Aurora C# Propulsion Design Theory

[nuclearslurpee (OP)]

Propulsion design in Aurora is a frequent subject of discussion on this forum, particularly in the form of questions from less-experienced players. On the other hand, a frequent criticism of ship designs which are posted here is that they are “too slow”, often because they do not dedicate a sufficient fraction of ship mass to propulsion. Engine power modifier choice and the resulting impact on fuel consumption or fleet operating range is another confusing subject, even Steve himself prefers to stick to a 1.0x EP modifier rather than trying to work out the intricacies of speed versus fuel consumption. Many other players will outsource their engine design work to specially designed calculator spreadsheets or programs.

In this post, my intention is not to give the final, definitive answer to propulsion design. Nor do I intend to somehow replace the calculators designed by other members of this community. What I do intend to do is lay out, conceptually and theoretically (math ahoy!), a framework for engine design that encapsulates and explains the fundamentals of this process. My goal is to enable those who are interested in doing so to design well-optimized propulsion systems by themselves, to give those who prefer the calculators an understanding of the concepts which underlie those tools, and to give all readers a better understanding of how the various propulsion mechanics and components work together in Aurora.

This post is organized as follows: in Section (I) I define the basic terms and quantities which are used throughout including the concept of “propulsion” in Aurora. In Section (II) I derive the Aurora Propulsion Equation, which with clever application yields the optimal propulsion design. In Section (III) I demonstrate practically how the Propulsion Equation can actually be used to design a propulsion system and why this method is the most effective approach despite its relative complexity. In Section (IV) I extend this analysis to consider the additional effect of crew quarters on propulsion design, since the crew needed to run the engine can be considered part of the propulsion from a ship design perspective. Finally, in Section (V) I close by giving some general ideas about what reasonable fleet speeds and ranges might look like or how they might be determined by the player.


Table of Contents

• Definitions
• The Aurora Propulsion Equation
• Ship Design Using the Propulsion Equation
• Accounting for Crew Requirements
• How Fast Should a Ship Be?

I. Definitions

The term “propulsion” here refers to the ship components necessary to get a ship from one place to another under its own power in a finite amount of time. Conventionally, this is considered to include the sum of the total engine mass and total fuel mass.

    (1)

Mp = propulsion mass in HS
Ne = number of engines
Me = mass of a single engine in HS
Mf = total fuel mass in HS

Alternatively, dividing Eq. (1) by the total ship mass gives the propulsion fraction:

    (2)

Fp = propulsion fraction
Fe = total engine mass fraction
Ff = total fuel mass fraction

For the purposes of this post I will generally keep things in terms of the actual component masses, since these are more intuitive and familiar quantities.

As an alternative to the above definitions, it is reasonable to consider the mass of crew quarters required to support the engines, in which case Eqs. (1) and (2) are modified to give:

    (3a)

    (3b)

Mc = crew quarters mass
Fc = crew quarters mass fraction

The effect of including crew quarters into the propulsion mass will be briefly touched on later.

A number of other quantities are relevant to propulsion design, including

Ms = total ship mass in HS
Pe = engine power (EP) per HS of engine mass from technology
Cf = fuel capacity in litres per HS of fuel mass, usually 50,000 L/HS
?0 = fuel consumption efficiency base value from technology
?e = engine power modifier or “boost”, limited by technology
R = ship range in km, which depends on these quantities
V = ship speed or velocity in km/s, which depends on these quantities
Td = deployment time in months, only relevant to calculations involving crew quarters

Thermal signature reduction, while an element of an engine component design, has no effect on propulsion and is not covered in this post.

As a final note, it must be said that the following analysis assumes a continuous distribution of all quantities. In reality, most quantities in Aurora are either discrete (e.g. engine size, EP modifier) or subject to rounding (e.g. net fuel efficiency). Therefore, the optimal solutions in-game will almost always differ slightly from those presented here.


II. The Aurora Propulsion Equation

Here I will derive the propulsion equation and show how the optimal engine-to-fuel mass ratio of 3:1 arises. The application of these results will be covered in the following section.

To begin, the range and velocity of the ship must be expressed in terms of the quantities laid out in Section (I). The velocity is the simpler of these and is expressed as:

    (4a)

    (4b)

    (4c)

EP = total engine power

The range is somewhat more complicated but still straightforward to derive:

    (5a)

    (5b)

    (5c)

T = fuel endurance in hours
? = overall fuel consumption efficiency

The complications arise from the fuel consumption efficiency, which is the product of three terms:

    (6a)

    (6b)

    (6c)

    (6d)

For missile engines, there is also a fourth term which I will not go into here. The resulting expression for the ship range is then:

    (7)

Eq. (4c) can be rearranged into an expression giving the EP modifier as a function of the desired velocity. Doing so and dividing both sides by the range gives the Aurora Propulsion Equation:

    (8)

Here there are five terms, from left to right:

• The design criteria term, containing the desired ship speed and range
• A numerical conversion factor
• The engine technology term, containing the factors which are usually fixed by the player’s tech levels. This term implies that the maximum engine power and minimum base fuel consumption will give the best performance, as expected.
• The ship specification term. The ship mass is almost always set by the player at the beginning of the design process, The number of engines should be as low as possible, again as expected.
• The component mass ratio term, which we will now address. Note that the factor Ne*Me represents the total engine mass rather than the mass of a single engine, which is why Ne appears in two different terms.

