Reactor Statistics Computer

So, just what is that little red computer with the big tables trying to say?

A General Math Note

This computer has columns labeled dy/dx and d^2y/dx^2. If you're calculus-savvy, you're recognize these the first derivative and second derivative, respectively. If you're not, don't worry! This computer will do all the scary calculus math for you.

Whether or not you know calculus, though, you do need to know what those actually mean. The first and second derivatives describe how some quantity changes relative to another quantity, in this case to time. dy/dx describes the rate at which some quantity changes over time, e.g. how much pressure changes over time. d^2y/dx^2 describes how that rate changes over time, how much the change itself changes, e.g. how much the pressure changes change.

If a quantity's dy/dx is positive, it is said to be increasing over time, e.g. pressure is climbing. Similarly, if dy/dx is negative, the quantity is decreasing over time, e.g. pressure is dropping. Neither necessarily mean pressure is positive or negative; just that it's changing in a positive direction (increasing) or changing in a negative direction (decreasing).

If d^2y/dx^2 is positive, we say dy/dx is increasing over time, e.g. the rate at which the pressure is climbing/dropping is increasing. Similarly, if dy/dx is negative, we say dy/dx is decreasing over time, e.g. the rate at which the pressure is climbing/dropping is decreasing. Notice that neither necessarily tell us if dy/dx is negative or positive, just how much it changes.

Also, you may see some numbers written with an e, a positive or negative sign, and then another number afterwards, e.g. 4.572e+006. This e has nothing to do with the natural constant e; rather it's a calculator/computer's shorthand for scientific notation, short for "times ten with a positive/negative exponent of [number afterwards]". So, for instance, 4.572e+006 would also be 4.572 x 10^6, which would also be 4,572,000.

A Slightly Less General Thermodynamics Note

No doubt you've seen all the rows labelled "heat capacity" or "thermal energy" as well. Again, the computer will measure and calcuate all these qualities for you. The important thing is understanding why it's measuring and calcuating them in the first place. That means brace yourself for a thermodynamics lesson! But not too much; while this is stuff most people don't learn until college, it's introductory-level material, so it's not particularly formula or number-intensive.

Let's start tackling these big thermodynamics concepts SS13 uses with something small: atoms. Gases like oxygen, carbon dioxide, and, presumably, plasma are made up of loads of these tiny buggers, all zipping about at different speeds and directions. Some are moving incredibly fast, some are moving incredibly slow, most are in-between. We give the average velocity of all these particles a particular name, that is, temperature.

These particles can be used to perform certain tasks, namely increasing other particles' temperature. We call this process heat and the capability to do so heat energy or thermal energy. (It's a bit more involved than that, but this bit's not really simulated in SS13.)

Heat entails a transfer of thermal energy, (in fact, the thermodynamics defines temperature in terms of energy transfer) and there are multiple mechanisms for this transfer. In a thermo-electric generator, we're particularly concerned with conduction, that is, energy transfer through collisions. This is the part where our old pal Newton and his laws of momentum comes in and creates quite a fracas, but the geist of is that when two particles of different velocities collide, the higher-velocity particle loses some velocity while the lower-velocity one gains some. When this process occurs over and over amongst a huge number of particles, we get a temperature change. This process is how the combustion chamber and furnaces heat up the hot loop gases.

Now, we mathematically compute thermal energy in number of ways. SS13 (and by extension, the reactor statistics computer) defines thermal energy in terms of energy transfers computes it as theproduct of temperature and heat capacity. Heat capacity describes how a particular substance or set of particles receive or, more pertinently, transfer thermal energy, i.e. how they heat up or cool down. It depends on three factors:

Type of substance: Different substances take different amounts of thermal energy to experience a temperature change. We express this as a constant called specific heat. (In real life, it's amount of energy needed to cause a given temperature change in a given amount of substance, but SS13 considers these simple variables.)
Amount (i.e. concentration) of substance: Obviously, the more particles you have, the more collisions that occur, and thus the greater temperatue changes you can induce.
Change in substance's temperature: As you'd expect, the more thermal energy you have, the greater the temperature changes you can induce. Conversely, the more thermal energy you transfer, the more your own temperature will change.

