Author Topic: A formal look at various efficiencies  (Read 1621 times)

0 Members and 1 Guest are viewing this topic.

Offline Iranon

  • Captain
  • **********
  • Posts: 473
  • Thanked: 32 times
    • View Profile
A formal look at various efficiencies
« on: November 03, 2016, 06:48:48 AM »
1) Let's assume we have a fixed tonnage budget for propulsion, i.e. engines and fuel, and we're interested in the trade-off between performance and fuel efficiency.

Let x be the proportion of fuel in our propulsion tonnage.
(1-x) is therefore our engine proportion. Keeping speed constant, this is proportionate to the inverse of our power multiplier.
Specific fuel consumption is proportionate to power multiplier ^2.5
Our range is therefore proportionate to x(1-x)^2.5
I find it more useful to map fuel use to speed at constant range than to range at constant speed: (x(1-x)^2.5)^0.4
Standardising for 1.0 as the highest possible speed, achieved at x=2/7, we get (x(1-x)^2.5)^0.4*1.4/(2/7)^0.4

Google calculator (just put the last function into a Google search field) gives us a nice graph with value pairs if we mouse over it.
This is ready for use with no further thought, I'm not aware of any hidden pitfalls.

*

2) Now let's look at the effect of engine tonnage on cost and fuel efficiency. Speed is kept constant. We use a standard size for every single engine.
We simplify things a little and think of our ship as consisting of engine and payload, x being the proportion allocated to engines and (1-x) therefore being the payload.

Power is kept constant, so power multiplier is proportionate to 1/x.
Fuel consumption is therefore proportionate to (1/x)^2.5
Fuel efficiency is therefore proportionate to (1/x)^2.5/(1-x)
Standardising for 1 at the most efficient setup at x=0.714286, we get ((1/x)^2.5/(1-x))/8.11686

With power multiplier above 1.0, the engine cost is the same no matter the size. Cost efficiency of the propulsion plant is therefore 1/(1-x), the theoretical optimum being an infinitesimally small engine with infinite power multiplier.

With power multiplier below 1.0, cost of a single engine scales quadratically with power multiplier, so engine cost is proportionate to  1/x. Cost efficiency of the propulsion plant is therefore proportionate to (1/x)/(1-x). Standardised for 1 at our most cost-efficient setup, achieved at x=0,5, we get 1/(4x-4x^2)

*

Putting ((1/x)^2.5)/(1-x))/8.11686 , 1/(1-x), 1/(4x-4x^2) into the Google search field gives you these graphs (fuel efficiency, cost efficency > 1.0, cost efficiency <1-0). For a useful overview we may want to zoom to have about 0.15 to 0.75 for x and 0.5 to 6 for f(x).

While I find this useful, this needs a little more caution than 1).
We count everything that isn't engine as payload. That includes bridge, engineering spaces, armour (can't do away with the first layer), and all sorts of other things we may not think of as mission tonnage. So a seemingly very fuel-efficient design with 70% engines may not carry a lot of stuff we actually care about, dramatically lowering practical efficiency.
What we count as overhead and what as mission tonnage isn't even fixed: for a general purpose warship armour may be mission tonnage, if a given speed in nebulae is a non-negotiable requirement some or all may be overhead.
Likewise, our ship will need to carry some fuel at the cost of payload, so our ship with the compact high-power engines may not be quite as cost-efficient as the graph implies. And if we'd need >40% of engine weight in fuel, corresponding to the 2/7 of propulsion tonnage as in 1), we probably dropped the ball.

Comments about correctness, clarity, usefulness or considerations I neglected are warmly appreciated.

EDIT: Assuming 5%/10% of ship size as overhead to be subtracted from the effective payload, one gets
((1/x)^2.5)/(0.95-x)/9.7130565 , 1/(0.95-x)*0.95, 1/x/(0.95-x)/4.43213
or
((1/x)^2.5)/(0.9-x)/11.7365 , 1/(0.9-x)*0.9, 1/x/(0.9-x)/4.93827
« Last Edit: November 07, 2016, 06:43:52 PM by Iranon »
 
The following users thanked this post: zaze

Offline TCD

  • Lieutenant
  • *******
  • Posts: 157
  • Thanked: 6 times
    • View Profile
Re: A formal look at various efficiencies
« Reply #1 on: November 03, 2016, 01:44:57 PM »
Hmm, I'm afraid this is all a bit complicated for me, how am I supposed to use these?

