Re: A small rocket-science brain teaser

From: Androcles (dummy_at_dummy.net)
Date: 10/16/04 

Date: Sat, 16 Oct 2004 19:13:04 GMT

"sal" <pragmatist@nospam.org> wrote in message
news:pan.2004.10.16.17.14.44.663219@nospam.org...
> This occurred to me during a recent argument over rockets and I
> thought I'd post it, in case anyone else is also amused by it.
>
> Let's suppose I've just invented a new gun. Instead of firing
> ordinary bullets, it shoots little rockets -- sort of like a "pocket
> bazooka".
>
> The little rocket engines have an exhaust velocity of 900 feet per
> second. (I'll throw in some photons later on just to keep this "on
> topic" for a relativity group.)
>
> One question came up immediately, and after I realized how to answer
> that one, a few other questions cropped up.
>
> 1) I want the rockets to hit the target with as much momentum as
> they can. How fast should they go?

Well, the only possible answer is "as fast as possible".
It depends on the burn time, the thrust and the mass.
The smaller the mass the greater the terminal velocity.
The longer the burn the greater the terminal velocity.
I'd suggest they should burn until they hit the target.
The problem you run into is that the propellant is part
of the mass and that reduces the initial acceleration.
However, increasing the mass at the target also increases
the momentum. If your little rockets are ALL propellant,
they end up with zero mass at a high velocity. SRB's
are an attempt to approximate this condition and as you
know a seal gave out resulting in the Challenger disaster.
You can indefinitely increase the length of the SRB
until the mass of the propellant exceeds the thrust needed
to lift it against gravity, under which conditions propellant
would be wasted with a huge flame at ground level,
until the mass reduces to less that the constant force the
thrust exerts, at which moment the rocket will commence
lift-off. So we need to know the thrust. The same SBR
in orbit would commence acceleration instantly, of course,
since it would not be held back by gravity.
Changing the diameter of a SRB changes the thrust.
Changing the length changes the mass and then burn time.

>
> 2) The Army hears about my new design, and they like it; they buy it.
> But they don't care about momentum -- "stopping power", in modern
> parlance. All they care about is _energy_. So, to make the army
> happy, how fast should the rockets go?

I'd suggest they should burn until they hit the target and then flame out,
having used all the propellant. Without knowing the mass of the "bullet",
the mass of the propellant and the thrust, it is impossible to quote a
speed.

>
> 3) The Special Forces want some, too. But they want them _silenced_.
> Can they do that, if they use the Army version of the gun?

Don't fire them straight away. Throw them with a catapult, air rifle or
spring
cannon. You need a new gun. If you fire them at 900 fps from the weapon
with a timed fuse, then (neglecting any loss of velocity from air
resistance)
they'll still accelerate when the fuse time out. The exhaust will fall
straight
down to the ground, which, in the frame of the rocket, is moving backwards
at 900 fps. As the rocket accelerates, the exhaust will fall increasingly
forward
as well as down.

>
> 4) The Air Force wants them, too, but some relativitist on their
> research staff says chemical rockets are passe. They replace the
> chemical rockets with photon rockets. How fast should their
> version send its projectiles, to carry maximum momentum to the
> target? (See, I told you I'd get it back on topic.)

>
> I found this entertaining partly because it seems like there's not
> nearly enough information here to answer the questions -- but there
> apparently is. (Except maybe #4 -- I'm not sure about that one...)

It is calculable, but not from exhaust velocity alone. We'd need to know
if you had a single pencil beam from a laser, or two or more lasers and
a couple of flashlights.
Androcles
>
> --
> I can be contacted through http://www.physicsinsights.org
>

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