Shuttle Speed Up Dilithium Calculation?
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in The Bridge
Could someone post the math used to calculate the dilithium necessary to speed up shuttles, according to mission length?
It's about 300 for a 3-hour mission, but less than 600 for a 9-hour, and the shorter it gets, the slower it falls. I'd really love to see this formula, please educate me
It's about 300 for a 3-hour mission, but less than 600 for a 9-hour, and the shorter it gets, the slower it falls. I'd really love to see this formula, please educate me
1
Comments
I second the motion.
That's awesome having it charted out like that, well done. I hope you didn't spend the full 3 hours charting it!
Awesome!! Thanks for compiling this and sharing!
Simply having a table gets the job done, though it's not as elegant as a formula.
i would be happy with an example of something similar to this, even if it did not fit exactly.
(My interest is not actually for the game, i'm trying to learn something.)
Thanks!
so @Bobkyou does your software do fractional exponents too?
What I did was called regression analysis, where you try to find the formula between two sets of variables. The most common ways to do this are with a ti-83 graphing calculator, a spreadsheet such as LibreOffice, or by hand (which is miserable).
I'll show a quick example using google spreadsheet, since it's free and doesn't require you to install anything.
1. Go to https://docs.google.com/spreadsheets/ and select Blank at the top.
2. Copy the following data into the spreadsheet
3. Click and drag across column A and column B at the top, so that both columns are highlighted.
4. Click Insert -> Chart
5. In the pane that opens up click Chart Type and change it to Scatter plot
6. Click Customize, click on Series, click Trendline, click on Show R2.
A trendline is trying to find a trend in the data, such as increasing or decreasing, and draws a line on the graph, in the case the blue line.
The default type the spreadsheet tries to use is a linear formula (f(x)=mx + b). Google spreadsheet also supports exponential, polynomial, logarithmic, power series, and moving average formula.
The r squared tells you how closely the trend line matches the data. The closer to 1 it is, the more likely you are to have found the proper formula. In this case we have an r2 of 0.435, which is horrible, but we could already tell that by looking at the trendline and comparing it to the data.
7. Since a linear formula clearly doesn't fit the data, lets try another type. To make it easier to compare, lets start a new trendline rather than changing the one we already graphed.
Click Data on the pane on the right, click Add Series, select Column B, and hit OK.
8. Click customize in the pane on the right, click series, click Apply to and change it to the 2nd series of data that, even though that series of data is identical to the first. Click Trendline, and change the Type to Exponential. Click show r2 and change the label to Use Equation.
As you can see, the red line that we've drawn on the chart looks like it matches the data. The r2 is showing 1, which means its either an exact match or it's close enough that it's rounding to 1. The formula we ended up with is f(x)=1*e^(0.2*x). E is called Euler's number, if you aren't familiar with it.
At 168 hours, by Spock's math we'd observe 379,749,833,583,241 tribbles. The formula gives us 391,106,102,111,038 which is wrong, but close enough.
This was just a quick and dirty example, if you want a full lesson there's bound to be decent guides somewhere on the internet.
Spock: 1,771,561. That's assuming one tribble, multiplying with an average litter of 10, producing a new generation every 12 hours over a period of three days.