At the same time, we know that the Jumbo 64 has a fuel mass of 32000 kg. At a density of 5000 kg/m^3, you only need 32000 kg/ 5000 kg/m^3 = 6.4 m^3 to hold 32000 kg of fuel. So, if fuel is really 5000 kg/m^3, then the Jumbo 64 only uses 6.4/36.8*100 = 17.3% of its volume to hold fuel. The rest of it is just empty, wasted space. I don't believe that likely; the simplest explanation is just that liters are NOT, in fact, liters.

Either meters are not really meters, liters are not really liters, or full fuel tanks are almost entirely empty space. Liters not actually being liters only invalidates the numbers you see when you're fueling fuel tanks, as that's the only place that liters are ever counted. And hell, where does it actually SAY those are liters? I only see it in the wiki. No fuel tank descriptions say liters. However, meters are clearly intended to be meters. And if fuel density is really 5000 kg/m^3, then you NOT ONLY have to account for why fuel tanks are almost entirely empty space, but ALSO the "odd" coincidence that when you use a REALISTIC density for fuel, the mass of the fuel in the fuel tanks exactly matches what you would expect if the fuel tanks are, in fact, mostly filled with fuel like they SHOULD be.

Again, the simplest explanation I see is that liters are not liters. I think I'm just gonna call them "kerbal gallons" (kals) due to the fact that the value of 1 kal being close to the actual value of the gallon, and also due to the similarity that gallons are an inconvenient and confusing unit, too.

Edited September 8, 2013 by |Velocity|

[Captain Sierra]

There is a massive problem with your math. The jumbo 64 is 2.5 meters in diameter, not 1.25.

[Johnno]

There is a massive problem with your math. The jumbo 64 is 2.5 meters in diameter, not 1.25.

Diameter is not the same as radius.

[arq]

No, the volume math was correct. He used 1/2 the diameter, you're just misremembering the equation.

Not that it matters because at the end they're all just numbers, but my preference would be that a 'unit' of fuel be adjusted to correspond to one or ten liters. That would involve just changing the actual capacity numbers in all the tanks, and possibly the mass of the fuel.

I would just like to be able to talk about fuel in 'liters,' rather than 'units'. It just doesn't sound as awkward.

[Captain Sierra]

No, the volume math was correct. He used 1/2 the diameter, you're just misremembering the equation.

Not that it matters because at the end they're all just numbers, but my preference would be that a 'unit' of fuel be adjusted to correspond to one or ten liters. That would involve just changing the actual capacity numbers in all the tanks, and possibly the mass of the fuel.

I would just like to be able to talk about fuel in 'liters,' rather than 'units'. It just doesn't sound as awkward.

Oh, my bad. Yeah, I did forget that the equation calls for radius not diameter.

[Respawn]

The units could be anything. you don't know the state of the substance in the tank.

It could be pressurized or not, it could be cooled, or even heated.

Anyhow the units seem to correlate to mass not volume, so its not liters nor gallons.

You could fill a 1 liter tank with 1 liter of oxygen, or if you wanted you could fill the 1 liter tank with "860 liters" of oxygen,

but you would have to cool the oxygen down to a liquid state to achieve that.

At this point the oxygen would weigh 860 times more than it would in gaseous state but still only occupy a volume of 1 liter.

Whether the fuel is pressurized or not the "units" of fuel refer to the fuel mass not the apparent volume of the tanks,

even though it looks like they've tried to keep mass fairly consistent with volumetric size.

[capi3101]

Well...let's do some math. Almost every fuel tank in the game (exceptions are the Round-8 and Oscar- has a wet mass to dry mass ratio of 9:1 - the best example of course being the X200-16 tank (mass 9 tonnes, dry mass 1 tonne). That means that the fuel in that tank weighs eight metric tonnes, and a metric tonne is of course 1000 kg or 1,000,000 g. So, the fuel in that tank has a mass of 8,000,000 g. Now by definition, one gram equals one cubic centimeter equals one milliliter, so the volume of fuel in the tank is 8,000,000 milliliters.

With me so far? We know that the fuel in the X200-16 tank consists of 720 units of liquid fuel and 880 units of oxidizer; this is totally consistent with the 9:11 fuel to oxidizer ratio that the game utilizes. 1600 total units (720 + 880 = 1600) between the two = 8,000,000 milliliters, so therefore a single unit equals 5000 milliliters (8,000,000/1600 = 5000), or 5 liters.

There's your answer: one unit equals five liters.

You could also think of it as one unit equals 0.5 decaliters, though I don't know if that's a common unit of measure in practice in countries that practice the metric system (such as Mexico, where Squad is based) or not.

I suppose by extension, one unit has a mass of five kilograms and represents a volume of .005 cubic meters. Pretty sure that's consistent with the listed 5 kg/L density; I'll have to do more math on tht one.

[Respawn]

Yes capi3101 is more or less right.

