On the Economics of Fuel Economy

[skoormit (OP)]

I recently compared the total effective cost for tugs with 50% engines vs tugs with 40% engines using my current tech level (improved nuclear thermal, composite armor, 90% fuel consumption) and ship designs.

The tug designs:
     A) 40 2kt engines @50%, 5ML fuel, plus etc. (tractor beam, bridge, eng space, et al.). 88,471t, 2893km/s, 127.9bkm, 1894.9BP
     B) 40 2kt engines @40%, 3ML fuel, plus etc. (tractor beam, bridge, eng space, et al.). 86,222t, 2375km/s, 137.5bkm, 1365.1BP
ETA
     C) 50 2kt engines @40%, 4ML fuel, plus etc. (tractor beam, bridge, eng space, et al.). 106,625t, 2378km/s, 146.9bkm, 1653.6BP

The barge:
     1 Large cargo hold, 5 shuttle bays, bridge/engspace/crewquarters, No Armour. 128,277t, 363.3BP

Total effective cost includes the cost of fuel harvester stations required to produce the fuel consumed by the tug.
My fuel harvester stations are 10x harvester modules, refuelling system, 1 large fuel storage, et al. Total cost each: 387.1BP.
     (You can put more modules on a station to pay less per module in total cost, but this ends up being less than 10% of the total cost as is.)
With my current NAC structure and refining tech, a single harvester station at a 1.0 sorium accessibility planet produces ~0.82ml/year.

Total effective cost includes the cost of the ships needed to transport the fuel from the harvesters to where the tugs will refuel.
In my current game, the nearest/best sorium mining source is 17.3bkm from my HW.
A medium tug (293.9BP) with a 5ML unarmoured fuel station (91.9BP) brings home 6.4ML per year from that source.
The tug uses 0.27ML fuel per year.
All told, that's a net cost of ~63BP per ML/year for the fuel transport ships.
This cost will scale roughly proportionally to the distance involved (but the time required to load/unload the fuel is a constant).

I factored in cargo load and unload time based on a 30bkm round trip haul and assumed that these tugs are never idle. (I never have idle freighters.)
I calculated overall throughput in terms of standard cargo holds delivered per year. (One large hold equals five standard holds.)

The results:
     Tug A (50% power) moves 6.15 standard holds per year at a total cost of 2651.8.                          That's 2.32 holds per year per 1kBP cost.
     Tug B (40% power) moves 4.98 standard holds per year at a total cost of 1908.5.                          That's 2.61 holds per year per 1kBP cost.
     Tug C (40% power, +25% engines) moves 5.65 standard holds per year at a total cost of 2242.3. That's 2.52 holds per year per 1kBP cost.

But there is a hidden cost here. The cost of slowness.

Because Tug A hauls the barge about 23.6% faster than Tug B, you need about 23.6% more Tug Bs to equal the same throughput.
That means that a fleet using Tug Bs has 23.6% more "dead cargo" cost than a fleet with the same throughput using Tug As.

What is the cost of "dead cargo"?
You could consider it equal to whatever it cost you to make that cargo, multiplied by the amount of time the cargo is dead.

If you are hauling typical planetary installations, the cost is 120BP per 25kt cargo space.
If you are hauling infrastructre, the cost is 2BP per 2.5kt cargo space (which is 1/6 the cost per kt of installations).
If you are hauling low-grav infrastructre, the cost is 4BP per 2.5kt cargo space.

Since a barge is full half the time and empty half the time, the cost of dead cargo per year, on average, is half the cost of a full load of cargo.

My fleet is hauling installations a large majority of the time, so I calculate the cost of dead cargo based on the cost of installations.
To wit, a large cargo hold has a yearly dead cargo cost of 120 * 5 / 2 = 300BP.

The amended results:
     Tug A (50% power) moves 6.15 standard holds per year at a total cost of 2951.8.                          That's 2.08 holds per year per 1kBP cost.
     Tug B (40% power) moves 4.98 standard holds per year at a total cost of 2208.5.                          That's 2.25 holds per year per 1kBP cost.
     Tug C (40% power, +25% engines) moves 2.52 standard holds per year at a total cost of 2542.3. That's 2.22 holds per year per 1kBP cost.



