Slosh Baffles

So much time is spent discussing rocket engines that one of the most important parts of a rocket is glossed over: the propellant tanks. A significant amount of engineering goes into them, despite their simple appearance.

A rocket’s liquid propellant tank involves a number of considerations, such as propellant boil off, corrosion of the tank material, cryogenic insulation, slosh compensation, and pressurization. In space, without one g of gravity constantly pushing down, simply getting the propellant to the engine is a problem, since there is no force pushing the propellant into the rocket’s thrust chamber.

All of those issues must be dealt with using the least amount of mass, because of the rocket equation.

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NASA stopped painting the space shuttle’s external tank white after two launches and saved on roughly 272 kg of dry mass.

Indeed, propellant tanks tend to be one of the largest contributors of mass to a spacecraft. An oft made comparison is that rocket propellant tank walls tend to be proportionally thinner than aluminum cans in order to skimp on mass. In Children of a Dead Earth, armor tends to beat out propellant tanks in terms of mass, which immediately begs the question: why don’t we use a Monocoque design?

A Monocoque design builds the propellant tank into the outer skin of the spacecraft, rather than having separate propellant tanks at all, and it is used by a number of rockets in modern times, such as SpaceX’s Falcon 1. Thus, armor doubles as propellant tank as well.

 

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The Saturn V used a semi-monocoque design.

However, when a propellant tank suffers an external force such as that from a projectile, a water hammer, or a fluid shockwave forms within the tank, which can and usually will destroy the propellant tank. Thus, a monocoque propellant tank need not even be penetrated to be disabled. Enemies can simply hit the armor of the spacecraft hard enough to trigger a water hammer, and never even have to get close to penetrating the armor to render the spacecraft unable to move.

As a result, propellant tanks are kept separate from the armor skin. It costs more mass, but not significantly more, because it means the propellant tanks can be made much thinner.

Since Children of a Dead Earth takes place entirely in space without gravity, getting the propellant from the tanks into the rocket engine doesn’t happen automatically. There are a number of solutions to this issue, from ullage rockets (small solid fuel rockets designed to push the spacecraft forward, forcing the liquid propellant to the rear of the craft) to pressure diaphragms to piston expulsion devices.

 

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Designs for both various pressurized diaphragms and a pressurized piston.

 

In Children of a Dead Earth, surface tension devices, or systems which use the surface tension of the propellant to pull it towards the engine, in tandem with a turbopump injector are used. They do not need the additional pressurized gas that pressure diaphragms require, and the turbopump feed needs only slight pressurization of the tanks, yielding thinner walls.

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Several designs of turbopump fed bipropellant rockets. Nuclear Thermal Rocket designs are much simpler, requiring a simple propellant pump, and using an external power source rather than a turbine.

The lower pressure of the propellant tank also is valuable for avoiding water hammers for when the spacecraft undergoes rapid acceleration. Low pressure tanks also makes it easier to compensate for slosh effects with anti-slosh baffles within the tank.

On top of those considerations, cryogenic propellants may need to be insulated, although this is much less of a problem in space, as spacecrafts are not built in atmosphere, and so there is no convection of room temperature air always around the craft. Some propellants are corrosive to a lot of materials, and can only be stored in propellant tanks of certain materials. Finally, cryogenic propellants boil away at a slow but steady rate, and this too needs to be taken into account.

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Assembly of the first stage of the Saturn V.

A last note on tank mass. Spherical tanks once again save the most mass, however, cylinders fit much better in cylindrical spacecrafts (discussed in blog post Why Does it Look Like That? (Part 2)), so capsule shaped propellant tanks are used.

All in all, there are a lot of details to worry about, and they all add mass, which is very troublesome for any spacecraft designer. After all, recall the rocket equation:

\Delta v = v_e \ln \frac{m_0}{m_f}

Where \Delta v is the final delta-v of your spacecraft, v_e is the rocket engine’s exhaust velocity, and \frac{m_0}{m_f} is the mass ratio, or the wet mass divided by the dry mass. Recall that the wet mass is the total mass of the spacecraft including propellant, and the dry mass is the total mass except for the propellant.

In a previous blog post, Burn Rockets Burn, I went over the fact that the only drives with reasonable thrust for space combat are chemical propulsion and nuclear propulsion. In our case, combustion rockets or solid core nuclear thermal rockets. This limits your exhaust velocity to single digits of km/s. Also recall that while thrust scales up with the number of engines, exhaust velocity remains constant.

