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Most Efficient Mass
(For USI-LS version 0.5.0)
Do you need a recycler? What about that greenhouse? Is it better to take one big crate of Supplies or several MiniPaks? Recyclers, converters, and containers all add mass, so is it always worth it?
Well, it depends. The 'best' combination of life support equipment changes with the length of the mission, the number of Kerbals you take to complete that mission, and your own preferences for safety margins. On that note, none of the duration values amounts below include the 15 day grace period Kerbals get for remaining unsupplied, so if something is listed as good for 28 days of life support you can actually get by for 43 days. In practice, you may want to ignore that to leave a buffer for a bad transfer, or you may want to count on that 15 days for a crew of 5 since it reduces your required life support load by 75 Kerbal-days.
Storage:
The MiniPaks and inline life support tanks all have a dry mass of their max Supplies * .0002. In other words, their wet/dry mass ratios are all the same, so full tanks are all equally efficient at storing Supplies. For example, nine 1.25m tanks (500 Supplies each) are equivalent to one 2.5m tank (4,500 Supplies). If the mission requires 5,250 Supplies, it is best to bring one 2.5m tank (4,500 Supplies), one 1.25m tank (500 Supplies) and three MiniPaks (3 * 100 = 300 Supplies), for a total of 4,500 + 500 + 300 = 5,300 Supplies. It is certainly possible to bring one 2.5m tank and two 1.25m tanks for a total of 5,500 Supplies, but that wastes mass: either you end up hauling far more Supplies than you need, or, if you partially fill one of the tanks, you waste mass on empty tankage.
There may be cases where it is desirable to take multiple smaller tanks rather than one large tank for the same amount of Supplies; the major advantage to this is the ability to place those tanks on different parts of a vessel. For example, suppose you are conducting a mission that, on the whole, requires 4,300 Supplies but includes a landing operation that will require 100 Supplies. A lander may benefit from a MiniPak but suffer from overloading (and certainly waste fuel) if you try to make it carry a 2.5m tank solely because you can fit all of the mission's Supplies into one. The better option is to put a 2.5m tank on the orbiter and use it to top off the lander's MiniPak before starting the surface operation. If the mass is critical, you always have the option of emptying the MiniPak in the VAB--just remember to re-fill it from the main tank before you begin the surface operation.
The inline containers and all of the converters have Mulch storage so you don't need to worry about adding more; the main reason to add dedicated Mulch storage (there's a MiniPak for it) would be for cases where you want to save Mulch for reprocessing but do not wish to place converters on every vessel. For example, you may decide that a Jool orbital station that has several different attached landers does not require full life support conversion on each lander, but the mission duration for each of those landers is long enough that you do wish to retain your Mulch in order to get the most use out of the main station's converters and Fertilizer.
Consumption:
By default, Kerbals use 10.8 Supplies per day to produce 10.8 Mulch. With recyclers, Kerbals use less--how much less depends on the type and number of recyclers. When using converters, one unit of Fertilizer eventually turns ten units of Mulch into eleven units of Supplies. It won't do this at one time, but rather the result is that one unit of Supplies can be consumed and converted back eleven times for each unit of Fertilizer used. When calculating the number of Kerbals a converter can sustain, you must figure out the total consumption per day--after recyclers--and then compare this value to the output of Supplies per day for your converters.
Recycling:
Recyclers reduce consumption by a set amount in exchange for ElectricCharge: no other input is required. For this reason, recyclers are the go-to first choice to reduce the life-support requirements for a mission. For example, the RT-5000 Inline Recycler will reduce Supplies consumption by 79% for three Kerbals, so the mission for three that carries this recycler will require 21% of the Supplies that a mission without the recycler will require. The rationale is that a recycler uses energy to reclaim various useful components from Mulch--things such as water, residual oxygen, and so forth--so that the net effect is reduced consumption. Some processes are more efficient than others, which explains the differences in recyclers, but since Supplies and Mulch are abstractions and not broken down into individual components, it makes sense and saves processing time to take recycling as an abstraction, as well: rather than simulate every part of the reclamation, recyclers provide the net effect of reduced consumption.
