Re: railguns

Mostly good thinking, but an important figure in the input data was off
by four orders of magnitude and no consideration was given to the hit
probabilities, so here goes:

bbrush wrote:

> Max engagement range is 36".	Equals 36 million meters.

Max railgun range is 30", but it doesn't matter much for the
calculations.

> Turn length is 7.5 minutes which gives you a turn of 450 seconds.
> A kton of TNT is equal to 6.31*10^8 joules

Sorry, no. Not unless modern explosives are more than ten thousand
times stronger than TNT is, and I'm pretty certain they aren't...
otherwise we would've stopped using TNT in non-nuke warheads decades
ago. See my other post for this.

> Now, with these numbers you can figure that the absolute minimum 
> speed of a projectile has to be around 80,000 m/s.  Anything lower
and it l> iterally will not be able to make it from max firing range to
the target in 
> one turn.

80 km/s is speed 36... that's about twice the speed of my
slowest-moving capital ships, and slower than my fastest escorts. If
they can survive running into space dust at those speeds, they're not
going to have *that* much problem with small slugs.. and that's quite
apart from the fact that some of my ships can *outrun* those slugs :-/ 

> Since 7.5 minutes is way to long for a time-to-impact for a ballistic

> weapon we need to bump it up significantly.  So lets take it up to oh

> around 1 minute (600,000 m/s).  That's still a long lag, but not too
bad.  

Yes, it is. Assuming the standard scale - Thrust-1 ~ 1 g - a *Thrust-1*
target will be able to get up to about 17 km away from your projected
target point during that minute. Even if you're talking about Renegade
Legion-style Leviathans, a sphere with a 17km radius leaves quite a few
possible true target points  - and the MT railgun has a 17% hit rate at
that range (against all targets, regardless of thrust rating - but
after running these calculations I'm more and more inclined to make
railgun hit numbers dependent on target thrust :-/ ). Anyone care to
figure out how many slugs you'd need to fire to achieve this hit rate?

> Ok, now assume a projectile of 1 gram (itty bitty).  So we have
> 
> Energy=.5*.001*600,000^2=1.8*10^8 joules, or about 1/3 of a kton of
TNT

Um... no. Only about 43 kg of TNT... Question for you naval
historicians: how much TNT was there in a 16" naval grenade? 

Since there is space dust, micro-meteorites etc out there, my ships
(some of them flying *faster* than this slug, remember) are likely to
suffer similar hits quite often in normal operations - without taking
any noticeable damage from them.

> A 10 gram projectile will be 1.8*10^9 or about 3 kton of TNT

430 kg of TNT.

> Now just to get silly, let's take our velocity up a bit, say to
around 3.6
> million m/s.	

It isn't silly. It is necessary, unless you want to fire a several
thousand slugs in each shot...

> That gives us a time-to-impact of 10 seconds. 

Yes please. Now that thrust-1 target can't move more than about 500
meters away from where you thought it would be, before the slug
arrives... starts looking as if we might actually have at least a
prayer of hitting the target :-)

> We'll use our 1 gram projectile again.
> 
> Energy =.5*.001*3.6 million ^2=6.48*10^9 joules

Which is still "only" about 1.5 tons of TNT. Starts getting nasty, but
nowhere close even to a small nuke.

> Just for reference 3.6 million m/s is equal to about .01 c, so you're
going > to see some minor relativistic mass shifts

The mass increase at .01c is ~0.005%... rather easy to take account
for, I think :-/ The mass shift stays below 5% until above .3 c.

Regards,

Oerjan Ohlson
oerjan.ohlson@telia.com

"Life is like a sewer.
  What you get out of it, depends on what you put into it."
- Hen3ry