1 Liquid fuel unit = 5kg

1 Oxidizer unit = 5kg

1 Monopropellant unit = 4kg

1 XenonGas unit = 0.1Kg

They are mass units not volume units,

but as suggested stock parts does seem to follow a certain volumetric density rule.

But they wouldn't have to.

[Kerbart]

Capi3101 comes out with the right number, although based on the wrong assumption (1 gram equals 1 cubic centimeter).

When you look at the wiki entry for the X200-16 tank it lists "800 units of fuel" and in the sidebar "360 L fuel, 440 L Oxidizer"

With a dry mass of 500 kg and a liquid mass of 4000 kg (the SI unit for mass is kg, not g) those 800 units have a mass of 4000 kg, or 5 kg/unit ("L" which is obviously not liters), as Respawn pointed out.

The external volume of this tank is À×¼D²×h = 3.1415 × .25 × 6.25 × .9375 = 4.6m³

Kerosene (which is basically what the Saturn 5 rockets used) has a mass of around 800 kg/m³ (depending on temperature) so you'd need 2.25m³ to store those 360 "L"

LOx (which I assume is used as oxidizer) has a mass of around 1140 kg/m³ so you'd need 1.93m³ to store those 440 "L"

That gets you a total volume of 4.18m³ used to store propellant which is remarkably accurate, as the fuel volume obviously will be less than the outside volume (just take a look at the inside of a Saturn 5 rocket, although those are of course a bit more advanced than the above ground pools that Rockomax uses for their X200 tanks)

[Starwaster]

Well...let's do some math. Almost every fuel tank in the game (exceptions are the Round-8 and Oscar- has a wet mass to dry mass ratio of 9:1 - the best example of course being the X200-16 tank (mass 9 tonnes, dry mass 1 tonne). That means that the fuel in that tank weighs eight metric tonnes, and a metric tonne is of course 1000 kg or 1,000,000 g. So, the fuel in that tank has a mass of 8,000,000 g. Now by definition, one gram equals one cubic centimeter equals one milliliter, so the volume of fuel in the tank is 8,000,000 milliliters.

With me so far? We know that the fuel in the X200-16 tank consists of 720 units of liquid fuel and 880 units of oxidizer; this is totally consistent with the 9:11 fuel to oxidizer ratio that the game utilizes. 1600 total units (720 + 880 = 1600) between the two = 8,000,000 milliliters, so therefore a single unit equals 5000 milliliters (8,000,000/1600 = 5000), or 5 liters.

There's your answer: one unit equals five liters.

You could also think of it as one unit equals 0.5 decaliters, though I don't know if that's a common unit of measure in practice in countries that practice the metric system (such as Mexico, where Squad is based) or not.

I suppose by extension, one unit has a mass of five kilograms and represents a volume of .005 cubic meters. Pretty sure that's consistent with the listed 5 kg/L density; I'll have to do more math on tht one.

More like 6.25 not 5.

160 units = 1 cubic meter.

So, a resource with a density of 0.00625 (water) = 1 metric ton = 1 cubic meter. (water's special that way)

[tavert]

Now by definition, one gram equals one cubic centimeter equals one milliliter, so the volume of fuel in the tank is 8,000,000 milliliters.

This is horrendously wrong. A gram is a unit of mass. Cubic centimeters and milliliters are units of volume. No definition will ever equate a unit of volume with a unit of mass. If you assume a constant density for some specific substance, then you have a ratio of proportionality between mass and volume.

The origin of referring to KSP fuel/oxidizer units as "liters" is previous versions of KSP where the right-click context menu for fuel tanks actually listed liters as the unit of fuel. But this was also before fuel and oxidizer started being counted separately.

Currently, the units from the resource bar are not well-defined. The so-called "density", or proportionality ratio between mass and "resource units" is well-known.

[Talisar]

I'm not certain where this originally was, but Greys did some math to figure out the amounts of various fuels to volume:

I was dealing with this recently and the basic issue is that units of resource are not liters; they're also not the same between resources.

Based on analyzing the volumes vs resources of a few stock parts I have determined that:

LF/Oxy = 173.913 units/m^3

Monopropellant = 129.87 units/m^3

Xenon = 4875 units/m^3

Battery = 1785.714 units/m^3 & 5.6 tons/m^3 (because electricity doesn't have weight*)

And Taniwha did a lot of math to help me get the capacities of my tanks in line with the stock parts. It's spread out quite a bit, but if you're interested you can go through the first several pages of my release thread to see the math discussions: http://forum.kerbalspaceprogram.com/showthread.php/30673-0-21-x-Spherical-Fuel-Tanks-Pack-%28Updated-09-04-13%29

Maybe it will help out a bit.

[capi3101]

To be honest, my answer was bothering me for most of the weekend...it is based on several assumptions, foremost that the density of the fuel was roughly equivalent to water (not a bad assumption necessarily as it turns out - kerosene has an average density of 0.8 g/cc and liquid oxygen is 1.141 g/cc; a 9:11 ratio would give a fuel mixture that's got a density of about .988 g/cc and water is 1 g/cc under standard conditions - learned that the first year of meteorology school at OU). One milliliter does equal one cubic centimeter by definition, that's a given - you can look that up under "cubic centimetre" at Wikipedia.

