From: sfaber@intgp1.att.com
Subject: Re: [RIFLE] [RELOADING] Load development
Organization: AT&T

From article <CHB6MA.FE7@fc.hp.com>, by bartb@hpfcla.fc.hp.com (Bart Bobbitt):

# Todd Enders A262 857-3018 (enders@warp6.cs.misu.NoDak.edu) wrote:
#
# : Indeed good advice.  One of the raps against 6.5mm cartridges, especially
# : with 140 gr. bullets is that "they don't group" at 100 yds.  However, if
# : tested at 200 or 300 yds, the groups, on an M.O.A. basis are *tighter* than
# : at 100 yds. The bullets just needed a little time to "settle down" in their
# : trajectory.
#
# I've heard for many years of these `raps' with just about all bore sizes.
# So some time ago, I did some tests to find out what causes this `wait until
# they settle down [go to sleep is a common expression]' philosophy.  When
# bullets were fired at muzzle velocities fast enough to spin them too fast,
# they always grouped smaller in MOA at longer ranges than shorter ranges.
# When fired just fast enough to spin at the lower end of their required RPM
# range, groups were equal in MOA through 300 yards or thereabouts.  Groups
# did enlarge due to velocity spread and time of flight which is what the
# laws of physics predict.

I read a similar account in Handloader recently where the author tried
to answer a question about overstabilization.  He mentioned how complicated
it was and then proceeded with the bullet going to sleep story.  I still
couldn't figure it out.  The bullet should become more stable due to the
decreased drag down range, and the bullet is more stable if spun faster
initially, so what makes it group poorly at short range?  It sounds
like the story is that an overstable bullet is actually spiraling in
initially where a marginally stable bullet isn't.
I guess this may make sense if the precession rate of the bullet
is slow enough so that it is laterally displaced resulting in a spiral
path.  The precession rate will be proportional to the drag divided by
the angular momentum along the spin axis, so if this angular momentum is
high (high spin) the precession rate could be low enough to cause this in
an "overstable" bullet where in a marginally stable bullet it would precess
too fast to notice the displacement.

Steve

From: sfaber@intgp1.att.com
Subject: Re: [RIFLE] [RELOADING] Load development
Organization: AT&T

From article <CHJ0pn.16w@fc.hp.com>, by bartb@hpfcla.fc.hp.com (Bart Bobbitt):

# That's exactly what happens when a bullet is spun a bit too fast when
# it leaves the barrel.  Its centrifugal force is just enough to cause it
# to wobble, but as soon as its spin rate slows down enough to where the
# centrifugal force no longer causes it to wobble, it will fly point on
# quite well.  During the time the bullet wobbles a bit and its axis isn't
# tangent with its trajectory, it presents different attitudes to the
# atmosphere it's flying through, so it tends to take a spiraled path to
# through the air.  When its RPMs are a bit lower, it now flies straight
# through the air in a much straighter path.

OK, I understood your theory of unbalanced bullets and overstabilization,
but I was thinking of the perfectly balanced bullet case.
Even a perfectly balanced bullet will wobble - precess and nutate
to a greater extent according to the drag to spin ratio.

Does Mann's book show a spiraling path to the target?
How big a spiral?  Does the spiral increase and then converge, or
does it just diverge?  What would the nature of the forces be that
would make it converge again if it does?  If it diverges for a
while and quits, then it seems that the observed divergence would just be
worse at long ranges, unless the spiral is totally reproducible.