Clearly, slower is more cost effective. But it's not an overwhelming difference.
The cheaper your cost of dead cargo, the better tug B looks.
The closer your sorium source, the better tug A looks.

One other minor cost: the fleet using tug B will need 23.6% more shipyard capacity, which costs more to create and uses more workers.

The creation cost is theoretically amortizable over the lifetime of the tugs.
It's non-zero, but I don't think it's a major factor.
It does make it take longer to ramp up production.

The worker cost is ongoing.
It only matters if you are facing a labor shortage.
My race is nowhere near a labor shortage, so I'm ignoring that cost.
But if labor is tight for you, that's a small point in favor of Tug A.

[Scandinavian]

I think you get a closer comparison if you let design B have 50 engines instead of 40. For a tug this makes sense, as you want to have the same engine power available.

The effect directions are similar, but the magnitudes get smaller.

[skoormit (OP)]

I think you get a closer comparison if you let design B have 50 engines instead of 40. For a tug this makes sense, as you want to have the same engine power available.

The effect directions are similar, but the magnitudes get smaller.

It turns out to be slightly worse that way.
I've added TugC to the post.

[nuclearslurpee]

I'm not sure what the conclusion is meant to be here. It looks like the idea is that more efficient engines are generally better on a cost basis, but by a small enough margin that either approach is probably fine. I would say this generally agrees with practical experience, there is not really an "optimal" approach but rather the decision is based on larger strategic factors.

A major consideration, which I do not see here, is that not all BPs are created equal, as the same BP cost may reflect very different mineral requirements and not all TNEs are rated equally. For example a tug with 40x engines at 50% efficiency may generate the same engine power as a tug with 50x engines at 40% efficiency, but the latter will actually cost only 80% as much gallicite as the former. Even though the bigger tug will add additional build costs in extra armor, etc. requirements based on size, saving 20% of your gallicite can be instrumental in keeping the economy afloat while continuing to expand your navy full of gallicite-hungry fast warships.

Another key consideration is the ever-present need to place tomorrow's colonists on today's moon, yesterday. Given the option to build a bigger ship of the same speed (Tug C above) or a same-size ship of the lower speed (Tug B above), the former is often going to prove its worth when a time-sensitive mission occurs. Needing to deploy colonists to a new system to solidify a claim before the NPR can do the same thing is often a very relevant concern for example, the faster your tug the more likely you win this race.

Fuel logistics are also often a more salient concern than fuel economy. You may easily be able to produce enough fuel to run your fleets, but getting it where it needs to go when it needs to get there is a trickier business. Lower fuel consumption often has the biggest impact by reducing how much volume of fuel needs to be transported, while reducing the amount of needed production is less of a consideration.

[skoormit (OP)]

I'm not sure what the conclusion is meant to be here.

You sound like me at the end of nearly every student paper I ever marked. 

Think of this piece as more of a case study than a persuasive essay.
The intent was not to discern certainty, but to present thoughts to a candid world, and hope for thoughts in return.

A major consideration, which I do not see here, is that not all BPs are created equal, as the same BP cost may reflect very different mineral requirements and not all TNEs are rated equally. For example a tug with 40x engines at 50% efficiency may generate the same engine power as a tug with 50x engines at 40% efficiency, but the latter will actually cost only 80% as much gallicite as the former. Even though the bigger tug will add additional build costs in extra armor, etc. requirements based on size, saving 20% of your gallicite can be instrumental in keeping the economy afloat while continuing to expand your navy full of gallicite-hungry fast warships.

This is a fair point.
I tend to simplify the "cost" side of things by just considering the BP required.
That simplification seems to work fine for my empire; I keep a close eye on stocks, income and outlay of all minerals, and I expand my mining operations with a particular attention to circumventing any shortfalls.
A more granular analysis of cost would certainly benefit empires feeling a crunch in a particular mineral.

Minor point about relative costs: a comparison of tug/freighter options shouldn't be concerned with the relative cost per ship, but about the relative cost per throughput.
The tug with more, less powerful engines costs 20% less gallicite than the other one and has the same total engine power, but it outweighs the other one by more than 20%, meaning you have to build more of them (and more barges) to move the same amount of cargo per year.
On a throughput basis, the savings for the big slow option is closer to 10% for my scenario with the ~128kt barge.