The mass ratio term can be analyzed to give the optimal ratio of engine and fuel masses. Specifically, since the other terms are effectively fixed values, in order to maximize the design criteria (V, R) it is necessary to find the maximum value of the mass ratio term. This is done by solving Eq. (1) for the fuel mass, substituting the result, and seeking to maximize the resulting term:

    (9)

We then make the following substitution and take the derivative of Eq. (9), after factoring out the propulsion mass:

    (10a)

    (10b)

    (10c)

    (10d)

Briefly, to summarize the importance of the result in Eq. (10d):

• For a ship design intended to reach a specific target velocity and range, it is always optimal to have a 3:1 ratio of total engine mass to total fuel mass.
• If this ratio is greater than 3:1, the implication is that the ship could be designed with a higher engine power modifier (i.e. boost factor) yielding the same performance with a smaller engine and larger fuel mass.
• Conversely, if this ratio is less than 3:1, the implication is that the ship could be designed with a lower engine power modifier yielding the same performance with a larger engine and smaller fuel mass.

Aside from small rounding or discretization errors, the only time a 3:1 ratio should not be rigorously adhered to is when the necessary EP modifier is outside of the current or maximum technological limits. Notably, early-game commercial ships may use engines with a maximum EP modifier of 0.5. Usually, not as much fuel is needed to reach an acceptable range and the engine-to-fuel ratio will be greater than 3:1. However, since the commercial engine limits the EP modifier to 0.5 at maximum, no better design is possible.

Finally, it is worth noting that Eq. (8) can be written in terms of the propulsion fraction rather than exact masses:

    (11)

Rewriting the Propulsion Equation in this form gives a useful insight: ship propulsion performance tends to improve as ship size increases. In practice, if V and R are fixed as design criteria by the player, this means that the propulsion fraction decreases slowly as the ship size increases. In terms of ship design, this means that larger ships can dedicate a larger fraction of their mass to mission payload e.g. weapons, hangars, sensor suites, etc.

Additionally, it is worth noting that if the player chooses to use a single engine design to save on research expenditures, so that Ne is proportional to Ms, ships of different sizes will have the same performance and propulsion fractions. This can simplify the process of fleet design somewhat for the player on a tight research budget.


III. Ship Design Using the Propulsion Equation

At this point, I have derived a so-called Propulsion Equation and used it to show that the optimal engine-to-fuel mass ratio is 3:1 exactly. However, thus far aside from some general observations I have not demonstrated how to actually design a ship with this equation.

Broadly speaking, there are three ways a player might use this information. A common design pattern is to choose a fixed propulsion fraction and design to a target speed or range. For example, many players will design a ship with 33% of its mass as engine mass (propulsion fraction 0.44). In this case the free parameter remaining to be solved is the engine power modifier, which can be obtained directly.

For a target velocity the EP modifier is:

    (12)

In this case, the result is a ship with fixed engine mass, fixed maximum velocity, and as much range as possible given those constraints.

A second method is to instead fix the range to solve for the EP modifier:

    (13)

In this case, the result is a ship with fixed engine mass, fixed maximum range, and as much speed as possible given those constraints. While this method is not as commonly used by most players, it is arguably a better approach for fleet design as usually a fleet only needs a specific range to fulfill its mission, while more speed is almost always desirable.

Both of these methods use the insight from the Propulsion Equation that the optimal engine-to-fuel mass ratio is 3:1. However, we can also use the Propulsion Equation directly to design an optimal engine to achieve a target speed and range simultaneously. To accomplish this, simply rewrite the total fuel mass in terms of the engine size (Mf=Ne*Me/3) and substitute this into Eq. (8):

    (14a)

    (14b)

Then using Eq. (4c) the engine power modifier is obtained:

    (15)

Aside from rounding errors, Eqs. (14b) and (15) give the most optimal engine that yields a desired speed and range.

At this point one might ask why anyone should bother with this more complicated method. In fact, it seems much simpler to use Eq. (12) or (13) to reach a desired speed or range, and then get as much possible performance in the other quantity for a given propulsion size. If, for example, one uses Eq. (12) to design an engine to reach a preferred speed but the range is more than desired, they could after all simply reduce the propulsion mass until the range seems reasonable. This is true, if and only if the player intends to research a single engine design and use it for all ships in a fleet.

The method given in Eqs. (14) and (15) is much more powerful when the player chooses to invest additional RP into designing multiple engines, up to one engine per ship size/class in the fleet. In this case, assuming that the player wants the ships in the fleet to have roughly equal speeds and ranges (excess of either is of course wasted unless the fleet doctrine requires breaking into subfleets during an operation), in general the optimal propulsion mass will not be the same for ships of different sizes. If all ships in a fleet share the same R, V, and Ne, then from Eqs. (14b) and (15) the engine difference between two ships of different total sizes will be:

    (16a)

    (16b)

It is apparent that a larger ship will achieve the same range and velocity as a smaller ship with a smaller relative engine mass (and fuel mass! Remember the 3:1 ratio) and a higher engine power modifier. In other words, by using this design approach the tonnage of a larger ship which is available for weapons, hangars, armor/shields, etc. will be maximized.

