Why does it look like that? (Part 3)

Previously, we examined why lasers and exhaust look they way they do, in addition to spacecrafts’ shapes. Now we’ll look more closely at one specific part of spacecrafts: the heat radiators.

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Fleet Carrier cutaway, also showing all radiators glowing at peak temperature.

Heat radiators are necessary for spacecrafts in order to cool their internal systems. Nuclear reactors produce tremendous amounts of waste heat, and other subsystems produce smaller yet substantial amounts as well. Nuclear-enabled naval ships on Earth can cool their reactors via convection since they are sitting in an enormous bath of coolant already: the ocean. Aircraft and ground craft also have the air to use as coolant to constantly soak away heat.

No such solution exists in space. The lack of any sort of fluid medium in space prevents convective cooling, and there exists no solid material in space to support conductive cooling either. This leaves the one remaining method of cooling: radiation. All materials always radiate photons via Blackbody Radiation, and the amount and kind they do depends on the temperature: hotter materials emit much more energy.

This is where heat radiators come in. These are already in use on the ISS.

Heat radiators on the ISS on the right and bottom. Solar panels on the left.

They are flat panels with tiny pipes running through their entirety, pumping in scalding hot coolant through one side, and cooled off coolant out the other side. In this way, the radiators form a closed coolant loop with the system that needs cooling. Each set of radiators cools a different system, which is also why some radiators glow orange hot, some glow yellow hot, and some don’t even glow at all (well, they’re actually glowing in infrared, too cold for the visible spectrum).

Unfortunately, you can’t simply dump all of your systems’ coolant loops into a single loop and pipe them through a single enormous radiator because of the second law of thermodynamics. Closed thermodynamic systems will maximize entropy over time. Put another way, heat always flows from hot to cold.

This means that if you have a nuclear reactor running at 1000 K (degrees Kelvin) with its radiators dumping out heat at 1000 K, and you hook it up to a crew module running at 293 K, you have a problem. The crew module and nuclear reactor coolant loop will combine to yield a temperature partway between the two. This will still cool off the nuclear reactor, but then it heats up the crew module until the people inside are cooked.

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Module design of a radiator. Silicon Carbide ceramic core with Stainless Steel finish.

Why are radiators shaped like that? Heat emitted is directly proportional to surface area, so flat plates are the most mass-efficient way to radiate heat: maximum surface area, minimum volume. The jagged shape is to allow them to be retracted inwards to temporarily reduce heat signature (if enemy missiles are homing on you) or to protect them from damage.

Certain other designs of radiators exist, but many of them have issues. Liquid droplet radiators use a liquid pumped between a sprayer and a collector. The liquid allows a much higher temperature since the boiling point of the material is the limiting temperature instead of the melting point for solid radiators. Problem with this is that temperature is by far not the limiting factor of radiators. Silicon Carbide and other similar refractory ceramics can be heated to excess of 3000 K without melting. Even more exotic materials, like Hafnium Carbide, can exceed 4000 K (For comparison, the Sun’s surface is 5778 K) without melting! Their material properties are weaker at that temperature, but they remain still usable as radiators, and as long as they are never dropped below a certain temperature, they will never crack from thermal expansion stress. For reasons I’ll outline below, the internal systems will never emit coolant hot enough to take advantage of these refractory materials’ high melting points.

Another kind of liquid radiator, the Belt Radiator.

The radiators can never be hotter than the system they cool due to the laws of thermodynamics. However, the nuclear reactors in game can reach up to 3000 K, yet the radiators rarely ever exceed half that. In fact, for one of the reactors used for power production only in game, the reactor core never exceeds 1688 K and the radiators radiate at 1200 K. This reactor’s design is shown below.

13 MW electric solid core nuclear reactor.

Why are the temperatures so low when the materials used can withstand temperatures twice as high? Two things: the machinery between the reactor core and the radiators all needs to be able to withstand this heat, and the system works best when the temperature drops.

The reactor uses a thermocouple to convert the heat gradient from the reactor into power (note that a turbine-powered system would have somewhat similar limitations). The thermocouple first must withstand the high temperatures. Thermocouples require materials with high Seebeck Coefficients, and these materials tend to have low melting points. On top of that, the high temperature difference involves very significant thermal expansion stress, which is also not something these materials are good at withstanding.

Secondly, thermocouples are most efficient when the temperature drops significantly across them. This yields an interesting optimization problem. If the temperature drop from reactor to thermocouple is high, then the temperature drop from the radiators to space must be low, and the reverse is true. Remember that radiators perform best when their temperature is high.

