Shot distribution that works against you.

by **Wobbley** 7/26/2023, 11:36 pm

First topic message reminder :

Most people think that guns shoot their bullets in a single modal “Gaussian” distribution. This would have the majority of bullets hit within a bullet diameter or so of center. This would mean that a shot that breaks while pointed at say the 8 ring will land inside the 8 ring as often as not. But guns appear to shoot with a “Bi-Modsl distribution.

Shot distribution that works against you. - Page 2 Img_0210

This is a bimodal distribution. While there is a central thickening, most bullets don’t land on the center of the group. In short, the group is hollow to some extent with most of the impacts landing in a ring around the point of sim. One reason for this is that most bullets are over-stabilized and over-stabilized projectiles spiral around the trajectory (Mode2) and have random shot placement due to ballistic variance (Mode1). Pistol bullets are generally over-stabilized (quite a bit).

So consider the picture below. It shows the point of aim (the small cross) centered on the 8 ring at 10:30. The dotted ring represents this bimodal distribution. The diameter of the ring is roughly proportional to the distance. So at 50 it’s twice as big as at 25. What all this means is that you called an 8 on the line but you look and the shot is a 7 almost a 6. Why? If you look at the dotted circle the majority of the bullets will land outside of the ring. Couple that with a poor shooting pistol/ammo combination and you get shots way off call. This is why I try to load ammo that shoots well inside the “X-ring” sized groups at 25 yards. At 50 it will be just outside the “X-ring” group size. And it’s why when you shoot slow fire at 25 yards on the B-16 target, as often as not your score will average higher than at 50.

Shot distribution that works against you. - Page 2 Img_0213

by crmath 8/8/2023, 11:20 am

One question it raises with me is can we assume the precession "rotation" always starts in the same direction when the bullet leaves the barrel or does it start in a random direction, in which case it could hit the target anywhere in the circle even if the velocity was the same shot to shot.

Steve,

Thanks for the response. Good questions and comments.

The computational model uses the bullet’s aerodynamic attempt to align its spin axis with its trajectory to initiate precession. Since gravity always shapes trajectory with the same magnitude in the same direction, the answer is yes. In the real world there will always be perturbations that will affect the actual point of impact. I chose velocity as it’s likely to be a major contributor. If the perturbations become large enough, the effect on point of impact could be anywhere on the circle and the ‘volcano’ becomes the worst case limit. If the perturbations became chaotic enough I suspect that the truly random Gaussian distribution would expand to overwhelm the precession-induced circle and we would be hard pressed to separate the two effects without aggregating thousands of shots. As Ashley noted, “The juice wouldn’t be worth the squeeze”.

As you note, our bullet holes should be elongated due to angle of attack (the angle between spin axis and trajectory axis). That angle may never approach ten degrees for practical marksmanship distances. The amount of elongation should be something like bullet length times the sine of ten degrees. For a bullet that’s an inch long the elongation should be around 0.17 inches (0.085 inches toward the nose and toward the base). That should be enough for the unaided eye to notice. Perhaps the angles of attack our bullets experience are much smaller. That would mean the diameter of the ‘volcano’ would be smaller, too.

Hope this helps…

Bob

by Star loader 8/8/2023, 8:21 pm

Wobbley wrote:Most people think that guns shoot their bullets in a single modal “Gaussian” distribution. This would have the majority of bullets hit within a bullet diameter or so of center. This would mean that a shot that breaks while pointed at say the 8 ring will land inside the 8 ring as often as not. But guns appear to shoot with a “Bi-Modsl distribution.

This is a bimodal distribution. While there is a central thickening, most bullets don’t land on the center of the group. In short, the group is hollow to some extent with most of the impacts landing in a ring around the point of sim. One reason for this is that most bullets are over-stabilized and over-stabilized projectiles spiral around the trajectory (Mode2) and have random shot placement due to ballistic variance (Mode1). Pistol bullets are generally over-stabilized (quite a bit).

