15 September 2012, 22:48
SmokinJGibby, everyone is tired of hearing your "benchrester shooters use the slowest twist they can to stable a bullet". There are other reasons too, but you wouldn't know that. You only know what you paraphrase.
You're wrong about the 7 twist isn't the best twist for the .224. Equally wrong that you interpreted those books you read wrong. Maybe you better take a look at this:
: 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.
# 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.
# 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.
: 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.
# 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?
#
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.
16 September 2012, 01:38
GeargnasherFirst off Larry, that the little test Joe showed in the chart above DIRECTLY correlates to your comment about 8 twist being the desired rate for the bullet in question, and he showed you that it 'taint necesarily so. If you can't see that, you might as well forget trying to understand what I'm about to tell you. That test revealed some interesting results, can you explain why? You throw books that you probably haven't even fully understood at us and say WE are the ones who don't understand your theory. Let me show you, in ballistic terms with which you claim to be familiar, why your theory is innacurate in its ability to describe what is really going on with our cast bullets at HV, and you'll see that, outside of extreme cases, accurate, linear flight paths have nothing to do with the bullets being out of balance or not "overspinning" them.
When a spin-stabilized projectile pops out of the muzzle, it is accompanied by two different types of barrel harmonics and about 40% of the powder energy in the form of muzzle blast. These forces combine to make the bullet yaw slightly in a random direction upon exit. The aerodynamic forces on the nose of the yawing bullet are countered by the gyroscopic forces of the angular velocity, which react (as a neat function of gyroscopes) at 90 degrees to the wind force against the yawing nose and slightly ahead of the center of gravity of the bullet, provided it is spining fast enough, moving fast enough, and of the appropriate shape. This perpendicular force acting on the center of pressure of the bullet ahead of the center of gravity is called the Magnus force, and is the most important force for keeping the bullet stable. Static stability is balance, dynamic stability is the balance of the magnus force against yaw, a setup of opposing forces made possible by the gyroscopic force of the rotation. I will assume you've read and understand enough about this to know about the spiraling nose, the different attitudes a bullet can have in flight, and why, so I won't go into ALL of the forces affecting the bullet, only those necessary to stabilize one. So, there is a stability factor for each bullet at launch that must be met or the bullet will fly off in an ever-increasing spiral, usually in a BAD way, and not at particularly high velocities either. If the static AND dynamic balance is sufficient to reach a minimum stability factor, the yaw is cancelled out usually within about 5,000 caliber lengths from the muzzle, which is not very far. If the bullet is dynamically stable at muzzle exit, it will virtually be dynamically stable for the remainder of the useful range. As forward velocity decreases with range, the spin rate deteriorates proportionally much less, so the damping effect of the magnus force increases and the bullet flys even more true, leading many to observe "going to sleep" of bullets at longer ranges. This actaully begins to occur just a few yards from the muzzle if things are done correctly. If the statically balanced bullet is spun faster than the minimum for dynamic stability at muzzle exit, the only real negative effect is that the bullet will maintain the same orientation downrange as it did when leaving the muzzle, meaning as it goes "over the top" or passes the apogee of the trajectory it will be flying nose-up, which increases the yaw of the nose, rather than the nose turning to "follow the arc" as it does when not overspun. This is only a significant factor when shooting at extreme upward angles, as you would with long-range artillery, not with sporting rifles which under most conditions will be fired fairly close to horizontal. The conclusion is that the only things that will cause a bullet to "cone" as it goes downrange are loss of static balance or loss of dynamic balance. Static balance is lost when a bullet is damaged at launch, out of balance badly, or experiences more yaw forces coming out of the muzzle than the dynamic balancing "system" can handle. The other possibility is that the dynamic force or static force is interrupted by a phyical collision with something, the dynamic balance is overcome by a shift in the magnus force to the rear (overturning moment) due to aerodynamic forces that come into play as the bullet is "retarded" downrange, such as going subsonic.
So, in review, the bullet's dynamic stability reduces the yaw of the nose (spiraling of the nose around the flight path while the CG point follows the line) until the bullet has almost no perceptable wobble by 5,000 caliber lengths. Dynamic stability depends on forward motion, rotational motion (gyroscopic effect), and the magnus force to be in balance, and the rotational motion (angular velocity) need only meet a minimum for the "system", anything over the minimum isn't necessary but is a bonus for horizontal shooting. In fact, as the angular velocity increases, the the distance required for the launch yaw to be dampened DECREASES, meaning the bullet "goes to sleep" sooner, because it actually increases the magnus force by increasing the "lift" due to air moving across the rotating nose of the bullet. "Overspun" really only means that it is spinning faster than necessary, not that it is spinning so fast that a (insert negative effect of your choice or invention) begins to occur. In fact there aren't any negatives from the 'overspinning' unless your launch sucks and throws the bullet out with so much yaw that it cannot possibly become dynamically stable, such as launching froma damaged crown or at the worst possible point in a vibration curve. If the bullet isn't statically balanced, there is no hope for it either, and it will fly out in ever-increasing circles until somebody shouts "Eureka! There's an RPM threshold that affects all bullets fired over 144K RPM! It MUST be that pesky dynamic balance making wild sprirals out of our trajectories like so many unbalanced car tires! We must reduce our rifling twists to compensate for the fact that we have no idea what's really going on or how to fix it!". What REALLY is the issue is there is a STATIC balance problem due to poor loading techniques that is causing excessive yaw at launch, and dynamic balance never had a chance. DON'T blame dynamic balance issues for causing the problem due to "overspinning", it's the STATIC balance that's the bugaboo, and this is why the RPM Threshold Theory cannot be substantiated.
