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.

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.

 

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.

 

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.

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.

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:

Where is the final delta-v of your spacecraft, is the rocket engine’s exhaust velocity, and 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 (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 (~7.4), and to get three times that, 15 km/s, you need a mass ratio of (~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.

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.

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.