# Re: more physics (short)

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Ok, I can't find a copy of the rocket equation set up for relitivistic
speeds.  Could someone forward a copy to me.

Oh, should the exaust velocity be considered in ship time or 'real' time?

Kelly

At 6:37 PM 6/2/96, Timothy van der Linden wrote:
>>I went over the Bussard paper and found 14E6 as the upper exaust vel for p
>>+ 11B.  Which obviously isn't what I'm getting.  Eiather I miscalculated
>>the watts per Kg (I sent my equations for that in another letter) or I
>>misread Bussards paper.  (I suppose I could write him.)  I'ld hate to write
>>off about 15% of spec impulse if I didn't need to.  (See table below.)
>
>>If you know how to get the exaust speed from Mev numbers let me know.  I'm
>>sure those numbers from the papers are correct.
>
>Watch carefully:
>
>The reaction as found in my tables book:
>
>H + 11B --> 3 4He + 8.7 MeV
>
>Let's assume energy conversion is 100% and ALL reaction products will be
>accelerated in the 100% effective lineac.
>
>First turn MeV in to Joules:
>
>8.7 MeV = 8.7E6 * 1.602E-19 = 1.394E-12 Joule
>
>Then determine the weight of the particles in kg:
>
>H + 11B is approx 12 u (u=atomic mass unit)
>
>12 u = 12 * 1.661E-27 = 1.993E-26 Kg
>
>Thus the energy per kg is:
>
>1.394E-12 / 1.993E-26 = 6.995E13 J/Kg
>
>(Don't use much more significant numbers, if you do use them you need to
>define some things more accurate and cannot simply think that 11 H weighs as
>much as 11B.)
>
>Using E=0.5 m v^2 I still get v=11.8E6 m/s, so I really wonder how Bussard
>can get a higher velocity, unless he dumps some of the reaction mass instead
>of accelerating it.
>
>>I was working up the following table of the fuel mass ratios needed to get
>>to or from certain speeds given the exaust velocities.
>>
>>NEW numbers
>>
>>Fuel --> Exhaust
>>Vexh                75E6m/s     100 E6m/s  125 E6m/s 150 E6m/s
>>
>>p + 11B --> 3 4He
>>  11,800,000 m/s       576.0     4,790.0    39,900    332,000
>>
>>6Li + 6Li --> 3 4He
>> (Combined)
>>  17,800,000 m/s        67.6       275.0     1,120      4,570
>>
>>3He + 3He --> 4He + 2 p
>> 20,300,000 M/s         42.5       138.0       472      1,620
>>
>>De + 3He --> 4He + p
>>  26,500,000 m/s        16.9        43.5       112        287
>
>Of course ;) I get completly different numbers (at least for higher Vend)
>
>  674  2,680  82,000  1,200,000
>   73    181   1,728     10,000
>   44     97     708      3,377
>   18     34     154        509
>
>I assume this time relativistics is the origin (for 0.5c gamma=1.15 which
>means its not almost equal to 1 anymore) for our differences
>
>>Amazing how touchy the fuel ratios are to changes in exaust vel/specific
>>impulse.  Look at the difference between 6Li + 6Li and 3He + 3He!  ;)
>
>Well yes, that is because of the energy per kilogram of fuel. Which is 3
>times higher for 3He + 3He. (This is what my "magic" number f says)
>
>
>Timothy

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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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