The relationship of power to accuracy by Tom Gaylord from Pyramyd Air” /> The relationship of power to accuracy, airguns report post” />

Wednesday, October 01, 2008

Jacob's conundrum
The relationship of power to accuracy

by B.B. Pelletier

I received this question from Jacob this past week.

I have a question about the relationship of power to accuracy. Consider the Daisy 953 with about 500 fps and the Gamo Nitro 17 with about 900 fps. The Daisy shoots much smaller groups at close ranges. Since the Gamo will shoot a much straighter trajectory, will there be a distance at which the accuracies of the two guns become equal and then from longer distances the Gamo will be more accurate? Or will the Daisy always be more accurate regardless of range? I used these two guns as examples, but would like to know if the answer would apply to other air rifles as well.

The ballistic cone
Ballistic projectiles travel in an arc; that, we all understand. The arc a projectile follows is actually a drop from the instant the projectile leaves the muzzle. At that point, all the "push" ends and gravity takes over. Where the projectile strikes the earth depends on its velocity, which starts diminishing at the muzzle, too. The angle of the bore to the plane of the earth is another factor that determines where the projectile lands. Also, bullets radiate from the straight-line trajectory in all directions, landing in a circular pattern--a so-called cone of fire.

Farther than you think!
Several years ago, the U.S. Army used millimeter-wave radar to track the flight of various black powder bullets to settle an age-old argument. Some said that if a bullet leaves the muzzle at 1,200 f.p.s., there is no way it could travel as far as a mile (1,760 yards) before striking the earth. In fact, those bullets were monitored by radar and traveled anywhere from 2,800 yards to 3,900 yards before striking the earth when their bores were inclined 30 degrees above the horizon upon firing. That test settled the argument of how far bullets can go, but it overlooked all the other things a bullet does while in flight.

Pellets don't travel as far because of their high aerodynamic drag. But they do travel 400-500 yards.

Instability
A bullet or pellet spirals around its own center of mass as it flies. The direction of spin determines the direction of the spiral. If the bullet or pellet is made very uniform, this spiral may be very small. So small that it isn't readily apparent for a long distance from the muzzle. However at some point in its flight, the bullet will begin to spiral as a result of destabilizing. Here's an interesting fact. If the range at which the bullet performs (such as the distance to the target) is shorter than the range at which it destabilizes, that bullet (or pellet) will be accurate! If, however, the range to the target is farther than where the bullet destabilizes, it'll be inaccurate.

More instability
An unstable bullet or pellet may also yaw in flight. I see this all the time in my testing. A yaw is when the axis of the pellet is not parallel to the line of flight. It is seen in targets as an oval hole. Like a spinning top, the yaw will sometimes correct itself and the bullet/pellet will become stable again. There is far more chance for a pellet to stabilize than a bullet, because a pellet has high drag that tends to stabilize it all the time.

Once off track, the problem always gets worse
However, if the bullet/pellet is spinning too slow to stabilize, it'll never recover from the yaw. A yawing bullet/pellet has even higher drag than a straight-flying bullet/pellet, and the high air pressure on the side of the yawing bullet/pellet will continue to push it off course over time (which means over distance).

Keyhole
The extreme yaw condition is called a keyhole, and represents the bullet passing through the target sideways. I have seen that with pellets a few times, but I can't lay my hands on any pictures right now. However, during some testing of a reduced power load in my trapdoor Springfield .45-70, I captured a perfect keyhole at 50 yards. The bullet is tumbling end over end in flight, and the farther it gets from the muzzle, the less likely it will land near any other bullets fired from the same rifle.


Four bullets from a .45-70 rifle landed in this pattern, several inches up and right from the aim point at 50 yards. Three of the bullets were yawing badly, but the fourth one was a perfect keyhole.


So your question boils down to two things. First, is the pellet accurate at any range? Because an inaccurate pellet is not going to suddenly reverse its tendency in flight and become accurate. That is what the term ballistic means: a projectile that is unguided during its flight.

The second part of the question is this: the farther you go from the muzzle, the more likely it becomes that the pellet will destabilize. So, your Daisy 953, which is such a tackdriver at 10 yards, may not be able to stay on paper at 100 yards. Your Gamo Nitro that can't keep up with the 953 at 10 yards may be able to shoot a 12" group at 100 yards. So, the answer is "yes," there is a point at which the Nitro becomes more accurate than the 953 simply because of its greater velocity.