So consider the picture below. It shows the point of aim (the small cross) centered on the 8 ring at 10:30. The dotted ring represents this bimodal distribution. The diameter of the ring is roughly proportional to the distance. So at 50 it’s twice as big as at 25. What all this means is that you called an 8 on the line but you look and the shot is a 7 almost a 6. Why? If you look at the dotted circle the majority of the bullets will land outside of the ring. Couple that with a poor shooting pistol/ammo combination and you get shots way off call. This is why I try to load ammo that shoots well inside the “X-ring” sized groups at 25 yards. At 50 it will be just outside the “X-ring” group size. And it’s why when you shoot slow fire at 25 yards on the B-16 target, as often as not your score will average higher than at 50.

by bruce martindale 8/9/2023, 2:02 pm

AHA! with the above discussions it now occurs to me why I was always told that a bullet hitting high plugs out while a bullet at the same angle of attack but hitting low in the same ring plugs in. It’s base the bullet coming down into the target. Any base yaw adds to your favor for a low shot and at best cancels out the angle effect for s high shot.
Is that the reason? Not that I ever get any of those…

by Star loader 8/9/2023, 2:22 pm

Jon Eulette wrote:Calling shots at 50 yds.......Did it look like a 10? Did it feel like a 10? You have to have both! Next time you shoot, shoot your shot. Ask yourself both questions (look and feel). If you don't have both then most likely the shot will not be on call.
When we shoot/train, we should learn to know what a 10 looks like and feels like. The feel is recoil based. Was my grip, stance and arm the same during recoil? It is a learned feeling of replication. If your arm feels different in recoil than your typical felt 10 shots, most likely it will not be a 10. Did you relax your arm during the shot? Did you relax your stance/core during the shot? Did you relax your grip?
Also slightly forced shots (not waiting for the shot break, but helping the shot off) can look like a 10 but not be a 10 because the shot was forced off.

My shot distribution is if it looked like a 10, and felt like a 10, it's a 10. Simple as that. Using excellent pistols and ammunition ensures this.

Jon

I agree with you Jon . Graphs , Histograms and Biomodals are for someone who dreams a lot. My old armorer told ne to get the best pistol and known good ammo , then go to the range and learn how to shoot it . Maybe by the time you are knee deep in brass you will have figured it out .
Some people know all of the theories but never learn how to align the sights and break the shot !

by crmath 8/9/2023, 2:32 pm

Star,

I couldn’t agree more. Still, it’s fun to poke around at the technical stuff. It keeps me out of trouble on rainy days.

I’m not much of a pistol shot but I was a High Master with a service rifle in the 1980s. Won some state championships, had a couple of top-five regional finishes and was a firing member on a national champion team. Maybe my interest in technical things held me back. Maybe not.

Bob

by crmath 8/10/2023, 8:36 am

bruce martindale wrote:AHA! with the above discussions it now occurs to me why I was always told that a bullet hitting high plugs out while a bullet at the same angle of attack but hitting low in the same ring plugs in. It’s base the bullet coming down into the target. Any base yaw adds to your favor for a low shot and at best cancels out the angle effect for s high shot.
Is that the reason? Not that I ever get any of those…

Bruce,

Interesting question. I’ve given it some thought and here’s my take.

I agree with what you are saying but am unsure about the magnitude of the effect. The angle of the trajectory at 50 yards is downward about 1/2 degree, which works in our favor regardless of of the precession angle. I’m not sure I would set my zero to be a click low to take advantage of it.

I’m just elated to hit the X ring at all.

Bob

by Allgoodhits 8/10/2023, 3:37 pm

Excellent post and follow up thread. Thank you.

I have developed the ability to be pretty good at calling my shots maybe 90-95% of the time. I often have a friend who insists on spotting and calling out value. I politely tell him not to. I only want him, if he insists to verify my call, by clock in general area, not value. Value, albeit nice is not important. Concentration of shots, and true call is what matters to me most. Not having the gun sighted properly is a different matter.

From time to time, that 90-95%, I will call out wide 2 oclock. I generally call out either "center, loose center, clock position, wide clock position or the dreaded unknown". On some of the unknowns or wide calls, he will say X or ten, I reply either "it shouldn't have been (not on call) or then it was luck". During training I don't like luck. During a match, I'll take as much luck as I can get. Matches are the only time score matters, and even then, it shouldn't matter the most. I think many of us fail on that one.

by Ed Hall 8/10/2023, 5:50 pm

Actually Bruce, I think you have it upside down. The bullet is falling as it travels through the target, which means the hole is higher on the front (target) side of the backer and lower on the backside. When a plug is placed in the target, the flange is positioned flat on the target instead of following the original trajectory. The backer pulls the plug downward slightly due to the hole through the backer traveling that way. This slight downward pull tends to move the plug away from the ring for shots on the lower edge and toward the ring for shots on the upper edge.

by crmath 8/10/2023, 8:35 pm

Ed,

Good point. I can’t disagree with your logic. I think my response to Bruce needs the caveat that the magnitude of the effect depends on the direction of precession.

