AIRGUN BALLISTICS
Some preliminary remarks. 
By Robert Beeman
 19 Sept 2006
 

When adult airguns first started to became widely popular in the United States in the 1970s, the power of airguns generally was indicated by their muzzle velocities, expressed in feet per second (fps) or meters per second (mps). Although Crosman started their air rifle production in 1923 with .22” caliber, it was .177” caliber that became America’s favorite caliber until late into the 1980's. At that time, .177” caliber accounted for over 95% of the sales of adult airguns in the U.S. and there was a rather narrow range of pellet weights and styles available. Because of this, and because velocity generally is more understood and recognized by the public, velocity figures were used to give a feeling for the power of the various airguns available. At that time, it was like we were comparing the speeds of different kinds of cars, not locomotives and bicycles. When we were considering sporting air rifles of the same caliber, all firing rather similar projectiles with rather low energies, “effective accuracy” was the key consideration.

Velocity indeed is a key factor in airguns, perhaps even more so than in firearms. The higher the velocity is, the flatter is the trajectory of the pellet. Thus higher velocity means that we can be less concerned with the exact determination of range, as a faster pellet would be closer to the line of sight than a slower one. This is one of the key reasons that hunters of small game often select high velocity cartridges. It was realized that most shooters cannot accurately judge distance in the field, few of us can. With small targets, it is often more important to have a flat shooting gun, with which the shooter can more easily hit the small critical area of that target, than to have a projectile with greater energy. Higher velocity means a faster "lock time", or exit time, the amount of time that elapses between the actual trigger release and the projectile emerging from the muzzle.  A faster exit time means that the flight line of the projectile will be closer to the shooter's intended sight line. The sight line is, of course always moving around as the shooter is aiming. Shorter lock time is of even greater importance to the new and poor shot than it is to a very highly trained shooter who can control the gun's movement to a greater degree after trigger release. Higher velocity means greater effective accuracy; this is of very special importance when one considers the extremely small critical areas of the kind of  game and other targets fired upon by airgunners. We must be very careful not to confuse "effective accuracy", the only kind of accuracy that really counts in the field, with "theoretical or benchrest or machine rest" accuracy.

Higher velocity also can mean greater actual accuracy. While working on an airgun injury case, the Crosman Airgun Company and I conducted independent tests which revealed that a .177” (4.5 mm) caliber match air rifle became more and more accurate as its muzzle velocity was increased from 400 fps to 700 fps. The very top match air rifles fire a 177” (4.5 mm) pellet of about 8 grains at muzzle velocities of about 550-650 fps. It had long been felt that muzzle velocities in the 550 to 650 fps range resulted in the greatest air rifle accuracy. This conclusion was reached because most match airguns fired in this velocity range and they were the most accurate airguns in existence. While this may be the optimum velocity for some airguns, the selection of these velocities for indoor match shooting also may be a function of other factors such as custom and the ease of manufacturing, cocking, and shooting a gun of that velocity.

Inherent accuracy may or may not increase, as velocity is further increased over this indoor optimum, but, for airguns used outdoors, “effective accuracy” greatly  increases. This is because, as velocity is increased, not only does the trajectory becomes flatter but side winds do not have as much time to affect the pellet’s path. Thus a higher velocity airgun makes it easier to place the pellet more precisely on the intended targets at varied, and generally unknown, distances. The drawbacks of lower velocity are not factors to paper target match shooters. They fire in windless, indoor ranges at exactly known distances.

The increase in actual effective accuracy, which can accompany higher velocity in outdoor airguns, perhaps is the primary reason why so many American gun makers have increased the velocity of airguns that are used outdoors.

To get some perspective on airgun velocities, consider the muzzle velocities of some well-known guns: A typical "BB" gun imparts about 250 to 350 fps to a light (about  5 grains [0.32 grams]}, .174” (4.4 mm) steel ball. A .22” ( 5.5 mm) rimfire cartridge rifle has a regular-speed muzzle velocity of about 1025 to 1145 fps. Ten pumps in a Daisy Powerline 880 or Crosman Powermaster 760  BB/pellet pneumatic will fire pellets at about 570 to 670 fps. Ten pumps in a Benjamin M342 .22 caliber air rifle, produces about 640 fps. Ten pumps gives about 605 fps in the .177” Crosman 1400 or 695 fps in the .20” Sheridan air rifle. The muzzle velocity of a Beeman R-1 air rifle ranges about 590 to over 1100 fps, depending on model and caliber. A .38" Special (9 mm) firearm or .45" (11.4 mm) ACP firearm wadcutter bullet moves at about 770 fps muzzle velocity, but is extremely dangerous due to its great weight. In terms of the more familiar miles per hour, the BB gun sends out its projectile at about 170 miles per hour, while a top level adult air rifle will rush its projectile out at over 750 miles per hour. Plaintiff lawyers in airgun cases often dwell on the velocity of airguns as a measure of their danger. However, one must temper any considerations of velocity with the mass of the moving object; obviously most of us would choose being hit with a BB at 170 miles per hour rather than by an automobile, or even a hard baseball,  going “only” 60 miles per hour!

