Mass… Velocity… Twist… Drop… ?!? WTF! This Ain’t Rocket Science… Or Is It?
© 2002, 2003 by Tom Holzel, with Jim Baumann
With premium air rifles costing as much as they do, figuring out what particular brand and model to buy can be
quite confusing. On what do you base your choice? The first step is clearly deciding how much money you can
afford to spend. This will determine the quality level, and the features of the gun. After deciding this, the next most
important factor is to chooser the correct caliber for the gun’s intended purpose. If you are going to own only one gun,
this can be an agonizing choice. Here’s the approach I used to decide between a 5mm and .22-caliber Theoben
Eliminator rifle for hunting in southern England.
As a long time air rifle crow hunter in the U.S., I recognized that to English farmers, hares, not crows, are more of a
nuisance, so they would be the varmint of choice in my new home in Oxfordshire. With crows, long range is more important
than high power, so for that task the longer reach of the 5mm would be the obvious choice. Would that caliber also be the
optimum for fur bearers? When I examined the published performance I was puzzled by the ballistic data given the Eliminator
on the Theoben website (http://www.theoben.co.uk/). Their highly regarded 5mm rifle is listed as having a muzzle velocity of 880 fps,
with 840 fps remaining at 50 yards. Energy figures are quoted as being 24.5 ft/lbs at the muzzle and 22.4 ft/lbs at 50 yards.
These figures indicate the Crosman Premier pellet used loses only 4.5% of its velocity over 50 yards — yet drops by 23% the
next 50 yards. The .22-caliber figures were equally confusing.
There are two ways to determine the trajectory of a pellet: Empirically on the range — this is the most reliable method–or theoretically
(and much more rapidly) by means of a ballistics software program. To help me clear up the issue, I bought an air rifle ballistic
program developed by Jim Baumann of Lame Rabbit Software (Note: Jim is apparently no longer in business). Let’s see how the two
calibers fare (at least on paper).
To use ballistic software, one needs to know (or find out) the correct ballistic coefficient (BC) of the pellet being tested and therein
lies the rub. The BC of a pellet is an extremely complex function that changes depending on a pellet’s range and velocity.
A pellet can have an excellent BC at one muzzle velocity and at one optimum range–and then flop miserably as the velocity is
changed, or the measuring range altered. In the case of the superb 5mm Crosman Premier recommended by Theoben,
Jim Baumann has measured its BC as is high as 0.040 at 25 yards, but more commonly at 0.0308 at 50 yards. The big
advantages of the 5mm Premier pellet are that of high, repeatable quality and that it has a high BC. But — unlike many other
pellets–it maintains its BC to well over 900 fps. We use 0.0300 at 950 fps for the maximum usable power of this pellet.
To complicate matters even more, BC varies from shot-to-shot! Below is a sample of a series of shots measuring BC of a
5mm Crow Magnum (Eliminator) with chronometers set at 10 ft and 45 yards from the muzzle.
To determine maximum usable range, the shooter has to decide how many inches of rise above the telescopic line of sight is he willing
to aim at intermediate distances. With 12-lbs-ft rifles this is usually 3-inches. But with a FAC rifle this is usually 2-inches — or less.
And the shooter must determine his own personal field marksmanship. Then, knowing the pellets BC, ballistic software lets
us plot the trajectory for different sight-in (“zero”) ranges.
Chart 3 shows the trajectories of the two calibers when sighted so as to result in a rise of two inches, each at two different power settings.
The lower power settings are those which the Theoban website says result in the highest accuracy; the higher settings are those used by
many American varmint hunters for maximum effectiveness. Recognize that with all mechanical devices, (your car, for example) extracting
more power results in more rapid wear & tear.
Notice (chart below) that if we also allow two inches of drop, we can achieve an absolute maximum theoretical range (blue line) of the two calibers
of 63 yards for the .22-caliber, and 72 yards for the 5mm. But, accuracy will probably hold up over the farthest reaches of our neat graphs only
as wishful thinking.
What this means is that while ballistic computer plots of air rifle rounds are useful as starting points, complex second-order aerodynamic
factors begin to dominate at the higher ranges and velocities — that is, much beyond 60 yards. Also, wind deflection alone can double group
size from 50 to 70 yards.
But wait — can I even hit the 3-inch “kill zone” of my target out to 70 yards? Certainly not from a standing position. However, when shooting hares,
I will almost certainly be either sitting, or probably even lying down. But even using a bipod, will any air rifle shoot that accurately out to 75 yards?
In the field I can realistically put three out of four shots inside a 2-inch circle from the seated position at 50 yards. If the pellets’ flight continued
perfectly, that would result in a 3-inch circle at 70 yards. But perfection never happens.
