Okay, so I followed up and got my head around the math, and I wanted to share my findings as this all ties back to the initial question of this thread i.e. what should a "standard speed" look like?
To sum up, the Reddit post shared by Iceranger is completely right as expected. The optimal ratio of engine to fuel component size is 3 HS of engine to 1 HS of fuel barring small discretization errors and running up against tech limits. Interestingly, this ratio is completely independent of the engine power modifier and so by itself this ratio does not tell us what modifier is optimal (although it does invalidate my argument about engine vs fuel size efficiency), however the math is there to figure out the answer and it turns out that the answer depends strongly on the design doctrine for your ships.
So to start off I'll sum up the math from that Reddit post, we have expressions for ship speed and range in terms of various tech level values, design parameters, and target values. Anyone else who wants to please feel free to double-check this of course.
Ship speed/velocity:
V = Cv * Me * Fp
Cv = 750 * EP
EP = base engine tech level in EP/HS
Me = engine power modifier
Fp = Fraction of ship mass dedicated to propulsion components, i.e. engines and fuel storage
Ship range:
R = Cr * Fp^1.5 / (Me^2.5 * Ne^0.5)
Cr = 6.75E+4.5 * Cf * HS^0.5 / eta
Ne = number of engines
Cf = fuel storage size in L/HS
HS = total ship size in HS
eta = fuel efficiency tech level
The design parameters are Me, Fp, and Ne, as everything else is either a tech that we always want to use the latest level of or a parameter we set earlier in the ship design (ship size, in this case). Out of these parameters: Fp is usually determined by our ship design doctrine based on what we think will give us a good balance of weapons and speed; Ne should be as small as possible for efficiency, but since warships need redundancy in their important components we usually don't want Ne = 1 except on fighters/FACs, and additionally if we are reusing the same engines for multiple sizes of ship classes we have to compromise on this parameter; this leaves Me as the design parameter to optimize and we can do this in several different ways.
(1) Select speed, get Me, get range.
Me = v / Cv / Fp
R = Cr * Cv^2.5 * Fp^3.5 / (v^2.5 * Ne^0.5)
Very straightforward and simple. Good for fighters/FACs and if you're not worried about having a long range as long as your fleet has a uniform speed in combat. Another approach is to set a minimum speed (e.g. for survey ships or transports) and see how much range you can get out of it.
(2) Select range, get Me, get speed.
Me = Cr^0.4 * Fp^0.6 / (R^0.4 * Ne^0.2)
v = Cv * Cr^0.4 * Fp^1.6 / (R^0.4 * Ne^0.2)
Only slightly more complicated in terms of how much work you have to do to find Me. You can use this approach to ensure that all of your fleet units have a specific range, but this is often not really necessary if you have a functioning fleet logistics arm unless you expect to be sailing from X to Y at top speed without any resupply stations along the way. Probably a better use here is for commercial and survey ships that need long ranges. Another idea is to set a minimum operating range and see what kinds of speed you can get out of it.
(3) Optimize some relation between range and speed. If you're not able to precisely define the mission parameters of your fleet, this could be a useful approach to get a "balanced" fleet that can perform a variety of missions adequately. This is where calculators may not be as much help, the above two cases are easy but if you want to optimize a particular function of R and v you may have to DIY.
Example: Optimize the product R*v:
R*v = Cv * Cr * Fp^2.5 / (Me^1.5 * Ne^0.5)
Optimal Me is the minimum value available from your tech.
This is a rather simplistic example that shows an important point: if we optimize some product of R and v, to whatever powers we might choose to emphasize one over the other, we always end up with either the minimum or maximum engine power modifier as the optimized result (unless it drops out entirely). So products are not a useful optimization function.
What about addition? We can't add R and v directly because they have different units, but we can add scaled versions by dividing by target values Rt and vt:
Let Qt = R / Rt + v / vt
Qt = Cr * Fp^1.5 / (Rt * Me^2.5 * Ne^0.5) + Cv * Fp * Me / vt
dQt / dMe = 0 = Cv * Fp / vt - 5 * Cr * Fp^1.5 / 2 / Rt / Ne^0.5 / Me^3.5
Me = [(Cr / Rt) / (Cv / vt)]^(2/7) * (25 * Fp / 4 / Ne)^(1/7)
Obviously, this is the most overcomplicated approach so far, and you could certainly get even more complicated if you wanted (root mean squares, anyone?). Probably for most people it will suffice to optimize for speed or range and tweak the target value a few times until they're happy with both values.
Okay, so to tie back to the original question: what is a good "standard speed" for a given tech level? To answer this question I pulled the tech values from the Aurora DB for base engine tech, min/max engine power modifiers, and fuel efficiency tech and just set them up as somewhat arbitrary tech levels. Since a standard TN start gives the player NTE engine tech but only the baseline/conventional modifier and fuel techs (0.5, 1.0, and 1.0 respectively) I set this as TL1, and each successive tech level increments each tech if possible. Additionally, I set Fp = 0.4, Ne = 4, Cf = 50,000 L/HS, and the ship size 200 HS (10,000 tons). 40% of space dedicated to propulsion is a reasonable estimate (perhaps a bit low?), and four engines for a 10,000-ton destroyer makes sense if you want to re-use the engines for 5,000-ton frigates and 15,000-ton cruisers or something similar.
