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lau
Non-abelian, simple sexaginta! Male + silly bits.
Joined: Jun 18, 2006
Age: 60
Posts: 7700
Location: Somerset UK
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 Posted: Sat May 17, 2008 6:04 pm Post subject: |
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| Orwell wrote: | | richie wrote: | Maxima is available for Windows. And I used to do all my electronic calculations from simple Ohm's law in DC circuits to
calculating RCL impedances using a Quattro-Pro spread-sheet program back in the nineties... |
I'm on a Mac. I'm trying to see if I can get access to Mathematica, but I'm not too confident about it. |
Mathematica costs money. Why bother?
Also, spreadsheets are pretty good for this sort of thing. I once wrote a helicopter simulation in a spreadsheet.
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Orwell
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Joined: Aug 09, 2007
Age: 19
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| Posted: Tue May 20, 2008 9:24 pm Post subject: |
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| lau wrote: | | Orwell wrote: | | richie wrote: | Maxima is available for Windows. And I used to do all my electronic calculations from simple Ohm's law in DC circuits to
calculating RCL impedances using a Quattro-Pro spread-sheet program back in the nineties... |
I'm on a Mac. I'm trying to see if I can get access to Mathematica, but I'm not too confident about it. |
Mathematica costs money. Why bother?
Also, spreadsheets are pretty good for this sort of thing. I once wrote a helicopter simulation in a spreadsheet. |
The money issue was why I lacked confidence. I'm not gonna spend $50 to RENT a computer program for a semester, that's a load of bull. I'm trying to see if my teacher will let me use her copy (I'm doing just one calculation, so it's not like I'm really robbing wolfram research).
How did you do that in a spreadsheet? I think I'm going to try a couple different approaches to this, and hopefully at least one will work out reasonably well.
Since it's a long-range ballistics, my initial calculations (ignoring air resistance) had a max height of over 500 Km above the ground. I stopped a moment and realized that that's significant enough that you could no longer reasonably assume the force due to gravity to be constant. So now I'm going to try a lower angle (it will require a higher initial velocity of course, I previously fired at 45º) because I don't know how to account for a changing acceleration due to gravity. 
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yesplease
Velociraptor
Joined: Dec 29, 2006
Age: 27
Posts: 441
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| Posted: Wed May 21, 2008 2:54 am Post subject: |
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| Orwell wrote: | | I'm on a Mac. I'm trying to see if I can get access to Mathematica, but I'm not too confident about it. |
What about Portage and Octave? |
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wolphin
Velociraptor
Joined: Aug 16, 2007
Posts: 442
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| Posted: Wed May 21, 2008 7:43 am Post subject: |
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You don't need mathematica or matlab - I was just suggesting, if you had access to one of them, that would make it relatively easier - but it's not absolutely necessary by any means.
These folks here: http://octave.sourceforge.net/ claim to provide a mac os version of octave, which is very similar to matlab (no need for portage or fink or such, apparently)
With octave, you should be able to find plenty of differential equation tutorials using matlab, for the most part, it should be the same for octave. |
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lau
Non-abelian, simple sexaginta! Male + silly bits.
Joined: Jun 18, 2006
Age: 60
Posts: 7700
Location: Somerset UK
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| Posted: Wed May 21, 2008 9:07 am Post subject: |
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Hmm. On looking back, I see that you want to...
| Orwell wrote: | | ... calculate what it would take to fire our textbook halfway across the country to hit its author... |
Now, the first problem is that you haven't specified which country. The launch velocity wouldn't need to be very great, if the country were Vatican City.
If the country happens to be a larger one, I suspect that an answer of "approximately 11.2 kilometres per second" will suffice. That is escape velocity. In the absence of air resistance, if you can reach orbit, you can pretty much choose where to come down.
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Orwell
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Age: 19
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| Posted: Wed May 21, 2008 3:57 pm Post subject: |
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| lau wrote: | Hmm. On looking back, I see that you want to...
| Orwell wrote: | | ... calculate what it would take to fire our textbook halfway across the country to hit its author... |
Now, the first problem is that you haven't specified which country. The launch velocity wouldn't need to be very great, if the country were Vatican City.
If the country happens to be a larger one, I suspect that an answer of "approximately 11.2 kilometres per second" will suffice. That is escape velocity. In the absence of air resistance, if you can reach orbit, you can pretty much choose where to come down. |
I'm in the United States, firing from Cincinnati, Ohio, to St Olaf College in Northfield, Minnesota. After correcting for the curvature of the Earth, it is a horizontal distance of slightly over 1000Km. This isn't exactly a realistic problem we're doing (as has been noted, the book would vaporize at such speeds, plus the max height reached is significant enough that we really shouldn't assume acceleration due to gravity to be constant) but my partner doesn't care about any of this and my teacher doesn't have enough of a mind for physics to notice.
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lau
Non-abelian, simple sexaginta! Male + silly bits.
Joined: Jun 18, 2006
Age: 60
Posts: 7700
Location: Somerset UK
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| Posted: Wed May 21, 2008 4:50 pm Post subject: |
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Well, I'm feeling lazy...
http://en.wikipedia.org/wiki/Orbit_equation
Consider your book as just a satellite of the Earth. As such, it will have an elliptical orbit. The above gives your the formula for such orbits, which will form a family based on the eccentricity and the h^2/mu terms.
You require that set of the ellipses that intersect the surface of the Earth in two places 1,000km apart.
That will give you a set of possible firing angles/speeds. You could then choose the angle that requires the lowest speed. I'd guess it would be around the 45 degree mark, as we're not going to be wildly at odds with the case for normal ballistic parabolas.
I leave the detail to you... 
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pakled
"Bless his Heart"
Joined: Nov 13, 2007
Age: 51
Posts: 3281
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| Posted: Sat May 24, 2008 8:47 pm Post subject: |
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don't know how helpful this would be, but search for references to the Paris Cannon the Germans used in WWI (fired about 100+ miles). There was also a guy who sold Saddam Hussein a cannon that would fire from Iraq to Tel Aviv (was actually built, maybe tested, but never used). This was prior to GWI (as opposed to the current GWII).
There may be some of his research posted on the Net, somewhere. |
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Orwell
Outer Party Member
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| Posted: Sat May 24, 2008 11:13 pm Post subject: |
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| pakled wrote: | don't know how helpful this would be, but search for references to the Paris Cannon the Germans used in WWI (fired about 100+ miles). There was also a guy who sold Saddam Hussein a cannon that would fire from Iraq to Tel Aviv (was actually built, maybe tested, but never used). This was prior to GWI (as opposed to the current GWII).
There may be some of his research posted on the Net, somewhere. |
That's pretty amazing. I'll probably throw some of that in to my write-up on the history of theories of projectile motion.
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