Let's test the validity of my math... okay, by definition, density equals mass per volume and we're dealing with the volume of a cylinder, which is pi*radius^2*height.

Forumlae here: rho = m/V, V=Àr^2h, thus rho = m/Àr^2h.

Solve for h: h*rho = m/Àr^2, h = m/Àr^2(rho)

Let's look for the heights of the X200-8 and FL-T800 tanks (both contain 800 units)

For the FL-T800:

h = 800u/À*(0.5m)^2*(1u/.005m^3) = 800u / (157.0796u/m) = 5.09 m

For the X200-32:

h = 800u/À*(1m)^2*(1u/.005m^3) = 800u/ (628.31 u/m) = 1.27 m

I know that's wrong...

Looking at the wiki this morning, I might've made a bad assumption just then with the radii. Let's try those "actual size" figures instead.

For the FL-T800:

h = 800u/À*(0.625m)^2*(1u/.005m^3) = 800u / (245.4369u/m) = 3.26 m

For the X200-32:

h = 800u/À*(1.25m)^2*(1u/.005m^3) = 800u/ (981.7477 u/m) = 0.81 m

Also wrong...

At this point I'd suggest the OP go with the information that's already been linked to this thread; so much for my valiant attempts at answering the question correctly...

@Kerbart: You do know you linked the entry for the X200-8, right? I see nothing wrong with your math, necessarily, but that may be a point of confusion for some. Might want to edit that post.

[tavert]

Yeah I was disputing your equating mass units with volume units, not the second part about cubic centimeters being equal to milliliters which is indeed correct based on the definition of a liter.

The densities of the planets and oceans in KSP have been established to be way out of line with reality, so I don't see any reason to think the densities of the fuels will match reality either. And any speculation about the internal structures of KSP parts are just that, speculation.

[wasmic]

No, the units are neither a measure of units or mass - for example, a tank that could hold more than 1000 xenon would only be able to hold around 5 LF and 5 Oxidizer. At the same time, one unit of XenonGas weighs less than one unit of LiquidFuel. Therefore, the volume that a "unit" corresponds to would be different depending on the thing being measured, screwing everything even more up.

[LameLefty]

Now by definition, one gram equals one cubic centimeter equals one milliliter, so the volume of fuel in the tank is 8,000,000 milliliters.

This is horrendously wrong. A gram is a unit of mass. Cubic centimeters and milliliters are units of volume. No definition will ever equate a unit of volume with a unit of mass.

When SI units were first defined way back when, the gram mass was indeed defined to be the equivalent of one cubic centimeter of (distilled) water. It's not defined that way NOW, but a couple hundred years ago, it was.

[tavert]

When SI units were first defined way back when, the gram mass was indeed defined to be the equivalent of one cubic centimeter of (distilled) water. It's not defined that way NOW, but a couple hundred years ago, it was.

Key: "of water." Not of other substances. Mass and volume are fundamentally different quantities. The origin of the kilogram's value was indeed based on fixing the density of water at a specific measurement point as the conversion factor, but measurement precision has gotten much better since then. Reasonably soon the kilogram will probably be redefined from its current artifact-based version to an "electronic kilogram" that is derived from taking the value of Planck's constant as a definition instead of a measured quantity (like how they redefined the meter to be derived from the speed of light 30 years ago).

[LameLefty]

Key: "of water." Not of other substances. Mass and volume are fundamentally different quantities.

I'm an engineer. I've known this since high school, way back in the days of stone knives and bearskins, shortly after the period of time when dinosaurs roamed the Earth.

Save the pedantry.

[tavert]

Considering the number of people here who are not engineers, and the statement you were quoting was the incorrect assertion that "by definition, one gram equals one cubic centimeter," pedantry is necessary to avoid misinformation. Just because something is trivial to you doesn't mean you should assume it is trivial to anyone else. Statements you consider obvious can be safely ignored, but that doesn't mean they're obvious to everyone else.

[LameLefty]

For the purpose of this discussion, especially with non-technical people, it's a distinction that makes no difference.

And in case others wish to consider the matter further, Wiki has a decent article, replete with extensive footnotes and references. Pay special attention to the original 1795 definition of the gram, then go back and re-read my post, in context.

http://en.wikipedia.org/wiki/Gram

And lastly, this thread serves as a good reminder to us all to keep Wheaton's Law in mind at all times:

http://knowyourmeme.com/memes/wheatons-law

[tavert]

Water vs anything else, "distinction that makes no difference"? Yeah no. Don't be wrong, or you will get corrected. Granted there's a difference between simple ignorance and making false statements in such a way that other people will think you know what you're talking about. Your post made no incorrect statements, so no problem there.

But technicalities matter in a technical discussion. Glossing over them as if they are irrelevant is not the right way to enlighten those who don't yet understand the subject.

Edited September 10, 2013 by tavert