This means the more efficient the reactor is at producing power, the harder it is to cool the system. On the other hand, a low efficiency reactor is very good at cooling itself. This problem yields two different valuable qualities that are inversely proportional to each other, and no local maxima can be found for both simultaneously.

In the end, for the above system, the somewhat reasonable point for both properties was at 1688 K for the reactor and 1200 K for the radiators.

Color temperature of Blackbody radiators.

That 1200 K temperature is why the largest radiators on spacecrafts glow orange. In fact, you estimate the temperature of radiators by their color, and from that you could estimate their purpose.

What about inter-reflection? Inter-reflection of radiators is a problem, since the heat from one radiator can be re-absorbed into another. This is exacerbated by Kirchhoff’s Law of Thermal Radiation, which states that the emissivity and absorptivity of a material is identical for any given wavelength of light.

Tail end of a spacecraft, showing how radiators will re-absorb each other’s heat radiated to some degree.

Blackbody radiation emits not simply perpendicular to the emitting surface, but in a full hemisphere of directions. Note that the intensity does fall off with the cosine of the angle from the perpendicular, however, so emission is most intense perpendicular to the radiator, and it falls to zero directly parallel to the surface. This does mean that these radiators will suffer inter-reflection, which will reduce their total efficiency, but they still will do the job, and can still be placed next to each other at narrow angles to each other.

Finally, can these radiators be armored? The answer is yes, contrary to what other sources may claim. Radiators are simply panels with material with tubes hollowed out in them to pass coolant through. One can simply increase the panel thickness beyond the tubes to add monolithic armor, and the refractory nature of the radiator materials means they will remain very strong even at orange-hot temperatures.

But, thicker monolithic plating reduces the efficiency of the radiators, because it will negatively impact the Heat Transfer Coefficient of the convection-radiation system. Thus, this yields yet another optimization problem, with radiator protection being inversely proportional to radiator efficiency. One will generally find that the added mass and poorer efficiency is often a fair trade for radiators that can actually withstand a serious beating.

That’s all for radiators! Next time, we’ll look into moment-to-moment space combat itself.

Why Does it Look Like That? (Part 2)

We’ve looked at lasers and engine exhaust, now let’s take a look at the spacecrafts themselves. They look something like cylinders with glowing prongs on the ends. Soft science fiction would have you believe spacecrafts would like anything from fighter jets to battle ships to strange, blocky constructs. Taking inspiration from NASA or SpaceX, one might assume future spacecrafts would simply look like rockets. So why do they look like they do in game?

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Something to note: All spacecrafts in game are spaceflight-enabled only, and are not designed for in-atmosphere operations, because the game takes place entirely in space. Atmosphere-enabled spacecrafts would look closer to modern fighter jets or to the space shuttle.

So, why is the shape a tapered cylinder? This spacecraft is a collection of internal modules (crew modules, propellant tanks, powerplants, radiation shields) wrapped in armor, with some external modules (heat radiators, rocket engines, and gun turrets). From the cutaway, you can clearly see the internal modules.

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Due to the rocket equation, mass is a premium on spacecrafts, as having heavy spacecrafts exponentially increases the amount of propellant needed to get your spacecraft around the solar system. Thus, everything needs to be as low density and light as possible.

So what exactly makes a spacecraft massive? Here’s a sample mass pie chart pulled from ship design of the above craft:

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Aside from propellant, armor is by far the heaviest part of the spacecraft. This immediately implies one thing: Armor must be a convex hull to save on mass. Concave shapes always have greater surface area than a comparable convex shape, and thus will always be heavier. The more concave the shape is, the more massive the armor will be.

If armor must be convex, then the shape of the spacecraft must likely be a geometric primitive: a cone, a cylinder, a tetrahedron, a sphere, a prism, a cube, and so on. (Maybe The Borg were on to something…)

The ideal shape, the one that has the greatest volume with the lowest surface area, is a sphere. But there are numerous problems with a sphere.

The other significant consideration governing spacecraft design is cross sectional area. In combat, the cross section of a spacecraft is the primary factor which determines the range of enemy projectile weaponry. A smaller cross section yields a harder target to hit, and requires the enemy to get closer to be able to hit it. Spheres are awful in that regard. Their cross section is a giant circle, easy to hit, easy to destroy, just aim for the center.