The magic range may not be 100 yards. I just used that distance to make a point. What if the real distance at which the Nitro passes the 953 for accuracy is 157 yards? Then, it would make no practical difference to you, because you're never going to intentionally shoot either rifle that far.

Jacob, I saved the best for last. Is it your Nitro that is less accurate, or could it be a flaw in your hold that renders the rifle less accurate? Breakbarrel spring-piston airguns are the absolute most difficult shooting implements to master, while a single-stroke pneumatic like your 953 is one of the easiest. I haven't tested the Nitro, but I have tested the Gamo Whisper, whose barrel should be very similar to the Nitro. I got many groups well under a half-inch at 25 yards. Can your 953 do as well?


This 5-shot group from a .177 Gamo Whisper with H&N Match pellets went into a 0.325" group at 25 yards.

50 Comments:

At October 01, 2008 7:24 AM, Blogger gtctex said...

Very interesting BB. Any changes for round balls from smooth bores(both with and without choke) and rifled barrels?

 
At October 01, 2008 7:50 AM, Anonymous Dr. G. said...

B.B.,
It seems that several of your recent blogs have targeted our interests quite accurately, based on all the engaging replies over the past couple weeks.

Related to today's interesting blog, I could swear that sometimes when shooting the .25 Condor on CO2 outdoors (note lowered fps), as the pellet passes through a sun field at around 20 yards I momentarily catch a glimpse of the pellet spiralling (not rotating on its own axis like a perfectly thrown football) in a wobbly manner around an imaginary line of sight to the target. I was wondering if I am really seeing this (6-24X scope used) or if it were some kind of optical illusion. It seemed to me that the pellet was wobbling more than a 1/2" around this line of sight, but it is hard to believe that it would be anywhere near that much given that the actual accuracy of this application is around 1/2."

Also, thank you for responding to my query regarding the noise level of the shrouded AA 410 vs. Condor.

- Dr. G.

 
At October 01, 2008 8:20 AM, Blogger Joe in MD said...

400 to 500yd range???

While a pellet can go that far if one is, say, shooting from the rim of the Grand Canyon, in practice 120yds is more than enough for the maximum range. I plugged 1100fps with a .5BC (rediculously high, on purpose), with a launch angle of 24degrees into Chairgun. This resulted in a range of about 120yds for a 6' tall person shooting offhand until the pellet impacted the ground. With more realistic velocities and BCs, the range is more like 80 to 100yds but a bit of a safety factor never hurts.

 
At October 01, 2008 8:54 AM, Blogger B.B. Pelletier said...

gtctex,

You ask several important questions, but I don't have the smoothbores to test any of them. The best answer I can give is there probably is a difference.

B.B.

 
At October 01, 2008 9:02 AM, Blogger B.B. Pelletier said...

Dr. G.,

I saw the same spiraling pattern back in the 1990s, because the range I tested on was oriented generally east-west. The sun was at my back in the morning and I first saw the spiral you speak of.

I reported it in The Airgun Letter under the title "Do pellets spiral?".

Then, several years later, I discovered that Dr. F.W. Mann had documented it very well in his book, "The Bullet's Flight fro Powder to Target," back in the early days of the 20th century.

A good test is to shoot through multiple tissue-paper targets that have all been aligned by a laser. Then you can actually plot the spiral. But you don't even need to go to that much trouble. Just shoot at individual paper targets at different ranges and compare the points of impact.

Yes, pellets do spiral, and the most accurate ones spiral the least.

B.B.

 
At October 01, 2008 9:05 AM, Blogger B.B. Pelletier said...

Joe,

I was referring to the max distance a pellet can fly with the bore inclined 30 degrees to the horizon - just like the .45-70 bullets in the same reference.

B.B.

 
At October 01, 2008 9:25 AM, Anonymous wayne said...

B.B. & All,

Great info for a novice like me...

I'm sucking it up like a thirsty hog in a bucket of beer..

Wayne,

AARR&R

 
At October 01, 2008 9:34 AM, Anonymous wayne said...