I was brushing up on the chapter on motion of a rotating projectile in
Moulton's book on Methods of Exterior Ballistics (1920s) where he
did the theory associated with experiments similar to your Mann's
with projectiles fired through cardboard screens.  Moulton discusses
the firings of 3" projectiles at Aberdeen Proving Grounds.
He does not address any translational motion or spiraling in his
theory except for drift due to rifling twist, and only deals with
measurements of the angles and periods of nutation and precession
and how these damp out with time.  Here is a summary:
He derives the gyroscopic motion of the projectile and defines a
quantity "S" that is inversely related to the rate of spin (or
stability).  The value can approach 0 as the spin increases, and can
reach a value of 1 where it is at the verge of total instability.
(It is also proportional to the torque on the bullet by the wind drag.)
The bullet's spin axis will make a small angle "theta" to the
bullets path that will increase and decrease between 2 values, theta1
and theta2.  This action is called nutation, and its period "P" is
calculated and varies with "S" and the initial conditions which
determine the initial angles.  Good projectiles and guns give
small inital values of theta, so the result for the nutation period
is P= tw/(v*sqrt(1-S)) where tw is the twist length and v the
velocity.  Then there is precession where the axis sweeps out a cone
shape around the bullet path line.  The bullet is found to transition
between different modes of wobble, a fast precession where the axis
sweeps a about 360 degrees each nutation period, and a slow precession
where it only sweeps a fraction, typically 1/4 a circle each
nutation period. There are 3 modes of this slow precession which
vary by the way the precession speeds up or slows down on each
nutation bob ( the precession is not a constant speed).
Next - how are these oscillations damped?  Even if the velocity and S
were constant and the bullet moved in a straight line, the oscillations
would be damped in the following manner:  The fast precession mode would
have theta1 and theta2 both decrease and merge together resulting in
a more stable configuration with the bullet pointed where it is
going.  The slow modes would have theta1 and theta2 merge but increase,
resulting in a less stable situation.
Now add in the effect of changing v, S, and the effect of a curved
trajectory on the damping and the result is that all modes have
theta1 and theta2 approach each other and decrease toward stability.
The rate of this damping is expressed as an equation, but I have
not figured out how to calculate the coefficients quantitatively
yet.  It is shown that a bullet will follow the path of its curved
trajectory so that theta(1,2 merged) remains a constant or decreases
due to increasing S downrange.

Overstabilization is discussed only in terms of a bullet where S
is too low a value to allow the bullet to follow the curved trajectory
in this manner.  If this is the case I would expect to see an effect
that would increase down range, but it seems we don't see this in
practice.

Steve Faber

From: ohk@tfdt-o.nta.no (Ole-Hjalmar Kristensen FOU.TD/DELAB)
Newsgroups: rec.guns
Subject: Re: Bullet's Angle in Flight
Date: 11 Dec 1997 07:15:03 -0500

bartbob@aol.com (Bartbob) writes:

# Over the years, I've heard all kinds of comments, theories and the like
# regarding the angle a bullet has while going downrange.  For example, if the
# bullet is properly stabilized by its spin rate and is fired at an upward angle
# of, say 15 MOA (like for a target about 500 yards away), does the long axis of
# the bullet:
#
# Remain at +15 minutes up angle for its entire flight?
#
# or
#
# Stay parallel to its trajectory path and point down as the trajectory goes
# down?
#
# and
#
# Do rifle bullets and larger artilllery/naval projectiles have the same
# characteristics in this regard?
#
# I'm curious to know what others believe.

I have been thinking of the same problem over the years, but I have no
really good answers. However, I have a couple of data points, both
derived from military experience.

1. I once saw a high-speed film of a projectile in flight, I think it
was 155mm, but it may have been bigger. The nose of the projectile was
running in a circle around the direction of flight, not very large,
but obviously following a corkscrew trajectory.

2. The 107mm mortar is not fin-stabilized as most mortars are, but
spin-stabilized. The initial angle of flight is about 45 degrees, yet
it comes down with the nose first.

A rifle bullet is governed by the same laws as a larger projectile,
but the relative magnitudes between the air forces, gyroscopic
effects, and gravity need not be the same. A projectile of large
diameter has a much larger moment of inertia, of course, and the
ballistic coefficient is larger, meaning that inertia has relatively
more influence than the air forces.  Nevertheless, if the projectile
is properly stabilized, I believe rifle bullets and military
spin-stabilized projectiles will show approximately the same
behaviour.

The reason for this, I believe, is that if the spin is appropriate,
the balance between the gyroscopic forces and the air forces is such
that the projectile will either tumble, do the corkscrew motion with
its nose, or align itself with the direction of flight (which could be
viewed as an infinitesimally small corkscrew motion).

