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=== Solar Sail Cost=== | === 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 | 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. | Assertion: Solar Sail cost increases as the square of the distance. | ||
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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). | 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. | 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, <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. | 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. | ||
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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.) | 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.) | ||
<ins><After reading that the last author forgot to record observations fo<u>r the power output of the frame i</u>tself, 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.></ins> | |||
{| class="wikitable" | |||
|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 | |||
|} | |||
====== <ins>Method and things to mention</ins> ====== | |||
<ins>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.</ins> | |||
====== <ins>Findings</ins> ====== | |||
<ins>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. </ins> | |||
<ins>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).</ins> | |||
====== <ins>Conclusion</ins> ====== | |||
<ins>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.</ins> | |||
<ins><End of addition></ins> | |||