Finally, we have pressure. Pressure is just the force of all those particles colliding with the container. When you increase their temperature, you increase both the frequency of these collisions and the force with which they collide with (and vice versa). When you decrease the size of the container, the volume, you do the same thing. Simple stuff.

Reactor

This page displays information about the thermo-electric generator (TEG). Much of it is the same information you'd see from checking the generator itself or the Power Checker PDA app. The Instanteous table shows measurements of various quantities right then, at the very moment. The Average table shows the average of the of all the measurements so far, including all the previous measurements, divided by number of measurements.

Just what is being measured and averaged? All these following familiar quantities:

Engine Output: Electricity output of the TEG, in watts.
Hot loop temperature (in): Temperature of the gas exiting the hot loop and going into the TEG, in Kelvins.
Hot loop temperature (out): Temperature of the gas entering the hot loop and going out from the TEG, in Kelvins.
Hot loop pressure (in): Pressure of the gas exiting the hot loop, going into the TEG, in kPa.
Hot loop pressure (out): Pressure of the gas entering the hot loop out of the TEG, in kPa.
Cold loop temperature (in): Temperature of the gas going from the cold loop into the TEG, in Kelvins.
Cold loop temperature (out): Temperature of the gas going out of the TEG into the cold loop, in Kelvins.
Cold loop pressure (in): Pressure of the gas going from the cold loop into the TEG, in kPa.
Cold loop pressure (out): Pressure of the gas going out of the TEG into the cold loop, in kPa.

Combustion Chamber

This page displays information about the tiles the map defines as combustion chamber, which, sanely, just includes the tiles where actual combustion can take place, rather than the walls or airlocks. The total tables display info about all the tiles in the combustion chamber, calculated as the sum of the measurements of a particular quantity for each tile of the chamber. The per tiles tables displays similar information, but it is calculated as an average of all those measurements. Since the amount of measurements is basically the same as the number of tiles, this is effectively average of a quantity per each tile.

As with the Reactor page, the Instanteous table shows various measurements of certain quantities right now, at the very moment, while Average table shows the average of the of all the measurements taken so far, including the previous measurements.

What does all that mean? Well, you could interpret all the combinations this way, using oxygen concentration as an example:

The Total oxygen concentration of the combustion chamber is the sum of all the measurements of oxygen concentration for each tile of combustion chamber. This is essentially, how much oxygen there is the entire chamber.
Oxygen concentration per tile would be the average of those measurements. This is also, essentially, how much oxygen there is in the entire chamber but represented as an average oxygen concentration per tile.
Instanteous...per tile shows average concentration of oxygen per tile of the combustion chamber, at the moment.
Instanteous...total shows the total concentration of oxygen for the whole combustion chamber, at the moment.
Average...per tile shows the average of those calculations of average oxygen concentration per tile , including all the ones from before. (Yes, it's an average of averages.)
Average...total shows the average of all those measurements of total concentration of oxygen.

The Chamber page measures and calculates averages just like the Reactor page, but it uses a completely different set of quantities:

Oxygen: Concentration of oxygen in the chamber, measured in moles
Plasma: Concentration of plasma, also measured in moles
Carbon dioxide: Concentration of carbon dioxide, measured in, you guessed it, moles.
Nitrogen: Concentration of nitrogen. Did you guess it would be in moles? Because it's in moles.
Temperature: Temperature of the gases in the burn chamber, as measured in Kelvins. This affects the how much plasma and oxygen will be consumed as the combustion goes on as well as how high the pressure is.
Fuel burnt: Amount of oxygen and plasma being burned, with rate of oxygen burning having higher representation. Not only does initial chamber temperature affect the amount of fuel being burned, but that amount will itself affect how much the temperature of the chamber changes.
Pressure: Pressure of the gases in the burn chamber. Pressure is calculated using the ideal gas law, so concentration and temperature of gases will affect the pressure.
Thermal energy: Energy of all the gases in the chamber. Similar to real life thermodynamics, this is calculated as temperature of all the gases times their overall heat capacity.
Heat capacity: Amount of heat all the gases in the chamber can hold. Also similar to real life thermodynamics, this is concentration of each gas times their specific heat. The difference in heat capacity of the gases before and after a plasma combustion reaction will affect how much the temperature of the gases in the chamber changes, and both heat capacity and thermal energy affect gas temperature.
- Relatively speaking, plasma has the highest specific heat of all the gases, while carbon dioxide's specific heat is distantly behind. Nitrogen and oxygen have the same specific heat, which is slightly behind that of carbon dioxide (just like real life!)
Molality: The concentration of all the oxygen, plasma, carbon dioxide, and nitrogen, as well as any possible trace gases. While the more chemistry-minded will know molality to be moles over kilograms, this is actually just moles of these gases.

