External Ballistics (Continued)

Continuing our discussion of external ballistics let's look at what bullets do under different conditions and see what affects what. While the majority of the discussion below deals with rifles projectiles, the principles apply to shotgun and pistol projectiles as well. I suggest that you read the rifle section first. If you pay attention you will see that many effects are quite small and have no real affect at reasonable ranges. Too many people worry about inconsequential increments. I had one fellow brag to me that a certain load gave him less drop (according to published data) than the brand he had been using. According to the published data the difference amounted to less than 2" at 500 yards. Huh? (And, he was hunting deer in the NY woods.) If you are one of those rare people that really can hit consistently at extremely long ranges you may have some things to think about. For the majority of shooters, however, what happens inside of 300 yards is what really matters.

By the way, most folks tend to visually over estimate the range and think that something is farther off than it is.  If you have never done range estimation, try this.  Find a large open field and laser or measure off a real 400 or 500 yards and then turn around and look at your buddy standing at the start point.  If you don't have a laser or long tape measure simply find a long straight road, set your odometer to 0 and then drive.  Each 1/10 of a mile is 176 yards.

Please note that this a fairly long page with lots of tables and runs about 21 screens worth at 800 x 600 screen resolution, so you might want to print it out (landscape orientation works best). MS FrontPage says 68 seconds to load at 28.8.

| Rifle External Ballistics | Shotgun External Ballistics | Pistol External Ballistics |

Rifle Ballistics

The tables below are based upon the assumption of a telescopic sight mounted 1.5 inches above the centerline of the bore. The velocities are for illustration purposes only and may not be attainable in your particular rifle. Unless stated otherwise the bullet used for these calculations is the GI M80 Ball bullet with a G7 ballistic coefficient of .195 as derived by the Ballistics Research Laboratory, Aberdeen Proving Grounds and using a program designed for the G7 drag model (mainly because I have verified data). While some of the tables go out to 1000 yards I have purposely cut many of the tables off at 600 yards since the data makes the point intended. Longer ranges are listed only where the effect under discussion only really shows up at extreme range.  I have also rounded velocity and drop numbers to eliminate meaningless precision.

A NOTE: As previously mentioned the drag models for G1 and G7 can't really be compared. However, the G1 "equivalent" for the M80 type bullet is about .397 according to the published data for the Hornady and Sierra FMJ-BT 150 gr bullet and this number will provide a fairly close match of trajectory for ranges under about 500 yards. For other bullets use your ballistics software to determine what works best for you.

Velocity VS. Trajectory

Many people falsely believe that velocity makes a really big difference in the bullet's trajectory. In the table below using the cartridge data described above note how it takes a velocity increase in muzzle velocity of about 200 f/s to make a less than 1/2 minute of angle (1.5") difference in point of impact at 300 yards when all are zeroed at 225 yards. Unless you have Superman's eyes you can't see that difference at that distance, let alone hold to it. So much for worrying about that last foot-second for most field shooting! Spend your time practicing marksmanship.

However, for those with the skill (which are few and far between) to make use of improved trajectory and wind drift (which we'll discuss later) at greatly extended ranges the extra velocity can provide an edge. For the vast majority of shooters it is a moot point.

Effect of velocity on trajectory
(Zero=225 yards)

Effect of velocity on point blank range
(Maximum ordinate = 3")

If you are sharp eyed you will notice in the table above a slight change in the maximum ordinate. This would indicate that if you crank up the velocity you can achieve a slightly longer point blank range. In the table below I have adjusted the zero range of the 2500 and 2900 f/s loads to match the 3.0" maximum ordinate of the 2700 f/s load.

With the 2500 f/s load the point blank range (-3" low) occurs at about 245 yards, with the 2700 f/s load at about 265 yards, and for the 2900 f/s load at about 285 yards As you can see, changing the velocity by 200 f/s gives us only about a 20 yard change in a point blank range. Is all that fuss getting an extra 200 f/s really worth it? Not unless we are talking about drop at very long ranges.

Zero Range VS. Trajectory

Too many shooters zero their rifles at too short a distance and thus lose the advantages of a more useful trajectory. For the most efficient use of trajectory you want to keep the actual point of impact vs. point of aim within the vital zone of your target for the greatest distance possible. Your critical zone size will vary depending on your intended target but ± 3 - 4 inches is a good compromise for most uses.

The table below shows the effect of different zeroing ranges. You can see that a good zeroing range for the .308 / 150 gr is somewhat greater than 200 yards. (200 meters might be a workable choice but 225 - 250 yards works very well) Looking at the first set of tables (above) with the 225 yard zero you can confirm this. This data holds true for most other cartridges of similar bullet weight and velocity. For a more in depth discussion of zeroing visit the Zeroing Page by returning to the main ballistics menu page. (I suggest that you read all these ballistics pages in the order suggested for maximum benefit.)