The corkscrew motion probably comes from the fact that if you push at
a gyroscope, it will respond with a movement in a direction at right
angles with your push. If the air forces (drag) tries to push the nose
further out of alignment with the trajectory, it will respond by
moving the nose at right angles to the push. Thus, it will start to
move in a circle. I have not done any calculations, but I would think
that after a while (if it is properly stabilized) those small
oscillations induced by either a change of direction of fight or any
crosswind, will die down, and the projectile will align itself with
the new direction of flight. As the rifle bullet is travelling in an
approximately parabolic trajectory, the direction of flight is
continually changing, so I would expect a very small corckscrew motion
at all times, but aligned with the instantaneous direction of flight.

Hopes this makes some sense. I really should go read Dr. Mann before
shooting my mouth off, I guess.

Ole-Hj. Kristensen

From: bartb@hpfcla.fc.hp.com (Bart Bobbitt)
Newsgroups: rec.guns
Subject: Re: [RIFLE] [RELOADING] Load development
Date: 4 Dec 1993 21:32:08 -0500

: What do you mean by 'spiraling'?  If you're saying that it's doing the
: equivalent of a barrel roll done by aircraft, I can't see the physics 
: allowing that motion of the bullet.

Neither could someone else about ninety-some years ago.  So he made some 
very interesting tests.

Read Dr. F.W. Mann's Book, `The Bullet's Flight from Powder to Target.'  It
has excellent examples of this.  Thin paper sheets placed every few feet 
between muzzle and 100 yards show the exact spiral path of the bullet.
It even shows how the angle of the bullet relative to its down-range path
is determined.  Great reading.  Even though it was first printed in 1907.
Physics hasn't changed much since then.

BB

From: Gale McMillan <" gale"@mcmfamily.com>
Newsgroups: rec.guns
Subject: Re: Short-range instability ( was RE: The 50 yard Sermon )
Date: 25 Apr 1997 13:22:09 -0400

Stephen Swartz wrote:

# Hey Guys:
#
#   I can see how aerodynamic effects and the forces created by
# the center of mass and center of aerodynamic pressure being
# in two different places on a bullet can cause the "flight path"
# to be affected.
#
#   I'll even buy this spiral flight path thing HOWEVER the great
# question that was never answered (at least this time around) was:
#
#   "But why would the spiral be **different** every time?"
#
# (remember, group size is a function of each bullet following a
# different flight path; not that the flight paths in general are screwy)
#
#   In other words, if each bullet consistently follows the *same*
# "spiral path" around the arc of flight, you would expect to see
#
# -  bullet holes at different relative positions for different distances
# -  different group sizes (in moa) the further you go out due to
#     differential environmental effects (wind, etc)
# -  different flight paths due to each bullet being different
#
# but not *smaller* (in terms of moa) group sizes!!!
#
# Or are we claiming that the dispersion around the *spiral itself*
# gets smaller the further out you go????
#
# This wouldn't seem to make much sense . . .
#
# A spiral path in and of itself- even if the spiral gets smaller- may
# explain how a *single* bullet tends to "home in" on a given
# flight path
#
# BUT
#
# does not explain how *successive bullets* follow/don't follow
# each other more or less closely!
#
# Did I explain this right?
#
# Steve


The difference in muzzle velocity between rounds causes the bullets to
go through the paper at close range at different points of the
spiril. You will see this more frequently as time goes by due to the
numbers of tight twist barrels being used in this fad of shooting overly
heavy, long bullets.  Shoot a 55 grain bullet out of a 9 twist barrel
etc. There has been posts in this thread indicating that the dispersion
of shots would be in seconds and minutes of angle proportionate to the
distance checked.  Then I ask why not check every thing at short range
and eliminate shooter error.  We shot 18000 rounds of 50 cal ammo during
a contract.  The guns were sighted in and function tested at 100 yards
and averaged 1.5 moa groups.  When these same guns were tested at 600
yards you would expect the groups to run 1.5 moa or 9 inches.  The 600
yard targets ran as small as 3 inches and never any larger than 6 inches
as an average.  Any that shot larger than 9 inches were inspected and re
tested.

Gale McMillan