Additionally, the nuclear powerplants and nuclear thermal rockets emit tremendous amounts of radiations. The crew modules need to be both far away from these systems and/or heavily shielded against them. A sphere is a poor shape for both of these things.

Finally, it’s a lot harder to pack things into a sphere. Packing things into a cylinder is much easier, and packing them into a cube is easiest. With a sphere, you end up with a lot of unused space at the edges.

This leads us to the next shape, the cylinder. A cylinder is second to the sphere in terms of greatest volume to surface area ratio. Cylinders, if made long and thin, can have an extremely small cross section for their volume, making them very hard to hit. Additionally, they naturally provide distance between the powerplants and the crew modules, because of their length, lessening the need for radiation shielding. Modules, such as propellant tanks, pack very nicely into this shape, and waste little space in this way. An additional benefit of the cylinder is that it can be rolled very quickly to bring a broadside of weapons to bear.

Next, why the taper? Why not a simple cylinder? Sloped Armor is a way to drastically increase the effectiveness of a simple monolithic plate of armor. A plate of armor angled at 45 degrees reduces penetration by approximately cos(45 degrees), or about 29%, no small benefit!

A gradual taper from the start of the cylinder to the end takes advantage of sloped armor. Projectile weapons attacking from the front as well as from the side will similarly be reduced in effectiveness by this slope.

Thus, there you have the reasons behind the shape of combat enabled spacecraft. More on the heat radiators later.

Why does it look like that? (Part 1)

Children of a Dead Earth never compromises scientific accuracy for anything, especially not visuals. This leads to a lot of counter-intuitive visual effects, so this is a page explaining some of them.

The first thing you may wonder is why lasers appear to be visible and slow moving in the game, since they obviously are not in real life.carrier taking fire4.png

Those are not lasers, not the orange beams, not the red beams, not the purple ones! Those are all pyrotechnic tracers on projectile weapons. Tracer rounds are used to correct accuracy of bullets, and the differing colors are different pyrotechnic colorants (which all use real world emission spectra data to approximate their real life color). Different colors are used between different weapons to help targeting software distinguish between them.

This is an actual laser in game:laser hit.pngThe violet flash up high is a ship tens of kilometers away firing a violet laser, and the violet flash on the ship with ejected glowing matter is the laser impact. The actual beam is invisible, and all you can see is the firing location, and the impact location. The firing location is visible due to diffraction. When the laser is not in the visible range of light, all that you will see is the ejected matter, and the subsequent red or orange glow of melted armor.

Next up, why does engine exhaust look like that? I’ve seen SpaceX’s rockets launch, and their exhaust looks nothing like that.engines.png

First, the shape. One usually finds rocket exhaust to appear as curving away from the nozzle, possibly with bright shock diamonds. As a rocket gets higher in altitude, the curvature lessens, because the air pressure lessens. In space, with no atmosphere, the curvature vanishes entirely, and the exhaust plume expands outward linearly.

The angle of expansion is dependent upon two things: the exhaust velocity of the rocket itself, and the temperature of the plume at nozzle exit. The temperature is important because it directly governs the outward velocity of the plume: hotter temperatures means the gas expands faster. A plume which expands at the same speed as the rocket’s exhaust velocity will have a 45 degree angle of expansion. As you can see in the above image, the angle is less than that, so the exhaust velocity must be greater than the expansion velocity.

Second, why is it transparent rather than a bright orange or white plume? In atmosphere, the air pressure compresses the exhaust as it tries to expand, which causes it to curve back in on itself and form shock diamonds. As a result, the temperature of the gas remains hot, hot enough to keep emitting tremendous amounts of light. In space, the exhaust gas expands unrestricted, and the temperature drops immediately as soon as the exhaust leaves the nozzle. This is simple gas laws: in an unrestricted vacuum, a gas will expand in volume and reduce in temperature as the kinetic collisions between the molecules lower rapidly.

Finally, what about the shimmering effect? Is that supposed to happen in a vacuum? It does, whenever the gas’s index of refraction differs from that of the medium it is in (in this case, vacuum, which has an index of refraction of 1). In the above image, the exhaust is dissociated methane, and the carbon expelled does have a refractive index different enough from vacuum in the visible range. However, you will find that other engines, such as rockets which have only pure hydrogen in their exhaust plumes, will not have this shimmering effect, since hydrogen has an index of refraction very close to 1 at visible ranges.

That’s all for now, more to follow!