1) is this telling me that a 72:28 engine to fuel ratio will be the most fuel efficient? So if I always want my 10kt ships to have 40% propulsion tonnage, I should build a single engine of size 28.8kt and 11.2kt of fuel space to maximize fuel efficiency?

 

Offline Iranon

  • Captain
  • **********
  • Posts: 473
  • Thanked: 32 times
    • View Profile
Re: A formal look at various efficiencies
« Reply #2 on: November 03, 2016, 02:42:45 PM »
Not quite. 2/7 fuel (slightly less than 28%; maybe easier to design with if you think of it as 2 part fuel and 5 parts engine, i.e. 40% of engine weight) is the least fuel-efficient setup that makes sense, namely the the performance-optimum.
If you want to find out how much speed you lose for cutting the performance-optimal fuel load in half, you'd check at 1/7 (around 0.143, around 0.91 of maximum achievable speed).
« Last Edit: November 03, 2016, 02:44:54 PM by Iranon »
 

Offline TCD

  • Lieutenant
  • *******
  • Posts: 157
  • Thanked: 6 times
    • View Profile
Re: A formal look at various efficiencies
« Reply #3 on: November 03, 2016, 06:29:11 PM »
Ah okay, thanks. I had it backwards. So I should always think of 2/7 as my optimum performance, then look at if the range that gives is acceptable, and if not gradually move to say 3/7 accepting that range/efficiency will be improving as speed decreases?
 

Offline Iranon

  • Captain
  • **********
  • Posts: 473
  • Thanked: 32 times
    • View Profile
Re: A formal look at various efficiencies
« Reply #4 on: November 03, 2016, 07:28:44 PM »
You should move to less than 2/7 fuel, and constant range is assumed.
For ships that aren't meant to refuel others, you can ignore anything to the right of 2/7, as that'd use more fuel while being slower.

Performance-optimal would be ~0.286, or 40% of engine tonnage, for 100% of achievable speed and 100% fuel we can use without wasting any.
At  0.2, or 25% of engine tonnage, we achieve 97% of our maximum speed but only use 0.2/(2/7)=70% as much fuel.
At ~0.167, or 20% of engine tonnage, we achieve 94% of our maximum speed using (1/6)/(2/7)=58% as much fuel.
At ~0.091, or 10% of engine tonnage, we achieve about 80% of our maximum speed using (1/11)/(2/7)=32% as much fuel.
At ~0.048, or  5% of engine tonnage, we achieve about 65% of our maximum speed using (1/21)/(2/7)=17% as much fuel.
At ~0.010, or  1% of engine tonnage, we achieve about 36% of our maximum speed using (1/101)/(2/7)= 3% as much fuel.
« Last Edit: November 03, 2016, 07:37:13 PM by Iranon »
 

Offline TCD

  • Lieutenant
  • *******
  • Posts: 157
  • Thanked: 6 times
    • View Profile
Re: A formal look at various efficiencies
« Reply #5 on: November 04, 2016, 08:01:31 AM »
You should move to less than 2/7 fuel, and constant range is assumed.
For ships that aren't meant to refuel others, you can ignore anything to the right of 2/7, as that'd use more fuel while being slower.

Performance-optimal would be ~0.286, or 40% of engine tonnage, for 100% of achievable speed and 100% fuel we can use without wasting any.
At  0.2, or 25% of engine tonnage, we achieve 97% of our maximum speed but only use 0.2/(2/7)=70% as much fuel.
At ~0.167, or 20% of engine tonnage, we achieve 94% of our maximum speed using (1/6)/(2/7)=58% as much fuel.
At ~0.091, or 10% of engine tonnage, we achieve about 80% of our maximum speed using (1/11)/(2/7)=32% as much fuel.
At ~0.048, or  5% of engine tonnage, we achieve about 65% of our maximum speed using (1/21)/(2/7)=17% as much fuel.
At ~0.010, or  1% of engine tonnage, we achieve about 36% of our maximum speed using (1/101)/(2/7)= 3% as much fuel.
Wow, the 94% speed for 58% as much fuel is very dramatic. It looks like 1:4 is a pretty good balance for most uses. Very helpful. Thanks for explaining this Iranon.
 