Joe & B.B.

We are dealing with this now at the range. How far will in the worst case, most powerful, maybe Condor or AR6, with 16 gr pellet at the 30 degrees. And when it falls, does it fall like hail maybe, almost straight down, gravity only, or is it still carrying speed?

Bottom line, how dangerous is it still? at 120 yards, 180 yards, 300 yards, 450 yards.. will it still penetrate skin? or like getting hit with hail..

Wayne,
AARR&R

 
At October 01, 2008 9:37 AM, Anonymous twotalon said...

Joe in md
I plugged some numbers into chairgun because your estimate of 80 -100 yds sounds REALLY wrong.
Starting with a .22 16 gr exact with a BC of .5 at 1100 fps, then asking for max range....
Chairgun comes up with a 36 degree angle for a range of nearly 3000 yds with a remaining energy of 14 ft/lb.

When dealing with real world BC and velocity of different pellets, chairgun says I could be shooting my Talons anywhere between 200-550 yds max depending on pellet and velocity.
Don't think for a minute that anything beyond 100 yds is not in danger. Run some real numbers and ask for max range...particularly with some high BC pellets.

twotalon

 
At October 01, 2008 9:41 AM, Anonymous UW Hunter said...

I have an RWS 34 Panther that I've been shooting for a few months now and I have been very happy with the power and accuracy of the gun. I feel like the trigger pull is a little heavier than I like. Is there anything that can be done to reduce the trigger pull weight of the T05 trigger? Also, is there any reason that I should not install an over travel screw in the trigger guard? Like I said, I am very happy with the gun and the trigger for that matter, but I think these minor changes would really make it nice. I am also considering installing the Pro Guide Spring Retainer to see how that feels. Any opinions would be appreciated.

 
At October 01, 2008 9:43 AM, Blogger B.B. Pelletier said...

Wayne,

A diabolo pellet will fall like hail, but a solid bullet will fall with force. So keep solids off the range. 500 yards is considered the max range for diabolo pellets regardless of the initial energy.

B.B.

 
At October 01, 2008 9:48 AM, Blogger B.B. Pelletier said...

UW Hunter,

The Diana trigger can be worked over, but the T05 is not straightforward. I'm not the guy to ask, but maybe Rich in Mich could do something for you.

The overtravel screw sounds fine as long as you don't mind the asthetics.

As for installing the Pro Guide, remember that I said my 34 powerplant was already pretty calm. However, I do see a difference with the Pro Guide installed. I would do it.

B.B.

 
At October 01, 2008 10:48 AM, Anonymous Anonymous said...

In the paragraph where you described yaw of a pellet, I believe you meant to say it happens when the axis of the pellet is not *parallel* with the line of flight, rather than perpendicular. Perpendicular would give a maximum yaw of 90 degrees.


Roy

 
At October 01, 2008 11:07 AM, Blogger B.B. Pelletier said...

Roy,

Thank you! That is so important that I'm correcting it right now.

Good eye!

B.B.

 
At October 01, 2008 11:30 AM, Anonymous Anonymous said...

BB,

On accuracy: I adjusted my scope for first intersection hit at 15 yards. I moved my target out to 30 yards, adjusted focus bell but kept the windage and elevation setting constant (the same as at 15 yards setting). My poi was one half inch high from point of aim at 30 yards.

Using Chairgun, I can try different values of fps until I match my poi at 15 and 30 yards. Is this some sort of a reliable poor man's chrono? Please correct me if I am wrong.

I got 815fps, the two intersecting points at 15 and 37 yards, 19.8 grains, .22, 0.032BC, 1 inch kill zone.

Dave

 
At October 01, 2008 11:55 AM, Anonymous Anonymous said...

B.B.

Does the destabilization happen at a particular point (more or less) or as a gradual process?

Keyholing at 50 yards for a high-caliber gun sounds pretty serious. Is that a routine occurrence or does it mean there is a real problem? Sometimes my IZH61 looked like it was keyholing at 20 feet or so, but the problem never lasted.

Matt61

 
At October 01, 2008 12:18 PM, Anonymous Anonymous said...