One caveat exists: in general, due to rounding and discrete parameter values in Aurora, it is rarely possible to get an exact match of range and/or speed between two ships using this approach. Often this will result in small amounts of excess speed and/or range which can be construed as wasted tonnage in a fleet setting. However, the overall fleet design will be as close to optimal as possible, provided of course that the player is willing to invest into the necessary research.


IV. Accounting for Crew Requirements

In Section (I) I briefly alluded to the possibility of accounting for crew quarters in the design process. To conclude this post I will show briefly how this is done.

The Propulsion Equation in the form of Eq. (8) remains unchanged, however the substitution for fuel mass is determined from Eq. (3), yielding in analogy to Eq. (9):

    (17)

The crew number requirement for an engine is simply the product of the engine size and EP modifier. The total crew quarters size, in tons, is the product of the crew number and the cube root of the deployment time in months. Thus, the total crew quarters size in HS (1 ton = 0.02 HS) is expressed as:

    (18)

Noting that this has the same engine mass factor as before, we can still make the substitution of Eq. (10a) into Eq. (17) as we did with Eq. (9), yielding:

    (10a)

    (19a)

    (19b)

    (19c)

    (19d)

Interestingly, the relative fuel mass is unchanged from the previous case, however the relative engine mass is reduced by a small amount. This is often negligible, however for high engine power modifiers or long deployment times the change can be on the order of 5% smaller engine mass compared to the previous case. This is in practice most likely to be apparent when designing survey ships due to their long deployment times, since high-boost ships such as fighters usually are optimized solely for high combat speed rather than range and are subject to large deviations from the optimal point due to rounding of small component values.

Returning to Eq. (8) and again rewriting it in terms of the propulsion fraction gives:

    (20)

Substituting Eq. (19c) into Eq. (4c) gives:

    (21)

Substituting this into Eq. (20) finally gives:

    (22)

This can be verified by taking the deployment time as zero, and showing that Eq. (22) in this case is identical to Eq. (15). Solving the resulting quartic equation, which can be done analytically with some effort, yields the optimal propulsion fraction and then the propulsion fraction and/or mass. An easier solution to implement, given the discrete nature of the engine power modifier in Aurora, may be to create a lookup table instead.

It should be noted, for completeness, that the approach of choosing a fixed propulsion size and designing for a target speed or range remains possible. For a target velocity the engine power modifier is found as:

    (23)

Meanwhile, for a target range:

    (24)

This gives a sextic equation which cannot be solved analytically, to the best of my knowledge. However, I have developed an approximation which works well over the reasonable range of deployment times (using this approximation for, say, a 20-year deployment time is not advisable):

    (25)

In general, the effect on range is minimal (range itself only varies with the square root of the additional term).

The difference between this analysis and the preceding sections is largely one of design philosophy, i.e. whether one considers the crew quarters needed to run a propulsion system as part of that propulsion system for the purpose of allocating space on a ship.


V. How Fast Should a Ship Be?

While it is not the intention of this post to prescribe a fleet doctrine, given that I have laid out a method to devise propulsion systems for a specified speed and range it makes sense to briefly consider what would be reasonable benchmarks for those values. Range depends strongly on the ship role, and for a main warship fleet should generally be sufficient for a fleet to travel from Earth or another major naval station to any frontier system of the player’s empire - and then either back again, or else to wait on station for a tanker to catch up. Thus, I cannot say very much about the ideal range for a fleet.

However, the ideal speed is perhaps a more interesting question. Comparing against other technologies at a similar level to a particular engine technology is one possibility, and in this case an interesting comparison is to beam fire control speeds. The table below compares reactor, drive, and beam FC speed technologies at various RP amounts, with the beam FC speed tech placed in a row so that its RP cost is in the same range as the reactor and drive technologies in that row.



Why use beam fire control speed? Aside from the obvious, in a meta-gaming sense the BFC speed at each tech level implies how fast the game expects ships to be going at a point in time when the RP cost of the tech becomes reasonable for a typical race.

That being said, for beam-armed fleets the speeds after Nuclear Pulse do strike me as low, and I would probably recommend aiming for the next speed up in your propulsion design (e.g. at Ion Drive level, aim for a fleet speed of 5000 km/s rather than 4000 km/s). Beam ships do need the extra speed to close range more quickly, and the BFC speed can match this with a mere +25% size which is not too costly.

For missile fleets however I think the speed in the same row as the player’s drive tech is reasonable. Missile fleets do not need to move as quickly, even at 80% of the speed of a beam-armed fleet a missile fleet in full reverse can cause their opponents to require 5x as long to close the range which should be ample time to fire off enough missiles to decide the battle. The lower speed means a lower propulsion mass which allows more magazine space or larger salvos as desired.

