Aurora 4x
VB6 Aurora => Bureau of Ship Design => Topic started by: Iranon on January 31, 2014, 05:18:24 AM
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Let's say we set a speed requirement and weight allowance for propulsion (i. e. engines + fuel).
Let's standardise our weight allowance w on a weird but helpful unit: "the weight of a 1. 0-power engine needed to reach the design speed at the full design size". Yes, it's ugly. No, we won't have to standardise speed on "the airspeed of an unladen swallow".
Examples:
If we could reach our design speed with 1. 0 power engines but have nothing left over for fuel, w is 1
If power 1. 0 engines without fuel would require twice our weight allowance, w is 0. 5
The fuel we have available is (w-1/p), in the same awkward unit. Because we know the efficiency modifier for a given power multiplier, our range at the desired speed and weight is proportional to (w-1/p)/p^2. 5
Now my hillbilly maths failed even harder at letting me go anywhere elegantly. I just plugged in some values of w, differentiated the buggers with respect to p, and eyeballed the results for anything interesting.
Eureka: Maximum range at a given design speed and weight was always reached when fuel weight was 40% of engine weight.
All those long range missiles or independent (i. e. neither tankers nor tankees) long range craft using more space for fuel than engine are wasteful. Get close to a 2:5 ratio between fuel and engine, and adjust the power multiplier accordingly.
You may want erring slightly on the side of bigger engines: Achieving almost the same range on less fuel is an advantage, and if we're using a single big engine we get a further boost in efficiency.
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I solved this last year. http://aurora2.pentarch.org/index.php/topic,5659.0.html (http://aurora2.pentarch.org/index.php/topic,5659.0.html)
It turns out that, for a given range and a fixed amount of (engine + fuel) there is an optimum that gives the maximum speed. It occurs when the fuel is .2857 of the total tonnage, and the engine is .7143. The engine to fuel ratio is 2.5. I can show how I did this if anyone's interested.
Note that this ignores the gains in fuel economy for a larger engine. I'm still working out how to include those, particularly if multiple engines are involved.
For unitary missile engines the optimum fuel fraction is .2391 and the engine is .7609 with a ratio of 3.182. All of this assumes that you can vary the engine power modifier infinitely, so they don't translate well to very high-speed missiles (or ships). However, it should be of some help for building slower, longer-range weapons.
Your result agrees with mine for ships, but you didn't take into account the gain in efficiency from larger missile engines. (This isn't a criticism. I'm an engineering student, and have to do stuff like this for school.)
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Well, I feel a bit silly now :)
I deliberately mentioned engine size only as an aside, as that may not scale freely:
designing additional engines for the last few percentage points of efficiency may not be worth it, especially if larger engines cause maintenance concerns or we'd prefer slightly more redundancy over slightly more efficiency. But in either case, relatively less fuel is preferable.
Good to have more detailed hard info than I got - I had often used 1:3 in practice. Thanks!
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I deliberately mentioned engine size only as an aside, as that may not scale freely:
designing additional engines for the last few percentage points of efficiency may not be worth it, especially if larger engines cause maintenance concerns or we'd prefer slightly more redundancy over slightly more efficiency. But in either case, relatively less fuel is preferable.
Depends on if we're discussing ships or missiles. For ships, I'm in agreement with you. Actually, I don't even pay attention to this due to research costs and other design considerations. For missiles, this improves performance a lot. There is one caveat, however. The missile ratio assumes infinite scaling in the power multiplier. That's not true in practice, so you'll often need more engine than is strictly optimal.
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In my experience there is no such thing as the most efficient ration of fuel and engine. Both for ships and missiles.
The usual thing is that you want a desired speed and a desired range. It's rare you only want one thing. Then there is something called research cost, fuel production and build/maintenance cost to consider. This means you can't just make one engine for every class of ship you want to build so you normally want to keep to as few engine models as possible.
Yes there is a sweet spot between engine power level and the amount of fuel from a mathematical perspective and it can be important to understand that. But in practice it often have little relevance.
At least that is my experience playing the game...
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It does require some qualifiers. The optimum holds true mostly for independent things that aren't expected to regularly transfer fuel in either direction, and even then we're constrained by tech.
For example, if we are willing to sacrifice a lot of range for a little speed (carrier-bound fighters, short-ranged missiles) we're unlikely to have researched a high enough power multiplier for the ideal setup. Here a shotglass of fuel and the highest-powered engines we can make will have to do.
But if you design an engine specifically for long range missiles or an independent cruiser meant to boldly go where no-one has gone before, and you' d have to use more than 40% its weight in fuel, you should probably consider using less stressed engines.
