Difference between revisions of "Dyson Sphere"

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{{Note Box|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.}}
 
{{Note Box|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.}}
  
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== TL;DR ==
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Based off the data accumulated below, a structure point generates 96 KW, a cell point generates 15 KW, NO MATTER HOW FAR AWAY FROM THE STAR.
 +
 +
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
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or for a general case
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LUMINOSITY * 4 * π * (RADIUS * 0.0191) ^ 2 * (15 + 96 * 0.08), in KW
 +
 +
As for solar sails, they output 36 KW each, times the luminosity. But still independent of the distance from the star.
 +
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== 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)
 
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)
  
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Further code inspection could lead to the complete understanding of the Dyson sphere power computation. But I can understand that some people would prefer to make more "conventional" research and that direct code inspection could spoil that fun. So should I continue and extend this post with more information?
 
Further code inspection could lead to the complete understanding of the Dyson sphere power computation. But I can understand that some people would prefer to make more "conventional" research and that direct code inspection could spoil that fun. So should I continue and extend this post with more information?
 
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[[Category:Astronomical Objects]]
 
[[Category:Astronomical Objects]]

Revision as of 03:23, 22 June 2021

In The Real World

A Dyson Sphere is a hypothetical megastructure that completely encompasses a star and captures a large percentage of its power output. The first appearance of a Dyson Sphere is in the 1937 Science Fiction novel Star Maker by Olaf Stapledon. This book inspired physicist and mathematician Freeman Dyson to formalize the concept in a 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 - the sheer quantity of resources and technological advancements required to achieve one can only be dreamed of by the human race, for now.

In DSP, the player's goal is to construct a Dyson Sphere, though there are indications in pre-release footage that it may be possible to stop at a partial sphere, as well as construct more than one layer of sphere. It is also expected that players will be able to construct Dyson Spheres around multiple different stars in the same save.

In The Game

In Dyson Sphere Program, constructing a Dyson Sphere is one of the primary goals for "completion" (though the game cannot really be completed, as you can continue playing 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. At the default range of a Dyson Swarm, each solar sail provides 30 kW of energy, and they are inexpensive to manufacture so can be launched in the thousands. However, the player will soon realize that Solar Sails have a lifespan after which they disappear. The base lifespan is 1800 seconds (30 minutes). Thus, the maximum energy obtainable from a Dyson Swarm is dependent upon how many solar sails they can manufacture and fire, per half-hour, 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 a Gas Giant host planet in the way to block their view on occasion.

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 comprised 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, it does not need to be a proper 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 a number of 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.

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 nearby Dyson Swarms into the Shell to create a hexagonal-lattice panel between the frame segments. The Solar Sails' energy output is combined with that of the Frame segments, and the lifespan limitation of Solar Sails in a Swarm is negated - they last forever once placed in a Shell.

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 were absorbed into the Shell from a Dyson Swarm 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 Frame segments or Small Carrier Rockets will be returned to the player.

Mathematics

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, NO MATTER HOW FAR AWAY FROM THE STAR.

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

As for solar sails, they output 36 KW each, times the luminosity. But still independent of the distance from the star.

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 Followup 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 formular is similar, but with 36kW instead of 100kW. Might need checking.