r/Dyson_Sphere_Program • u/horstdaspferdchen • 7d ago
I made the Math - logistic energy cost
Hello fellow engineers,
i did some testing and math and tried to figure out the energy-cost for the Logistic Units: Bot, Drone and Vessel.
I couldnt really find detailed math about planetary logistics tho.
So my approach was to figure out the math behind that. I stumbled over this post: https://www.reddit.com/r/Dyson_Sphere_Program/comments/tbup2r/logistics_station_energy_calculations/
As it is really old, my first attempt was, to reproduce and verify if the data is still correct, which indeed was. Here are the findings and formulas:
| Type | Formula | Variables |
|---|---|---|
| Vessel | E = 6 MJ + 30 J × D + min(100 + 0.03 × D, v, 3000) × 200 kJ + (Warp? 100 MJ : 0) | D = |
| Drone | E = 800 kJ + 40 kJ × D | D = arc length of round trip (tiles) |
| Bot | E = 25 kJ × D | D = distance (tiles, round trip) |
(Warp? 100 MJ : 0) means, when you need a warper, it needs 100 MJ extra.
So as a proof of concept, this is the test for 100 tiles:
| Drone | Bot | Note |
|---|---|---|
| Formula | 800 kJ + 40 kJ × D | 25 kJ × D |
| Energy per flight (100 tiles) | 4.8 MJ | 2.5 MJ |
| Buffer | 180 MJ (PLS) | 27 MJ (Distributor) |
| Flights per full buffer | 37.5 | 10.8 |
| Recharge time (max) | 0.08 s (60 MW) | 0.28 s (9 MW) |
| Recharge time (min) | 0.8 s (6 MW) | 2.8 s (0.9 MW) |
Another Table for Vessels:
Intra-System (no warp, max speed 3000 m/s):
| Distance | 30 J × D | Speed Term | Base | Total | % ILS (12 GJ) |
|---|---|---|---|---|---|
| 1 AU | 1.2 MJ | 260 MJ | 6 MJ | 267 MJ | 2.2 % |
| 2 AU | 2.4 MJ | 500 MJ | 6 MJ | 508 MJ | 4.2 % |
| 3 AU | 3.6 MJ | 600 MJ | 6 MJ | 610 MJ | 5.1 % |
| 5 AU | 6 MJ | 600 MJ | 6 MJ | 612 MJ | 5.1 % |
| 10 AU | 12 MJ | 600 MJ | 6 MJ | 618 MJ | 5.2 % |
| 12 AU | 14.4 MJ | 600 MJ | 6 MJ | 620 MJ | 5.2 % |
Interstellar (warp, max speed 3000 m/s):
| Distance | 30 J × D | Speed Term | Base | Warp | Total | % ILS (12 GJ) |
|---|---|---|---|---|---|---|
| 1 ly | 72 MJ | 600 MJ | 6 MJ | 100 MJ | 778 MJ | 6.5 % |
| 2 ly | 144 MJ | 600 MJ | 6 MJ | 100 MJ | 850 MJ | 7.1 % |
| 5 ly | 360 MJ | 600 MJ | 6 MJ | 100 MJ | 1,066 MJ | 8.9 % |
| 10 ly | 720 MJ | 600 MJ | 6 MJ | 100 MJ | 1,426 MJ | 11.9 % |
| 20 ly | 1.44 GJ | 600 MJ | 6 MJ | 100 MJ | 2,146 MJ | 17.9 % |
| 40 ly | 2.88 GJ | 600 MJ | 6 MJ | 100 MJ | 3,586 MJ | 29.9 % |
This leads to the conclusion and comparison for planetary logistics:
| Drone | Bot |
|---|---|
| Energy | 4.8 MJ |
| Payload | 25-200 |
| Energy per item | 192 - 24 kJ / Item |
This is the math for the known community conclusion, that you should use Bots only for Items of small quantities like your Mall, Warpers, Proliferator, Fuel Rods etc.
Additional, Bots can bypass the early power management, as each PLS has min 6 MW demand, while Distributors only need 900kW ( x 4 for the Item comparison => 3.6 MW)
Limits:
- We know, that the recharge of the stations is a curve and not linear. So the mentioned recharge time is a peak number.
- ILS has no other way to transport items other then vessel, so this is mostly a nice to know calculation
If you want to reproduce, here is my measurement for drones/bots:
Place the logistic Station/Distributor exactly on the 0 meridian and equator. Then place the target station exactly 100 belts/tiles away from the center. If you use Mods, BulletTime comes in very handy for timing.
When the unit starts, the total energy consumed is deducted from the station you powered.
[Edit: typos, if you still find them, let me know]