Effect of different zeroing ranges on trajectory
(Muzzle velocity = 2700 f/s)

Ballistic Coefficient VS. Trajectory

The ballistic coefficient of the bullet effects the bullet's trajectory, although at reasonable ranges not as much as some folks believe. The following table is based on otherwise identical commercial 165gr bullets in both flat based and boat tail configuration at a nominal muzzle velocity of 2700 feet per second zeroed at 225 yards with published G1 ballistic coefficients of .400 and .460 (+15% for the BT). We could get really picky and remember that the G1 coefficients are based upon the flat base model which is not a true match for the characteristics of the boat tail bullet which are more closely matched by the G7 model. However, it is probably close enough for field (500 yards and less) use.

Note that until the bullet gets way out past Ft. Mudge that a nominal 15% change in ballistic coefficient doesn't do very much. (Yup! You read it right. At 1000 yards with a 225 yard zero you've got to hold between 31 and 35 feet high to hit your target.)

Effect of ballistic coefficient on trajectory
225 yd zero

The effect of cannelure on ballistic coefficients

The effect is quite small and varies with the shape and depth of the cannelure and seems to vary between about 3 and 12 percent. The table below shows the difference between several bullets that are identical except for a cannelure.

Environment vs Trajectory

Ballistic tables are generally based upon what is called "standard" conditions, which is generally taken to mean "sea level," 59°F, a barometric pressure of 29.53" Hg, and 78% humidity (known as "Army Standard Metro") or  "sea level," 59°F, a barometric pressure of 29.92" Hg, and 0% humidity (known a "ICAO").  All of the above tables are based upon the "metro" conditions. In real life, on any given day the actual conditions may be quite different than the so-called "standard" conditions so there could be some interesting things that go on. Let's see...

For example, at higher altitudes the air is thinner so there is less drag on the bullet. However, it is also true that at higher altitudes the air is generally colder, the speed of sound is thus lower, and therefore transonic drag occurs at a lower velocity. Also, on a warm day the barometric pressure tends to be higher which increases drag but the higher temperatures tend to decrease drag slightly. In effect most things tend to pretty much cancel each other out--but not quite.

The following tables assume the standard M80 ball ammo at 2700 f/s with a 225 yard zero as used in the first table above (all of which were done for "standard" conditions). They will give you some idea of what the various changes will do independently. In each table below only the particular item has been changed. The other conditions remain at "standard."

Altitude Changes

Temperature Changes

It must also be pointed out that temperature changes also affect chamber pressure. While the affect varies with the type of powder, with IMR type powder there is about a 1000 - 1500 pound change for every 10°F change in temperature. This would give you about a 3% velocity change for every 20°F. (Which, as we have seen, doesn't have a big effect on trajectory until you are out past Ft. Mudge.) Ball powders are another matter. Their change may not be linear and at the extremes of temperature they may show dramatic if not catastrophic changes.

Since the effect of temperature changes on internal ballistics is difficult to predict the only way to get accurate data for temperature variances is to actually test the load in question under the conditions expected.

Humidity & Barometric Pressure

I thought I'd be real complete and tabulate trajectory changes due only to humidity and barometric pressure changes. There was a difference between "standard" humidity (78%) and dry (20%) and between "standard" pressure" and ± 1" of Hg at normal rifle ranges.  These changes amounted to less than .2" at 500 yards and 3" at 1000 yard for the humidity change and 1.1" at 500 yards and 19" at 1000 yards for a 1" change in barometric pressure. Thus it is really of interest only to statisticians and long range target shooters.

And Now The Real World
(Average conditions where you might be shooting)

The chart below will give you an idea of what you can expect in the "real world." Conditions are based upon actual typical weather conditions during the month of January in The People's Republic of NJ and the month of August in Prescott, AZ, to give a good spread.

Note that the data from NJ may be skewed because of all the air pollution and political BS in the air (which tends to adversely affect bullet performance) and may not reflect actual results under similar climatic conditions in other states.

Bullet Weight vs Trajectory

Well what about changing bullet weights? The table below shows the differences in trajectory between three different bullet weights in the same cartridge. The muzzle velocities are based upon published data and the different velocities are what can be expected for the different bullet weights in the .308 with a "standard" length barrel. The bullets are commercial softpoint flat base bullets of the same design from the same manufacturer with published G1 ballistic coefficients of .358, .400, and .431. Zero in all cases was 225 yards. Notice that the 180 gr bullet, even though it started out 200 f/s slower than the 150 gr bullet, is traveling faster at 500 yards and beyond and its shows less drop at very long range.

