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Re: Physics help (I found it!)
- To: T.L.G.vanderLinden@student.utwente.nl (Timothy van der Linden)
- Subject: Re: Physics help (I found it!)
- From: kgstar@most.fw.hac.com (Kelly Starks x7066 MS 10-39)
- Date: Fri, 17 May 1996 09:37:28 -0500
- Cc: KellySt@aol.com, kgstar@most.fw.hac.com, stevev@efn.org, jim@bogie2.bio.purdue.edu, zkulpa@zmit1.ippt.gov.pl, hous0042@maroon.tc.umn.edu, rddesign@wolfenet.com, David@InterWorld.com, lparker@destin.gulfnet.com, DotarSojat@aol.com, neill@foda.math.usu.edu, 101765.2200@compuserve.com, MLEN3097@Mercury.GC.PeachNet.EDU
I found it!!
>At 11:31 PM 5/16/96, Timothy van der Linden wrote:
>>Hi Kelly,
>>Rex letter made me look back at out letters from last week.
>>When I use the following numbers:
>>Vexh=0.0667c (2E7 m/s)
>>dV =0.3c (9E7 m/s)
>>and the classic rocket formula:
>>M=Exp[dV/Vexh]
>>I get:
>>M=90
>>and not the 148 (or 150) you seemed to get.
>>Is this the reason for the confusion that had arised?
>>Timothy
>Well thats part of it. It certainly doesn't give me a warm comfident
>feeling when our numbers are that far apart! Eiather we're talking about
>something fundamentally different and don't realize it, one of us has a
>blown calculator, or one of us is badly misappling some equation.
>Kelly
Wait a minutte?!! The rocket equation (as cut from one of Rex's lates
E-mails) is:
Vend = the velocitie at the end of the acceleration burn or the Delta V in
our case.
Vexh = the exhaust velocity
M = starship mass (= Mi initially; = Mbo at burnout)
Now from the rocket equation
Mi/Mbo = exp(Vend/Vexh)
And your numbers tim were:
dV = Vend =0.3c (9E7 m/s)
Vexh =0.0667c (2E7 m/s)
Mi/Mbo = exp (9/2) = exp(4.5) = 90
I however wasn't computing a Vend of .3c. I was computing to 1/3rd c, I.E.
10E7 m/s.
Mi/Mbo = exp (10/2) = exp(5) = 148
We were both talking about something fundamentally differnt, but didn't
know it! The difference was all due to the slightly different Delta V.
The Exponential makes a hellish difference given even slight differnces in
the speed assumptions.
(See why I always want to see examples with numbers and units with your
equations Tim?)
So a 55 to 1 fuel ratio with a Vexh of 2E7 m/s:
55 = exp (?/2E7)
or
2e7 * Ln (55) = 80E6 = .267c
So we can still get a burn down from over 1/4th c with the same fuel ratio.
Giving a touch under 17 years for a flight time to Alpha C. Much better
than I was afraid of.
:)
Kelly
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Kelly Starks Internet: kgstar@most.fw.hac.com
Sr. Systems Engineer
Magnavox Electronic Systems Company
(Magnavox URL: http://www.fw.hac.com/external.html)
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