Conversion:
Converters (sometimes also called 'greenhouses') restore Mulch to Supplies with the addition of ElectricCharge and Fertilizer. The process is essentially that for every ten units of Mulch, the converter adds one unit of Fertilizer and returns eleven units of Supplies. Each converter comes with a small amount of storage for Supplies, Mulch, and Fertilizer. The conversion process is exactly the same across the three converters that ship with USI-LS--meaning that you get the same amount of Supplies from a given amount of Mulch and Fertilizer. The larger converters do save mass over multiple smaller converters of equivalent total capacity, but the main difference between converters lies in the rate of conversion: the larger converters turn Mulch back into Supplies faster than the smaller converters. This is important because if you forget to provide enough converters, your Kerbals will consume Supplies faster than you can replace them.
It is also important to note that you can convert quickly enough to keep up with Kerbal consumption but still build up a store of Mulch: if your Supplies storage is full, converters stop converting (they won't throw extra Supplies out the airlock), but your Kerbals are always converting Supplies back into Mulch, so Mulch will build up at the same rate that Fertilizer is consumed; i.e., very slowly. Keep in mind that Kerbals will throw extra Mulch out the airlock, so if you want to be able to convert all of it, you'll need to plan accordingly and take extra tankage for the Supplies produced.
One Kerbal needing life support for 12 days or fewer may as well just haul Supplies. 10.8 Supplies per day for 12 days is 129.6 Supplies (.1296 tonnes) which fits in two MiniPaks (.02 tonnes each) for a total mass of .1696 tonnes.
One Kerbal needing life support for 13 days to 67 days should use the smaller recycler. The RT-500 Recycling Module has a mass of .1 tonnes, an efficiency of 60%, and supports one Kerbal. While using it, the Kerbal's Supplies consumption drops to 4.32 Supplies per day.
On extremely long missions, the better efficiency of the larger recycler (79%) eventually overcomes its vastly increased mass (3.75 tonnes)--not to mention the complete waste of two of the Kerbals out of its three-Kerbal rating--but long before the mission reaches this point, it makes sense to add converters.
A small converter (Nom-O-Matic 5000, .154 tonnes), which comes with space for with 50 units of Supplies (.05 tonnes) and 50 units of Fertilizer (also .05 tonnes), has a total mass of .254 tonnes and if filled, it will cover a recycling Kerbal for 138 days--except for one small problem: the small converter can only produce 2.8512 Supplies per day and the Kerbal, even with the RT-500 recycler, consumes 4.32. A net consumption of about 1.47 Supplies per day is very low but it is still consumption, which means that you will run out. The converter will delay the end, but at the given rate the Kerbal will run out of Supplies after 34 days. This may be acceptable--for example, on a mission to Minmus--in which case you can reduce mass somewhat by reducing the load of Fertilizer to 8.82 units (a 34-day supply), but it will not do for a longer-term mission.
Two small converters (Nom-O-Matic 5000, .308 tonnes) with 4.32 units of Supplies (.00432 tonnes) and 100 units of Fertilizer (.1 tonnes) have a mass of .41232 tonnes and will cover the Kerbal for 255 days. Note that we bring only one day's worth of Supplies this time; it's not necessary to bring more than one day's worth when running a converter at a surplus. Instead, we use the one-day supply as a catalyst (to generate Mulch) and let the converters take it from there. Each 100 units (one MiniPak) of Fertilizer adds approximately 254 days to the Kerbal's maximum mission time (that one day's worth of Supplies makes up the 255th day above); if you add a MiniPak of Fertilizer (100 units) to the aforementioned load, your Kerbal can eat for over a year in space.
The mass-saving benefits of taking Fertilizer over Supplies cannot be overstated: if you send a mission with converters, a recycler, and a single 3.75m Fertilizer tank with 15,000 Fertilizer, it would extend the mission time by over 90 years for an extra mass of only 18.5 tonnes (3.5 for the tank and 15 for the Fertilizer). Contrariwise, sending a 3.75m Supplies tank would extend the mission by only eight years for the same total mass.
