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Re: Physics help (I found it!)

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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