Dyson Sphere

The Dyson sphere is the ultimate end goal of the Dyson Sphere Program. It is a permanent mega-structure built around a star that constantly produces huge amounts of power, which can then be brought to that star system's power grid using Ray Receivers.

Main Info

A Dyson sphere has 2 components: Solar Sails, which form the bulk of the Dyson sphere's power generation; and Small Carrier Rockets, which form the framework that gives the Dyson sphere its structure.

Launching Solar Sails without a Dyson sphere frame in place is possible, in which case they form a Dyson swarm. However, the Dyson swarm is not a permanent installation, and Solar Sails will expire after a set amount of time. The lifespan of each Solar Sail can prolonged with the Solar Sail Life upgrade.

Item	Output	Energy and Material Cost	Description
	1 sail in swarm 36 kW	Using rare ores: 50 ores, 80MJ per 1MW	Solar Sails in the Dyson swarm will expire after enough time passes. The base lifespan is 1.5 hours, and can be increased with the Solar Sail Life upgrades. Once a Solar Sail is integrated into the Dyson sphere, it becomes permanent. An unlimited number of Solar Sails can be in the Dyson swarm at any time; it is only limited by the rate at which Solar Sails are launched. For comparison, Solar Panels cost 150 ores and 130MJ per 1MW.
	1 structure point 96 kW	Using rare ores: 3500 ores, 5800MJ per 1MW	Each node in the Dyson sphere requires 30 structure points. The number of structure points required for frames between nodes is based on each frame's length.
	1 cell point 15 kW	Using rare ores: 120 ores, 200MJ per 1MW	Once a shell in the Dyson sphere is enclosed by frames, it absorbs Solar Sails that are in orbit to form cell points. The number of cell points required to fill a shell is based on its area. Each node with at least 1 built structure point consumes up to 30 sails per minute from the swarm to fill nearby shells.
	6~15MW	Without any Ray Transmission Efficiency research: takes ~333% of produced energy from Dyson swarm/sphere With Ray Transmission Efficiency Level 3 researched (the highest available with Structure Matrices): takes ~204% of produced energy from Dyson swarm/sphere	Used to transport energy from the Dyson swarm/sphere to planets in that star's system. Power consumed from the Dyson swarm/sphere is not equal to the amount of power produced, due to innate inefficiency. Without any upgrades, the efficiency is only 30% (meaning 70% of the power from the Dyson swarm/sphere is lost). This can be improved with the Ray Transmission Efficiency research. After researching Planetary Ionosphere Utilization, the Ray Receiver can consume Graviton Lenses to double its power for 10 minutes. After researching the Dirac Inversion Mechanism, the Ray Receiver can generate Critical Photons instead of power. This greatly increases the load on the Dyson swarm/sphere to 120MW, or 240W when using a Graviton Lens.

In the game

In Dyson Sphere Program, constructing a Dyson sphere is one of the primary goals for "completion" (though you can continue playing the game indefinitely after researching all technologies and building a complete Dyson Sphere). Building a Dyson sphere takes a few stages:

The Dyson Swarm

Players typically start testing their ability to build a Dyson sphere by first launching several Solar Sails into a Dyson swarm, which is an orbital ring around the host star of a loose collection of Solar Sails. They do not link up to one another, instead working independently to provide energy. Each solar sail in a Dyson Swarm provides a base 36 kW of power (regardless of their orbital radius), which is then scaled by the star's luminosity. Solar Sails are inexpensive to manufacture, so the player can launch them in the thousands. However, the player will soon realize that Solar Sails have a lifespan after which they disappear. The base lifespan is 5400 seconds (1.5 hours), which can be upgraded to a maximum of 9000 seconds (2.5 hours) with the Solar Sail Life upgrades. Thus, the maximum power obtainable from a Dyson swarm is dependent on how many Solar Sails the player can manufacture and fire, per Solar Sail lifespan, on a continuous basis.

An additional hindrance to maintaining a Dyson Swarm is that the EM-Rail Ejectors used to fire the Solar Sails require a line of sight to the target orbit. This can become more difficult to achieve depending upon how many EM-Rail Ejectors the player constructs, whether their planet has a significant axial tilt, where on the planet the EM-Rails are placed, and whether there is another planet blocking the EM-Rails' line of sight (an especially common occurrence when launching Solar Sails from a satellite of a Gas Giant).