Two Kerbals needing life support may, with one exception, just as well consider recyclers to be essential mission equipment rather than simply haul Supplies. For missions shorter than 15 days it is not technically necessary to bring Supplies at all; as before, the recyclers offset their own mass penalty at 13 days, and for missions longer than 15 days, recyclers always provide the most mass-efficient option. 2 Kerbals use 21.6 Supplies per day, so over the course of 15 days, the minimum mass needed would be .324 tonnes for 324 Supplies and another .06 tonnes for the tankage (3 MiniPaks), for a total mass of .386 tonnes. With 2 RT-500 recyclers, 2 Kerbals use 8.64 Supplies per day, so over the course of 15 days, the minimum mass needed would be .1296 tonnes for 129.6 Supplies, .2 tonnes for the recyclers, and .04 tonnes for the tankage, for a total mass of .3696 tonnes, or .0164 tonnes less.
The only exception, and indeed only sensible reason to bring the Supplies instead of the recyclers would be offset the need for electrical generation to run the recyclers: it is conceivable that missions this short are running in early career when a space program may not have large solar panels or other reliable electrical generators available, in which case it is advisable to bring batteries to cover the Kerbals' direct ElectricCharge requirements and Supplies, which need no electricity to be consumed. Batteries are heavy but are certainly more mass-efficient than solar panels that you don't have yet.
Two Kerbals using two RT-500 recyclers require four Nom-O-Matic 5000 converters to produce Supplies in excess of their consumption. There are use cases for three converters instead of four: since these two Kerbals consume 8.64 Supplies per day and three converters produce 8.5536 Supplies per day, this reduces net consumption to .0864 Supplies per day. Because this is extremely close to net zero consumption, this kind of arrangement makes a lot of sense provided that the mission will be shorter than the maximum amount of time these converters can run. If these converters are packed with Fertilizer (150 units total) and bring a starting amount of 8.64 Supplies, they will last two Kerbals for 190 days before the Supplies run out. If we fill the on-board Supplies tanks, we can extend that time to 206 days. Because the net consumption is so low, this figure is very close to the theoretical maximum operating time of 208 days.
Such an arrangement is fine for orbital stations that are not constantly occupied: just leave Mulch there and let the converters run while the Kerbals go home. Alternatively, you can keep the station full of Fertilizer and send an occasional MiniPak of Supplies to offset the slight deficit: however, after the eighth such run, it is more mass-efficient to have a fourth converter. However, there is much to be said for using a three-converter arrangement for one-time or shorter-duration missions: it works for almost any mission in Kerbin's sphere of influence, and may even be enough for an asteroid capture mission--though that may push the limits of what you can expect.
With four converters and two recyclers, the savings in Fertilizer offsets the mass penalty over using recyclers alone at 45 days. There is no period where it is better to use converters and no recyclers; in order to keep up with consumption, it becomes necessary to use the big inline Nom-O-Matic 25000-I, but that converter masses at 1.52 tonnes. This is .02 tonnes better than ten of the smallest converters, but this arrangement is still a victim both of its own mass penalty and its high consumption; when compared to a converter-recycler combination, it starts behind the mass efficiency of the fewer needed converters and never catches up to the consumption efficiency of the recyclers.
It is also informative to look at the possibility of sending the RT-5000 recycler on a two-Kerbal mission even though the RT-5000 is rated for three Kerbals. The RT-5000 saves the mass of the two RT-500 recyclers (.2 tonnes total) but of course it is more massive (3.75 tonnes), so the net effect is a mass gain of 3.55 tonnes. On the other hand, the RT-5000 has a rating of 79% versus the RT-500's 60%. This means that the RT-5000 is the better choice on those missions where the 19% of Supplies savings equal more than the 3.55 tonnes of extra mass. This is equivalent to 2,950 Supplies and necessary tankage, which would be six 1.25m tanks. 21% default consumption (from the 79% efficient recycler) means that two Kerbals consume 4.536 Supplies per day, so to even begin to be worthwhile, this mission must take longer than 650 days ... except that we have not yet considered converters.
Two converters are needed to keep up with these Kerbals' consumption; they mass .308 tonnes. They each carry 100 Fertilizer for an additional mass of .2 tonnes. The remaining mass difference is taken up by five 1.25m tanks and one MiniPak carrying 2,522 Fertilizer, for a grand total of 2,722 Fertilizer. 2,722 Fertilizer can become 29,942 Supplies which can supply these Kerbals for 6,600 days, or roughly 15.5 years. Unless planning an absurdly long-term mission, it simply does not make sense, mass-wise, to bother with the big recycler for only two Kerbals.