I tried some crap Daisy .22 pellets once and at about 30 yards, almost all of them hit the target sideways. I'd say about 1/3 of the pellets fit the bore while the other 2/3 pretty much fell down the barrel. I could hear a distinct difference with the loose fitting pellets so I quit using them. I think I was pretty much dry firing my gun. I wish there was somewhere locally that carried .22 pellets. The cheap Daisys are the only ones available locally and it is so expensive to ship lead. Very frustrating.

 
At October 01, 2008 12:24 PM, Anonymous UW Hunter said...

I was a little bored so I searched around my garage and found a spring that was the same size as the sear spting on my T05 trigger. I replaced that spring with the one I found and now my trigger pull is extremely light. It feels great. I think I will install an over-travel screw and I also found out how to install an second stage adjustment screw. That should make my rifle awesome. Any reason I should not do any of this? I know that I should bang on the but of the rifle to make sure that it doesn't misfire. That doesn't seem to be a problem.

 
At October 01, 2008 12:37 PM, Anonymous wayne said...

Anon, .22 cal crap pellets,

Pyramyd gives you the 4 tin free, and free freight on orders over $150 I think, (I'm buying as a dealer now, I don't get the 4 tin free or free freight until $3,000) there pellet deal is like wholesale to consumers....Bite the bullet (sorry for the pun) and buy a bunch now, before the price goes up, it will for sure... Not only that, supply is often not there...

I stocked very heavy in the JSB and Kodiak, in .177 & .22 Exacts and Heavies, that shoot so well in almost all my higher power air rifles.. And the 7.0 hobby and basic, for the lower power air rifle.

Air rifles can be different within the same model.. so it might be best to buy small, and test, then stock up like crazy...

Wayne,
Ashland Air Rifle Range

 
At October 01, 2008 1:14 PM, Blogger B.B. Pelletier said...

Dave,

Your "poor man's chrono" will give you an approximation, but nothing more. It relies on a computed BC, which will be wrong unless it was measured by a real chrono.

A ballistic pendulum will do the same thing, and is entirely empirical. However, it must be calibrated with a chronograph.

I think the Chrony is the best poor man's chronograph.

B.B.

 
At October 01, 2008 1:17 PM, Blogger B.B. Pelletier said...

Mattr,

The M16 had a terrible keyholing problem before they changed the twist rate. Any time an elongated bullet isn't stable it will start to yaw and then keyhole.

My example was pretty extreme, at only 50 yards. If that cartridge had been just 100 f.p.s. faster it might have been stable out to 100 yards.

B.B.

 
At October 01, 2008 1:18 PM, Anonymous Dr. G. said...

Wayne,
You might want to check with your attorney before writing emails that could come back to haunt you later in a lawsuit, meaning that it can now be shown that you have been made aware of some hazards and thus you may now have a higher level of liability. This is similar to writing a letter to the town clerk, stating that a hazardous pothole exists on Main Street - now, being forewarned, the town has an obligation to act or it risks being held liable should an accident occur.

- Dr. G.

 
At October 01, 2008 1:20 PM, Blogger B.B. Pelletier said...

UW Hunter,

Don't just bang on the butt. Hold the rifle in various attitudes and bang on it to try to make it fire. If it doesn't, your trigger job can possibly be trusted.

One other thing, if the spring you used ever loses its strength, how will that affect the trigger pull?

B.B.

 
At October 01, 2008 1:34 PM, Anonymous UW Hunter said...

B.B.
Good point about the spring losing its strength. I used this spring as an experiment but I will replace it with the factory spring until I can locate a high quality spring and purchase it in a few different wire thicknesses. I don't know anything about the spring I found. It could be from a ball point pen for all I know. I will probably use a spring of higher quality and a wire thickness in between my experimental one and the factory spring. That, combined with the second adjustment screw mod should give me the results I'm looking for while retaining the safety of the mechanism.

Thanks

 
At October 01, 2008 1:50 PM, Anonymous Scott298 said...

B.B.-Scott298-quick question-has anything happened to Air Arms-I have noticed that their web site is down. I've been trying to save up for the tx200 mk111 -am I running out of time? Thanks

 
At October 01, 2008 2:24 PM, Blogger B.B. Pelletier said...

Scott298,

Not that I have heard. Pyramyd Air maintains a close association with Air Arms and as far as I know, business is going great.