Gas Loop

This page indicates various readings from six meters in the following locations in Engineering:

Cold loop radiator meter: Attached to the portion of the cold loop exposed to cold space.
Hot loop combustion meter: Attached to the part of the hot loop inside the combustion chamber
Hot loop outlet meter: Near the TEG, where the hot loop's gas exits the TEG.
Cold loop outlet meter: Also near the TEG, where the cold loop's gas comes out of the TEG.
Hot loop inlet meter: Near the TEG as well, where the hot loop's gas supply goes into the TEG.
Cold loop inlet meter: Once again near the TEG, where the gas in the cold loop enters the TEG.

Like the Reactor and Chamber pages, there are Instanteous tables, with the meter's readings right at the very moment, and Average tables, based on all the average of all the previous meter readings of a certain quantity.

It also features the exact same quantities as the Chamber page, but for the section of piping the meter is on rather than a whole room. Assuming nothing goes wrong, these meter readings should hopefully apply to the whole, but in any case:

Oxygen: Concentration of oxygen, measured in moles.
Plasma: Concentration of plasma, also measured in moles,
Carbon dioxide: Concentration of carbon dioxide, measured in, you guessed it, moles.
Nitrogen: Concentration of nitrogen. Did you guess it would be in moles? Because it's in moles.
Temperature: Temperature of the all the gases in the measured portion of piping, measured in Kelvins.
Fuel burnt: Amount of oxygen and plasma being burned. This should hopefully be zero.
Pressure: Pressure of all the gases in measured section of piping. Pressure is calculated using the ideal gas law, so concentration and temperature of gases will affect the pressure.
Thermal energy: Energy of all the gases in the portion of piping. Similar to real life thermodynamics, this is calculated as temperature of all the gases times their overall heat capacity.
Heat capacity: Amount of heat all the gases in the section of piping can hold. Also similar to real life thermodynamics, this is the concentration of each gas times their individual specific heat values.
- Relatively speaking, plasma has the highest specific heat of all the gases. Carbon dioxide's is distantly behind, and nitrogen and oxygen have the same specific heat, which is slightly behind that of carbon dioxide (just like real life!)
Molality: Concentration of all the oxygen, plasma, carbon dioxide, and nitrogen inside the piece of piping, as well as any possible trace gases, in our ever-present friend moles.

So what?

Here's an answer from the coder who made the patch for this computer, kremlin, taken from a thread discussing the merits of the long-held 66 O2/33 Plasma ratio:

hi,
the 2:1 ratio is not always ideal, it's too ~~rich~~ lean of a burn for most relevant engine states
there is a tool that will help you discover exactly what you are looking for, you can read about it here [this page]

i created it to answer exactly the kinds of questions you're asking
if you have any questions about it, don't hesitate to ask
secondly, be very careful at how much you read into one line of source code from a year ago. the way this thing works is not straightforward and very prone to misunderstandings and misconceptions. i can promise you, that even if you read all of the FEA source, you still would not have a clue what is going on in a hellburn

You can read the thread for the rest, but kremlin's post is clear: it's a tool for precisely assessing hellburn setups. It answers questions that the public release and periodic checks of the Engine Output Computer can't precisely answer. For example, how's this new O2/plasma mix affect the power output? Is it continually exponentially rising? Or is there a huge increase that plateaus later? Some combination of both? How does it compare to previous setups? And, perhaps most importantly, did this setup produce more/less power because of the new mix or some other factor perhaps yet to be even considered?

It answers questions about failed hellburns too. For example, is your power output plateauing after some point? Perhaps your setup is losing so much gas that the combustion chamber can't power through it. Or, maybe the pipes are fine, but your combustion chamber is simply too weak and not producing enough heat for good results. Heck, it could just be that it's simply burning through plasma and oxygen too quickly. Hellburns can splutter out for plenty of reasons. This computer can help you ascertain which one.