For three Kerbals, we have reached the point where we can make use of the RT-5000 recycler's full capacity. However, the same concerns exist here as for the two-Kerbal case: the gains in recycling efficiency simply do not match the mass penalties of taking three RT-500 recyclers for most missions, and Nom-O-Matic converters only exacerbate that issue by extending life support too efficiently for the recycler to catch up quickly. On the other hand, when sending many Kerbals on a large expedition or a deep space mission, the RT-5000 can make up for that penalty: it can do this by raising the recycling efficiency cap.
Multiple recyclers work together: for example, on a four-Kerbal mission that takes both an RT-500 and an RT-5000, the RT-5000 reduces consumption by 79% for three Kerbals and the RT-500 reduces consumption by 60% for one. USI-LS does not assume that individual Kerbals are assigned to specific recyclers or anything like that, so the net effect is that the two recyclers combine their efforts to reduce consumption by a total of 74.25%. If you add another RT-500, even though the total crew rating is one more than crew present, the extra recycler is not wasted. Each additional RT-500 reduces vessel-wide consumption of Supplies by 6.48 per day (equivalent to 60% for one Kerbal) until the total recycling reaches the rate of the best recycler running. Mathematically, the extra recycler ought to increase the rate to 84.25%, but because no recycler can reduce consumption past the highest-rated recycler on the vessel and the highest-rated recycler in this case is 79%, that is the maximum. If, for example, only RT-500 recyclers were taken on this mission, one could bring one thousand of them and never have better than 60% recycling. On the other hand, you only need one best recycler; for almost all purposes RT-500 recyclers, with their tiny mass but still good efficiency, will do the best job of making up the difference.
In truth, the RT-500 recyclers have such a good mass ratio that they are the best choice for most missions anyway. Does this mean that the RT-5000 is useless? Not at all: with a longer mission or a larger crew, the RT-5000 will win out eventually because 79% recycling is greater than 60% recycling. With converters, it takes a lot longer, but eventually, the RT-5000 becomes the all-round best choice for a three-Kerbal mission. It happens on day 4309.
To put things in perspective, it takes 37.5 RT-500 recyclers to equal the mass of a single RT-5000; put together, this is enough to provide 79% recycling to a crew of 31 Kerbals. That is well past the point of needing to seriously consider MKS or some other base-building mod that provides larger and more efficient recyclers and converters.
In summation, for missions of three or more Kerbals, you will almost always want to take RT-500 recyclers, either on their own or to supplement a single RT-5000 (or another high-efficiency recycler), and the mass of the RT-500 is so low that you'll almost always want to max out your recycling before you begin adding converters. You will want the converters, of course, but there is little point in using them with anything less than maximum recycling.
A final note: the Mobile Processing Lab carries a four-Kerbal, 50% recycler. It also has a mass of 3.5 tonnes: what this means is that you can get better recycling using four RT-500 recyclers and for 3.1 tonnes of mass savings. Therefore, the only sensible reason to bother with the MPL recycler is because you're taking a lab anyway for scientific research; otherwise, it simply isn't worth the trouble.
How did we find that information? How can you figure it out for parts other than the parts included in USI-LS?
First, we need to define terms:
- D is the mission length, in days.
- R is the rate of consumption, in
Suppliesper day. - M is the mass of static parts, such as a recycler or converter, in tonnes.
Here is the formula for the mass of Supplies, tankage, and static parts:
Total Mass = D * R * .001 + Ceiling( D * R / 100 ) * .02 + M
The first part of the sum covers the mass of the needed Supplies: days of Supplies needed times consumption per day equals total Supplies needed. Supplies mass .001 tonnes per unit, so total Supplies needed times .001 equals tonnes of Supplies to take.
The second part adds the mass of the containers you are using to carry the Supplies. It was mentioned before, but bears mentioning again that all default containers have a dry mass of their total capacity times .0002, so a 3.75m tank that carries 15,000 Supplies masses 15,000 * .0002 = 3.0 tonnes. 150 MiniPaks that carry a total of 15,000 Supplies mass ( 100 * .0002 ) * 150 = .02 * 150 = 3.0 tonnes, as well; the difference is only in part count. Of course, the empty mass of the container is a fixed value no matter how much you choose to fill it; if you only intend to take one unit of Supplies, you still need at least a MiniPak to carry it. For this reason, the ceiling function, Ceiling( D * R / 100 ), calculates the minimum number of MiniPaks necessary to carry the total needed Supplies: total Supplies (given by days times consumption, as before) divided by 100 Supplies per MiniPak equals number of MiniPaks, rounded up. This is multiplied by .02 tonnes per MiniPak to give total tankage mass; it is up to you to decide whether to consolidate these MiniPaks into larger tanks.