Offline Iranon

  • Captain
  • **********
  • Posts: 473
  • Thanked: 32 times
    • View Profile
Re: A formal look at various efficiencies
« Reply #6 on: November 04, 2016, 06:34:31 PM »
Additional thoughts for 2)...

Much of the time, our speed requirement may be such that we consider engines below and above 1.0 power.
I hadn't thought about combining the cost efficiency graphs because I thought it'd be complicated... fortunately, it isn't:

A unified graph naturally needs to join the partial graphs at whatever x corresponds to a 1.0-power engine; one of them needs to be multiplied by a constant greater or equal to 1.
As given, they reflect the "standard" speed requirement achieved with 25% tonnage of 1.0 power engines.
If a higher speed is required, the low-power efficiency curve (1/(4x-4x^2) by default, used to the right) is multiplied by the same factor.
If a lower speed is required, the high-power effiiciency curve (1/(1-x) by default, used to the left) is multiplied by the inverse of the factor.

Incidentally, the  graph shows that the "standard" propulsion setup - 25% 1.0 engines - is absolutely pants: a local maximum, deviating from it to either side is cheaper.
There are some requirements where they are borderline reasonable, but I avoid 1.0 power engines on principle.
« Last Edit: November 04, 2016, 06:37:16 PM by Iranon »
 

Offline Jorgen_CAB

  • Commodore
  • **********
  • Posts: 667
  • Thanked: 1 times
    • View Profile
Re: A formal look at various efficiencies
« Reply #7 on: November 07, 2016, 05:46:00 AM »
I really appreciate your dedication to engine versus fuel efficiency. But when do you actually have engine to fuel ratio as the primary objective of any ship design?

I find that design constraints are rather what speed and range I desire in contrast with other things that never make me able to produce a ship with a ratio of engine to fuel efficiency for range. Different ships with the same engine might have different constraint on their design concept.

I usually just have a operational range as one parameter and engine size as another, they rarely coincide with each other very well. The rest is just a measure of how much speed I will sacrifice for fuel efficiency. One engine might also often be used in multiple ship types and sizes and make up different weight ratios in different ships.

In general smaller ships tend to have more powerful engines and larger ships less powerfully engines for fuel efficiency. Mainly to reduce the necessary logistical and infrastructure investment in fuel production as well as upgrading, retrofitting and maintenance of my ships. It is a fairly straightforward process to calculate the optimal fuel to engine ratio for best range, but that seem rarely to be important when designing the concept of your fleet objectives.

But I might just be wrong and missing the overall picture. Some practical examples would be nice... :)
« Last Edit: November 07, 2016, 09:55:25 AM by Jorgen_CAB »
 

Offline Iranon

  • Captain
  • **********
  • Posts: 473
  • Thanked: 32 times
    • View Profile
Re: A formal look at various efficiencies
« Reply #8 on: November 07, 2016, 04:14:57 PM »
Fuel:Engine ratio isn't really a design objective in its own right, but an indicator of how one balances two other objectives (performance and fuel-efficiency)... or failed to do so (at x>2/7 for non-tankers).

I'm generally happy to sacrifice 3% speed for 30% fuel savings, so I don't like to go above x=0.2. Where exactly we draw the line for what kind of design isn't important at all, hat is important is that we draw it somewhere:
If we blithely use overpowered engines and carry the same weight in fuel to meet our operational range requirements (x=0.5, f=0.88), we use 4  times as much fuel than we need to for the performance we get (x=0.125, f=0.88). Alternatively, we could increase speed considerably at half the fuel consumption (x=0.25, f>0.99).
In more practical terms,  using a mix of 100HS*2.0 engines + 100HS fuel would be slower and shorter ranged than 150HS*1.5 in engines and 50HS fuel, at twice the fuel use.
Something I'd probably like even better is downscale the design by 10%, use 1.35 power and an accordingly reduced fuel load. But that's overthinking it, 50HS fuel is fine assuming our range and speed requirements were sane in the first place.