It's also a nice guideline for larger decisions. . . e. g. if I want a fighter wing able to operate on its own, I'll add enough tanker versions to get the total fuel of the wing between 25 and 40%. Less is ok (independent operations may be nice but not the top priority), but if I'd need more there is probably something wrong with my plans.
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You basically need to know that the sweet spot between engine size and fuel is about 2/3 engine and 1/3 fuel if I'm not mistaken. If you bring more fuel you might rather use engines with a lower multiplier (if range and not speed is your goal)... more or less. This is if memory serves me right, have not looked up the numbers lately. Calculating the exact point is usually not very important, just knowing the roughly most optimised configuration will probably be enough.
For ships this is usually never important at all, not even commercial ships. It can be important for missiles or mostly for drones, for missiles you usually just want the highest possible multiplier that you can get so the missile is as fast as possible, unless you are designing some sort of super range missiles.
When I design a fighter for example my primary concern is to give it a certain speed and range based on doctrine, not on what is most efficient for it's maximum range. A fighter usually only need fuel for making its final run against a target, fighter-tankers take care of the longer range when needed. A fighter only need perhaps half too a billion km in range or so, perhaps slightly more the longer into a game you get. Even from a RP angle I can't really justify long range independent fighters instead of just designing a long range fighter tanker that can be attached to each wing as is needed depending on the range I want my fighters to strike at, it give me much more flexibility.
The same goes for ships, refuelling tankers is more useful than stuffing all your ships full of fuel you only need very rarely. The only ship that I can reasonably find important to apply this to would be exploration ships (as you suggested as well) that you send out for several years. But your fuel efficiency technology quickly get down to very low levels so this also become pointless as you can easily keep the ship in space way longer than their deployment time (unless you build generation ships that is) anyway.
I have seen many threads about the optimum engine/fuel ratio and they often end up talking about hypothetical cases that are not practically applicable to the game most of the time. Although, I do agree as I said above, that having the basic knowledge of the optimum weight between engine/fuel in regard to optimum range is good to know as a reference.
Perhaps you should include some real applicable examples for its use in the game would go a long way to show exactly when and why it's good to use this optimum solution. Such as presenting some hard examples of missiles, fighters and ships that use the optimum engine/fuel ratio for range and what their uses would be to capitalize on the efficiency. I think this would make the discussion a little more informative for those that are not as experienced with the game.
So, please don't look at my remarks as a negative critique, its not meant to be, but rather as an encouragement to complete your analysis with some real practical examples to show when it is smart to use it.
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In my experience there is no such thing as the most efficient ration of fuel and engine. Both for ships and missiles.
Haven't we done this before?
The usual thing is that you want a desired speed and a desired range. It's rare you only want one thing. Then there is something called research cost, fuel production and build/maintenance cost to consider. This means you can't just make one engine for every class of ship you want to build so you normally want to keep to as few engine models as possible.
This is true for ships, but not for missiles. Given the complexities of shipbuilding, I don't even consider this number when I'm doing that.
It's also a nice guideline for larger decisions. . . e. g. if I want a fighter wing able to operate on its own, I'll add enough tanker versions to get the total fuel of the wing between 25 and 40%. Less is ok (independent operations may be nice but not the top priority), but if I'd need more there is probably something wrong with my plans.
Actually, I don't think this works. The math is based on how the engine power multiplier scales with size. Offboard fuel will wreck that.
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For missiles I guess this can get sort of useful. But in practical terms I think we mostly pick whatever the highest multiplier there is and then slap on fuel to give it a desired range, the rest goes into warhead and agility depending on the need. Of course using more than half the engine size in fuel will not be optimal. But I think that many missile designs use much less fuel than what is optimal in favour of high speed (or bigger yield) since high speed means the missile is more likely to hit something and evade enemy AMM/PD. It obviously depend on what maximum multiplier you have, but we can't just assume that every missile design uses very high multipliers.
When designing a missile with extra long range in mind we should obviously know the optimum in case we want to lower the multiplier below the maximum.
An optimised missile design would in this case be 50% engine, 25% fuel and 25% warhead. But I often find this to make missiles with too much range at lower multipliers, such as x4 or something for that technology level and thus either increasing the size of the warhead or engine is preferable over that much fuel. At x5-6 multiplier then 25% fuel might be a good choice.
As en example with ION tech engines and maximum x4 multiplier and a size four missile and 0.7 fuel efficiency a missile with 50% engine, 25% fuel would have 24000km/s speed and a range of slightly over 200 million km. I think that such a range might many times be a little too much, it does not have to be but it depends on the size and quality of fire-controls and other sensor systems in use.