DEFINING AIRGUN POWER:

Although the muzzle velocity of airguns has been the primary yardstick by which adult airguns have been compared in the past, this figure does not have a lot of significance in the real world. To start with, it is velocity at the target, not at the muzzle, that really counts in field use of an airgun. The field shooter and hunter is most concerned with how hard his projectile hits the target, and that involves not only velocity but projectile weight, projectile shape, and numerous environmental factors. An airgun projectile ricocheting from a hard surface, or even touching a leaf or grass blade, may lose much of its power and accuracy.

Some individuals, notably those who feel more comfortable when the world is reduced to fewer and simpler considerations, like to say that muzzle energy is the only true measure of an airgun's output. While that might be considered true from a physicist's standpoint, because muzzle energy is a combined function of both projectile velocity and mass, it downplays some extremely important considerations, such as trajectory, wind deflection, penetration, expansion, wound channel size, and the very inertia of the projectile.

Nevertheless, muzzle energy is the most meaningful way to compare the power of airguns. Giving gun power in terms of energy is the most practical way to compare guns of different caliber and projectiles of considerably different weight. This is now necessary as the market has become more sophisticated and it is important in preventing unfair, unrealistic legal comparisons of airguns and firearms. Comparing guns by energy, generally muzzle energy, also better compares the true efficiency of various guns. A quick examination of the Beeman, and other top line airgun catalogs, shows that the more powerful spring piston air rifles are much more efficient in .25” caliber than in smaller bores. Some of the most powerful spring piston airguns, such as the Beeman Kodiak, generally are not even offered in .177” caliber because the powerful air flow of such guns literally is strangled by the small bore.

Airgun energy generally is expressed in foot pounds. It is well worth considering, in practical terms, what a foot pound represents. One foot pound is the energy that a one pound object releases when falling one foot (ignoring the friction of air, which, from a very rough practical sense over very short distances, we may do for very dense objects). Thus, one can roughly consider that a gun firing with a muzzle energy of 12 ft./lbs. is about the same as dropping a 16 oz. hammer head from about 12 feet. Extend that to a 30 ft. drop for a 30 ft./lb. gun. Imagine being hit by that falling hammer head and you are doing a very crude visualization of the gun’s potential hitting strength.

II. Penetration:

In European airgun factories, airguns commonly are tested by firing against a shielded hard steel "splash plate". If the pellet explodes into fragments the gun is considered to be in good condition. Note that a magnum spring-piston air rifle can continue to explode its pellets against a steel plate to over 35 yards!

Americans frequently test their airguns by firing into soft wood. Unfortunately wood probably is one of the worst possible testing materials because its grain, type, and condition varies tremendously with wood species, dryness, etc.. However, some very rough "ballpark" ideas of penetration can be had by this method. These notes refer to .177” caliber airguns. Guns firing at 630 fps will usually completely bury their pellet into soft pine or redwood. An 800 fps sporter will frequently tear completely through a 1” finished board, splintering out the rear as the pellet leaves! Aluminum beverage cans provide more uniform testing material, but maximum penetration depends on hitting them exactly square. A 640 fps match test air rifle could go right through six cans. A magnum sporter could rip through over 10 cans. Even a match air pistol could go completely through four!

Ballistic putty is one the best materials for testing airgun projectile penetration. It is relatively uniform and so dense that penetration depths can be rather easily measured from the surface. It is far denser than flesh. A soft lead, round nose pellet from a 780 fps gun will penetrate a total of about 3/4" into this material at room temperature at about one foot firing distance.  (Don't forget to add the length of the projectile when measuring penetration depth!).

There are several other good materials that can be used for penetration testing. The outstanding airgun author Tom Holzel champions the use of Ivory soap bars. Most forensic and ballistic laboratories use various specialized media such as ordnance gelatin and ballistic clay. We will consider those materials in separate articles.