Probably the website is just down.

B.B.

 
At October 01, 2008 3:00 PM, Anonymous BG_Farmer said...

BB,
Interesting topic. I've seen keyholing a few times when a rifle's seal dries out and the velocity falls a lot. I suspected that there was a relationship to the twist rate (i.e., a minimum velocity for a given twist rate and pellet form), and you seem to confirm this.

 
At October 01, 2008 3:08 PM, Blogger Il Bruce said...

The Air Arms "Home" page is screwy. Try starting on another page. Like this one.

http://www.air-arms.co.uk/PRODUCTS.htm

Bruce

 
At October 01, 2008 3:13 PM, Anonymous wayne said...

Dr. G.

That's good advice, I've been working with him already on many issues around this, and I'll be sure he reads these comments..
B.B. I hope this is not making you or anyone liable here.. We are asking questions so we can do the right thing in the future..Air gunning advice, not legal advice, is all were are receiving here, and thank you all for it...

Our current plan is to have that safe distance in any direction, and "blinders" on the sighting in and shooting booths, limiting the height and width of a possible shot. We are even thinking of a drop down door, in front of the booth, to insure a "cold fire". We are still designing these booths the first prototype is being worked on now..

The Field Target course will be in the creek canyons, and should be very safe.. Our Eco minded land manager has plans to teach about the rocks, plants, wild foods, and native American life styles at each field target lane, on sign posts at each rock or plant of special note. You get extra points if at the end you pass a test.. What do you think?


Thanks, Dr. G., so much for your concern..you guys are so great!

Wayne,
Ashland Air Rifle Range

 
At October 01, 2008 3:20 PM, Blogger B.B. Pelletier said...

BG_Farmer,

Yes, there is a definite relationship[ between spin rate and stability. It varies with the length and diameter of the projectile. In the 1800s a formula called the Greenhill formula was used to predict the right spin rate for bullets, and thereby determine the rifling twist rate.

But diabolo pellets also use high drag to stabilize themselves, so the spin rate is not as crucial.

B.B.

 
At October 01, 2008 5:24 PM, Anonymous Anonymous said...

BB,

Wow! Thanks for that more than complete reply to my question. It was a pleasure to read and I can't believe I have a conundrum named after me!

Thanks a lot,

Jacob

 
At October 01, 2008 7:04 PM, Anonymous BG_Farmer said...

BB,

Thanks -- Greenhill formula gives me something to look at.

RE: "Tales of the Tuners" (from yesterday) sounds great.

Wayne,

Slavia 634 sounds pretty good...If it stands out in your (now) massive collection, must be a winner.

 
At October 01, 2008 8:30 PM, Anonymous The Trout Underground said...

This is another interesting post; now that my hanger-queen CFX is on its way (again) to the warranty repair folks for yet another mainspring repair, I'm back to shooting my little 953 at ranges up to 65 yards (haven't tried further, but then, I was using a peep sight and just got the scope mounted).

(And yes, I'm considering saving my pennies for a Discovery or TX200 - just as soon as my $700 billion bailout arrives.)

Most interesting has been researching pellets, ballistic coefficient and long-range firearms shooting.

For example, RWS Hobbys and Gamo Match pellets are excellent at 10 meters, but their barely discenerable ballistic coefficients mean they're hardly printing at 30 yards (a high ballistic coefficient means a projectile loses less energy as it travels through the air - at least that's how I understand it).

Gathering all the pellet ballistic coefficient information I could find, I discovered that wadcutter pellets are a horrifying .009 or so, while published Crosman Premier Lite BCs seem to range from .019 to .026 (depending on the source, though I think the higher BC is probably the heavy version).

That's far, far lower (and less efficient) than the .5 bc used above to calculate maximum pellet travel distance and the .6-.7 bc's of long-range target bullets.

Suddenly, I can see why airguns become such a challenge to shoot even at moderate ranges

Looking solely at the numbers, I started shooting up my supply of 7.9 grain Premier Lites, confident I'd selected the best ammo for distance shooting with my 953 - right up until the point where I tested other pellets.

at 21 yards, the CP Lite was more accurate than the handful of other domed pellets I tried - except for the Gamo Hunters, which astonishingly printed higher on the target, and with similar accuracy.

