From: bercov@bevsun.bev.lbl.gov (John Bercovitz)
Newsgroups: rec.guns
Subject: Re: Trajectory Question
Date: 9 Nov 92 23:48:23 GMT
Organization: Lawrence Berkeley Laboratory, California


 
 Hey Dan, when you or I send in an opus and Jim moderates and sends it out
 from magnum@cs.umd.edu, does that make it a "magnum opus"?  Hyuk, hyuk,
 hyuk, hyuk, I slay myself.
 
 Sorry.

 [MODERATOR:  AAAAAAAAUGYHHHHHHH!}

In article <9211091828.AA04413@sweetpea.jsc.nasa.gov> weed@sweetpea.jsc.nasa.gov
(daniel weed 283-4162) writes:

#replying to an article by John Bercovitz  (JHBercovitz@lbl.gov)

# >Sounds like your gun is pretty loose.  This is 7.5 inches at the 25 yard

#I was amused by your comment that my gun must be "loose", because all of
#your analysis is an attempt to "prove" that a .45 auto with a VERY loose slide
#and a VERY loose grip, will still not show any variation in impact point
#with different bullet energies.

No, I was assuming a low-friction slide and a loose grip.  Low-friction and
loose are not necessarily partners.  The spindles on your car have low-friction
but are not loose while farm equipment is often loose but has high friction.
I assumed the low friction to favor my side of the argument and the loose
grip to favor your contention.  Couldn't be fairer.  8-)

#A "loose" .45 will shoot inaccurately and inconsistently.  Mine, while not
#blueprinted, gives me results consistent enough to notice different loads
#vary in mean impact point.
#I agree that my evidence shows only what my gun will do, when I shoot it,
#from one stance, on Saturdays.  However, I remind you that I am not the 
#first and only persion to notice that higher energy loads hit the targets
#lower.  This whole thread started because someone noticed just that, and
#several others have also commented on same.

The guy who started the thread noticed the phenomenon in a rifle.  Actually,
what he noticed is that one of his light bullet loads struck much lower while
one did not.  This is pretty standard since barrel whip is a major factor
in point of impact for rifles.  In ordinary handguns, the barrels are too 
short to whip.  Many other people have noticed the difference in point of
impact in handguns but not for the gov't model, I think.  I sure haven't in
the 38 super, 10 mm and 45 gov't models I've owned.

# >I don't think you understand what I wrote.  The only resistance to slide 
# >motion other than its inertia is the recoil spring and a little bit of slide-
# >to-frame friction.  Do you see any other resistance to its motion?

#Most certainly.  I agree slide friction is the smallest force.  Slide
#momentum is significant, the recoil spring is very significant, and the
#most significant force is the one you are missing - that of the mainspring.
#Remember the gun is not cocked after firing, and the slide must cock the
#hammer.  This about doubles the energy required to move the slide over the 
#recoil spring alone.

Good point.  The hammer does take quite a bit of force and it happens just
at the period in the cycle when the bullet is still in the barrel.  However,
this force is not too much larger than the recoil spring force as I recall. 
Since I got zilch barrel rise from the recoil spring, I expect that a few
times zilch is still small.  However, I think there is another factor missing
which may be modestly significant, but more about that below.

#In the Shooting Times article, again on page 14, Rick Jamison writes to 
#explain why heavier bullets hit higher:
#"The reason is that the bullet is still in the bore as the muzzle begins to 
#elevate under recoil.  This can be calculated mathematically.  But what left 
#no question in my mind was an X-ray photograph of the firing of a .45 auto. 
#The bullet was clearly seen still in the barrel as the muzzle was elevating."

I think I'd better grab that article and take a look.  Sounds interesting.
How much tilt was he observing?  As I showed in an earlier post, the 
barrel must tilt enough to cover the bullet's drop and the height of the
sights above the slide.  That amounted to some 2 parts in a thousand
while the revolver rose some 15 parts in a thousand.  All I've been 
trying to say since the beginning (so who can remember the beginning?)
is that revolvers have wild dispersions due to different bullet weights
while 45 autos have virtually none.  