[kilo]

I do not have an idea about how to improve your calculation, but I thing the fuel transport calculation misses an important point. From my point of view, you want to keep the fuel harvesters running 24/7, which requires your fuel transports to cycle faster than your harvesters need to fill their tanks. In this case, speed becomes important for your tanker fleet. This is an argument for speed. You can save Galicite though by using a two stage transport system. The first ship or fleet cycles between the gas giant's harvester fleet and it's innermost moon, while the second fleet loads the fuel on the moon and transports it to the final destination. This allows you to reduce the construction cost per ship and increase the fuel efficiency drastically. The cycle times become irrelevant, as the moon can buffer as much fuel as you like. For a fuel mining operation the speed of the transport ships is completely irrelevant as long as there is no bottleneck when it comes to throughput in the first cycle.
This can be very different when it comes to military action, when you need to react fast to a changing environment on the battlefield. Depots can help as a buffer and by shortening supply lines, but you will still need replenishment oilers, which need to be significantly faster compared to a tanker, as they have to be able to keep up with the task groups.

To my mind, the same applies to bulk good freighters. Let us assume you are building automated mines on Earth and shipping them to a certain destination. There are two rate limiting steps here, which are the construction of the mines and the logistics. The slower process is what limits your expansion of the mining operation. This can either be the construction or the distribution, but I do not see where ship speed is important in this equation. As long as you can ship as many mines to the destination per year as you are building, you should be golden.

This is not an argument against express shipping. There are situations in which speed is important. It might be convenient or even essentially on manually controlled operations or when you build an outpost close to the enemy's territory. It is not essential when transporting installations and minerals between colonies, especially when they circling between these locations until the end of time.

[skoormit (OP)]

...As long as you can ship as many mines to the destination per year as you are building, you should be golden.

If cargo in transit were as useful as cargo at the destination, then speed would not matter per se. It would only matter as a component of throughput (which is speed times capacity over distance).

But installations in transit aren't providing value for us.
Installations that have reached their destinations are providing value for us.
So it stands to reason that, all else being equal, we should prefer that our installations reach their destinations sooner rather than later.

Example:
You are deciding between two options for transporting automines from a production planet to a mining planet.
The production planet will make 100 automines per year.
The automines produce nothing while at the production planet.
Option A will use 100 ships, each making 1 round trip per year carrying 1 automine.
Option B will use 1 ship, making 100 round trips per year carrying 1 automine per trip.

Both options have the same throughput: 100 mines per year.
But if the total cost is the same for both options (accounting for ship cost, fuel cost, fuel transport cost, amortized shipyard cost, and whatever else applies), then option B is far superior.

With Option A, for each year that passes you will have 100 mines in transit for half a year each--a total loss of 50 mine-years of production.
With Option B, for each year that passes you will have 100 mines in transit for about 1.8 days each--a total loss of about 0.5 mine-years of production.

49.5 mine-years of production per year is worth a lot more than zero, for sure.
How much it is worth, exactly?
I'm pretty sure it's worth exactly as much as it costs to make 49.5 mines.
Because that's what you have to pay to get 49.5 mine-years of production per year.

So, in this contrived example, I'm willing to pay up to the cost of 49.5 mines more to implement option B.

[Jorgen_CAB]

When it come to a tug would it not be very easy to calculate which one is more efficient by looking at how fast it is in relation to the fuel it uses up and the amount of fuel a particular harvesting station would produce by being deployed sooner rather than later. There just will be a better choice... I have not done the calculations on this but I bet a 50% fuel engine will almost always win this as the production capacity of the harvesting station will vastly outperform the fuel cost of delivering the station to it's destination. You obviously also have to at some point consider that fuel is not an infinite source, but at some point the efficiency simply is good enough that most fuel sources will feel infinite (more or less)

I think you probably can do similar calculation with construction and/or mining facilities as well. How much minerals will a mine produce being deployed sooner rather than later etc...