Lemme see; the Hunters are heavier and have a lower ballistic coefficient, yet they're shooting flatter? I guess they fit the barrel better, and are more efficient in the gun.

Testing at 50 yards was eye opening; the Hunters were simply more accurate than the CP Lites - by a noticeable margin. But then again, long-range firearms shooters use fairly heavy match bullets for their higher BCs and ability to retain energy at 500-1000 yard distances, so why not the same with pellets?

Naturally, using a 425 cfs popgun at those ranges is hardly an invitation to accuracy. With the peep sight, at 50'+ ranges I'm happy to simply hit the 5.5" square pellet trap (it makes a satisfying "thunk" as a reward for a steady hold).

Even with the peep sight cranked all the way up, at 50 yards I have to hold so high on the target it disappears below the bottom of the hooded front sight.

Now that I've got the scope from my CFX mounted on the 953, my greed for accuracy is growing, though I'm already noticing keyholing at 50 yards.

At 60 yards, I'm looking at better than two feet of pellet drop; at 70 yards, it's more than three feet, and at 80 it's closing in on five feet. At that point, pellet velocity has fallen below 240 fps (the online ballistic calculator I use doesn't accept muzzle velocities lower than 500 fps, so I'm interpolating some).

In one sense, using a low-power 10 meter gun for longer ranges is a little silly, but from another perspective, I'm enjoying the challenge of long-range shooting without leaving my little 3 acre piece of heaven, and during the winter, I can shoot 10 meter in my garage with the same gun.

Those are two excellent advertisements for popguns like the 953 specifically and airgunning in general.

Thanks, BB. Now if you could only get the Gamo folks to fix my CFX right this time... 8-)

 
At October 01, 2008 8:38 PM, Anonymous Anonymous said...

B.B.

Is it fair to say that for accuracy, you want the heaviest bullet that the bore will spin?

Matt61

 
At October 01, 2008 9:38 PM, Anonymous Herb said...

Accuracy & Precision

To be a twit, should are accuracy and precision be used carefully? Accuracy in statistics means how close to the true value, and precision refers to the variation in repeated tests/samples.

 
At October 01, 2008 10:04 PM, Anonymous Vince said...

trout underground -

.177 Gamo Hunters are not heavier than CP 7.9's - my first clue was when I noticed that they chrony higher. Gamo had, for quite some time, listed a wrong weight for the pellet. They have since corrected it, and now list that pellet at, I think, 7.56gr.

As for the .177 Gamo Match pellets at longer ranges - at least for plinking I have some guns that do very well with them even at 60 yards, like my CFX. Other guns, like my BAM B20 are useless with that pellet. But for some reason the .22's don't shoot long-range worth a darn in any of my guns.

 
At October 01, 2008 10:31 PM, Anonymous Herb said...

Impact energy - I've wondered about how much energy a pellet would have also when it impacts at a distance. The ballistic coefficient isn't a constant, but would vary with the velocity of the pellet, and how fast the pellet is spinning at any given moment.

I've done a lot of bird hunting and had lead shot, size 7-1/2 (.095 inches, 2.41 mm), drop all around me when shot from the other side of a dove field. It is hot, but won't puncture the skin. (wouldn't want to get hit in eye though...) Round shot has a high BC compared to average pellet.

When shot for maximum range, wouldn't the projectile fall to earth at "terminal velocity?" That is the maximum speed that the projectile could obtain if dropped from a very great height?

The overall point is that all the various ballistic programs are set up assuming "normal shooting" parameters. So the programs can just use a single constant which is good for probably less than a 30%(?) drop in muzzle velocity. It would seem that inevitability that imperfections in the pellet would cause the pellet to start tumbling instead of spiraling(spinning). Once the pellet is tumbling, obviously the BC would change dramatically. Thus I can't image that the ballistic programs could predict anything useful in terms of maximum range, or terminal energy.

 
At October 01, 2008 11:22 PM, Anonymous Anonymous said...

Herb, you are right...If ya shoot da pellet inta the sky, say a 26 gr flathead, it will hit the ground 'round 250 fps, which is about 2 1/2 ftllbs., which may kill a mouse or insects, but that is all.