Robert Beeman, (founder of Beeman Precision Air Rifles in California) believes that down-range pellet instability is primarily caused by two factors:
First, any random tipping of the pellet as its skirt loses final contact with the edge of the muzzle; and second, the imperfect distribution of the pellet’s
mass about its spinning axis. In both cases the pellet can begin to wobble more — and then less — and then more again — during its flight.
This wobble becomes more acute the faster and the further the pellet travels. Combine this with the minute shot-to-shot variations of power and it
becomes easy to see why even with the best high-powered, long range air rifles, perfection is unattainable.This brings us to the next consideration — “terminal ballistics”–the effect of the pellet on the target.
Chart 5 shows us that the energy the two rounds carry at two different power settings. The reason the 5mm loses energy slightly faster is that its
ballistic coefficient (BC) is less — 0.0300 vs. 0.0340 for the .22-cal.. This is almost always the case, that larger pellets have better BCs than
smaller ones. In the case of the Premier, Jim Baumann believes the cause has to do with a pellet’s length which has been optimized for long range.
What is interesting about this chart is that, although the 5mm Premier pellet leaves the muzzle with more energy than the .22-cal H&N Barracuda,
because the Barracuda has a slightly better BC, loses energy less rapidly. But think on this: By increasing power above the Theoben optimum,
how much range and extra energy are we really gaining?
Yet it is not energy but “lethality” that we seek. What is the difference? Firstly, let us go to the sight-in range of 60 yards. Of course the 5mm
round is traveling a lot faster than the heavier .22. And the equation for energy is well-known: E= mv2/2. In other words, increasing the velocity
just a bit results in a whopping increase in energy. But there’s a major snag.In my experiments shooting into an animal flesh simulator (Ivory soap), I discovered that a .177-cal Hobby pellet penetrates 7.5 to 8-inches
when carrying 15 lbs-ft of energy. A .22-cal Hobby pellet only penetrates 5 to 6 inches with the same energy. The reason for that should be clear.
The .22-cal pellet must clear out a wider wound channel per inch of penetration. Indeed, with these experimentally derived figures, the .22-cal
creates a short, fat wound channel with a volume of 0.19 cubic inches, while the.177-cal pellet creates a long skinny wound channel of 0.185
cubic inches — in other words the same wound channel volume — an amazingly close experimental confirmation (and a great advantage of
using Ivory soap for these tests).
Now here’s the high-velocity catch: Shooting both of these pellets into a critter with a diameter of only 2.5-inches means both pellets will exit
the animal — and carry with them unspent energy. But the .22 will have dropped off half its energy in this example. Since it can penetrate
5 inches, and exits after half that distance, so it has used up half its energy or 7.5 lbs-ft. The .177-cal pellet can penetrate three times as far,
so it will exit with 2/3rds of its energy intact. It will have dropped off only 1/3 of its energy, or 5 lbs-ft. Thus the fatter .22-cal pellet will have delivered
50% more energy to the target; energy that is, of course, more destructive, or more “lethal.” (Of course, these depths are theoretical in that they
apply to Ivory soap which may or may not be an accurate flesh simulator. If the pellet hits bone, a lot more of its energy is transferred to the animal
– in most cases, all of it.) But there’s more to the energy story.
This over-penetration gave me the idea for a real hollowpoint pellet — an egg cup design that would really open up. The result was Dr. Beeman’s
Crow Magnum hollowpoint pellet. It will double in caliber inside a varmint and almost never exits the critter. However the 5mm Crow Magnum
hollowpoint BC is only 0.0263 at 900 fps. So you will have to experiment to see if the higher lethality of the Crow Magnum pellet is worth its
slightly lower efficiency.
Jim Taylor, a world famous big game hunter, wrote in the November 1947 issue of American Rifleman that his experience with the
E=mv2/2 high-velocity equation did not comport with his extensive personal experience — so he made up his own lethality index –
the Taylor Index. His equation is:
TI = (grains*velocity*caliber)/7000.
Note that velocity is really given short shrift in this equation; it is no longer squared. Because Taylor was using really big guns,
his numbers come out big — or, put the other way round — when we plug in air rifle values, they come out very small. So I modified the
Taylor Index and call it the Taylor Value. Instead of dividing by 7000, I divide by seven.
Using that modification, we can calculate the Taylor Value for the Eliminator 5mm and the .22-cal pellets at 60 yards. They are:
TV5mm60 = (14.3grs * 729fps * .20-in)/7 = 292
TV22cal60 = (21grs * 601fps * .22-in)7= 422
Wow — the .22-cal comes out 44% more lethal at 60 yards than the 5mm. Now we can see where the .22-caliber’s fur-punching
reputation comes from!