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For missiles I guess this can get sort of useful. But in practical terms I think we mostly pick whatever the highest multiplier there is and then slap on fuel to give it a desired range, the rest goes into warhead and agility depending on the need. Of course using more than half the engine size in fuel will not be optimal. But I think that many missile designs use much less fuel than what is optimal in favour of high speed (or bigger yield) since high speed means the missile is more likely to hit something and evade enemy AMM/PD. It obviously depend on what maximum multiplier you have, but we can't just assume that every missile design uses very high multipliers.
I'm well aware of this, and as I said earlier, we've been over this before. The fact that a piece of math is not useful in all cases does not mean we shouldn't share it.
An optimised missile design would in this case be 50% engine, 25% fuel and 25% warhead. But I often find this to make missiles with too much range at lower multipliers, such as x4 or something for that technology level and thus either increasing the size of the warhead or engine is preferable over that much fuel. At x5-6 multiplier then 25% fuel might be a good choice.
Umm, that's not the optimum. The optimum is to have fuel equal to 31% of the engine. A Fuel/Engine ratio of .5 is always too high, unless you've bottomed out your power multiple.
Perhaps the best way to state the optimum missile engine rule is as follows:
The missile's fuel should always be as close as possible to 31% of the engine size, unless you are operating at either the maximum (lower percentage) or minimum (higher percentage) values for the power multiplier. This will always give you the best possible combination of speed and range.
This is a fact, and takes your objections into account. The only other marginal case to mention is when multiple missile engines are involved. That's rare, but it does happen. For example, two size 3 engines would have .9x the fuel consumption of a single size 5 engine of the same power. If the optimum is technically a size 6 (fuel is 1.86 in that case), the size 5 will have 38% more range.
As en example with ION tech engines and maximum x4 multiplier and a size four missile and 0.7 fuel efficiency a missile with 50% engine, 25% fuel would have 24000km/s speed and a range of slightly over 200 million km. I think that such a range might many times be a little too much, it does not have to be but it depends on the size and quality of fire-controls and other sensor systems in use.
Actually, this is an instructive case of how optimization can help. An actual optimum missile would have 57% engine, 18% fuel, and 25% warhead. There are three ways that the engine can be optimized, and I will illustrate all three of them. (I did this numerically, not experimentally, so I had to assume perfect scaling of the power multiplier. Implementing this will give slightly different values due to granularity. Also, I assumed starting range was exactly 200 mkm, so there will be some error there.)
1. Keep the power multiplier at x4. Range will drop to 157.5 mkm, but speed will increase to 27630 km/s.
2. Keep speed at 24000 km/s. Range will increase by 9.3%, to 218.5 mkm.
3. Keep range at 200 mkm. Speed will increase by 3.6%, to 24865 km/s.
While the last two may not look like much, consider that you've gotten (in the case of #2) over half the benefit of the next tech level at no additional missile cost. When you do this when you first build the missile, it can help a lot.
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As I stated above, the numbers were from my memory and they were 3/4 engine and 1/4 fuel and not 2/3 engine and 1/3 fuel. I didn't really look it up I just winged it. I just know it was in that ballpark. :)
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Regarding groups of fighters: I assumed an independent wing of uniform tonnage and speed - nothing to increase sensor footprint or slow them down. We get an ideal of 40% of engine weight if we ignore the engine size multiplier altogether, this still works as an upper bound if fuel isn't distributed evenly.
Usually we'll want to go slightly lower, there are fiddly details (I listed some earlier) which preclude an absolute ideal.
Short-ranged fighters and tankers are more efficient than uniform long-range designs. : If we move most of the fuel to dedicated tankers and use the weight reductions for more weaponry, we need fewer fire controls sets for the same firepower. Not that this is necessarily the best use, we may prefer them smaller and faster.
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Regarding groups of fighters: I assumed an independent wing of uniform tonnage and speed - nothing to increase sensor footprint or slow them down. We get an ideal of 40% of engine weight if we ignore the engine size multiplier altogether, this still works as an upper bound if fuel isn't distributed evenly.
Usually we'll want to go slightly lower, there are fiddly details (I listed some earlier) which preclude an absolute ideal.
I don't think the math on this actually works. The 40% comes from an assumption that there is a simple tradeoff between fuel and engine, which doesn't quite hold for a tanker/fighter force. You can't move engine from the fighters to the tankers if you decide to raise the amount of space allocated to propulsion like you could in a more conventional setup.
Short-ranged fighters and tankers are more efficient than uniform long-range designs. : If we move most of the fuel to dedicated tankers and use the weight reductions for more weaponry, we need fewer fire controls sets for the same firepower. Not that this is necessarily the best use, we may prefer them smaller and faster.
I will agree with this, although the math isn't quite there. When you're tanking, fuel-efficiency becomes as important as raw range, simply to avoid placing too much of a strain on the tankers. I've had to re-engine a bunch of survey craft because they were using too much fuel. Their range actually went down slightly, but that was because they were carrying a lot less fuel.