 
At October 01, 2008 11:25 PM, Anonymous The Trout Underground said...

Vince: Thanks for the Gamo pellet info. I suppose I would have discovered the "new" weight when I went to order more of the "miracle pellet," but it's nice to know the laws of physics haven't been entirely repealed.

 
At October 01, 2008 11:31 PM, Anonymous Terence said...

A ballistic pendulum will do the same thing, and is entirely empirical. However, it must be calibrated with a chronograph.

With some trepidation I query this statement. Before chronographs the ballistic pendulum was the standard way of measuring muzzle energy (cf "The Gun" by W.W. Greener 8th Edition).

Surely a ballistic pendulum gives a direct value not an empirical one? If the mass of the projectile, the mass of the pendulum and the perpendicular rise of the pendulum are known then the energy of the projectile can be calculated directly. The one caveat is that law of conservation of momentum applies to elastic collisions - so a steel BB or full metal jacket shot against a steel pendulum plate would give the best results.

However even with a lead-pellet one can approximate an elastic collision if the mass of the pendulum is chosen with care and the pendulum has a front surface that will slow the pellet without distorting this.

I managed to achieve these criteria in a physics lab session in the sixth form (final year at high school). The "bob" of the pendulum was a blackboard duster with the felt facing forward and covered in several layers to corrugated paper. The mass of the pellets and the bob were determine using laboratory balances and the rise of the pendulum by an observer sighting through a theodelite against a vertical scale.

With this set-up we measured the muzzle energy of my BSA Meteor to a value close to its published energy of 8 ftlbs. As far as I remember I was unaware of the published figure so I did not fudge the figures.

BTW I agree with Wayne, the BSA Meteor is a great plinking weapon - 49 years and still in production!

Terence

 
At October 02, 2008 1:06 AM, Anonymous Herb said...

ballistic pendulum -
I remember doing this experiment in high school physics about, well many many years ago. We had essentially a zip gun and shot a 22 rim fire round into the end grain of a 2x4 suspended by eye hooks and fishing line. I can't imagine such a neat experiment now!

Anyway, you don't want the round to have an elastic collision. You want it to actually stick in the pendulum so that all the energy is transferred to the pendulum.

Knowing the weight of the pellet, and how much the pendulum was lifted would allow you to calculate the muzzle velocity or energy.

However that is only part of what you need to know. It doesn't tell you anything about the ballistic coefficient of the pellet. Thus you'd have to also do the experiment at the target distance. At any distance, it would be hard to hit the ballistic pendulum squarely so that it swings directly away, and not at some angle.

A chronometer would make both measurements easy...

 
At October 02, 2008 5:42 AM, Blogger B.B. Pelletier said...

Terrence,

Yes, the ballistic pendulum gives direct readings for ENERGY, but we were talking about velocity. For that, the reading must be empirical.

And, yes, ballistic pendulae were used for hundreds of years before modern chronographs became feasible. But that doesn't make them accurate.

You may not remember or be aware that the Cardews of the book fame (The Pellet's Flight, from Trigger to Target) manufactured a ballistic pendulum that they sold to the public for use with airguns. That machine inspired more discussion about its use than it provided useful data for airgunners.

Gary Barnes built me a ballistic pendulum for big bore airgun testing. We used it for a couple years at the big bore match at the Damascus airgun show. However, in the initial testing I discovered its weakness, which is the weakness of all such machines. A light, fast projectile expends more of its energy flattening out and partially vaporizing on the pendulum face, where a slower, heavier projectile of the same caliber deforms less and transfers a lot more energy to the pendulum. The result is that a round ball shot from a .458 rifle appears to have one-quarter the energy of a conical bullet at 40 yards, when it actually may have about half as much.

B.B.

 
At October 02, 2008 5:45 AM, Blogger B.B. Pelletier said...

Matt,

I would not say that. Accuracy depends on a number of variables, like the distance to the target, the external influences (wind), the fit of the bullet to the bore, etc. It's not possible to create a rule of thumb because of too many variables like that.

B.B.

 
At October 02, 2008 9:00 AM, Anonymous gtctex said...