Penetration is not completely a function of velocity, of course. A hard, pointed pellet like the Sheridan or Prometheus has excellent penetration but has less shock power than a mushrooming soft lead pellet. A sharply pointed pellet, like the Silver Jet pellet, also penetrates deeply but its softness allows some expansion for shock value. The Crow Magnums hollow point maximizes expansion.  A really hard projectile, such as a steel BB or dart, can have quite great penetration power, but its capacity for injury is greatly reduced by the low amount of tissue damage.

A very technical standpoint is appropriate when considering perforation or penetration in the forensics of human injuries with airguns. Technically speaking, the threshold levels for beginning penetration in human tissue are about 0.2J/mm² for bone, 0.1J/mm² for skin, and 0.06J/mm² for eyes.

Just as with high velocity firearms, over-penetration can be a problem with airguns. Some airgun projectiles may make a great impression by the number of telephone book pages they can penetrate, but the wound channel such pellets produce in the field may be so tiny as to have almost no knock-down effect. Unfortunately, the "acupuncture" effects of such projectiles and others, such as steel core pellets or darts, may mean more than just the loss of game to the shooter; they may mean a long, cruelly lingering death to an injured animal perhaps without the shooter even knowing that he scored a hit. Even pointed lead pellets may have undesirable over-penetration if used on very light game at close range. Such prey calls for the use of a hollow point pellet, or at least a flat head wadcutter pellet.

PELLET FLIGHT

The typical airgun projectile, with its characteristic diabolo (not diablo, that’s Spanish for devil!) hour-glass shape, is basically different from that of most firearm projectiles and thus some information about bullet performance may not apply nearly so well, or at all, to pellet performance. At the present time very little empirical information on pellet performance has been published. Much of that which has been published may have very little to do with the most basic points of pellet performance. For instance, many airgun shooters become very concerned if one batch of pellets varies in weight from another. Such differences may simply require a slight change in sight adjustments. Of somewhat more importance is the matter of weight variation within a given batch of pellets, but the significance of even this absolutely pales in comparison to the importance of the evenness of weight distribution within each individual pellet. Pellets with quite a significant weight variation could be extremely accurate in test firing, especially at close ranges, before trajectory differences become pronounced, if the mass of each pellet is evenly distributed within the design of that pellet. However, perfection of weight distribution, especially within a series of randomly selected pellets, is virtually impossible, but such uniformity is one of the keynotes of pellet quality - and thus cost and performance.  As in so many matters, there is no free lunch in the pellet business.

 The displacement of weight from a perfect arrangement within the design of a given pellet has both radial and longitudinal components. Considering only the radial component, a perfectly balanced pellet would have the center of weight distribution at the axis of the pellet. Pellets in the real world virtually always have their weight center slightly off center from the axis. As the pellet moves up the rifle barrel and a spin is imparted to the projectile by the rifling, the centerpoint of weight is going to follow a helical path rather than the straight axial path that a pellet itself makes as it passes up a perfectly straight bore. In pellets of even only moderate quality, the diameter of this helical path certainly must be less than a thousandth of an inch. The pitch of the helix is going to be very long, matching the pitch of the rifling. Thus, if this helix should somehow magically become visible, it would certainly appear, except under extreme magnification, as a perfectly straight line.