The Dyson Shell

The next phase of building a Dyson sphere is the Dyson shell. A Dyson shell requires additional technologies to unlock - they are composed not just of Solar Sails, but also Dyson Sphere Components. The player defines the location of Nodes and, for Nodes within a certain distance of each other, Frame segments to connect them. When enough Frame segments are defined such that an enclosed area is defined, that area can be designated as a Dyson Shell. This area can have any shape and does not need to be a regular polygon, though guidelines are available in the Editor for rectangular and triangular shapes.

Once the Nodes and/or Frame are defined, the player then uses a Vertical Launching Silo to fire Small Carrier Rockets to construct the frame. These rockets can be considerably difficult to make in large quantities, depending on the player's industrial setup. However, large-scale production is a necessity to construct the largest and most powerful Dyson spheres.

As soon as any Frame segment is put in place, the frame itself can begin to generate power, even before it is completed. Once all Frames encompassing a defined Shell are completed, it will draw any Solar Sails from the star's Dyson swarm into the shell, creating a hexagonal-lattice panel between the frame segments. The consumed Solar Sails' energy output is then combined with that of the Frame segments, and their lifespan is no longer a consideration - once a Solar Sail becomes part of the Dyson shell, it will last forever.

Deconstructing

It is possible to deconstruct a Dyson Shell, at any stage of its construction. Take note, however, that doing so will not return all of the materials to the player. All Solar Sails that had been absorbed into the shell will be jettisoned back into space, immediately beginning their lifespan countdown timer again. If left alone, they will spread out into an orbital ring. The Frame segments that were constructed of Small Carrier Rockets are converted into Solar Sails upon deconstruction, and these too join the new swarm and get a lifespan timer. No Dyson Sphere Components or Small Carrier Rockets are returned to the player.

The Dyson Sphere Editor

The Dyson Sphere Editor is used to design a Dyson swarm/sphere for the current star system, or modify existing Dyson swarms/spheres.

Orbit Designer

A star's Dyson swarm can contain up to 20 orbits. Each orbit's radius, rotation, and inclination can be freely adjusted, although an orbit cannot come too close to a planet's orbit. Orbits can overlap with each other, however. The player may also choose a color for the Solar Sails in an orbit, although this is purely cosmetic.

An orbit that currently contains Solar Sails can still be modified, although the existing Solar Sails will not move into the updated orbit and will remain in the original one until their lifespan runs out.

Clicking on an orbit in the list will pull up a panel containing information about it, such as its dimensions, total power generation, and number of Solar Sails.

Shell Designer

A star may have up to 10 Dyson shell layers. Like Dyson swarm orbits, each shell's radius can be adjusted, but cannot come close to a planet's orbit. Additionally, shells cannot overlap; their radii must be at least 1000m apart.

Shell Grid

The first step to designing a shell layer is to select what grid type to use. There are 3 triangular grids, 1 square grid, and 1 completely blank grid. The grid chosen will dictate where nodes and frames can be placed.

Build Plan Designer

There are 3 components of a layer: nodes, frames, and shells. Nodes are single points that are the endpoints of frames, and shells are closed polygons formed by frames. To design a shell, first draw a network of frames, then fill the framework with shells. The framework will be constructed from Small Carrier Rockets, and the shells will be formed by absorbing orbiting Solar Sails.

Researching the Dyson Sphere Stress System technology is necessary to build a larger Dyson sphere. Without any research, it is only possible to build a very narrow ring. Each successive upgrade expands the range of possible construction, until it is possible to fully enclose the star.

Notably, frames have 2 different types, geodesic and graticule. Geodesic frames directly connect their 2 endpoints, while graticule frames will attempt to follow the grid's lines. Both types still follow the curvature of the Dyson sphere grid, and the difference is largely negligible except when constructing close to the Dyson sphere's poles.

Frames have 3 different styles to build with, and shells have 7 different texture patterns. Additionally, the player can recolor nodes, frames, and shells with the Decoration tab. All of these changes are purely cosmetic.