BB,
When you did your penetration tests you observed that round balls penetrated more than the other pellets tested. Was the barrel used in those tests smooth or rifled, choked or not. Did the recovered balls show a change in shape?

 
At October 02, 2008 9:22 AM, Blogger B.B. Pelletier said...

gtctex,

The test was done in soap and no, there was no deformation. The barrels were all rifled. They were not choked, because spring gun barrels normally aren't. Choked barrel normally come on PCPs.

B.B.

 
At October 02, 2008 12:15 PM, Anonymous Herb said...

BB,

You said "Yes, the ballistic pendulum gives direct readings for ENERGY, but we were talking about velocity. For that, the reading must be empirical."

That just isn't correct. The ballistic pendulum measures momentum. Thus either energy or velocity, or both can be calculated from the experimental data. As you point out though, there are sources of experimental error (eg, pendulum not swinging directly away, pellet vaporizing, energy loss to heat...). A chronograph would tend to have fewer error sources, but would obviously depend heavily on an absolute calibration, and precision of the chronograph itself.

 
At October 02, 2008 2:49 PM, Anonymous Herb said...

gtctex ...

"Round balls from smooth bores" come out like a knuckleball pitch. The ball could be spinning any which way. Thus the cone of fire is very large. The whole point of rifling and a bullet instead of a ball is to create a predictable and repeatable spin of the projectile which stabilizes the ballistic path.

Don't think that rifling helps a ball very much. Think about miniball bullet in a rifle as used in the war of northern aggression (known in North as the Civil War) compared to ball round in smooth bore musket. the minball/rifle goes further and is more precise. Thus that combination has a much greater effective killing distance. I remember a demo with a smoothbore musket and ball at Fredricksburg. the demonstrator commented somewhat tongue in cheek that the safest man in the opposing line was his target. The ball could go up, down, left, or right, but almost certainly not straight!

The whole thing about firing at 30 degrees for maximum distance with a ball is bogus. The maximum distance would be influenced both by firing angle, and by direction of spin. For example, the maximum distance for a golf ball is achieved by a fairly shallow launch angle because the ball has backspin and climbs. I'd interpret the spinning as why the distances that BB quoted vary so much. The "short" rounds are spinning such that they dive to the ground, and the "long" distances are given by rounds that climb initially.

Maybe dimples would be an idea for ball ammo to reduce drag...

 
At October 04, 2008 1:34 PM, Anonymous Anonymous said...

BB,

Yips see that I'm going to have the last three posts on this, oh well...

Is "precess" used to describe the flight of a projectile? As I remember from college physics, precess refers to a secondary spinning around the axis which the object is spinning. Like a spinning top. Thus the tip of the projectile would make a corkscrew path around the ballistic path of the center of mass.

If you're shooting through a strong sideways wind I can see that the projectile would have a slight yaw. However I'd think that less than a circular hole would be more likely because the pellet was precessing than because it was yawing.

Sorry to be such a terminology nut, but as you know, clear communication is hard!

Herb

 
At October 04, 2008 5:50 PM, Blogger B.B. Pelletier said...

Herb,

As I understand it, precession is the movement 90 degrees to an outside force in the direction of spin. The wind causes precession like that.

Is that what you are asking?

B.B.

 
At October 05, 2008 12:38 AM, Anonymous Anonymous said...

B.B.,

I think so, but precession doesn't have to be 90 degrees. Think of a spinning tops and how they "wobble" about a vertical line through its center of gravity. The "wobble," which is a slow secondary spinning about the vertical, is precession. See:
http://hyperphysics.phy-astr.gsu.edu/hbase/top.html


As I understand yaw, the projectile (or plane...) would actually be "slipping" sideways through the air, like shooting through a strong crosswind. A crosswind would be slow compared to the speed of the bullet, but I do think a crosswind would cause a pellet to turn ever so slightly sideways. For example if a plane is trying to fly due north in a wind from the west, the plane would have to actually set a slightly westerly course to keep keep a due north heading. So in that situation the plane would have yaw, because it is oriented in a different direction than it is actually flying relative to the ground.

It would seem (arm chair gunnery!!) that a projectile would more likely be precessing than yawing. The precessing would increase wind resistance, and perhaps even cause the path of the projectile to noticeably corkscrew.

Herb

 

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