It seems we standardise our fleets along different lines.
There is little correlation between size and engine power multiplier in my fleets. I often build slow fighters designed for independent low-visibility operations spanning multiple years, I sometimes build highly stressed hangar-based ships >10000t.
Engines (usually 1 or 50HS) and speeds are fairly standardised in my fleets though, sometimes over multiple generations: initial fast fleet makes considerable design concessions to outrun all known enemies. Later additions keep the performance and improve on economy.
 

Offline Jorgen_CAB

  • Commodore
  • **********
  • Posts: 667
  • Thanked: 1 times
    • View Profile
Re: A formal look at various efficiencies
« Reply #9 on: November 08, 2016, 05:17:04 AM »
That was why I asked for some practical example ships to see when this is actually super relevant...

I looked at a game I had played for a short while with magneto plasma drives and an overall fuel efficiency of 0.7. I had a standard engine for fast ships at x1 power with a 0.63 fuel efficiency.

One ship I just quickly glanced at was a fast armored invasion ship (troop transport), 10000t and 4000km/s speed, same speed as my 12000t destroyers.

The ship had my standard 20 billion km range which is the standard range for a destroyer type military ship. 18 month deployment and 2.5 years on the maintenance cycle.

The engine made up 25% of the size of the ship but adding crew, maintenance and armor the engine displaced about 29% of the ship total size. The fuel was 5% but with maintenance and armor (no crew) it displaced 5.35%.

My larger ships and such as cruisers and carriers usually use 0.8 to 0.9 multiplier on the engine. This decrease research and fuel cost considerably and the engines are usually a bit bigger to reduce fuel consumption even more. I rarely research 50HS engines until later in the game when such engines are cheap in comparison with fuel efficiency technologies.

Another thing, in most of my military designs from destroyer and up they all have hangars and recon or strike crafts of some kind, this also mean I need extra large fuel reserves for those crafts... fuel I can use for traveling further if I have to. This also put a huge kink into the engine versus fuel ratio relationship a ship might need.

If I replace the above engine with a 0.9 efficient engine the speed dropped to 3600km/s and fuel efficiency was 0.48 instead of 0.63. With everything else the same I could add an additional 200t of mission tonnage.
« Last Edit: November 08, 2016, 05:41:21 AM by Jorgen_CAB »
 

Offline Iranon

  • Captain
  • **********
  • Posts: 473
  • Thanked: 32 times
    • View Profile
Re: A formal look at various efficiencies
« Reply #10 on: November 09, 2016, 05:49:59 AM »
Well, if you cede performance, you can naturally get better fuel efficiency and additional space for mission tonnage... but when so many things change at once, I find it hard to draw conclusion for overall design practice. I'd try to keep most things constant:

Code: [Select]
Vanilla class Escort Cruiser    10 000 tons     401 Crew     1883 BP      TCS 200  TH 1200  EM 0
6000 km/s     Armour 3-41     Shields 0-0     Sensors 1/1/0/0     Damage Control Rating 2     PPV 90
Maint Life 1.04 Years     MSP 294    AFR 320%    IFR 4.4%    1YR 274    5YR 4108    Max Repair 300 MSP
Intended Deployment Time: 6 months    Spare Berths 0   

25x1.5 Magneto-plasma Drive (2)    Power 600    Fuel Use 103.34%    Signature 600    Exp 15%
Fuel Capacity 750 000 Litres    Range 13.1 billion km   (25 days at full power)

10cm Railgun V3/C3 (30x4)    Range 30 000km     TS: 6000 km/s     Power 3-3     RM 3    ROF 5        1 1 1 0 0 0 0 0 0 0
Fire Control S00.7 40-6000 (3)    Max Range: 80 000 km   TS: 6000 km/s     88 75 62 50 38 25 12 0 0 0
Stellarator Fusion Reactor Technology PB-1.25 (30)     Total Power Output 90    Armour 0    Exp 20%

This design is classed as a Military Vessel for maintenance purposes

A fairly basic, moderately fast escort in the "standard" 25% engine tonnage configuration.
7.5% fuel is on the high side, but not entirely unreasonable.
What happens if we fit bigger engines at the expense of weaponry, without changing mission requirements or size of available shipyards?