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I don't think the math on this actually works. The 40% comes from an assumption that there is a simple tradeoff between fuel and engine, which doesn't quite hold for a tanker/fighter force. You can't move engine from the fighters to the tankers if you decide to raise the amount of space allocated to propulsion like you could in a more conventional setup.
I don't see the problem. If you increase the amount of space allocated to propulsion, every fighter - refuel version or not - would get the same upgrade. You are more limited by granularity and there's an absolute size limit, but the maths for optimum fuel:engine weights stays the same as for single craft.
I will agree with this, although the math isn't quite there. When you're tanking, fuel-efficiency becomes as important as raw range, simply to avoid placing too much of a strain on the tankers. I've had to re-engine a bunch of survey craft because they were using too much fuel. Their range actually went down slightly, but that was because they were carrying a lot less fuel.
Depends on our requirements. If we want the best combination of fighting ability and independent range (i. e. just refueled by tanker-fighters moving with us at the same speed), our maths applies.
If that independence requirement can slide and we accept the requirement to be topped up regularly by regular tankers, "don't waste fuel schlepping fuel with fuel hogs" takes precedence over the sweet spot for independent craft/wings.
Sorry if I seem stubborn, but I'd like to see where the disagreement comes from. If one of us is wrong with the maths or where it applies, that would be good to find out. If we simply make different tacit assumptions, it'd be good to know them,
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I don't see the problem. If you increase the amount of space allocated to propulsion, every fighter - refuel version or not - would get the same upgrade. You are more limited by granularity and there's an absolute size limit, but the maths for optimum fuel:engine weights stays the same as for single craft.
No, because you're attempting to treat an entire squadron as a single craft. While it's clever, the problem is that you are in an area where two of the underlying assumptions (free tradeoff and infinite scaling) hold very poorly. Let's say that during design, you end up with a .5 f:e ratio, instead of the .4 you would want. Normally, you would increase the amount of engine, and decrease the amount of fuel, but in this case, you can't increase the engine on the fighters because you don't have space, and putting the engine on the tankers won't help the fighters at all. That, plus limited engine granularity makes working with theoretical optima here somewhat academic.
Sorry if I seem stubborn, but I'd like to see where the disagreement comes from.
Perfectly all right with that.
If one of us is wrong with the maths or where it applies, that would be good to find out. If we simply make different tacit assumptions, it'd be good to know them,
I think it's a combination of both. I applaud your attempt to apply the math, but I'm not sure it's either correct or relevant.
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No, because you're attempting to treat an entire squadron as a single craft. While it's clever, the problem is that you are in an area where two of the underlying assumptions (free tradeoff and infinite scaling) hold very poorly.
The "infinite scaling assumption" holds much better if we use the squadron as an independent entity, so that's a reason for doing this rather than one against it.
Whether the "free trade-off assumption" is a problem depends on how we approach design - "Define requirements. Meet them." vs "Design something inherently efficient that hits most of the sweet spots. Check if it fits our requirements". It's less of a problem for the latter approach, which I find preferable because decisions are made on incomplete information. Easier, too.
Using your example:
Let's say that during design, you end up with a .5 f:e ratio, instead of the .4 you would want. Normally, you would increase the amount of engine, and decrease the amount of fuel, but in this case, you can't increase the engine on the fighters because you don't have space, and putting the engine on the tankers won't help the fighters at all. That, plus limited engine granularity makes working with theoretical optima here somewhat academic.
In descending order of laziness: don't change a thing about the designs, field less tankers until we hit the sweet spot. We lose range for general capability, i.e. more craft that actually do something - like shooting or snooping.
If range isn't negotiable but speed is, we can decrease the engine power multiplier.
If there's no wiggle room for either speed or range, we may have other options depending on our current fighter design. Like playing with the fuel carried by non-tankers, or the engines carried by everyone... both affecting and limited by size. Those won't be quite as straightforward, and there may be considerations more important than reaching a theoretical local optimum.
So I agree with you there: Maybe we can't hit the majority of the sweet spots (optimal fuel:engine ratio, concentration of armament to avoid wasteful use of fire control, matching MSP to possible failures if we use engineering bays, maybe even desired compromise between cost-efficient components and redundancy, matching maintenance life to deployment time where applicable) and get something that fits our requirements.
However, I'd prefer to try first. One advantage of "sweet" over "specced" design is that incremental component upgrades don't throw off the assumptions behind our design compromises.
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The "infinite scaling assumption" holds much better if we use the squadron as an independent entity, so that's a reason for doing this rather than one against it.
Infinite scaling might have been a poor choice of words. The problem is that we lose a lot of granularity when dealing with fighters, which can prevent us from reaching theoretical optima.