This means that the only way to squeeze out any more delta-v for your craft is by increasing your mass ratio. In particular, reducing your dry mass, or adding more and more propellant mass. Assuming you’ve reduced your dry mass as much as possible, getting more and more delta-v is simply a matter of adding enormous amounts of propellant tanks.

Since the delta-v scales with the logarithm of the mass ratio, consider this example. Suppose you have a spacecraft with an exhaust velocity of 5 km/s, either an excellent chemical rocket, or a middling nuclear thermal rocket. A mass ratio of e (Euler’s number, ~2.7) will give you 5 km/s of delta-v. To get twice that, 10 km/s, you need a mass ratio of e^2 (~7.4), and to get three times that, 15 km/s, you need a mass ratio of e^3 (~20).

To make things less abstract, remember that a mass ratio of 20 means your spacecraft is 19 parts propellant, 1 part actual spacecraft. At that point, your actual spacecraft will be ballooning in size, because even the densest propellants tend to be lower density than the actual alloys and ceramics of spacecraft components.

methane tanker.png
A methane tanker with a mass ratio of 29. Note that it is mostly just methane at this point (28 parts methane, 1 part spacecraft).

And how much delta-v do you need? Maneuvering in combat around a planet or high gravity moon, from what I’ve seen, requires around 5-10 km/s to remain effective in combat (for evading missiles, drones, and even the enemy fleet). Somewhat more is needed when planning interlunar transfers, and tens of km/s are needed for interplanetary traveling.

For anyone who has studied the rocket equation, this is all pretty elementary. However, there is one complication that appeared from the rocket equation which was not immediately apparent to me. Once you have a drive chosen, the exhaust velocity is absolute. Thus, to get more delta-v, you get a higher mass ratio, by adding more propellant.

But there is an ultimate limit to your mass ratio, and by extension, an ultimate limit to the delta-v of your spacecraft. Not only that, you can bump into that limit very quickly.

Most of my capital ships run Nuclear Thermal Rockets using Methane as a propellant (for reasons I’ll outline in later posts), which yields an exhaust velocity of about 6 km/s. I started making a tanker with the same engine to refuel my capital ship fleets, and I wanted them to have an enormously high delta-v in order to get just about anywhere. Yet, almost immediately, I started hitting a low delta-v ceiling, no matter how many propellant tanks I added.

This is because every propellant tank added has dry mass in addition to its propellant. Thus, each tank has it’s own separate mass ratio, and a spacecraft can never have a mass ratio that exceeds the mass ratio of its propellant tanks. This propellant tank mass ratio approaches very quickly, and it depends heavily on a number of different factors, primarily the propellant type, the tank material, and the aspect ratio of the tank.

Some numbers here. In game, I optimized Methane propellant tanks to yield a mass ratio of about 30, around 50 for Decane tanks, and several hundred for Water. Most propellants cap out at around 50. Given very exotic and expensive materials, this can be doubled or tripled, though this often runs into corrosion or insulation issues.

h2 tank.png
A hydrogen tank with a very high aspect ratio. High aspect ratios tend to yield better mass ratios. Despite this, hydrogen tanks tends to have abysmal mass ratio because of how low density hydrogen is. This particular tank has a mass ratio of 4.2.

So, given a Methane rocket with an exhaust velocity of 5 km/s, and an ultimate mass ratio of 25 from the propellant tanks, the most delta-v your spacecraft can ever conceivably have is about 16 km/s. Yikes! That spacecraft will never make any significant interplanetary journey unless there are copious fuel depots along the way.

This emphasizes just how critical propellant depots are in space travel, and especially in space warfare.

One final way to push these limits are through rocket staging, which involves discarding your propellant tanks after use. However, if your spacecraft is armored, this involves likely dumping off a lot of expensive armor as well. A better way to do this is to take a number of propellant tankers with you, and then scuttling them after you’ve drained them out.

In Children of a Dead Earth, this is the primary way to stage an interplanetary invasion. When there are no allied propellant depots along the way, one has to take a huge number of tankers along for the ride, and then simply scuttle them at various points along the way as they are depleted.

Whew! That’s all for propellant tanks! We didn’t even get to a comparison of propellants in this post. I’ll have to get to them in a later post, but for now, you have all the challenges involved with managing your propellant tanks in space warfare.

