12-30-2012: Getting the math right
I have to agree with a fellow writer whom I got to know while attending Launchpad earlier this year - the holiday time sure puts a major crimp in productivity. (You can see his post here: http://www.matthewsrotundo.com/blog/) I thought I would get some writing done this weekend but only managed less than 1,000 words. This morning I unexpectedly slept in later than I thought possible and then encountered problems when we got to the bookstore. Problems? Like what, you might ask. Well, since you asked, let me explain.
I prefer to keep the numbers I use in my books as realistic as possible. For example, if I say I want to be traveling past a certain point at a speed of 15 Km/sec then I had better be correct when I say how much acceleration I will have to apply and for how long to achieve that velocity. I have a spreadsheet that I rely on to do the math. Today, I found an error in it and it took me most of an hour to figure out which one of the equations I was using was wrong. Instead of writing, I spent time fixing the spreadsheet. Still curious? Okay - here's how it all went down...
A fleet is poised to attack a planet. They are stationed 50 million kilometers away. I first dumped in some numbers wondering how long it would take them to get there at 300G's acceleration. Simple - divide the distance in half (for acceleration and deceleration time), punch in 300 in my magic spreadsheet, and BINGO, the answer appeared - 3.6 hours. Multiply that by two for total travel time. The maximum velocity attained by this calculation was something on the order of 12% light speed. Too fast for me. So, I decided to just let them boost at 300G's for an hour and then coast for awhile and then decelerate at 300G's at the other end. I have a different set of equations for that. Total travel time turned out to be 1.3 hours - What? How can using less acceleration get me there faster? Red alert - red alert - red alert. Error - Error - Error. Must analyze.
It took a long time to find the problem and a longer time to run the numbers against several websites to ensure they were correct. The spreadsheet is now fixed. If you're interested in the spreadsheet I plan on putting it up on my web page in a few days.
Speaking of my web page. I will be uploading the new Galactic Alliance covers there as well as my spreadsheet. I've not had the time to update it recently (the darned holiday again). Check back in a few days if you're curious.
Happy new year! I hope 2013 treats everyone well.
I prefer to keep the numbers I use in my books as realistic as possible. For example, if I say I want to be traveling past a certain point at a speed of 15 Km/sec then I had better be correct when I say how much acceleration I will have to apply and for how long to achieve that velocity. I have a spreadsheet that I rely on to do the math. Today, I found an error in it and it took me most of an hour to figure out which one of the equations I was using was wrong. Instead of writing, I spent time fixing the spreadsheet. Still curious? Okay - here's how it all went down...
A fleet is poised to attack a planet. They are stationed 50 million kilometers away. I first dumped in some numbers wondering how long it would take them to get there at 300G's acceleration. Simple - divide the distance in half (for acceleration and deceleration time), punch in 300 in my magic spreadsheet, and BINGO, the answer appeared - 3.6 hours. Multiply that by two for total travel time. The maximum velocity attained by this calculation was something on the order of 12% light speed. Too fast for me. So, I decided to just let them boost at 300G's for an hour and then coast for awhile and then decelerate at 300G's at the other end. I have a different set of equations for that. Total travel time turned out to be 1.3 hours - What? How can using less acceleration get me there faster? Red alert - red alert - red alert. Error - Error - Error. Must analyze.
It took a long time to find the problem and a longer time to run the numbers against several websites to ensure they were correct. The spreadsheet is now fixed. If you're interested in the spreadsheet I plan on putting it up on my web page in a few days.
Speaking of my web page. I will be uploading the new Galactic Alliance covers there as well as my spreadsheet. I've not had the time to update it recently (the darned holiday again). Check back in a few days if you're curious.
Happy new year! I hope 2013 treats everyone well.
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