Whether the "free trade-off assumption" is a problem depends on how we approach design - "Define requirements. Meet them." vs "Design something inherently efficient that hits most of the sweet spots. Check if it fits our requirements". It's less of a problem for the latter approach, which I find preferable because decisions are made on incomplete information. Easier, too.
This may be the problem. I tend to set moderately firm requirements, and then try to meet them. Information is always incomplete, but experience and thought can generally result in good requirements.
If there's no wiggle room for either speed or range, we may have other options depending on our current fighter design. Like playing with the fuel carried by non-tankers, or the engines carried by everyone... both affecting and limited by size. Those won't be quite as straightforward, and there may be considerations more important than reaching a theoretical local optimum.
I think that this is going to happen most of the time. It's an interesting consideration, but definitely secondary to making the rest of the design work.
So I agree with you there: Maybe we can't hit the majority of the sweet spots (optimal fuel:engine ratio, concentration of armament to avoid wasteful use of fire control, matching MSP to possible failures if we use engineering bays, maybe even desired compromise between cost-efficient components and redundancy, matching maintenance life to deployment time where applicable) and get something that fits our requirements.
We usually can't hit very many. Part of my issue here is that you're focusing on one part of the design (and a fairly minor one, all things considered) to the point at which I think it will probably hinder the design.
However, I'd prefer to try first. One advantage of "sweet" over "specced" design is that incremental component upgrades don't throw off the assumptions behind our design compromises.
This doesn't make sense. Particularly with fighters, you can redesign the whole thing every time you get a tech upgrade without penalty. With larger ships, I just haven't seen this as a problem. You do sometimes lose a bit of theoretical performance over a clean-sheet design, but not enough to be a problem. And you still have a ship that's probably better than a "sweet" design.
WRT the specific problem of fighter squadrons and fuel, there's another assumption that I haven't brought up, but which actually pushes you to a worse result. Assume we have a given strike squadron, which takes two tanker-loads to refuel, and which must hit a target at its maximum range. The obvious solution is to give it two tankers. The better solution is to have one tanker go halfway with the squadron, then turn around and return home. It refuels, and heads back out to meet the squadron on the return leg. We've just doubled the effectiveness of our tankers at no additional cost.
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This whole tanker/fighter thing is kind of moot in the end. It will all depend on doctrine and the use of your resources as a whole.
You might want to have a long range fighter, let's say you choose to sacrifice some speed with a slightly lower multiplier and slightly more space for fuel. You might thin that it will be an inefficient design, but that depends on what type of tankers you have. You might not include any fast moving fighter/tanker but rely on slower tankers to escort fighter wings or be stationed in space for fighters to refule at during striking missions. There is also the total amount of fuel consumption as a whole to figure. You perhaps can't afford to have fast tankers follow the fighters all they way and like to build long range fighters with better fuel efficiency for that reason etc..
It's not all about one thing the consider.
In general my supply ships actually carry a few 750-1000t fast tankers. These generally have very good fuel efficient engines and is pretty fast (in comparison with normal ships) and can carry enough fuel to act as jumping point for fighter wings or bring fuel to task-groups in need without endanger the supply ship itself. This and I also would deploy more regular fighter/tankers with the carriers. But, building a long range fighter with more fuel efficient engines can be a viable option just to save the amount of fuel you will consume on such missions. Even more important if you don't deploy fighter/tankers with high speed engines.
In essence, the sweet spot is completely depending on the underlying assumptions.
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This whole tanker/fighter thing is kind of moot in the end. It will all depend on doctrine and the use of your resources as a whole.
Yes and no. Iranon's analysis was oversimplifed, but he wasn't entirely wrong in looking at the fighter/tanker ratio mathematically.
You might want to have a long range fighter, let's say you choose to sacrifice some speed with a slightly lower multiplier and slightly more space for fuel. You might thin that it will be an inefficient design, but that depends on what type of tankers you have. You might not include any fast moving fighter/tanker but rely on slower tankers to escort fighter wings or be stationed in space for fighters to refule at during striking missions. There is also the total amount of fuel consumption as a whole to figure. You perhaps can't afford to have fast tankers follow the fighters all they way and like to build long range fighters with better fuel efficiency for that reason etc..
This was stated earlier. He was assuming no offboard refueling, and no fuel supply considerations. The first is entirely a matter of doctrine, while the second depends on what the fighter is to do.
It's not all about one thing the consider.
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In essence, the sweet spot is completely depending on the underlying assumptions.
I'm in complete agreement, with the caveat that so long as we are clear about our assumptions we can arrive at optima that we would have struggled to find otherwise. In some cases (missile engines being the prime example) the assumptions are few and obvious, the analysis is simple, and the conclusion useful. In other cases, such as optimizing a wing of fighters, the assumptions made are far less obvious. (We're into a field that goes by names like Operations Research and Systems Analysis. It's something I'm interested in, and Aurora is actually a decent place to practice it.)
