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*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 ---------------------------------------------------------------------- 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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