Consider this, though. We all know that our bullets fall away from the centerline of the bore as they travel down range. Because our sights are always above the bore our bullets always start out rising, level off at ‘midrange’, then start to fall. So depending on range to the target, the bullet can be rising, flying level, or falling with respect to the line of sight when bullet meets paper. I remember from my small bore rifle days that with Anchutz iron sights a 50 foot zero (bullet rising) was pretty close at 50 yards (bullet falling). I would be surprised if pistol isn’t about the same.

An interesting aside is that the empty space between the paper target and the front of the backer will amplify the effect you describe. Several layers of repair center could leave enough space so, in addition to the hole in the backer being tilted, it’s also displaced - enough to visibly pull a plug when pressed firmly against the target and backer. Maybe a few thousandths.

I wonder how much the varying density of the cardboard backer itself affects bullet dynamics.

This is getting way too academic.

Bob

by Ed Hall 8/10/2023, 9:20 pm

Hey Bob,

Maybe Bruce was right side up and it had to do with 50 ft targets. My experience was mostly thinking of .45 holes at 25/50 yds. I'll have to get back into the math again, but I don't think the angle difference would be great enough to be seen on the rise portion of the trajectory. It becomes quite pronounced on the fall which increases much more rapidly, especially if you're trying to "lob" bullets with reduced loads.

At 850 ft/s, the fall is just less than 6 inches from bore at 50 yards - much less than half that at 25 yards. But a lot of reloaders are trying to get down in the low 700s. Maybe I'll dust off the slide rule and do some more numbers. . .

by jwax 8/16/2023, 8:58 am

Anybody have access to a high speed camera? Would be nice to see what typical bullets look like before target entry.

by rich.tullo 8/19/2023, 6:40 pm

Good work, I have noticed that SWC especially 185gn Magnus 201 Button Nose have a binomial distribution, Back in my Dad's day many would swear by 3.6 BE before optics and the formulation might have been different in the 1970's as compared to today. Today we mostly use 4.0 +/_ 1 th.

Accounting for the change of powder 3.6 is 3,8 BE. I have found with most cast bullets 3.8 BE is an accuracy load. That testing was done with a Kart Barrel and Kc Custom Wad gun from a bag at 50 yards. Best group out of that gun with 4.1 BE was 1.375 inch flyers included about 1.125 excluding the "flyer". I will also note the group was the same size with 185gn JHP and 4.5 BE.

The best group with 3.8 BE was 1 5/8 flyer excluded. So in a match , I suggest the difference in accuracy would not matter much, ceteris paribus, unless x count matters for a match win.

In our game I also suggest that wind , shootability, barrel and variance matters too. Some guns like a hotter round and bullet traveling at 700 FPS could have more variance on a windy day than a bullet at 750 fps.

i shot 2 ten x's ever in SF and both were with 4.5 W321 and in doors. That bullet may not have broke 685 FPS. That same load out doors on a windy October day was an utter disaster because the gun FTF about 7 times. In short what is optimum for accuracy may not be optimum for points.

by shootingsight 8/21/2023, 8:00 am

On the question of what causes the spiral, it occurs to me that if it were just the barrel, by shooting at consistent distance, and with consistent spin rate and consistent velocity, the bullet would always hit at the same part of the spiral, and there would be no bi-modality.

But there isn't.

While I'm sure that barrel adds to it, an element that is beyond control is the bullet CG. If the bullet were perfectly homogeneous, the bullet CG would be exactly at the bore centerline ... but it never is, due to imperfections in the bullet itself. So while the bullet is in the bore, it is forced to spin about the bore centerline, but as soon as it exits the muzzle, it wants to spin about the CG, so there is a sideways jump, leading to the spiral. Since the shooter cannot control the timing of the bullet in the chamber, you do not know which direction the bullet will jump upon exiting, so the initiation of the spiral will be random.

There are two reasons for rifling: one is that it takes any aerodynamic defects in the bullet shape, that would cause it to arc off in some direction, and rotates that arc, so it averages out. The other is that is stabilizes the bullet, because a rounded nose bullet, while having less drag, is aerodynamically unstable - objects want to fly with CG ahead of the center of aerodynamic pressure, not the other way around.

While I'm sure people have experimented, I wonder if there is anything to be gained by giving up on the BC, and going to a drag stabilized bullet, like a dart. This could be fired out of a smoothbore barrel, or at least a very slow twist, so you still compensate for the arc of the bullet, but you minimize or eliminate the violent jump.

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