Considering the above should not be difficult, but it requires a considerably greater stretch of the imagination to understand what must happen at the muzzle. A weight on a string swung around above ones head will follow a circular path. Consider that the pellet, with its off axial center of weight, is being spun around and around in the rifled bore but is restrained from flying to the side by the bore of the gun. Remember that because the projectile is swiftly moving forward, the path of the weight center follows not a circle, but an extremely elongated helix. When the spin of the weight center exits the muzzle it is going to cause the weight to fly off at a tangent from the spin, just as the weight on a string flies off at a tangent from the circle when the string is released. However, since the pellet's weight center has been traveling in a helix rather than a circle, it will fly off at a tangent from this helix. Depending on where it leaves the helix, this tangent might parallel the bore axis or point at some angle away from it, more likely away. However great or small the deviation of this tangent is from the axis of the pellet and the gun’s bore, two things must be kept in mind. First, since the tangent is flying off from a helix that has such a long pitch and such an extremely small radius, the helix would appear as a straight line if visible to the naked eye and the actual deviation from the axis is going to be extremely small. The deviation from the axial direction will be perhaps less than a millimeter to only a very few millimeters at a distance of ten meters from the muzzle. Second, we must not confuse this tangent of force with the actual path of the pellet. This tangent of force is simply an off center line of force attempting to push the comparatively large mass of the pellet off from the forward, axial path on which its forward inertia is taking it. However, we can see that a pellet with unevenly distributed weight, which is true to some degree of virtually any pellet, is going to start to tip, or "yaw", upon exit from the muzzle and it is going to be pushed further and further away from the axial path upon which inertia alone would take it. The uneven weight distribution thus has caused the pellet to start to tip at the muzzle and this tipping is going to become more and more pronounced, causing an ever increasing spiral of the flight path which will result in greater and greater deviation from the axial line of flight until a point of chaotic instability is reached. The pellet will then begin to tumble and become extremely inaccurate. Of course, the pellet is also subjected to force lines from the continual pull of gravity and from air movements caused by wind and heat waves. The above factors also probably are involved with the accuracy and point of impact changes that occur when a gun is tilted from the position in which it was sighted-in. If there is any damage, even very minor, at the muzzle or if the muzzle is cut even a microscopic amount off from square, the muzzle may impart a good deal of instability to the pellet.  The last one millimeter of a barrel can have more effect on accuracy than the entire rest of the barrel!

For an diagrammatic view of pellet precession and nutation, click on

The "conventional wisdom" is that a small variation is going to have less effect on a large projectile than an equal variation in a smaller projectile. However, in the absence of experimental evidence to the contrary, I believe that an airgun pellet's shape might be a greater factor than its mass under many conditions, within the normal range and velocity of airgun pellets. The length of most larger bore pellets is shorter in relationship to their diameter than in smaller bore pellets. It is possible that this relatively greater length of smaller bore pellets results in them tipping less, having less yaw, due to the tangent of force which develops when unbalanced pellets emerge from the muzzle. Also, the greater relative length of tail on the smaller diameter pellets may give a relatively larger area for air pressure to force the gyrating pellet back onto course. Since the tail of a diabolo pellet has a shape much like the tail on a shuttlecock, a feature not shared with most firearm projectiles, there may be a significant contrast here with typical firearm projectile behavior. Most firearm projectiles simply do not have most of their mass in the forward end with a large, flared, stabilizing tail behind.  Of course, a round ball, like a BB, or a lead ball, is not going to have yaw, or any functional result due to tipping,  in the usual sense, as a sphere presents the same shape surface regardless of how its axis may tip. A very uniform ball may have quite excellent accuracy to a surprising distance because of this.

The commonly observed greater accuracy of smaller diameter pellets versus larger diameter pellets may also reflect a difference in manufacturing tolerance in some designs. Almost all the attention to producing highly accurate pellets has been focused on .177” caliber pellets. The tolerances and sorting of larger pellets usually has not been held to as rigid a standard. Also, the design and configuration of a pellet which is highly accurate in .177” caliber may simply not be as conducive to stability, especially without careful consideration of proportion, in larger diameter pellets. The manufacturing perspective and tolerance in making .177" caliber barrels versus larger bore barrels may be a major consideration in some cases. Further, when comparing airguns which are supposedly identical, except for caliber, one generally is comparing guns with the same outside barrel diameter. The smaller bore barrel has greater weight and stiffness and thus considerably less barrel oscillation during firing. This difference is not as pronounced when comparing firearms of larger bore diameters. Also, as is the case in so many considerations of airgun performance, minute differences of various factors, which might have a great effect on airgun performance, might simply be swamped by the relatively tremendous force and projectile mass of firearms. Thus differences which would favor the accuracy of smaller projectiles in airguns may have little or no significance in firearms. We are just starting to understand airgun ballistics, but it is clear that we cannot simply consider them as if they were small firearms.  Many aspects of airgun ballistics will surely be shown to be partially or even fundamentally different.

Sometimes, experience reveals that theory springs from experience and not the other way around. After very extensive testing of Beeman and RWS magnum air rifles, the outstanding airgun author, Tom Holzel, found that .25” caliber clearly was the most accurate of the four calibers from .177” to .25”.
 

Testing and Studying Airgun Ballistics:  Airgun ballistics as a field is perhaps some decades behind firearm ballistics. Some would say that we are only now entering the 20th century. However, we have a tremendous advantage that the firearm testers did not have in 1900 or even very late in the century. We have some wonderful instruments and programs to speed the development of our field!