In general I would say that you want most of your facilities to be delivered as fast as possible as the transition times means loss of production. But when you look at transfer of things such as minerals or facilities you might not readily use all the time then speed is less of an issue and economy of transfer is more important. There also is a breaking point at around 25-30% fuel efficiency where the lower efficiency simply is not worth the investment anymore as size of the engines needed to get the speed simply becomes too great. Reduced fuel cost also becomes less of an issue rather than just produce more fuel instead.

[skoormit (OP)]

I bet a 50% fuel engine will almost always win this as the production capacity of the harvesting station will vastly outperform the fuel cost of delivering the station to it's destination.

I guess it depends on the relative size of the tugs and the station.

A 50% engine uses about 75% more fuel per EPH than a 40% engine.
A tug using 50s instead of 40s will reach the destination in 20% less time.
In that amount of saved time, will a station produce that much extra fuel?

My slow tug uses ~557kl/yr.
My fast tug uses ~979kl/yr.
Both are roughly the same weight as my harvester station, which has ten modules and can produce about 600kl/yr (with my naval admin mining bonuses accounted for).

Suppose it takes the fast tug a year to deliver a station, and six months for the return trip.
Then the slow tug would need 15 months to deliver and 7.5 months to return.
That's a 1.5-year round trip for the fast tug, consuming ~1.47ML of fuel.
The slow tug takes 1.875 years, consuming ~1.04ML of fuel.
So the fast tug needs 0.43ML more fuel. What does the faster trip gain me?
Just 3 months of fuel production from the station.
In that time, the station produces ~0.15ML of fuel.

The slow tug is better.
After all is said and done, delivering the station with the slow tug leaves me with an extra ~0.28ML of fuel.

But if my tugs were much smaller, the faster tug might be better, because the 20% time savings equals much more time, while the 75% extra fuel usage equals much less fuel.

If you cut the tug sizes in half, then the trip takes 50% longer and uses 2/3 as much fuel.
The station would then be harvesting ~0.225ML more fuel when delivered by the fast tug, and the fast tug would be using ~0.29ML more fuel per trip than the slow tug.

Cut the tug sizes in half again, and the faster tug will be the better option.

Of course, all this does not factor in the value of finishing the return trip sooner.
If you are going to build stations as fast as you can tug them all away, then using faster tugs means you get more stations built and delivered sooner.
But it costs you more fuel to do it that way.

If you are going to build stations at some given rate, then you will want to build enough tugs to handle that build rate, so that you always have a tug ready when a station is completed.
This will require 25% more slow tugs than fast tugs.
But the fast tugs are about 30% more expensive, so this really only saves ~2.5% of the cost of tugs for this job.

[Jorgen_CAB]

In addition to this the faster tug will also become more economically viable as your technology increase. As you get better fuel economy and fuel production values.

I would also say that in general you don't want to use giant tugs for a 50% efficiency engine. The tug probably should be around 25-35% the size of the thing it drags if at 50% efficiency, larger if less efficient engines. My main tugs tend to be around 50-100kt intended for stations and the stations are around 100-200kt in size. Thing like harvesters I tend to build in naval yards as I want to constantly produce them, so a  specialized yard with one or two slipways can constantly pump out large harvesters, the same for terraforming and mining stations. For tugs the max efficiency that is usable is around 30%, lower than that is not efficient. At 30% you can still just build the tug larger and have roughly the same speed but cheaper and better economy, so a 30% tug could be over 50% the size of the thing it drags and still be as fast, cheaper and consume way less fuel. But when you get to even less efficient engine it is very hard to get good efficiency and the reduction in fuel start to become not as important.

But you also need to look at overall total consumption of fuel as well as fuel is not actually infinite either, so both consumption and production efficiency is important overall. It is OK to loose some production now in order to get more out of fuel harvesters over time. So we can't completely disregard the importance of fuel economy in terms of absolute numbers completely. What I mean is we can't just stare our self blind on one type of efficiency.

[Scandinavian]

But you also need to look at overall total consumption of fuel as well as fuel is not actually infinite either, so both consumption and production efficiency is important overall. It is OK to loose some production now in order to get more out of fuel harvesters over time. So we can't completely disregard the importance of fuel economy in terms of absolute numbers completely. What I mean is we can't just stare our self blind on one type of efficiency.