That said, I'm going to take a look at some of the assumptions involved here, stating them as best I can and looking at how they would impact the outcome. This can be summed up as two questions:
1. What does the wing have to do?
2. What else am I trying to optimize?
Question 1 could be answered any number of ways. The most likely are: fixed speed and/or range, a certain amount of hangar space, or a certain number of missile tubes. These could be fixed by the carriers you have available, your doctrine, or experience with past battles. Usually, you'll get two out of the three as fixed, although sometimes you will only have speed or range as your variable.
Question 2 is probably getting the one that wasn't fixed in question 1 as high as possible while keeping cost as low as possible.
It seems simple, but the devil is in the details. Often, the way your fleet is already set up will drive what you do with new pieces to it.
For the wings we've been talking about here, fuel has a massive influence on how you set them up. If you're assuming that all fuel will be carried by the wing at launch, you'll probably go for maximum theoretical range even if it costs fuel efficiency. Offboard refueling raises the question of how big the tanker is, which brings that into design considerations. Are the benefits of offboard refueling (not having to carry fuel at fighter speeds) worth the added complexity and risk? (Keep in mind that there's no tooling for fighters.)
And then there's the logistical implications off all this. Fuel economy is far less important to the system defense wing that flies a mission once every few years from a planet with plenty of fuel than it is to a carrier's wing that flies every few months.
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It can become difficult to keep track of our assumptions were and what we were optimising for.
1) My wing of fighters + tanker-fighters was judged as an alternative to an original design of uniform long-range-fighters. In that context, I wanted to minimise the disadvantages as far as possible (nothing I can do about losing redundancy at range).
2) Fuel efficiency is relevant only as far as it limits range, I'm cramming maximum independent range and capability into limited tonnage. Why? Carting fuel with fighters is inherently wasteful. Right tool for the job: Tanker-fighters extend tactical range, supply vessels perform supply jobs.
The first assumption means our optimisation concerns are the same as for a single craft, because concerns for a wing of identical craft are the same as concerns for a single craft. Because of how I'd define a long-range fighter, it implies that the balance of speed and range is negotiable.
The second assumption means that, if speed and range are indeed negotiable, the optimal f:e ratio is straightforward to calculate. If we're already fitting the biggest engines we can and have room to play with our power multiplier, the sweet spot is at 0.4.
In practice, that's the upper bound rather than the ideal because assumption 2) is too extreme: fuel efficiency will be a very minor concern instead of no concern at all.
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Byron gave an example how we can refine our doctrine for a common missile profile if we ditch assumption 1).
We require less fuel for the same range than uniform long-range-fighters would, and can go lower on tankers than a straight equivalent.
Does the same hold true for most of our needs? If yes: does this affect just the ratio of tanker-fighters we want to field, or does it call for different design?
If we keep them away from the melee, we may relax the fighter-sized requirement. If we want to field a decent number and soften their role as a pure range extender, fuel efficiency may enter the picture. The resulting "tactical tanker" may be very different from our mainline fighter stripped of offensive payload for fuel tanks.
Other criticisms are valid if I drop either assumption.
If a mix of fuel efficiency and range is desired instead of pure range, the optimal fuel:engine ratio will be lower than 0.4, we can calculate the exact value if we can define the relative importances.
If speed isn't negotiable and I'm operating at the highest power multiplier, I can freely trade range and capability by adjusting the ratio of tankers. There is no obviously ideal fuel:engine ratio.
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Formal methods of coming up with the optimal solution for multiple simultaneous requirements would be nice to have, but the maths behind them is rather daunting. Possibly beyond my ability (economics background), definitely beyond my willingness to try.
Simple optimisation methods finding the sweet spots for fewer variables don't have that ability. Fairly easy analysis is sufficient for revealing questionable parts of our designs though. And I mean questionable, it's not an euphemism for wrong: "Is this a design mistake, or the least bad compromise for our tech constraints, assumptions, and resulting doctrines?"
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It can become difficult to keep track of our assumptions were and what we were optimising for.
1) My wing of fighters + tanker-fighters was judged as an alternative to an original design of uniform long-range-fighters. In that context, I wanted to minimise the disadvantages as far as possible (nothing I can do about losing redundancy at range).
And as such, it has merit. I'm just not sure that 40% fuel is more than mathematically ideal in that situation.
2) Fuel efficiency is relevant only as far as it limits range, I'm cramming maximum independent range and capability into limited tonnage. Why? Carting fuel with fighters is inherently wasteful. Right tool for the job: Tanker-fighters extend tactical range, supply vessels perform supply jobs.