Finally, it is worth repeating that I do not intend to give a comprehensive answer to the question of ideal fleet speeds, rather I am giving some general thoughts to accompany a design framework in which fleet speed is an input parameter. Ultimately, it is the responsibility of the player to consider all of the variables in their own game and select a fleet design speed accordingly.

[Zap0]

Some impressive math! My ship design bureaus are currently hiring :-)

Rewriting the Propulsion Equation in this form gives a useful insight: ship propulsion performance tends to improve as ship size increases. In practice, if V and R are fixed as design criteria by the player, this means that the propulsion fraction decreases slowly as the ship size increases. In terms of ship design, this means that larger ships can dedicate a larger fraction of their mass to mission payload e.g. weapons, hangars, sensor suites, etc.

Why is that exactly? Only if you increase the ship mass in relation to it's number of engines, meaning having larger and more efficient engines on a ship instead of more small ones? Or is there something else making larger ships more efficient irrespective of size/number of engines?
In either case, the application of that knowledge for warships will likely remain limited as restraining engine size has benefits in HTK and maintenance.

I'd also like to explore the limits of the usage of the the 3:1 fuel ratio from a practical standpoint. As this is a very theoretical approach it does not factor in fuel as a limited resource, which may cause somebody to want to include less fuel than the ratio suggests. For instance in freighters using such ratios would be absurd.
If an empire finds itself generally low on fuel/with bad access to it and therfore prefers ships with higher efficiency, how does the situation change when you set a specific fuel amount (or an amount per tonnage) as a design parameter?

There's another factor that may be worth looking at: fuel time. How long does a tank last? Assuming that you always want to have at least as much deployment time on a ship as it takes to run the tank dry (eventually plus some certain percentage of that or a fixed amount of time), does a given propulsion configuration reduce it's own efficiency by requiring a larger deployment time, meaning more crew? I'm imagining this may be an interesting thing to know for designing survey ships and serve as a reason to reduce deployment times and increase the boost factor.

A question: The crew requirement of engines is proportional to the increase in engine power in an engine, right? There is no reason to say many small, heavily boosted engines require a significantly larger amount of crew than fewer, slightly more efficient and therefore less boosted engines?

[misanthropope]

"hey you can easily get a lot more square footage for your housing budget, optimum is to buy a house in Kansas"

[Droll]

"hey you can easily get a lot more square footage for your housing budget, optimum is to buy a house in Kansas"

I was waiting for the TLDR, thank you. I can finally start my real estate empire.

[nuclearslurpee (OP)]

Rewriting the Propulsion Equation in this form gives a useful insight: ship propulsion performance tends to improve as ship size increases. In practice, if V and R are fixed as design criteria by the player, this means that the propulsion fraction decreases slowly as the ship size increases. In terms of ship design, this means that larger ships can dedicate a larger fraction of their mass to mission payload e.g. weapons, hangars, sensor suites, etc.

Why is that exactly? Only if you increase the ship mass in relation to it's number of engines, meaning having larger and more efficient engines on a ship instead of more small ones? Or is there something else making larger ships more efficient irrespective of size/number of engines?

Because a larger engine is more efficient than a smaller engine with the same EP modifier, purely due to increased efficiency from engine size (see Eq. 6c). Because of this, you would get more range out of the same amount of fuel (assuming 3:1 ratio). If you do not need so much range, it becomes possible to use a smaller engine with a larger boost modifier to get the same speed while bringing the range back down to the desired value.

For example: suppose I want to have 5,000-ton frigate and 10,000-ton cruiser designs for a INPE fleet with speed 4000 km/s and range 20 billion km, using two engines per ship for redundancy in case of battle damage. For the frigate, this can be accomplished using two size-16.8 HS engines with a 1.20x EP modifier along with 10.84 HS of fuel, so the total propulsion size is 44.44 HS. For the cruiser, using the same relative proportion would give me two size-33.6 engines and 21.68 HS of fuel for a propulsion size of 88.88, however this would have a range of 28.3 billion km which is much more than we need. Instead, we can push the EP modifier up to 1.30x and build size-31 HS engines along with only 19.46 HS of fuel - a total propulsion size of only 81.46 HS. That gives an extra 373 tons (3.7% of total mass) for weapons, armor, shields, etc. while giving the same speed and range as the smaller frigate.

To sum up: because larger engines are more fuel-efficient, you can get the same performance as a smaller engine using a higher EP modifier and lower mass fraction. It's a bit unintuitive but it works.

In either case, the application of that knowledge for warships will likely remain limited as restraining engine size has benefits in HTK and maintenance.

Certainly this gets into the questions of fleet doctrine which are beyond the scope of my post. However, it is worth noting that the benefits in HTK and maintenance are offset at least in part by the ability to mount extra weapons, armor, etc.  not to mention fuel use as you mentioned later.

I'd also like to explore the limits of the usage of the the 3:1 fuel ratio from a practical standpoint. As this is a very theoretical approach it does not factor in fuel as a limited resource, which may cause somebody to want to include less fuel than the ratio suggests. For instance in freighters using such ratios would be absurd.
If an empire finds itself generally low on fuel/with bad access to it and therfore prefers ships with higher efficiency, how does the situation change when you set a specific fuel amount (or an amount per tonnage) as a design parameter?