The "overspinning" only serves to increase the magnus force and better stabilize a statically stable bullet. "Overspinning" also serves to DAMPEN static balance imperfections rather than increase them as the RPM Threshold theory dictates, unless the static balance imperfections are so great or the yaw angle at muzzle exit is so great that they "cam over center" the dynamic balance force (the bullet nose yaws beyond the point where the dynamic stabilizing component can lasso it back on course), in which case the bullet sprials off in to RPM Theory land, causing some pretty wild, non-linear group dispersions downrange.
As you should be able to see by now,the RPM Threshold really isn't a balance issue exacerbated by too much rotational velocity, it's a point at which irrecoverable yaw is induced by a poor launch, and in fact there is not ENOUGH spin to induce sufficient magnus force to dampen the spiraling out of control. EVEN A PERFECTLY, STATICALLY BALANCED BULLET WILL "CONE" IF THE DYNAMIC BALANCE IS THROWN OFF AT SOME POINT IN THE TRAJECTORY, therefore coning is not necessarily the result of static balance issues as the RPM Theory dictates. If the magnus force shifts to "at" or "behind" the CG, or the bullet shape is wrong or changes during launch, the bullet will become dynamically unbalanced resulting in uncontrolled yaw. Uncontrolled yaw will deflect the bullet aerodynamically and in some cases make it trace the path of the surface of an expanding cone.
So above a certain forward velocity (exactly what point depends on the "system"), it gets more and more difficult to launch bullets without excessive yaw. Unbalanced bullets make the yaw even worse, causing non-linear dispersion. At this point someone will say "A-HAH! So you just substantiated the RPM Threshold theory!" but in fact this isn't the case, because the theory states that the non-linear dispersion is due to increased centrifugal effect from the unbalanced bullets being overspun. Actually any so-called "RPM Threshold" effect is observed ANY time a badly out-of-balance, damaged, or excessively yawed bullet exits the muzzle, although normally we call those "flyers" if they are anomalies, and "piss-poor shooting" if those "flyers" are the norm for the group. Overspinning only serves to correct imbalances (with possible exception of certain "nodes" in the RPM spectrum, of which I don't know any studies or information), but no amount of practically achieveable spinning will overcome a bad launch, a badly damaged bullet, or an unbalanced load, so the "RPM Threshold" becomes an excuse, to be blamed on "too much spin magnifying the unbalanced bullet".
I had the opportunity a couple of years ago to spin-balance some of my cast bullets and compare them directly to some common copper-jackeded bullets, and in fact in most cases my cast bullets were better. If static imbalance and centrifugal force were responsible for non-linear group dispersion, the jacketed bullets would certainly have shot worse at similar velocities, but they did NOT. The reason? My cast bullets were getting damaged and so were not coming out of the muzzle as true and balanced as the jacketed ones after all (even being better when loaded into the breech end). Now, when I identified and repaired the cause of the bullet damage affecting my cast projectiles, the group dispersion became linear, actually a little LESS than linear, tested at 50, 100, and 200 yards, albeit on different days.
Do poorly balanced bullets shoot better at low RPM/velocity? Yes, because they don't yaw as badly coming out of the muzzle and there is some chance for the (even reduced) gyroscopic stabilizing effect to take place and, combined with the magnus force acting ahead of the center of gravity to minimize the nose spiral, normalize the bullet to at least a reasonably tight, non-expanding helical path.
The yaw is what gets you as you increase velocity, not how fast the bullet spins as it goes downrange. So why is it easier to go faster with accruracy by simply going to a slower twist? Because the yaw gets you less. Why does the yaw "get" you less? I'm not really sure, but study of recovered bullets indicates that slower twists put less torsional stress damage on the bullet at muzzle exit. There are loading techniques that minimize this stress and allow less yaw at HV, fast-twist launch. Maybe, if even more really deep study is done here, we might be able to establish a Twist Rate Threshold Theory that will more accurately identify what's causing our HV accuracy issues.
So FINALLY, it's easier to shoot HV with slower twists with cast bullets, but it's all in the launch, not due to "overspinning". If you learn how to tame the factors affecting the yaw at launch, you don't have to worry how fast the bullet is spinning once it leaves the barrel as long as it is fast enough for dymanic stability to take place.
Those two separate barrel harmonic forces I mentioned in the beginning have LOTS to do with taming launch yaw, pressure curve shape has a lot to do with the rest. Like I said before, even on this thread I think, it's all about INTERNAL ballistics. If you start with good castings and get the launch right by controlling the mechanics and the internal ballistics, particularly what immediately proceeds from the first spark, the external part will take care of itself and you needn't get your knickers all knotted up about a particular rifling pitch.
Gear
......do you really expect anyone to think 25 yard groups (pages 2 & 6 specifically) impress anyone? 
Do you think claiming the 5 closest shots (was that also 25 yards? 
) and then pasting up all the other holes claiming them as "another load" fools anyone? 