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17 thoughts on “Slosh Baffles

  1. Interesting points about tanks and their minimum mass ratio.
    How do mass ratio vary with tank scaling? Bigger tanks have a better volume/surface ratio, so if pressure and armour thickness don’t increase, we could naïvely assume that walls won’t become thicker, improving mass ratio. What of it in practice?

    Also, the main reason given for cylinder over sphere is cross-section, which is a military requirement. Do you have collateral d… I mean civilian designs? Depending on their role, they could use ion drives – either for station-keeping or if decade-long cruises aren’t a problem.

    About disposable tankers, I’m not sure to follow the logic. If you want disposable fuel reserves, why not directly use an stage tank? It will be ditched before combat, so there is no need to armour it.
    Conversely, a tanker could use its own engines to depart before combat, to be reused later – or at least its core, as it may have to drop its empty tanks along the way.

    For water, is such great mass ratio obtained by keeping it frozen? Wouldn’t that be advantageous for a warship by having ice itself act as structure/shield?

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    1. So, one would think that larger tanks with the same pressure would require thinner walls proportionally, and indeed, I thought so, too. As it turns out, the minimum wall thickness required for a constant pressure scales up exactly proportionally to volume, so scaling tanks up or down has no effect on the mass ratio.

      I have made a few civilian designs, but not a lot. If decade-long cruises are not an issue, ion drives are absolutely back on the table. Though I’m not sure spending several decades on a single spacecraft without stops is something a lot of civilians would be very keen on unless you’re doing something significant like colonizing a new world.

      Simply adding more staging tanks is an issue because the thrust begins to drop very drastically, so you need more nuclear thermal rockets in addition to each staging tank. You could have staging tanks with nuclear rockets attached, but the reactors will need extra crew to maintain them over yearlong journeys, so at that point you might as well go with a separate tanker.
      Trying to save these tankers requires saving up delta-v before ditching them, which exacerbates things further and likely will require even more tankers to plan an invasion. It’s doable, but I think simply draining the ships dry and then scuttling them is much cheaper.

      Water has such a great mass ratio because of it’s density. Ice is actually really bad as a structure/shield. It has a tensile strength 100 times less than steel, and is only about 8 times less dense. It’s low melting point also means that a very weak laser could melt through meters of it without breaking a sweat.

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      1. Interesting!
        Do you have something to calculate a rough price for the ships? It would heavily depend on resources and industry controlled by the shipbuilder, I guess, but I am wondering what the cost difference is between extra tankers to be reused and less, but expandable tankers.
        Also, I guess that the tankers themselves make for a rather poor missile in combat, but how hard are they to stop when aiming at civilian infrastructure?

        For decades-long travels, I was thinking about automated haulers, for example asteroid bulk resource movers.
        Also, do you have space station designs? I am curious about the challenges of attacking or defending them.

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        1. Price is something I’ll go into on my next post. As you said, it’s very fuzzy, and unlike everything else in the game, there are no hard and fast equations to govern it.

          The main issue with the cost I brought up is how much the delta-v will increase if you try to reuse the tankers, as high as double the delta-v to get back home or to finish the journey. That’s a huge amount of additional propellant needed (remember that 2x the delta-v is likely much higher than 2x the propellant since the scale is logarithmic).

          There are some space station designs in game, but it became rather apparent early on that they are extremely difficult to defend. Because they lack any significant thrust, they are easy to target with any sort of mass. If something in space can’t effectively dodge, a projectile’s range against it is limited only by accuracy and whether or not it can reach the target. Essentially any sort of high velocity, high mass projectile launched a long ways away is guaranteed a hit if the enemy can’t dodge, and if it’s massive enough, no amount of point defense will deal with it. As you pointed out, simply flinging a tanker at a station fits this bill.

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  2. Not specifically related to the article, but what are your thoughts on laser thermal propulsion?
    http://www.projectrho.com/public_html/rocket/enginelist.php#laserthermal

    I’m not formally educated on the subject myself, but if I understand this right, it’s got an effective exhaust velocity competitive with magnetoplasmadynamic thrusters, with more T/W, without having to carry a nuclear reactor and requisite radiators.
    The one caveat is that you need a suitably powered(and friendly!) laser within range of your intended burn.

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    1. Laser Thermal Propulsion is a way to combine the higher temperatures of nuclear electric with the pure power and lack of needed radiators of nuclear thermal. It’s nice on the surface, but that one caveat is a big one.