It's actually not hard to modify the Propulsion Equation to use a fixed engine:fuel ratio. If we let, say, G be the engine:fuel ratio so that G*Mf=Ne*Me, then the Propulsion Equation becomes:



If we increase engine-to-fuel ratio G, the result is a larger engine is needed to achieve the same performance (and per Eq. 4c it will have a lower EP modifier). The consequence of course is that your overall propulsion size will be larger, thus your warship may be more fuel-efficient but also less capable in combat. This again gets into the realm of doctrinal choice which is more art than science.

With regards to freighters and other commercial ships, this is indeed absurd and I would not suggest using this method to design those ships. The "optimal" design for a freighter engine would usually end up requiring an EP modifier greater than 0.5 which is not even possible on a commercial ship, and I mentioned as much in my OP.

There's another factor that may be worth looking at: fuel time. How long does a tank last? Assuming that you always want to have at least as much deployment time on a ship as it takes to run the tank dry (eventually plus some certain percentage of that or a fixed amount of time), does a given propulsion configuration reduce it's own efficiency by requiring a larger deployment time, meaning more crew? I'm imagining this may be an interesting thing to know for designing survey ships and serve as a reason to reduce deployment times and increase the boost factor.

In theory, yes. However, the deployment time usually accounts for more than just the fuel endurance time as it also counts time when the ship is not moving while doing its job. A survey ship for example splits time between moving around and sitting still running surveys - thus the optimal deployment time depends on how long it takes to survey a body or location as well as on the average distance between those bodies or locations. Similarly, a warship fleet may spend large parts of its deployment time "on station" away from maintenance facilities, not moving and thus not using fuel but still running up the deployment clock. Thus once again deployment time becomes more of an art than a science. Personally, I try to choose deployment times so that my ships come back to the overhaul docks having just ticked past their clocks, since I'd rather deal with tired crewmen than a ship dead in space due to no fuel.

A question: The crew requirement of engines is proportional to the increase in engine power in an engine, right? There is no reason to say many small, heavily boosted engines require a significantly larger amount of crew than fewer, slightly more efficient and therefore less boosted engines?

This is true. While in my OP I expressed it in terms of base quantities, conceptually the crew requirement is proportional to the EP divided by your drive tech (EP per HS), which essentially means your crew quarters requirement is determined only by your design speed. Because of that, it is perfectly reasonable to not consider the crew requirement as part of the propulsion mass, and in fact I do not do this when I design my own engines. Ultimately it is a philosophical distinction; either approach is equally "optimal", it's all a question of bookkeeping.

Some impressive math! My ship design bureaus are currently hiring :-)

My people will be in touch with your people. 

"hey you can easily get a lot more square footage for your housing budget, optimum is to buy a house in Kansas"

The ability to mount 5% larger particle lances on my evil mansion of doom for the same budget is the best and only reason to move to Kansas I have ever heard in my life.

[davidr]

My head has just exploded trying to read this ( just a Maths "O" level ) and never liked solving equations.
nuclearslurpee , many thanks for the information - it must have taken some time to work out.

DavidR

[Jorgen_CAB]

I think the 3:1 engine to fuel ratio being the optimal have been known for a while... good to see it cleared up with some good math...

Of course it is only one part of the puzzle in terms if how a fleet doctrine is laid out overall.

Other considerations you need to consider are fuel consumption versus how active certain ship designs will tend to be versus the productivity of fuel extraction, fleet size and most importantly research costs. Large engines with a very high power to weight efficiency tend to be very expensive to research, not to mention if you also want a reduced thermal engine in addition to this.

When you design ships you also need to look at redundancy, emergency repair and maintenance times and costs. Large expensive engines can also eat up maintenance time and supplies as large expensive components do have an impact on the design for maintenance. From a maintenance perspective several small cheaper components are better than few larger more costly components.

Other considerations are the use of the same engine type in multiple ship types ans ship sizes and you also might have different speed requirement between ship classes as well depending on their strategic and tactical use. Research costs are a huge factor sometimes and it might require sacrifice on some other areas.

You often are also limited by how expensive Jump Engines you can build as to the maximum size you can afford military drives. I actually often design large capital warship with commercial engines so I can jump them with commercial jump drives... then I can build really big ships who are very effective in all but speed, these would be my Dreadnoughts and Super Carriers.

If every ship design have a specifically designed engine design your fleet might become very expensive research wise, even if it is optimised for both range and speed. But sometimes you do want that optimisation regardless. Although I rarely find that type of optimisation is the optimal priority for designing a ship, especially carriers as they need fuel for their parasites as well as its own engines. Nearly all of my capital ships have hangars and parasites of some kind.

Operational range is also something that can vary quite a bit over time or even by geography. You might want the same ship just small variations with more or less fuel as they are generally operating in different geographical areas of your empire (if it is large). This also will make a homogeneous design a bit difficult to make. You might have two different enemies that also need different consideration in engine design when considering speed. Sometimes there is such a thing as too much speed when it comes down to the nuts and bolts of economy.