A 10+ million ton gas giant is functionally infinite - I've never had one of those run out, and I get all my fuel from orbital refineries as soon as possible.

[skoormit (OP)]

The tug probably should be around 25-35% the size of the thing it drags if at 50% efficiency, larger if less efficient engines.

Did you come to this conclusion by analysis, or by intuition and experience?

Also, you are saying "efficiency" but I think you are meaning "power." This makes it hard to follow your reasoning at times.

[nuclearslurpee]

Did you come to this conclusion by analysis, or by intuition and experience?

Intuition and experience count for quite a lot in Aurora.

In this case, having a tug class ~1/3 the size of the stations being tugged is a balance between speed and fuel conservation. A larger tug will move stations more quickly, but you have to pay with fuel to move the extra tug displacement. A smaller tug will conserve fuel to an extent but takes longer in transit, which means your station is unproductive for longer. It is a balance of different factors which defies general analysis and often defies specific analysis as well, at least if you want to spend more time playing the game than doing math.

Generally, it is the case that optimizing a single metric in Aurora is not really the best approach. In this case we can analyze fuel consumption to death, but without any other considerations it is meaningless. How quickly can we move things from point A to point B? Is the value of lost production worth using a slower or smaller tug class? Tugs are also used for other purposes very often, so optimizing for a single use case may not represent the best overall design - in some cases speed is more important, in others fuel conservation becomes a more prominent concern.

We also are not considering the bottom line of economics here; that is, is the fuel usage from a single tug to get a FHS into position significant compared to the production from that FHS once it is deployed? It can easily be the case that fuel production easily exceeds demand, and fuel transport logistics are the dominant consideration. If a tanker or tug transporting fuel uses 2x as much fuel to go faster, but the consumption is only 2% of fuel carried compared to 1% with the more efficient design... well, would you rather have 99% of your fuel transported in 3 months, or 98% transported in two months? These are important considerations which are highly situational and usually defy straightforward analysis unless you are a trained logistics engineer.

[Jorgen_CAB]

But you also need to look at overall total consumption of fuel as well as fuel is not actually infinite either, so both consumption and production efficiency is important overall. It is OK to loose some production now in order to get more out of fuel harvesters over time. So we can't completely disregard the importance of fuel economy in terms of absolute numbers completely. What I mean is we can't just stare our self blind on one type of efficiency.

A 10+ million ton gas giant is functionally infinite - I've never had one of those run out, and I get all my fuel from orbital refineries as soon as possible.

That depends on how large your empire is and how much you want to spend time and resources shuffling fuel around, even a 10 million gas giant will start to reduce the production after some time and then also run out. How much fuel will your large military guzzle up moving around, usually allot. In the next version we will also have to factor in military patrols and a more spread out fleet with the consideration of pirates. Since I also almost always play multiple factions I need patrols of military ships that is not as fuel efficient as transport fleets. Since I also play on very slow technology progression I don't reach high end technologies very fast either with high fuel efficiency.

[Jorgen_CAB]

The tug probably should be around 25-35% the size of the thing it drags if at 50% efficiency, larger if less efficient engines.

Did you come to this conclusion by analysis, or by intuition and experience?

Also, you are saying "efficiency" but I think you are meaning "power." This makes it hard to follow your reasoning at times.

I probably was a bit inconsistent...

I obviously meant engine power such as 30% being of the more optimal design choice with the best speed to fuel efficiency trade-off, in my opinion any way. I have not done the math as that depends highly in the tech levels you currently have and I will not sit down and do it that methodically to be honest. The speed you want needs to be a trade-off between how important it is to get the thing to the place you need. Speed is also a strategic considerations as well as consideration of fuel efficiency.

I also meant that the Tug should be around 1/3 of the "total" size of the thing it drags (at 50% power), that seems a good trade-off between cost and efficiency. At 30% power you would want it to be almost at 50% of the total size so the tug would then be as big as the station it drags. The bigger the tug it also will burn more fuel just moving around itself.

In general I would not want to reduce speed by adding a less powerful engine, I would just make the tug larger in that case. In general a 30% power engine tug will be cheaper than a 50% power tug even if it is larger, both to build and move around at the same speeds... unless you want insane speeds that is for some reasons.