Endgame

To generate the terawatts of Dyson sphere power required for leaderboards, pro players have to take more things in consideration:

• Common yellow stars with ~1x luminosity will inevitably be phased out in favor of blue stars, the best of which have a ~2.5x luminosity.
• A Dyson swarm becomes less useful after days of playtime, because of its limited lifespan.
• The Dyson shell is a better long-term energy source than a Dyson swarm, as frames and sails absorbed by the sphere remain forever.
  • However, the Dyson shell itself has considerations when it comes to which grid pattern to use: the default triangle grid gives 15% less power than the crossed triangle grid (drawing triangles on 6-tris hexagons, so each triangle is just 3 trin and not 4), and the crossed triangle grid itself gives 15% less power than the perfect grid with fewer triangles can (you can disable grid by choosing it twice).
• The highest-luminosity stars, Blue Giants, are a necessity. With a perfect frame grid with 10 layers, the Dyson shell will yield 12TW. The best seeds have 3 Blue Giant systems, resulting in 36TW total.

• Note that while the game's optimization of Dyson sphere elements continues to improve over time, players should expect an increase in RAM usage and a decrease in game performance (lower FPS/UPS) as the number of sails/frames/shells increases.

Mathematics

Basics of the Dyson Shell

• Each Node has 30 Structure Points.
• Each Frame has a number of Structure Points based on the Orbit Radius of the Dyson Shell Layer. This number is rounded to multiples of 20. So two identical Layers with slightly different Orbit Radii can rarely have the same number of Structure Points.
• Each Structure Point produces ~95.8KW times the star's Luminosity. (This is definitely not a whole number, but it does seem to be a constant.)
• Each Structure Point takes one Small Carrier Rocket to build.
• Each Shell has a number of Cell Points based on the Orbit Radius of the Dyson Shell Layer.
• Each Cell Point produces 15KW times the star's Luminosity.
• Each Cell Point takes one Solar Sail to build.

This means the power produced per Small Carrier Rocket or Solar Sail only varies based on the star's Luminosity. The Orbit Radius only affects the maximum power output of the Layer (and possibly the continuous receiving uptime of the Ray Receivers).

Note: There are currently some bugs and inconsistencies in the UI as of version 0.9.27.15466.

• When selecting a Node in the Editor, the Structure Points listed includes 30 for the Node and half of each Frame attached to the Node. But the Generation Capacity is only for the Node.
• When selecting a Node in the Editor, the Generation Capacity listed includes the star's Luminosity multiplier; but when selecting a Frame or Cell, it does not include the multiplier.

Note

The information below is accurate as far as the assumptions made during the observations. Recent testing indicates that the mathematical "story" may be different than outlined below, and that the numbers merely lined up out of happenstance. This section will be updated once further testing has established the proper mathematical relationships.

TL;DR

Based off the data accumulated below, a structure point generates 96 KW, a cell point generates 15 KW and a solar sail generates 36 KW. Each of these is multiplied by the system's luminosity. These values do not depend on the distance from the star.

Thus the power formula for a completed Dyson Sphere is as follow:

LUMINOSITY * 4 * π * (RADIUS * 0.0191) ^ 2 * (15 + 96 * STRUCTURE_POINT_PER_CELL_POINT), in KW

or for a general case:

LUMINOSITY * 4 * π * (RADIUS * 0.0191) ^ 2 * (15 + 96 * 0.08), in KW

Dyson spheres around the same star do not block each other, so the best single-system power output is to find the brightest star and build the 10 largest spheres possible around that single star.

Maximum Dyson sphere radius

While the energy output of a sphere depends on the star's luminosity, the maximum energy output of a star depends much more on the largest possible Dyson sphere radius. It is possible to build up to 10 spheres around the same star. Additionally, spheres cannot be closer than 1000 units. This means that for a maxed-out system, the total power is proportional to:

(MAX_RADIUS * 0.0191) ^ 2 + (MAX_RADIUS * 0.0191 - 19.1) ^ 2 + (MAX_RADIUS * 0.0191 - 38.2) ^ 2 +... = (10 * MAX_RADIUS ^ 2 - 90000 * MAX_RADIUS + 285000000) * 0.0191 ^ 2

Substituting into the equation before,

MAX_POWER = LUMINOSITY * 4 * π * (10 * MAX_RADIUS ^ 2 - 90000 * MAX_RADIUS + 285000000) * 0.0191 ^ 2 * (15 + 96 * 0.08) kW for a general case

Here are some measured values from two separate seeds:

Mass	Luminosity	Radius	Type	Max sphere radius	Max power for a general case, TW
0.608	0.891	0.86	M	19100	0.205
0.955	0.989	1.05	G	21900	0.320
0.991	0.998	1.00	G	22200	0.334
0.434	0.358	0.26	White dwarf	23900	0.143
45.658	0.175	3.62	Black hole	55300	0.471
14.616	1.858	3.06	B	59900	5.945
0.403	0.929	16.79	M, giant	60600	3.048
94.557	0.197	3.79	Black hole	61800	0.674
49.419	2.462	4.36	O	74400	12.528
16.88	2.196	12.97	B, giant	199500	86.839
26.636	2.44	13.33	O, giant	216600	114.149
26.798	2.443	17.04	O, giant	216800	114.505

While it's difficult to make any concrete rules, we can see a general trend of maximum sphere radius correlating to mass and spectral class. More importantly, the maximum sphere radius increases by a factor of around 3 when the star is a giant, resulting in a huge increase in power output.

These results also imply that the best way to get a power production record is not to play on seeds with 10 O-type stars, but instead to look for seeds with multiple high-luminosity giants.

Note: Red Giants (Both M and K) have similar Max Sphere Radii to regular B and O stars, but with lower luminosity. Thus a regular O-type star will usually have a higher max power output than a Red Giant. It's only the Blue Giants (B and O) that are valuable, with O Giants often having 10x the max of a regular O-type.

Preliminary testing

Preliminary testing indicates that certain mathematical rules apply to Dyson shells as expected, while others do not, or apply in the opposite way as expected based on real-world physics (yet in a way that makes sense for a video game)

For this discussion, certain assumptions must be made based on observations in the editor:

A given frame segment in the editor covers the same radial arc, regardless of distance from the star.

This can be determined by counting the total number of large-grid segments defined in the editor (in 'square' mode). Regardless of the distance from the star, there are 24 such grids around the equator. This means that we can mathematically compare a 5x5 frame at different distances from the sun, to achieve some formulas.

With this in mind, a single 5x5 frame segment was actually constructed at each of two distances, for testing:

10,000m radius (default for Shell 1), 5x5 square equatorial frame:

• Frame Materials: 440
• Solar Sails to fill: 2,442
• Power Generation: ~78.8 MW

5,000m radius, 5x5 square equatorial frame:

• Frame Materials: 280
• Solar Sails to fill: 626
• Power Generation: ~36.2 MW

Solar Sail Cost

At 10,000 meter radius, it cost 2,442 solar sails to fill the panel. The similar 5x5 panel at 5,000 meter radius cost 626 solar sails to fill the panel. Because this amount is covering an area, the mathematical rule that Area increases with the Square of the Distance comes into play. The distance was doubled, so the Area should be quadrupled. 2,442 / 626 = 3.9, which is close enough to 4 to account for deviations based on distance from the equator.

Assertion: Solar Sail cost increases as the square of the distance.

Frame Materials (Rockets)

It takes 30 Rockets (Frame materials) to build each Node. Each of these panels was square, so 4 nodes, or 120 rockets for the nodes. This part is not variable. For the 10,000m frame, we are left with (440 - 120) = 320 Rockets for 4 roughly equal-length frame segments, or 80 rockets each.

A 5x5 frame segment is 1/24th the circumference of the sphere. At 10,000m, this is (10,000 * 2 * pi) / 24 = 2,618 meters in length. 2,618 meters, divided by 80 rockets, is 32.725 meters per Rocket (or 1 Rocket for every 32.725 meters, if you prefer).

To verify this, at 5,000 meters, remove the 120 rockets for the nodes to get 280 - 120 = 160 rockets for the 4 frame segments, or 40 rockets each. The 5x5 frame is still 1/24th of the circumference, so (5,000 * 2 * pi) / 24 = 1,309 meters in length. 1,309 meters, divided by 40 rockets, is again 32.725 meters in length. Therefore, at half the radius, half the number of rockets are needed for a frame segment, after accounting for the static number of rockets in the nodes.

Assertion: Regardless of the distance from the sun, frames cost 30 rockets per Node, plus 1 rocket for every 32.725 meters of frame segment length.

Power Output

Finally, let's take a look at the Power output. Before we begin, we must observe that before any solar sails are ever launched into orbit for a Frame, the frame itself generates power. One can presume this is the result of the frame having solar sails in its construction recipe.

Unfortunately, this author did not record observations of the power output of frame segments during construction, and so cannot presently derive their effects on the total power output. Suffice it to say, that the solar sails at half the distance appear to be generating approximately half the power. (this is the only part of the math here that goes against the expectation from real world physics - the same radial area is covered, so the same amount of energy should be captured, if not higher energy captured at closer distances. However, in video game terms, it makes sense to have a cost vs benefit of constructing closer to the sun.)