[brondi00]

Most of the comments are about fleet design philosophy and doctrine and OP already said this isn't about answering those questions.

Instead lets appreciate it for what it is.  Information that helps us understand the trade offs we are making when we design ships. 

I happen to agree with a lot of the caveats in the comments.  Especially about the research expense of custom designing every ship it's own drive system.  Which would be optimal but is not really practical.  I would bet OP also agrees.

But that doesn't mean the info he shared isn't really valuable. 

I happen to custom design drives for "important" ships, which depends on RP at the time.  But if my might empire is going to design a special 50,000 ton warship as the pride of the fleet, then that ship is getting everything as optimized as possible and custom designed just for it.  This information helps.

If I'm designing a small freighter for hauling minerals back then it gets whatever stuff is already researched and sitting on the shelf, even if its a drive from 2 generations ago that was sitting in the stockpile after its original ship was scrapped. 

So thanks OP, from me to you.  I appreciate this.

[nuclearslurpee (OP)]

I think the 3:1 engine to fuel ratio being the optimal have been known for a while... good to see it cleared up with some good math...

Of course it is only one part of the puzzle in terms if how a fleet doctrine is laid out overall.

Other considerations you need to consider are fuel consumption versus how active certain ship designs will tend to be versus the productivity of fuel extraction, fleet size and most importantly research costs. Large engines with a very high power to weight efficiency tend to be very expensive to research, not to mention if you also want a reduced thermal engine in addition to this.

When you design ships you also need to look at redundancy, emergency repair and maintenance times and costs. Large expensive engines can also eat up maintenance time and supplies as large expensive components do have an impact on the design for maintenance. From a maintenance perspective several small cheaper components are better than few larger more costly components.

Other considerations are the use of the same engine type in multiple ship types ans ship sizes and you also might have different speed requirement between ship classes as well depending on their strategic and tactical use. Research costs are a huge factor sometimes and it might require sacrifice on some other areas.

You often are also limited by how expensive Jump Engines you can build as to the maximum size you can afford military drives. I actually often design large capital warship with commercial engines so I can jump them with commercial jump drives... then I can build really big ships who are very effective in all but speed, these would be my Dreadnoughts and Super Carriers.

If every ship design have a specifically designed engine design your fleet might become very expensive research wise, even if it is optimised for both range and speed. But sometimes you do want that optimisation regardless. Although I rarely find that type of optimisation is the optimal priority for designing a ship, especially carriers as they need fuel for their parasites as well as its own engines. Nearly all of my capital ships have hangars and parasites of some kind.

Operational range is also something that can vary quite a bit over time or even by geography. You might want the same ship just small variations with more or less fuel as they are generally operating in different geographical areas of your empire (if it is large). This also will make a homogeneous design a bit difficult to make. You might have two different enemies that also need different consideration in engine design when considering speed. Sometimes there is such a thing as too much speed when it comes down to the nuts and bolts of economy.

Thanks for bringing up quite a lot of important doctrine points. Of course, I had to limit the scope of the OP to not dig into the doctrine questions, else I'd be writing an entire thesis on the subject of engine design in a game!    Perhaps a bit much...

Generally my intention was to clarify the mechanics involved in engine design and performance, and to provide the basic application which is in this case the optimization of the engines. Even if one uses this as a jumping-off point for modification to fit their own doctrine I think that is better than blindly throwing engines on a craft and hoping the design is good enough. For example, an important concept which many people miss is that fewer, larger engines are more fuel-efficient thus reducing how much ship mass is taken up for propulsion, of course that efficiency at the cost of research but for many players fuel is more limited than RP (and, of course, vice-versa, every game is different!). I see many ship designs with 10 or 20 smaller engines when just 2, 3, or 4 would save a lot of tonnage and fuel, simply because they are using the same engine on their small and large ships to save RPs.

In my mind, this post is the "fundamental science" that underlies Aurora's "applied science" in the sense of making clear what the rules are, with the implicit understanding that rules are meant to be broken. 

Most of the comments are about fleet design philosophy and doctrine and OP already said this isn't about answering those questions.

Instead lets appreciate it for what it is.  Information that helps us understand the trade offs we are making when we design ships. 

I happen to agree with a lot of the caveats in the comments.  Especially about the research expense of custom designing every ship it's own drive system.  Which would be optimal but is not really practical.  I would bet OP also agrees.

But that doesn't mean the info he shared isn't really valuable. 

I happen to custom design drives for "important" ships, which depends on RP at the time.  But if my might empire is going to design a special 50,000 ton warship as the pride of the fleet, then that ship is getting everything as optimized as possible and custom designed just for it.  This information helps.

If I'm designing a small freighter for hauling minerals back then it gets whatever stuff is already researched and sitting on the shelf, even if its a drive from 2 generations ago that was sitting in the stockpile after its original ship was scrapped. 

So thanks OP, from me to you.  I appreciate this.

Quite accurate, I appreciate your insights.