The problem is that your carrier is also serving as a tanker here, and it has to carry the fuel for multiple strikes. I've run into trouble with this before (in slightly different circumstances) so I'm probably more cautious than you are about it.
The first assumption means our optimisation concerns are the same as for a single craft, because concerns for a wing of identical craft are the same as concerns for a single craft. Because of how I'd define a long-range fighter, it implies that the balance of speed and range is negotiable.
This is theoretically true, but I'm not sure how well it will work in practice.
That said, I took a look at how this might work in my current game, and I was surprised by how well it did. My existing standard fighter happened (totally accidentally) to have a .4 f:e ratio, so I just copied the design, removed 75% of the fuel, and modified my standard tanker design to have the same speed. (For reasons I can't remember, it's slower.) The standard squadron ended up as 9 craft, either 8 fighters and a tanker or 9 fighters. The 9-fighter squadron had 126 missile tubes and cost 1427.4 BP. The 8-fighter squadron had 128 missile tubes and cost 1351.6 BP. However, because the tanker is carrying 75% of the fuel, I can't do the separate tanker range extension thing with a single squadron. Of course, I'm slightly hemmed in by the fact that each fighter only has a single size 1 engine.
The second assumption means that, if speed and range are indeed negotiable, the optimal f:e ratio is straightforward to calculate. If we're already fitting the biggest engines we can and have room to play with our power multiplier, the sweet spot is at 0.4.
In practice, that's the upper bound rather than the ideal because assumption 2) is too extreme: fuel efficiency will be a very minor concern instead of no concern at all.
At this point, I decided to do a sensitivity analysis. I wanted to check and see how big the sweet spot was. I re-did the original optimum equations for both standard engines (no size scaling) and missiles, for both constant speed and constant range. Then I looked at the ranges where the dependent variable would be at least 90% or 95% of optimum. The results were rather surprising (all numbers expressed as % fuel:engine):
Fixed Speed/Variable Range:
| Standard | Missile |
| 95% | 27.1-57.9 | 21.5-44.9 |
| 90% | 22.6-67.7 | 18.1-52.1 |
Fixed Range/Variable Speed:
| Standard | Missile |
| 95% | 21.3-71.3 | 17.0-54.8 |
| 90% | 15.8-90.8 | 12.7-68.8 |
A few caveats. First, these are assuming there are no limits on the power multipliers that can be used, and that fuel and engine space can be freely traded with no granularity. Second, the total propulsion space is assumed to be fixed, as is the first value. Third, the question is not if you can increase one variable at cost to the other. It's if you can make one better while keeping the other constant (or improving it slightly.)
I'm rather surprised at how wide the ranges are. This tells me that strict adherence to optima in ships is mostly unnecessary, unless you're way, way off optimum. For missiles, research is cheap and you can usually get closer to the optimum, so it's probably a lot more worthwhile to worry about those.
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We require less fuel for the same range than uniform long-range-fighters would, and can go lower on tankers than a straight equivalent.
This isn't true. You don't need less fuel than long-range fighters (except from reduction in the number of vessels involved) and you can replace redundant tankers with more fighters on a 1 to 1 basis, so you need exactly the same amount of fuel, just split up differently.
If we keep them away from the melee, we may relax the fighter-sized requirement.
I actually wouldn't do that, unless you're talking about going from 250 to 500 tons. I actually tried that with my designs, and I got about 4% more fuel per ton. It's not really worth it. Going with FAC-size ships is going to add a bunch of logistical headaches that will probably be more trouble than their worth, at least if you plan on integrating them into the same wing.
Formal methods of coming up with the optimal solution for multiple simultaneous requirements would be nice to have, but the maths behind them is rather daunting. Possibly beyond my ability (economics background), definitely beyond my willingness to try.
Simple optimisation methods finding the sweet spots for fewer variables don't have that ability. Fairly easy analysis is sufficient for revealing questionable parts of our designs though. And I mean questionable, it's not an euphemism for wrong: "Is this a design mistake, or the least bad compromise for our tech constraints, assumptions, and resulting doctrines?"
This I will agree with. I'm not willing to break out linear programming and the other forms of math involved here, although I could if I really wanted to. Honestly, I've found the best way to answer these sorts of questions is to do paper studies as far as possible. Build your hypothetical ships in the ship design window, and see how they work. (You could either set up a parallel simulation game to your main game, or just SM a copy of the parts you have upcoming with a special name so you know not to use it on a ship you're actually going to build.) Although in a lot of cases, that may not be necessary because you'll already have most of the parts you need.
I do a lot of this. I tend to run a big, high-tech 'flagship' game, and I've rebuilt my planned fleet for 6.4 twice over the past few months.