Once you have stepped up from using aluminum cans, Ivory soap, or ballistic putty you will need use of a chronograph. This simply is an instrument that measures the time a projectile takes to travel from one point (start screen) and another (closing screen). No longer do we have to put up with having to actually cut replaceable screens with our projectiles, now we can simply measure the tip between the shadow of a projectile passing one screen and the shadow of it passing the next screen or screens. Over the years, I have used the wonderful Oehler Chronographs, both in our airgunsmithing shop and in the field, and several other chronographs. I still recommend the Oehler machines as the very best, but the Oehler Personal Ballistic Laboratory Model 43, as their basic unit is called, now costs about $800. Check it out at www.oehler-research.com . For travel use and field studies, I have often used the Combro cb-625 Chronograph made in England ( www.combro.co.uk ) which not only is it very inexpensive, but it is so small that you can carry it in your vest pocket!  It has two microscopic sensors which read projectile shadows from the sun or even a room light. It just straps onto the muzzle of the airgun to be tested by rubber bands. Although so very handy and so very portable, I often have a hard time getting it to consistently read out velocity figures - getting the pellet to be right on the very tiny, critical sensory path can e very tricky. However, I have used it in many unusual places to be testing firepower - like various law offices when I have been engaged as an expert witness in airgun lawsuits or criminal investigations.  My current chronograph of choice is the CED Millennium Chronograph (www.cedhk.com )selling for only $179 as of November 2003 (generally you should not even bother getting it without the accessory infrared illuminators for about $79 unless you plan to only use it outdoors in full daylight.) The CED Millennium and the required illuminators and tripod can be transported in a good sized briefcase or pack.

The chronograph will give you velocity figures, but those figures are of very limited use without a good ballistic program on a computer. Again, many programs have passed through my facilities, but Dexadine's Ballistic Explorer seems to me to stand head and shoulders above any that I have tested - for easy of use and broad application. There are versions which will work in computers from DOS to Windows XP and the price is only about $50. You can get it from Oehler, but I suggest buying it direct from Dexadine at www.dexadine.com because the creator will actually answer your emails and calls - something that very few such makers will do.  I found the instructions to be typical of so many products whose instructions were written by someone who know TOO MUCH about the product to relate to the fellow who doesn't yet know which end of the wheelbarrow to hold! But, even I was able to get going with instructions and examples, from the "How To Examples" from Dexadine's own website.  You can download a free trial program for testing. This program is absolutely amazing in the things it will do and it covers the parameters so needed, and usually so neglected, for airguns - very close ranges, very low velocities, very light projectiles, etc. . Within an hour I was printing out all the graphs that I could want - even ones which showed the trajectory of a given pellet when fired up or downhill at various angles!! You really should back up the use of this program with the ballistic tables that I review in the Airgun Literature Review section of this website. The ballistic coefficient info, etc. in that reference is invaluable.

Testing Perspectives: The idea of airgun makers sending a sample to airgun writers for study is a good idea – but the big bugaboo is sampling.  A reviewer runs one test on one gun and then tells everyone that here is the gospel info for all time for all guns of this model and caliber!!  But he might just have had the best or worst, smoothest or tightest, etc. one ever made in that model.  One just cannot project firearm thinking and sampling methods to airguns – airguns are not so uniform or consistent as are firearms firing cartridges with rigidly controlled power sources. It would be best to send at least three specimens of anything to be tested for published specs- and to depend more heavily on the factory.  However, the factories are always dealing with the tightest, newest guns and may not be using the most efficient pellets for the job, or even pellets with which the shooters in another country are familiar. I relied on the shop guys (many of whom can be very rigid and unimaginative and without a statistical perspective) only so long as their results seemed to be reasonable – but whenever there was a real question, I studied the choice of guns and pellets and then did the testing myself!!   And we must get rid of the idea that one must test all calibers with the same kind of pellets. While that may seem, to persons who do not understand airguns and ballistics, to be the “fairest” way of doing it – it generally is not.  Different caliber pellets of the same design may vary enormously, between calibers, in length/weight ratios, diameter/weight ratios, etc. – and actually be very, very different in action!  Finding pellets of the same ballistic coefficients (BC) is far more important than selecting ones of the same design.  It is more important to say that the company has tested the guns with the pellets found to be most efficient for that gun in that caliber than to say that they have been blindly tested with all the same design pellets!  The talking heads and perpetual critics only know what they are talking about a little bit of the time!