Each of the above optimization methods is compared (for case 3, the addition method is compared as the product method is overly simplistic and useless). For the target speed I used a prescribed EP modifier linearly interpolated from 1.0 to 3.0 across the tech levels (i.e. 1.0 at TL1, 3.0 at TL14), and the target range is 20 billion km times SQRT(tech level / 5) (this is scaled to give 20b km range at ion drives which was arbitrarily chosen based on the starting ships in Steve's Imperium of Man fiction). The results are below in the table, noting that the EP modifiers are locked to the allowed range at each tech level - speeds in km/s, ranges in billion km.
Tech Level | Engine Tech | Base EP | Min EM mod | Max EP mod | Fuel eff | Target speed | Case 1 EP mod | Case 1 range | Target range | Case 2 EP mod | Case 2 speed | Case 3 EP mod | Case 3 speed | Case 3 range |
1 | NTE | 5.0 | 0.5 | 1.0 | 1.0 | 1500 | 1.00 | 19.1 | 8.9 | 1.00 | 1500 | 1.00 | 1500 | 19.1 |
2 | INTE | 6.4 | 0.4 | 1.25 | 0.9 | 2215 | 1.15 | 14.8 | 12.6 | 1.23 | 2361 | 1.25 | 2400 | 12.1 |
3 | NPE | 8.0 | 0.3 | 1.5 | 0.8 | 3138 | 1.31 | 12.2 | 15.5 | 1.19 | 2853 | 1.5 | 3600 | 8.7 |
4 | INPE | 10.0 | 0.25 | 1.75 | 0.7 | 4385 | 1.46 | 10.6 | 17.9 | 1.18 | 3551 | 1.63 | 4901 | 8.0 |
5 | Ion Drive | 12.5 | 0.2 | 2.0 | 0.6 | 6057 | 1.62 | 9.6 | 20 | 1.20 | 4515 | 1.70 | 6381 | 8.4 |
6 | MP Drive | 16.0 | 0.15 | 2.5 | 0.5 | 8492 | 1.77 | 9.2 | 21.9 | 1.25 | 5994 | 1.79 | 8603 | 8.9 |
7 | Int CF | 20 | 0.1 | 3.0 | 0.4 | 11538 | 1.92 | 9.3 | 23.7 | 1.32 | 7944 | 1.91 | 11483 | 9.4 |
8 | Mag CF | 25 | 0.1 | 3.0 | 0.3 | 15577 | 2.08 | 10.2 | 25.3 | 1.45 | 10847 | 2.08 | 15629 | 10.2 |
9 | Ine CF | 32 | 0.1 | 3.0 | 0.25 | 21415 | 2.23 | 10.3 | 26.8 | 1.52 | 14587 | 2.20 | 21150 | 10.6 |
10 | Solid AM | 40 | 0.1 | 3.0 | 0.2 | 28615 | 2.38 | 10.9 | 28.3 | 1.63 | 19520 | 2.36 | 28291 | 11.2 |
11 | Gas AM | 50 | 0.1 | 3.0 | 0.16 | 38077 | 2.54 | 11.6 | 29.7 | 1.74 | 26175 | 2.52 | 37852 | 11.8 |
12 | Plasma AM | 64 | 0.1 | 3.0 | 0.125 | 51691 | 2.69 | 12.84 | 31.0 | 1.89 | 36343 | 2.72 | 52220 | 12.5 |
13 | Beam AM | 80 | 0.1 | 3.0 | 0.1 | 68308 | 2.85 | 14.0 | 32.2 | 2.04 | 48881 | 2.91 | 69882 | 13.2 |
14 | Photonic | 100 | 0.1 | 3.0 | 0.1 | 90000 | 3.00 | 12.2 | 33.5 | 2.01 | 60203 | 2.92 | 87742 | 13.1 |
I'm not going to claim that this is a terribly informative data set, my aim is just to show what you can expect to see when you optimize for different quantities and how one might go about using this information to determine standard speeds for their fleets. In most cases, it's probably best to just optimize for a fixed speed or range (cases 1 and 2), and in this case using a calculator is probably the way to go if you want to get the best designs. However, if you really want to get into it you can devise various kinds of metrics that probably will work better than my examples in case 3, including messing with your choice of target values.
Anyways, hope this is at least mildly interesting to one of you nerds out there.
I imagine it won't be too far off practically, and it should not affect the theoretical optimal point at all.
Note that an engine's crew requirement is engine size x engine power boost, which is proportional to the engine power. Since the optimality is established based on given fuel range, tonnage and speed, under these conditions the total engine power is fixed. Thus in theory the total crew required by those engines is fixed. Of course practically the crew count for each engine needs to be an integer, so crew number for each engine is rounded up or down, which may result in certain engine compositions having slightly more or less crew, but the difference should be very small.
That makes sense. I'm still curious how it would shake out from the math and if there's any implications at all hidden away in there, but that's an adventure for another day I think.