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It looks like we see eye to eye on the major points that don't require digging deeply into assumptions, doctrine and other waffly things. Hooray, progress!
That sensitivity analysis looks useful, there seems to be a fair bit of wiggle room in how far you can deviate from theoretical ideals. The low end is especially interesting, as we save fuel (mostly relevant for ships) and require less engine power tech there. Looks like my previous aiming spot of 0.3-0.33 was reasonable. The numbers seem to imply I can drop considerably lower without wasting much performance, and save fuel in the process.
However: we could achieve the same speed and range on less weight. Important for craft struggling to stay within fighter/FAC limits, also worth looking at in high-performance craft where the last 10% in speed were expensive (in terms of weight).
The high end is costly in addition to sacrificing performance. The ship using 90.8% of its engine weight on fuel may be 90% as fast as the performance-optimal version, which doesn't sound too bad. However, it also uses considerably more fuel, and several times as much as it needs to for its performance (3.5 times as much as the other 90% speed example). This is bad.
It also needs a higher power multiplier, if we researched that at the expense of an engine tech things get downright terrible. And a fuel-to-engine ratio of 0.908 would not seem unreasonably large to people who didn't consider the mechanics, there is probably far worse out there.
This isn't true. You don't need less fuel than long-range fighters (except from reduction in the number of vessels involved) and you can replace redundant tankers with more fighters on a 1 to 1 basis, so you need exactly the same amount of fuel, just split up differently.
My phrasing was a little off: yes, you don't save fuel in the particular you outlined. Bit of an edge case, often enough it will. You can take just enough tankers to get the job done, while long-range fighters will carry dead weight if their tanks are larger than they need to be. You can also go halfway, top up the fighters, park the tankers, top up the fighters on the way back - this does save fuel.
You also get even more range if you deploy only part of your fighters but all the tankers - some types may be useless for the job, or you may want to keep some fighters around to protect your carrier.
Usual disclaimer: details differ in practice because granularity; this usually works in favour of the approach that leaves the designer more freedom (in this case the short-range + tankers option).
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However: we could achieve the same speed and range on less weight. Important for craft struggling to stay within fighter/FAC limits, also worth looking at in high-performance craft where the last 10% in speed were expensive (in terms of weight).
I decided to have a look at the math on this one. I looked at sizes of 105% and 110% of optimum, based upon an optimum size at 40% f:e for a given speed and range. The results were very surprising. The 105% size band went from 19.2 to 77.7%, while the 110% band went from 14.0 to 100.2%. I don't think I'm going to do missile engines, as that would require more math (which I've already done enough of today) and the results would be fairly similar.
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Just to clarify, you refer to allocating 5% or 10% more propulsion tonnage while keeping the whole ship at the same size?
In other words, 5% more propulsion tonnage than the performance-optimum would give us the same range/speed at 59.2% of the former fuel consumption?
1.05*(19.2/119.2)/(40/140)=0.592
Edit: There used to be something very wrong here. Sorry for the inconvenience.
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Just to clarify, you refer to allocating 5% or 10% more propulsion tonnage while keeping the whole ship at the same size?
In other words, 5% more propulsion tonnage than the performance-optimum would give us the same range/speed at 59.2% of the former fuel consumption?
1.05*(19.2/119.2)/(40/140)=0.592
Edit: There used to be something very wrong here. Sorry for the inconvenience.
That's exactly right. I held displacement constant for two reasons. First, it's usually how I design ships. Second, the math for variable displacement would be a lot messier.
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Oh, definitely the right way to do this... otherwise we'd have to know which percentage of the ship total we allocated to propulsion, which would change every time we fiddled with it, and it'd be all-around terrible to work with.
Does the maths lend itself to easy generalisation so we could plug in f:e ratios and get associated weight-efficiency and fuel-efficiency?
Standardising for the most weight-efficient setup, we'd have...
0.4, 1.0, 1.0
0.192, 0.952, 1.689
0.14, 0.909, 2.115
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Does the maths lend itself to easy generalisation so we could plug in f:e ratios and get associated weight-efficiency and fuel-efficiency?
You can. The equation I've been using so far is S=E+.4(1/E)^2.5, where S is the total size and E is the engine size. I then did an intersect on my graphing calculator at S=1.47 and S=1.54, for the 105% and 110% figures. F:E was calculated from (S/E)-1.
A bit of algebra gives me the equation E=(2.5*FE)^(-2/7). Plugging this back into the first equation gives us S=(2.5*FE)^(-2/7)+.4(2.5*FE)^(5/7). I checked this against my starting equation, and it works. Pulling out the coefficients and normalizing the whole thing gives us Weight Efficiency = .549762*(FE^(-2/7)+FE^(5/7)). This is actually a rather neat equation. I may see if I can do likewise for constant speed and constant range.