Math follow-up from another player

After reading that the last author forgot to record observations for the power output of the frame itself, I decided to do just that. Here is what I found...PS, feel free to use/edit my contribution to sound more coherent with the rest of the page.

Star Type	Luminosity	Orbit Radius (m)	Total # of Frame Parts Used	Total Power Output (MW)	MW per frame part = (power output / luminosity) / # of parts used )
M-type	0.863	18500	1000	82.8	0.09594438007
K-type	0.896	19200	1080	92.8	0.0958994709
F-type	1.089	19700	1080	112	0.09522837806
Neutron	0.655	22900	1240	77.8	0.09578921448
Black Hole	0.185	22900	1240	22	0.09590235397
O-type	2.165	22900	1240	257	0.09573120763
Red Giant	1.002	22900	1240	119	0.09577618956
G-type	1.01	22900	1240	120	0.09581603322
A-type	1.308	22900	1240	155	0.09556574924
B-type	1.651	22900	1240	196	0.09573865302

Method and things to mention

First, I want to mention that I did not think to measure the output of the nodes vs segments, so for these values it is looking at total # frame parts used. The frames observed were a circle at the top of the sphere with 4 nodes and segments going around to connect them. I did my best to keep the radius the same for all data points but some stars would not allow for the 22900m and I was forced to use a smaller radius on some stars, so feel free to throw out those data points if necessary.

Findings

As you can see by the table, each part launched into the frame produces a base output of roughly 0.096MW or 96kW. It is then multiplied by the luminosity of the star to get it's actual output after being launched.

As I set out to find some constant that represented the power output per frame part I did not know if distance mattered to it's output either. I had thought that the radius only changed how many parts were needed for that particular structure and that my calculations would show that the radius was moot for this experiment. However, even though I was pleased to see that the equation I used seemed to find that constant regardless of the distance, I hadn't started recording the radius at the time of setting up the frames and I accidentally had one (on the K-type star) at 19200m and another (the F-type star) at 19700m. These two data points are somewhat anomalous as they suggest there may be some range for the radius vs # of frames that make up the segments between the nodes (because they are at different distances but use the same # of frames) and that the power output may change slightly depending on where the frame sits within that range (because the MW/frame part rounds down to 95kW instead of 96kW like all the rest).

Conclusion

I know a lot more could be done to show more helpful information like "what radius should I build at to get exactly 5GW of power" but maybe this, coupled with the previous author's information, can help you understand the games mechanics just a bit more.

Another math example

I might have found a quite simple formula to calculate the power output of any Dyson-Shell without filling, meaning only parts shipped by small cargo rockets. Around a F-type Star with ~1.6L luminosity, i had 250 delivered parts and an output of 40MW. By simple division i come to the following formula:

Output = P * L * 100kW ;

P being the number of delivered parts (visible in any rocket silo screen of the system);

L being the luminosity of the star.

As for Solar Sails, I presume (!!!) the formula is similar, but with 36kW instead of 100kW. Might need checking.

Frame energy output formula

This formula for energy output works reasonably well for Dyson-Shells with only structure points and no solar sails.

Energy Output = Total structure pts * Star luminosity * 95.7

Example:

Total structure pts: 300 (short frame segment)

Star luminosity: 1.924

Energy = 300 * 1.924 * 95.7 = 55238.04 kW (55.2 MW)

Trivia

In the real world, a Dyson sphere is a hypothetical mega-structure that completely encompasses a star and captures some of its power output. Even capturing a small percentage of a star's power is an unfathomably large amount of energy, since stars produce an incredible amount of power constantly. The first concept of a Dyson sphere appeared in the 1937 science fiction novel Star Maker by Olaf Stapledon. This book inspired physicist and mathematician Freeman Dyson to formalize the concept in his 1960 paper "Search for Artificial Stellar Source of Infra-Red Radiation," published in the journal Science. There is no known real-world example of a Dyson sphere, as constructing one would require an immense quantity of raw materials and ultra-advanced technology, both of which are inaccessible to the human race (at least, for now).

Dyson Sphere Program

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• Blueprint
• Metadata

• Icarus
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• Stars and planets (names)
• Dyson Sphere
• Soil Pile

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