[Jorgen_CAB]

Thanks for bringing up quite a lot of important doctrine points. Of course, I had to limit the scope of the OP to not dig into the doctrine questions, else I'd be writing an entire thesis on the subject of engine design in a game!    Perhaps a bit much...

Generally my intention was to clarify the mechanics involved in engine design and performance, and to provide the basic application which is in this case the optimization of the engines. Even if one uses this as a jumping-off point for modification to fit their own doctrine I think that is better than blindly throwing engines on a craft and hoping the design is good enough. For example, an important concept which many people miss is that fewer, larger engines are more fuel-efficient thus reducing how much ship mass is taken up for propulsion, of course that efficiency at the cost of research but for many players fuel is more limited than RP (and, of course, vice-versa, every game is different!). I see many ship designs with 10 or 20 smaller engines when just 2, 3, or 4 would save a lot of tonnage and fuel, simply because they are using the same engine on their small and large ships to save RPs.

In my mind, this post is the "fundamental science" that underlies Aurora's "applied science" in the sense of making clear what the rules are, with the implicit understanding that rules are meant to be broken. 

I agree and I do also appreciate your thorough and well written insight into engine optimisation. I do think it is very valuable to many people to understand how to design an optimal engine. If you understand this you can then go to the next step and make sound decision for what you want to sacrifice in different areas or version of ships.

It is easier to make good decisions of you understand the fundamentals... then you can make good decisions for pros and cons of designs in terms of both tactical, operational and strategic reasons.

Me personally when designing a ship one of the the thing I look at is actually total fuel efficiency and then try to see how I can design an engine around those parameters. For example I generally want most capital warships to have around 30-60% fuel efficiency... If I can get inside that bracket I know roughly how much fuel I need to be able to produce and store in order to operate my fleets in a long term perspective.

My comment was mainly as a complement to your post in a general sense of importance to reflect on after you understand how to optimise an engine.

For me personally RP is almost always the biggest constraint because of role-play reasons. I always dedicate research complexes to specific fields and don't allow complexes to be switched between projects indiscriminately. In combination with usually running at 10-20% research efficiency a new large expensive engines might take like 5-10 years to develop in the first place... 

[nuclearslurpee (OP)]

For me personally RP is almost always the biggest constraint because of role-play reasons. I always dedicate research complexes to specific fields and don't allow complexes to be switched between projects indiscriminately. In combination with usually running at 10-20% research efficiency a new large expensive engines might take like 5-10 years to develop in the first place... 

I usually find that in the start of a game, instant-researching dedicated engines ends up taking a good chunk of RP, but as the game goes on and tech levels increase the relative cost of new engines starts to drop off, since tech costs for each tech level N increase as 2^N but engine development is only 5*EP (times the EP modifier if less than 1.0x) where EP scales at about 1.20^N. Once you reach the largest ship size you want to build, and your EP modifiers start to stabilize (usually around the 1.25x or 1.5x mark for everything except fighters, for me), it increasingly becomes economical to optimize engines instead of burning your way up the tech tree, which makes sense thematically as it should be more sensible to optimize the engine tech you've got as developing new tech gets harder.

I'll also say, your comments have me wondering about how the math looks if we set a desired speed and range but try to optimize fuel efficiency instead of propulsion mass. That sounds like something many players would find useful.

[nuclearslurpee (OP)]

I would apologize for resurrecting such an old post, but frankly I think it is a useful enough post to merit an occasional cheating of death, and more importantly I have a useful new contribution to add. While if I were to rewrite the OP today it would probably be somewhat different, I do stand by the major conclusions - Eqns. (12) through (15) remain completely correct and will give you the "most optimal" propulsion design in the sense of dedicating the minimum fraction of total ship mass to engine plus fuel load by maintaining the 3:1 ratio of engine to fuel mass.

However, it is a common rejoinder that the 3:1 ratio is not necessarily optimal when we consider various strategic factors beyond the perfect design of single ships. Legend has it that if you say "three-to-one engine-to-fuel ratio" into a mirror three times at midnight you will be haunted by Bloody Mary Jorgen. Some of these considerations, such as research cost for a series of optimal engines, have been somewhat mitigated since the OP was written by the change to component research costs; others, such as reducing the total build cost of a fleet, are worthy considerations but defy a simple analytical treatment which is limited to propulsion analysis only. However, one of the most important and oft-mentioned considerations is that of fuel consumption - this is a matter not only of raw fuel production but also logistics - the more fuel a fleet consumes in pursuit of that ivory 3:1 ratio, the heftier must be the tanker force that supports that fleet on extended operations.

In a comment I have given the straightforward modification of the Propulsion Equation, reproduced below, where G is the desired engine-to-fuel mass ratio. Commonly, this property ranges from 10 to 20 in most sensible designs I see posted on these forums, albeit not necessarily with any clear rhyme nor reason.

   

(All terms are as defined in the OP.) However, to be frank the concept of an arbitrary ratio is not terribly intuitive or useful to the average player. 3:1 is all well and good for optimization, but how does one relate a 10:1 or 15:1 ratio to actual fuel consumption to decide which is best? It is simply not very friendly for the purposes of designing a ship.

