Re: [HOE] Ummmmmmm... WOW! (minor spoilerish stuff, maybe)

[Dirk <darklord@dark-sky.net>]

Matt Crawford wrote:

> > Oh! and before I forget, the chances are that firing the weapon
> > while unbraced would start a character tumbling, rather than
> > rocketing through space, since it will (almost certainly) not be
> > held and fired along the axis of the person's center of
> > gravity. Just something else to think about. . . .
>
> OK, I'll take this one on as penance for posting so manay consecutive
> messages.  This time I don't know the answer (fast or slow spin) in
> advance.  But there will be some estimating ...
>
> I'm going to suppose a person's center of gravity is a bit above the
> navel and that a Chinese SGS assault rifle is fired from the shoulder.
> The mass of the bullet is 3.5x10^-3 kg and the velocity is 10^3 m/s.
> The impulse on the shooter is about 0.5 m from the center of mass,
> for a total imparted angular momentum of 1.75 kg m^2/s.
>
> Now for the tough part - the moment of inertia of a human about a
> diagonal axis.  About a vertical axis it would be roughly
> I1 = M W^2/2, where W is the width of the torso.  The moment of inertia
> around a "horizontal" axis would be somewhat less than I2 = M H^2/12,
> where H is the height.  (For comparison, the moment of inertia of a
> sphere about any axis is (2/5) M R^2.)  For an axis perpendicular to
> the navel-shoulder line I'm going to handwavingly take the average,
> and let H = 2m and W = 0.5m, M = 100kg.  I come up with 21 kg m^2.
> Dive the angular momentum above by this and get the angular velocity
> of 0.083 radians/second, or 0.013 revolutions per second.  About
> 3/4 rpm.  Darned annoying I'm sure, but not cinematically spectacular.
>
> Of course, a more powerful gun ...
>

Hmmm, now what would happen if they fired a burst of 3, 6, 9, or even 12
shots. I'm assuming the effects are cumulative...

--Dirk