      Space is huge, and laser range falls off painfully fast, even with extremely low wavelength lasers, and enormous mirror sizes to bounce the beam to the target. An expensive array of mirrors in low orbit around a planet or moon with huge laser batteries on the ground is feasible, albeit expensive. Beyond low orbits, however, the cost of trying to manage an array of mirrors that close together all throughout space is prohibitive.

      So basically, in low orbits, laser thermal propulsion is excellent, beyond that it’s not very useful. This might be good for low orbit combats, but then again, it means the enemy now can knock out your engine simply by evading your ship and taking out one or two of your mirrors. Mirrors are very difficult to armor, and at the huge sizes you’d need them, they’d be sitting ducks.

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      1. That does seem to limit your burns to where your station happens to be. Drat.

        Could it be used as a way to transfer vessels between friendly bases quickly and cheaply? You use one station to set up a transfer trajectory, and the destination base brakes the vessel when it arrives
        Like a railway, sorta.

        Also, couldn’t the laser itself double as a weapon? The mirrors might be fragile, but they could be used to focus the laser on hostile attackers.

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        1. Yeah, a laser railway between friendly bases might be a viable option, though you’d need an additional engine for corrective burns throughout the journey. Assisted takeoff and landing with laser propulsion definitely seems reasonable though.

          Absolutely, the laser would be able to double as weapon. The main issue though is that the mirrors would have difficulty dodging. As alluded in an above reply, anything that can’t dodge in space can just have large masses (rocks/ship debris/tankers/etc) lobbed at it from long ways away and no amount of point defense will save it.

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          1. Are docking ports or other means of temporarily attaching two ships together a thing? You could have a separate laser thermal tug from your warship to ease logistics. And-to mesh with another commenter’s question about civilian ships-whoever owns the laser could rent out laser time and tugs out to boost civilian ships.

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  3. Sounds like we might have large fleets. Will we need to manage trajectories and burns for each vessel individually, or might there be tools to command multiple vessels as a unit?

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  4. You know, this is one of those problems where a complex mechanical solution might exist. Rather than making it possible to draw fuel from any tank at any time, you could build your spacecraft to have lighter tanks – basically ballons full of frozen methane. Robots, possibly remotely controlled by the crew if your setting does not have full autonomy, would clamber over the structure of the ship and grab methane balloons, hauling them back to the main fuel feeder.

    The main fuel feeder would be something like a cylinder with a piston on top. You stick the methane balloon inside (control of their shape could make the ballons all cylindrical in shape) and attach the fill port at the bottom of the balloon to the bottom of the cylinder.

    Heaters in the cylinder side heat up the balloon fabric and a ram pressed down to basically empty the now liquid methane into a fuel feed tank which uses another piston or pressure bladder.

    Advantage is that since a given set of engines doesn’t need very much fuel per hour compared to the fuel carried (you only burn 1/5 your total fuel at once) it’s a lighter solution.

    Technically you could expose the methane ice to space directly and coat it with something to reduce boiloff, burning the entire chunk at once.

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  5. Hmm. This delta-V is troubling. Fortunately, my hard-sci fi story takes place farther in the future where fusion torch drives, advanced carbon nanotube materials, and Alcubierre Drives are available. This will greatly decrease the mass ratio for my spacecraft.

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  6. Since you mention dropping armor when drop tanks, I have to ask if you can choose to have unarmored drop tanks? There is little reason to armor them for interplanetary travel when you are going to drop most of them in the first few days of travel. You might need some ships to look like a katamari ball to get enough delta v but not having to throw away a nuclear engine is worth a lot of space dollars.

    There are reasons you don’t want to use drop tanks instead of tankers but it looks like they would serve slightly different roles. Drop Tanks on the way out of a gravity well and tankers when you are inside one or doing a capture burn.

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    1. Unarmored drop tanks would work great (turning your ship into a large katamari ball), but they increase your delta-v while heavily reducing your acceleration (since thrust stays constant and F = ma). When your acceleration is reduced so much, at best your travel time across the system increases significantly at best, and at worst you become unable to take off of high gravity bodies.

      Adding extra engines is very necessary to keep your fleet’s acceleration reasonable, and so either you’ll need to strap a lot more engines to your external tanks or you just use separate tankers. In either case, discarding the engine becomes something you’ll need to do.

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