# Re: New idea Laser launcher/scoop systems

```Reply to Kelly and Steve, worring about ratios

>Actually, now that I think about it there is a dangerous likely flaw in
>this fuel launcher idea.
>
>Remember a while back when I ran the numbers on fuel-to-payload ratios
>for different fuel types?  Remember that hydrogen came out at _minimum_
>to need 1,000,000 units of hydrogen to one unit of payload to reach even
>low relativistic speeds.

It's a long time ago already, so I dug up you formula:

/             2  \  ArcTanh[v]/a
|  r Sqrt[1 - a ]  |
f = | ---------------- |
\     r + a      /

f = fraction of mass that can be payload
r = reaction mass velocity (in lightspeed)
v = final spacecraft velocity (in lightspeed)
a = acceleration (in lightspeed --> 10 becomes 10/c)

Using a small r (0.081c) gives ratios of about f=1/45 which seems reasonable
compared to your 1:1,000,000. All this is for v=0.3c

For v=0.2 this ratio is down to 1:12, and for v=0.4 it is 1:180

With my own formulas I come to the same conclusion, some time ago I tried to
convince Kelly that with a 1:16 ratio we could come quite far.

Tim

```