Code: [Select]
Cinnamon class Escort Cruiser    10 000 tons     296 Crew     1299 BP      TCS 200  TH 1200  EM 0
6000 km/s     Armour 3-41     Shields 0-0     Sensors 1/1/0/0     Damage Control Rating 2     PPV 60
Maint Life 0.99 Years     MSP 203    AFR 320%    IFR 4.4%    1YR 205    5YR 3071    Max Repair 112.5 MSP
Intended Deployment Time: 6 months    Spare Berths 1   

25x0.75 Magneto-plasma Drive (4)    Power 300    Fuel Use 18.27%    Signature 300    Exp 7%
Fuel Capacity 150 000 Litres    Range 14.8 billion km   (28 days at full power)

10cm Railgun V3/C3 (20x4)    Range 30 000km     TS: 6000 km/s     Power 3-3     RM 3    ROF 5        1 1 1 0 0 0 0 0 0 0
Fire Control S00.7 40-6000 (2)    Max Range: 80 000 km   TS: 6000 km/s     88 75 62 50 38 25 12 0 0 0
Stellarator Fusion Reactor Technology PB-1.25 (20)     Total Power Output 60    Armour 0    Exp 20%

This design is classed as a Military Vessel for maintenance purposes

3 Cinnamons are 3% more expensive than 2 Vanillas for the same firepower... but they use less than 1/3 of the fuel and are 50% tougher. I kept armour thickness the same because this involves many other considerations, but the additional total armour and internal HTK certainly don't go to waste.
The moderately high speed requirement is also flattering to the Vanillas, with total cost of engines at 1200(V) vs. 1350(C). f we relaxed it to the "standard" 4000km/s and reduced the power multiplier accordingly,  the cost would be 800 vs. 600.

Imo, practical examples support the findings in the formal approach - compact propulsion plants are expensive in terms of fuel use and often don't save much if anything in the way of build costs.
I'll consider them if I have a reason to do so (e.g. unusual amount of overhead, compactness being desirable for reasons of hangar space or sensor footprint), but not for general use.
 

Offline Jorgen_CAB

  • Commodore
  • **********
  • Posts: 667
  • Thanked: 1 times
    • View Profile
Re: A formal look at various efficiencies
« Reply #11 on: November 09, 2016, 08:21:43 AM »
Yes I agree with the math and the principle that bigger more fuel efficient engines is generally cheaper and better from a cost perspective. Compact engines with a high power setting is only useful in short ranged ships. I think this should be common sense.

I often use power settings lower than one for reducing the fuel costs and increase the range of the ships with less space for fuel.

Although when doing your overall calculations you need to include the size the engine and fuel take up since the engine increase in size more than fuel due to maintenance and crew requirements.

One point on the ships above, they do severly lack in maintenance facilities, not that it is important for this comparison though. In general you need at least twice the amount of MSP (military ships) on ships than the most expensive component, one reason I stay away from big engines in the early game not withstanding research cost.

Also, overall fuel efficency of engines change the ratio of engine and fuel. If you have an overall fuel efficency of 50% the ratio of engine to fuel change accordingly for any given range. So as fuel efficency get better and your range requirement stay mostly the same these constraint with engine versus fuel ratio get less and less of an issue.

What I mean to say is that the engine to fuel weight are mainly important on really fast ships where you also want relatively long range. I think that those restrictions are probably not that common in general ship design.

I do however think it is very informative to explain that if you want to give ships exceptional range requirements you need to consider more fuel efficient engines when fuel exceeded a certain weight ratio of the ships engines, anything else is a waste of resources.

In basic terms it comes down to what resources you are willing to make a sacrifice on; build cost, range, fuel consumption, research cost, speed, mission tonnage, uppgrade/refitt issues and so on.

If we take Magneto Plasma tech as an example my military ships would likely have speeds varying from 2500-5000 km/s depending on role in the fleet. I would deem 4000km/s as a fast ship the likes of a Destroyer. Engines would range from 1.25 down to perhaps 0.75 in power efficiency depending on my needs, fuel consumption is allways an important issue, especially when you have lots of fighters and other parasite ships that have extreme fuel usage during operations.

