# Re: more physics (short)

```>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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