→In The Game
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=== Deconstructing === | === 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. | 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 == | |||
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 | |||
* 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 mathemetical 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 segments, 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. Tthe 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, <em>after accounting for the static number of rockets in the nodes</em>. | |||
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 <em>higher</em> 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.) |