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Velocities etc. to be got by solar sails

Posted by: Ekkehard Augustin - Tue Jun 21, 2005 7:35 am
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Velocities etc. to be got by solar sails 
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Post    Posted on: Wed Jun 22, 2005 4:23 pm
SawSS1Jun21 wrote:
Ah, integation by parts!
Actually that method is called numerical integration.

SawSS1Jun21 wrote:
If we assume some nominal accelleration continues throughout the remainder of the trip
No need to assume. Just copy the 1717th line of the Excel file a bunch more times and see the result. I just did that and found I made an error! The distance the second day is 93,002,400, not 93,000,100, because the speed is 100 miles per HOUR and not miles per DAY. The acceleration is miles per HOUR per DAY. Just goes to show that you should ALWAYS WRITE THE UNITS!. Anyway, the corrected calculation is much worse. You never get above 30,000 mph because the vehicle gets too far from the Sun too quickly! It passes Pluto at 27,567 mph after 6,263 days (17 years). Of course this ignores the Sun's gravity, the vehicle starting with Earth's orbital velocity and all sorts of angular momentum issues. As I pointed out in the orbital mechanics thread (OH NO, NOT AGAIN!), you would not just accelerate directly away from the Sun. It would require a much more detailed calculation to get real numbers. These are just rough, order of magnitude, back of the envelope calculations.


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Post    Posted on: Wed Jun 22, 2005 4:41 pm
campbelp2002 wrote:
Actually that method is called numerical integration.


Right. "by parts" is for integration of trig functions. It's been a while, cut me some slack.

campbelp2002 wrote:
No need to assume. Just copy the 1717th line of the Excel file a bunch more times and see the result.


Easy for you to say, you already built the 'sheet.

Yeah, I know you'd really have to make multiple solar orbits and it would be much more complicated than driving in a straight line, but it's a lot easier to illustrate the shortcomings of the original linear-on-top-of-linear estimate by keeping it one-dimensional. We definitely don't want to open the (I won't use the O-word again in the same post just to be sure) thread again!


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Post    Posted on: Wed Jun 22, 2005 5:19 pm
SawSS1Jun21 wrote:
It's been a while, cut me some slack.
It has been a while for me too. I barely remember that there is something called integration by parts, much less how to do it!

SawSS1Jun21 wrote:
Easy for you to say, you already built the 'sheet.
No, it is really easy for you too.

Cell A1 is distance; 93,000,000 at start.
Cell B1 is speed; 0 at start.
Cell C1 is acceleration; 100 at start.

Then
A2 = A1 + B1 * 24 (don't forget the * 24 like I did!). B1 is 0 so distance does not change yet.
B2 = B1 + C1 (New speed on row 2 is 100)
C2 = 100 * 93,000,000 / A2 * 93,000,000 / A2 (New acceleration on row 2 is 99.995)

Now just copy row 2 and paste to rows 3 - 10,000, or however many rows you want, where each row is 1 day. So simple. It took longer for me to describe it than do it.


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Post    Posted on: Wed Jun 22, 2005 5:27 pm
I have run more spreadsheets on Lotus 123 in DOS than I have on Excel, dude. And that was 'way back in college.

I can run Excel, but I'd have to either run it in the emulator (on my Linux box) or connect my OSX box (which I have been procrastinating on doing). 'Tis simply not an app I use at all. It would be quicker for me to write a shell script to do that calculation, but it may actually be more fun to make you do the math for me. (Sorry, cheap shot, I know... couldn't help myself). It's not that I'm lazy, it just that... well yes, I guess I'm lazy.


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Post    Posted on: Wed Jun 22, 2005 5:33 pm
Hey, I am lazier than you. Don't you go trying to out lazy me! :)
Doesn't Lotus do the same stuff as Excel? At least simple stuff like this?
(EDIT) Yes, a shell script would be a good idea too.


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Post    Posted on: Wed Jun 22, 2005 5:44 pm
Yeah, Lotus was the original spreadsheet. And I have not used it since college, which was in fact pre-Windows, (it may have been the ONLY spreadsheet then), thus showing how long it has been since I did any real spreadsheet work. We used it in Engineering Analysis to build graphs and such.

(EDIT) I could probably have done this in a command line loop, no script required. I could even break it down to seconds... See, what you've done! You've made me think about it too much!


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Post    Posted on: Mon Jun 27, 2005 12:21 pm
The old dead guys who came up with the idea of integration wrote:
int(u*dv)=u*v-int(v*du)


Unfortunately, it's easy to set it up in an infinite loop...

I might point out here that a solar sail has a maximum theoretical speed (I don't care about direction, so it's not really a velocity) of c. Of course, if the sail is relatively small in size, the payload is relatively large in mass, and the star it is near is relatively low in intensity (i.e. somewhere south of "quasar" status), it will likely take quite a while to get there.

A chemical rocket's top speed, however, is determined by the propellants, the engine construction, the dry weight of the rocket, and the amount of propellant carried on the rocket -- if you get an acceleration of 1000 m/s/s, but you only have enough fuel for 0.1 s, your maximum possible speed is 100 m/s.

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