The third part is the mass of your converters and recyclers, which is constant.
For the sake of estimation you can simplify the equation by removing the Ceiling function to get the following:
Total Mass = D * R * .001 + D * R * .01 * .02 + M
which simplifies to
Total Mass = D * R * .001 + D * R * .0002 + M
Total Mass = D * R * .0012 + M
There are three variables here, so what happens when we start changing them?
D, the number of days you need Supplies, is set by the mission's needs, so we will consider it constant.
Instead, to find the most efficient mass for a given duration of mission, we are going to tweak R and M. R is normally 10.8 times the number of Kerbals but is modified by both recyclers and converters. Recyclers reduce R by a percentage. Converters essentially divide R by 11 and turn it into a rate of consumption in Fertilizer per day, rather than Supplies--this does change the resulting equation a bit, but that will be explained below.
Not only do the different Supplies tanks have the same wet/dry mass ratio, but the densities of Supplies, Fertilizer (and Mulch!), and the masses and capacities of the associated tankage are equal, as well, so a 1.25m tank full of Fertilizer and a 1.25m tank full of Supplies, for example, have both the same number of units inside and the same mass. In other words, none of the default USI-LS parts change the .0012 factor of the equation: they restrict themselves to modifying R (they effect reduced consumption) and M (for them to work, you have to put them on the vessel).
For example, a recycler of 60% efficiency and a one-Kerbal rating multiplies one Kerbal's 10.8 by (1 - .6) to get the new R for that Kerbal (4.32 in this case). If you have more Kerbals or different recyclers, it is best to figure the total consumption separately and use that value for R, rather than try to fit multiple individual R-values into the mass equation.
When using a converter, you only need a day's worth of Supplies to start (these can be stored in the converter; no need for extra tanks), and the rest of the mass is Fertilizer. This does two things to the equation: it turns into an equation to figure total mass of Fertilizer needed by dividing the total Supplies required by the conversion ratio (11 for default parts) and it adds a term to figure the mass of Supplies needed for that one-day start (while subtracting it from the Fertilizer calculation).
Remember that every time you use a part to decrease R you must increase M to account for the fixed mass of that part.
Lastly, there is a caveat for converters and storage. Since converters come with built-in storage for some Supplies and Fertilizer, you don't need to add the dry mass of containers for that amount. However, it is easier to just reduce M by .0002 * FertilizerCapacity * NumberOfConverters so it gets picked up in the middle term of the equation: in other words, you essentially assign some of the converter's mass to serve as tankage, even though that mass is technically attached to the converter. For practical purposes, this means that you need to remember to fill your converters first and then attach extra tanks, or else the mass you add will not agree with the equation.
To finish we can look at the formulae for one Kerbal as an example:
Mass needed with no converters or recyclers:
D * 10.8 * .0012 + 0
Mass needed with RT-500 recycler:
D * 4.32 * .0012 + .1
Mass needed with two Nom-O-Matic 5000 converters:
10.8 * .001 + (( D - 1 ) * 10.8 / 11 ) * .0012 + .308
Mass needed with recycler and two converters:
4.32 * .001 + (( D - 1 ) * 4.32 / 11 ) * .0012 + .408
N.B: Remember that with converters, you need to add one day's mass of Supplies and subtract one day's mass of Fertilizer to get the correct mass. This is why there is an extra term on the front and a ( D - 1 ) in the middle.
If graphed, these equations show that the mass penalty of a recycler is offset by the consumption savings before day 13, which is effectively equivalent to saying that if you're going to take Supplies at all, you ought to take a recycler, too. Between day 13 and day 67, it makes sense to take a recycler but not a converter: this is because the recycler both masses less and than a converter and reduces consumption without requiring any mass inputs. After day 67, you should take a combination of a recycler and two converters.