So here’s the question I have to answer for myself:
5mm .22-cal Delta Max Range (yds): 63 57 22% in favor of 5mm Taylor: 292 422 44% in favor of .22-cal Pellet Pressure* 541 473 14% in favor of 5mm
What is more important — 22% more range or 44% more lethality? [New commentary] Or a 14% higher “Pellet Pressure”? *(Pellet Pressure is
the energy at the target divided by the cross-sectional area of the pellet. For example, 300PP is required to punch through the folded wing
feathers of a crow.) Notice that the 5mm pellet has a better PP (penetration) than the .22. This is one reason why in America, the 5mm pumped
up to achieve 950 fps with the Crosman Premier pellet has developed such a very strong following among varmint hunters. It results in a high
sustainable accuracy at the greatest ranges, with sufficient lethality to do the job. Future experimentation will reveal which of the two pellets
create a larger wound channel. It will be very interesting to compare the wound channel volume of the Premier vs the Crow Magnum pellets
as well. (After all that work to determine efficacy, it still remains a matter of opinion and personal choice!)
Chrony ballistic software.
Before you compute pellet trajectories, you have to measure the velocity at two distances–typically zero and 35 or 40 yards. Shoot five pellets
through the Chronograph at zero yards distance, then five pellets through it at 35 or 40 yards. Note that the Chrony does not require the white
plastic sun shields unless the sun is out and brilliantly clear. Even a hazy sun won’t give good readings with the shields in place. If you plan on
doing a lot of testing, buy two Chronys and shoot through both of them at the correct distances, at the same time. Then average the velocities,
throwing out any fliers.
The Chrony ballistic software is a very awkward and buggy product that can be used only after much fiddling about. But then it is extremely useful.
Here is a short-cut that works just fine.
Struggle to get the toolbar header to appear. Under “Project,” click to the “Trajectory Table” at which the screen (below) will open–except there
won’t be any numbers in the fields.
Fill in the variables in the screens marked “Range,” “Sight-in,” “Target” and “Bullet.” In order to fill in anything, you have to first erase
(not overwrite) anything in the blanks. Then (and this is the secret to making this product work) estimate your pellet’s ballistic coefficient,
and enter it in the B.C. field. You will also have entered a velocity value for either zero yards or 5 yards. Where the chart says “Velocity, 717fps” was where I entered the average
velocity at that range of 5 to 10 pellets. You will also will have changed the “Range” distances to 100 yards in 5 yard increments. Now, each time you enter an estimate of BC, all the chart figures change (or hit “Compute” to make them change) (Except the zero yards figures).
Then look at the “velocity (fps)” values for the other, more distant ranges you used to test your pellet with the Chrony chronograph–say the 45 yd value.
It will change with each new guess of BC. When the velocity of the table at 40 yards changes to the figure you obtained in the field–voilá–you will have
correctly guessed the pellet’s BC. Now the rest of the table’s figures will also be correct–energy, velocity, drop, etc. for all distances. Now you can
copy the drop figures to Excel to make a trajectory chart.
Since a pellet’s BC varies with its velocity and range, you can see that BC is not anything intrinsic to a pellet, such as its mass. Rather, BC is an
abstract factor used to make trajectory calculations come out right! The actual Chrony trajectory computation is quite accurate–within 1/2 inch
as far as I could tell (and even that difference is just as likely to be mine and not that of the program). For a more detailed explanation of BC,
check out this informative website.
Tom Holzel is author of The Air Rifle Hunter’s Guide, Velocity Press, (Sold by Beemans and Crow Busters). He was hunting editor for
American Air Gunner magazine and has written numerous air rifle reports including on the Theoben .22-cal Crow Magnum.
Has most recent article on air guns was with John Zent, Editor of the NRA magazine American Hunter, August 2002.
Jim Bauman is a professional ballistician and veteran air rifle user. He is the author of the “Lame Rabbit” air rifle software program
used to produce the data and charts for this article.
For an outstanding treatise of various aspects of air rifle ballistics–particularly internal ballisitics–see this excellent
For a tremendous trove of airgun knowledge, see Dr. Beeman’s comprehensive web site:http://www.beemans.net/ .
See in particular Dr. Beeman’s
article on Airgun ballistics at http://www.beemans.net/airgun%20ballistics.htm.
For a catalog of ballistic source material, see: http://www.goneshooting.co.uk/Ballistics.htm
A neat air rifle website is the British air rifle Review Centre.
For more air gun hunting, see: http://www.airgunhunters.com/index.html
Finally, another extensive listing of air gun material: http://www.airgun1.com/listings/adult_precision_air_guns.html