There is a more intuitive approach. Recall the Propulsion Equation (8) from the OP, which I rewrite here in a slightly different arrangement:

        (A.1)

Here I have set to the right-hand side the quantity Mf*Cf, which gives the total fuel volume in litres [sic]. This is a quantity which is much like speed and range in that it is readily comprehensible by the player and translates directly into useful in-game information. We can immediately combine these three quantities together to define a so-called mission profile parameter:

        (A.2)

Here we introduce the concept of a "mission", from the perspective of propulsion analysis, as "I need to go this far, at this speed, using this much fuel". This is, I think, much more useful information as it allows an astute admiral to judge whether he can afford to send his ships on a mission, or perhaps how many missions he can send his ships on, and to use this kind of calculation as a design parameter rather than finding out rather much after the Navy has been designed and built.

We can use this information to straightforwardly determine what size of engine we need for a given ship. We can write the result in a few different ways, but a good conceptual breakdown is:

        (A.3)

Here, on the right-hand side, we have three terms which represent conceptual groupings: the first term is the mission profile parameter already discussed; the second term represents your technology levels, which are essentially fixed for design purposes; the third term represents a design factor which is fixed by considerations outside the scope of this analysis - it is obvious that maximizing ship mass and minimizing the number of engines will be strictly optimal in theory (up to the limits of the player's tech level, of course), but in practice if the Admiralty requires a 32,500-ton battlecruiser which is to be built with three engines for redundancy against battle damage, then that is what we must design for them.

I hope this addendum is useful for players who are for whatever very good reasons not fans of the strictly "optimal" approach, or perhaps for those who mind find this a helpful roleplay tool which puts a little more power back into the hands of the admiralty instead of the ship design offices, for better or worse.

[Scandinavian]

Would this analysis change if you use a design doctrine that accompanies deploying fleets with tankers? Effectively you break the your total range into a "deployment range" where your ships are accompanied by their oilers, and a "mission range" where the oilers run off back to a safe(r) place.

It could also get you different speeds, but my intuition is that the fuel and Gallicite savings from accepting lower deployment speeds are negligible, since they only apply to the oilers.

It lets you essentially "outsource" maybe 10 % of total vessel mass to the tankers, which has both design and doctrinal advantages (that's 10 % of vessel mass you don't need to provide armor bands for, to take just the simplest cost saving), but I'd be interested in understanding whether it changes the fuel consumption and Gallicite cost profile specifically. (Total tonnage becomes more ambiguous when you allow part of the tonnage to run off and hide before you make your final jump).

[Jorgen_CAB]

Operational range in these calculations is the range you expect the ships to move without access to fuel. This can from a doctrinal perspective include tankers to extend the maximum operational range of a fleet. But the calculations only care about the actual operational range you desire from the design itself. If you intend to deploy tankers that is a doctrinal choice that will likely impact the desired operational range of any design.

Personally I often base engine designs around a specific range of fuel consumption.This makes it easy to estimate fleets long term perspective in terms of fuel usage. This makes it easier to design and manage the fuel logistics of a growing empire. Speed and operational range then just become a matter of engine size and amount of fuel.

It probably is not terribly uncommon to use the same engine in different designs with different conditions for either speed or operational range.

[nuclearslurpee (OP)]

Would this analysis change if you use a design doctrine that accompanies deploying fleets with tankers? Effectively you break the your total range into a "deployment range" where your ships are accompanied by their oilers, and a "mission range" where the oilers run off back to a safe(r) place.

It could also get you different speeds, but my intuition is that the fuel and Gallicite savings from accepting lower deployment speeds are negligible, since they only apply to the oilers.

It lets you essentially "outsource" maybe 10 % of total vessel mass to the tankers, which has both design and doctrinal advantages (that's 10 % of vessel mass you don't need to provide armor bands for, to take just the simplest cost saving), but I'd be interested in understanding whether it changes the fuel consumption and Gallicite cost profile specifically. (Total tonnage becomes more ambiguous when you allow part of the tonnage to run off and hide before you make your final jump).

Essentially for the purpose of ship design you are looking at the "mission range", hence the term "mission profile parameter". The decision of how to handle tankers is entirely strategic - basically, you would decide that you want to use tankers first, then work out what kind of deployment range (i.e., given a fleet that requires X fuel to go Y km, if you send tankers you want to have an effective strategic range of n*Y where n is however many refuels your tankers should provide), and then from that work out a suitable mission range.

What the propulsion design equations tell you is not how to choose these criteria, but rather once you've chosen the criteria how do you design an optimal engine for the job. All of the "thinking" so to speak happens when you actually choose those criteria based on the needs of the Empire - which means it can be some mix of the player trying to figure out the best mission profile to serve their needs, or it is a roleplay opportunity as you think about how your admirals and politicians might set these criteria. The latter is IMO the most interesting, as this means you can roleplay questionable decision making by the high command elements, and still translate that into a "good" ship design for the stated criteria, which IMO at least feels more realistic than making an intentionally mechanically bad ship design to simulate that (e.g., mismatching fire controls, underpowered reactors, etc.).