I also invest as much research into fuel efficiency as I can, that is generally more efficient the first four or five engine generations than building big research costly engines. In principal my ship engines up until Magneto Plasma are size five, just don't like size one engines on real ships, not a rational thing though.. ;)

In general I have no problem sacrificing speed for fuel efficiency, mission tonnage capacity and retrofit expediency on some types of military ships, generally the really big ships such as carriers. Ships wich are not suppose to be even remotely close with the enemy, or in ships that need both mission space and range, such as long range cruisers who operate alone or in small packs far from friendly bases. I often also try to target ships to a certain fuel efficiency, lower and it is OK with a more powerful engine and either I get more speed or more mission tonnage but also need extra fuel, but no point if it does not give me anything in return. The list goes on and on about what sacrifices I need to do in every design.

Engine to fuel efficency IS an important part of this process. It is certainly good to know when your designs start to waste resources.
« Last Edit: November 09, 2016, 08:32:03 AM by Jorgen_CAB »
 

Offline alex_brunius

  • Rear Admiral
  • **********
  • Posts: 854
  • Thanked: 22 times
    • View Profile
Re: A formal look at various efficiencies
« Reply #12 on: November 18, 2016, 07:24:57 AM »
( This is probably more in the suggestion realm, but I wanted to keep it in the same thread ).


In reality fighters, missiles and other high performance crafts often have 30-70% of their mass as fuel, with engines making up a fraction of the fuel tanks in size and weight.

For our primitive spacecrafts like the Space Shuttle for example it's even worse. The SS assembly has 2000 ton total liftoff weight (59% of it being the Solid rocket boosters). Shuttle empty weight is 78 ton + 25 ton of payload + 7 ton other (110 ton max weight). The 3 engines on the shuttle have a combined weight of 10.2 ton

This gives us the following:
Fuel and fueltanks: 1890 ton (95%)
Engine: 10.2 ton (0.5%)

Engine:Fuel ratio 1:185


Auroras equations and optimal Engine:Fuel ratios seems to be more based on ICE vehicles (cars)... And the worst part of it is that the very low tech (conventional) engines have obscene ranges and you pretty much don't have to worry about fuel ever.



How could the equations for fuel consumption be changed to model this better in Aurora? While still keeping part of the incentive to go for bigger engines to gain a small bit of fuel efficiency?

Basically:
  • Low tech(conventional) engines should have very bad efficiency and short range
  • Optimal Engine:Fuel ratio should be closer to 1:4 or 1:40, rather then 4:1


( 1:4 is not far away from the F-35 for example, it carries an 1.7 ton engine and 8.3 ton max internal fuel = 1:4.9 ratio )
« Last Edit: November 18, 2016, 07:26:44 AM by alex_brunius »
 

Offline Michael Sandy

  • Captain
  • **********
  • Posts: 487
  • Thanked: 15 times
    • View Profile
Re: A formal look at various efficiencies
« Reply #13 on: January 29, 2017, 04:35:45 AM »
I have some questions about ~10,000 ton parasite craft with boosted engines:

It seems to me that operating large craft with boosted engines runs the risk of golden BBs blowing the engines up, with secondary explosions potentially taking out the whole ship.

With fighters and LACs, that isn't as much of a concern, since any destroyed system is likely to be a mission kill, but losing a 10,000 ton craft because of a lucky meson hit would cause some questions for the design staff, I would think.

Having used boosted pocket battleships, or parasite battleships or whatever you call them, how often do you lose them to engine explosions?
 

Offline Iranon

  • Captain
  • **********
  • Posts: 473
  • Thanked: 32 times
    • View Profile
Re: A formal look at various efficiencies
« Reply #14 on: January 29, 2017, 05:28:52 AM »
Didn't happen so far.

I don't build that type of ship in numbers, and I don't risk them in brawls. If I build those:
No expense is spared to get very fast ships with the longest beam range my tech allows (including ECM/ECCM), for flawless victories against slower/shorter-ranged ships. Either they can safely destroy missiles in area defence while retreating, or they're only deployed once the enemy is out of missiles.
If forced into an ugly fight, they're held back to see if an opportunity presents itself - not expendable!
 

 

Sitemap 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51