# Re: New idea Laser launcher/scoop systems

```To Kelly,

>>OK, unfortunately (as you stated below) the paper didn't show all there was,
>>your numbers only showed a decrease of mass for lower exhaust-velocities.
>>I found out that for high exhaust speed the mass goes up because of the
>>extra kinetic energy (could be overcome by beaming) and for lower speeds the
>>mass goes up too, because of the waste of energy (ie. using fusion fuel as
>>reaction mass).
>
>I'm not sure I follow this.  By waste energy are you implying the same
>specific impulse ratio could be developed with lower fuel to reaction mass
>ratios?

I assume that with "impulse ratio" you mean "impulse velocity". Than the
So after "extracting" the energy of the fusion fuel, you could better dump
the excess mass without accelerating it! (Because if you accelerate it the
other mass could be accelerated less)

>>So one needs to find the valley between the (ever rising) hills.
>>The formula to do this:
>>
>>  BestG:=1+1/(f-1);                     (the relativistic gamma)
>>  BestV:=c*Sqrt(Sqr(BestG)-1)/BestG     (the accompanying velcity)
>>
>>The optimum exhaust-velocity is only dependent on the mass:energy ratio of
>>the fuel (thus not on the final velocity).
>>
>> f   exhaust velocity (in c)
>>200        0.09987
>>250        0.08935
>>300        0.08158
>>350        0.07554
>>400        0.07067
>>450        0.06663
>>500        0.06321
>>
>>(f is the mass:energy ratio (about 270 is the best for fusion untill now))
>>
>>The next table shows the ship:fuel ratios needed to accelerate upto the
>>final velocities that vary horizontally. Vertically the energy:mass ratios
>>of the fuel are varied.
>>Every time the optimal exhaust speed is used (this can be looked up in the
>>previous table).
>>
>>                  End velocity -->
>>      0.10      0.20      0.30      0.40    0.50    0.60    0.70
>>200     2.7       7.6      22.2      69.5     244    1032    5906
>>250     3.1       9.7      31.9     114.6     467    2338   16422
>>300     3.4      12.0      44.4     180.0     839    4896   41401
>>350     3.8      14.6      60.2     272.7    1439    9662   96907
>>400     4.1      17.6      79.8     401.4    2376   18191  213876
>>450     4.5      21.0     104.1     577.2    3805   32958  449882
>>500     4.9      24.7     133.8     813.9    5941   57820  908988
>> ^
>> +--- Energy:mass ratio of the (fusion) fuel
>>
>>
>
>Mass energy ration of what?  Kinetic energy to mass?  Thermal energy to
>mass? etc...

* Mass:energy ratio shows what part of the mass of a fuel can be turned into
energy. For a matter & anti-matter mix all mass can be turned into energy
and thus gives a ratio 1:1. For fusion fuel only about 1/300 part of the
total mass can be converted to energy so that means a ratio of 1:300.
Note. I've defined f as total mass divided by energy mass (f=mass/energy),
this way you always get ratios bigger than or equal to 1.

* Fuel:Ship ratio is clear I think, it shows what part of the total mass of
the starship is used for fuel and what is used for habitation etc.

>Your table apears to show that I could get lower ship to fuel mass ratios
>than I expected.

Yes, that what I'm trying to tell everybody for the last week. :)

If we content ourselves with a final velocity of 0.2c, we can accelerate and
decelerate having a total fuel:ship ratio of 12*12=144. (f=300) (Ofcourse we
still need to mine fuel for the homeward trip)
If we assume we are beamed away (and have to decelerate by ourselves) while
using the same fuel:ship ratio of 144 then we can decelerate from a velocity
of 0.385c (not in the tables)

Tim

```