# >If you assume the slide's motion is negligible, than you may be assuming
# >it is fixed in the gun which is an error.

#Lets contrast my analysis with John's. I assumed that the slide can be
#considered fixed to the frame while the bullet is in the barrel.  While
#this may raise eyebrows for a semi-auto, it is a good assumption for
#revolvers.  I chose this assumption because I know that the barrel/slide moves
#less than 1/8 of an inch while the bullet is in the barrel (for a 1911 style 
#.45 auto), and because I believe the countering effects of slide mass, recoil 
#spring and mainspring are significant.  By the way, the barrel is completely
#unlocked from the slide after the slide travels 1/4 to 3/8 of an inch - in
#a Colt 1911 .45 auto.

#John takes the opposite approach and assumes the slide is completely free to
#move backward while the bullet is in the barrel.  Totally free of any
#counter forces or friction.

Well, not totally free; I said the recoil spring was acting on the slide.
But as I've said many times, I was making an ideal case to demonstrate
the tendency.  There was no attempt to come up with the exact numbers.
I just wanted to show why a revolver tips a lot while an auto of this
type tips very little.  I think it's fairly common to idealize a case to
show the direction of the argument.  Of course we can always agree to
disagree on how much was lost when I idealized the problem.
 
#The reality of course, is somewhere in between (between NO forces being
#applied to the frame, and ALL the forces being applied to the frame).
#To look at what this implys, lets create some number "e", between zero and 
#one, which indicates how much impulse is applied to the frame by the bullet 
#momentum, divided by the total impulse.  Then lets give "e" an important 
#sounding name, like, say, the "coefficient of restitution". ;-)
#
#If "e" is zero, (John's assumption) then the slide movement is completely independent of the frame, and the bullets will all strike in the same place 
#(varying only by the external ballistic trajectory).  If "e" is one, then the 
#slide and frame are locked together - or its a revolver.  
#
#I have shown that the impulse applied to the frame ("e" = 1) is higher
#for the heavier bullet, causing the change in impact point.  This must
#also be true for ANY value of "e" OTHER than ZERO.  Therefore, even though
#I don't know what "e" is, my basic analysis is still correct, and is 
#supported by the preponderance of physical evidence.

You have shown that the heavier bullet tends to strike higher but you have
not shown that it causes it to strike significantly higher.  The physical
evidence you cite is that of your gun and Rick's article.  I think the former
is somewhat suspect as generally-applicable evidence for the reasons I've 
mentioned before.  The latter must be quantified to count.  I'll get the
article and take a look.  I have a lot of respect for Jamison's gun knowledge,
but although I haven't talked to him in a coon's age, and people change, I've
always thought of him as more conversant in rifles than handguns.

#Since "e" is at its maximum (one) for revolvers, I think both John and I can
#agree revolvers are likely to be more sensitive to bullet impulse than semi-
#autos, when it comes to changes in impact point.  Since "e" can never be
#zero, I maintain semi-autos are also affected, to a somewhat lesser degree,
#but still noticable to the shooter.

#To conclude any more than this will require scrapping both assumptions
#and digging in the the slide/frame equations of motion in MUCH greater
#detail.  I may get around to it in time.  

If you do get a round tuit:
I think perhaps a significant thing I left out is that there really may
be quite a bit of friction between slide and rails.  It may be enough 
to account for the small barrel rise which I showed earlier must occur.
I think the fact that the boreline does not go directly through the 
c.g. of the slide means the slide wants to rotate as it's pushed back.
This will cause increased friction.  I don't think you would see very
much of this in a long-railed gun like a CZ or one of those gorgeous
Neuhausen's.  However, a short-railed gun such as a gov't model should
tend to get a little self-actuation like a properly designed brake.

I have to say you've done a fair job of contrasting our analyses.
I think we now agree on everything except the magnitude of the effect.
And that we can determine by test.

#Anyone else who can shed some light on this, show equations, data, or 
#references, please join in!

You bet!  Also, anyone else feel like shooting a few groups at a reasonable
distance with 200 grain and 230 grain bullets and comparing the points 
of impact?  Dan and I have done our tests and they differ.  Obviously
we need more tests.  What we need is group sizes and displacements of 
their centers at given distances.

John Bercovitz     (JHBercovitz@lbl.gov)