Effect of changes in bullet weight on trajectory
225 yd zero

Look at the data. As they said on that TV show ""Verrryy Interessstink!" If you zero for the same distance there is no real difference in the trajectory out to where Ft. Mudge is located. So, if you know where your 150s go, if you switch to 180s and re-zero to the same distance you have an almost perfect trajectory match. However, we do know that when you switch bullet weights the zero usually goes out the window big time and if you don't re-zero all bets are off. Why? Because of the effect of barrel timing and recoil, and barrel whip (how the barrel vibrates as the bullet passes through it). These two things have a big effect with most barrels. However, as I intimated above, the difference in barrel timing and barrel whip with different bullet weights causes a much greater difference than one might expect and the differences show up in both the horizontal and vertical plane. I have seen several rifles that throw 165 gr bullets several inches to the left and high and throw 180 gr bullets several inches to the right and low at 100 yards compared to 150 gr bullets. There are some particular barrels such as those on some SMLE Mk4 Enfields which by some "magic" tend to throw heavier bullets slightly higher than would be expected and lighter bullets lower and these gems seem to hold the vertical deflection quite constant when bullet weight changes.

The Answer is Blowing in the Wind
(Wind Drift)

The final thing we'll look at is wind induced drift. To keep things manageable we'll look at the effect of both velocity and ballistic coefficient in this table. We'll use the same commercial 165 gr flat base and boat tail bullets with G1=.400 and .460 as before.

A couple of things to notice. At "reasonable" ranges (300 yards) the effect of BC or velocity on wind drift is not all that great--a 200 f/s difference in velocity or a 15% change in BC gives about a 1" difference in drift. There is less than a 3" difference between the worst case and best case at 300 yards with the average deflection being about 8" for the bullets under study. At 1000 yards a 200 f/s change in MV gives about 12" difference in drift and the worst case-best case difference is 23" and an average deflection of 128" for the flat based bullet and 106" for the boat tailed bullet. If you're a long range target shooter or a sniper you need to worry about these things. Otherwise, unless you are shooting in a gale, don't sweat the small stuff.

An addendum. I'm sure someone is going to ask, "How can you tell how fast the wind is blowing?" These rules of thumbs are taken from TC 23-4 on sniper training.

Another method of estimating wind velocity is by estimating the angle between a flag and its pole and dividing that angle by 4. If no flag is available a small piece of cloth, paper, or some grass may be dropped from shoulder height and the angle between vertical on your shoulder and where it lands can be estimated.  There are also available nifty "wind speed meter" available for shooters.  See www.kestrelmeters.com.

Shotgun External Ballistics

Most folks think that the trajectory of the 12 gauge rifled slug is close to that of a mortar. Since they don't think they could hit anything past 25 or 50 yards (which is probably true if they don't have a set of sights on their shotgun) they zero for slugs at 25 yards. Unfortunately, this short zero severely limits the effectiveness of the slug firing shotgun. Surprisingly, a slug's trajectory is quite flat out to about 125 yards (assuming the proper zeroing range). The biggest limitation of the shotgun slug is that penetration and trajectory drop off drastically beyond 125 yards due to velocity loss, so its maximum effective range is probably about 125 yards. (I still wouldn't want to be hit by a slug at 200 yards though!)

12ga Foster Type Rifled Slug (G1 = .109)
(20" barreled riotgun with ghostring sights)

While the 100 yard zero appears to be more useful than the 75 yard zero, the fact that most standard riotguns only will group into 8"-10" at 100 yards makes attaining a good 100 yard zero difficult unless sighted in at a shorter range with compensation for the distance. For those individuals using a rifled barrel shotgun with slugs for hunting or those lucky folks with the occasional "magical" riotgun that really groups 'em an actual 100yd zero may be preferred. A lot of folks find it easier just to zero them for 2" high at 50 yards (at which distance group size is usually quite good) which gives about an 85 yard zero which is probably the real optimum distance. Using a shotgun and slugs with a good set of sights one can completely control their environment with a 125 yard radius.

By the way, for those of you interested in such things (even though at typical buckshot distances it doesn't matter) the ballistic coefficients for buckshot are approximately as follows.  Note that the GS drag model should be used for spherical projectiles but since most programs don't handle the GS model I have converted them to the approximate G1 figures.

  The following is the data for 00 buckshot. A 75 yd "zero" is assumed.

Pistol External Ballistics

As with shotgun rifled slugs, most people believe that pistol bullets have such a curved trajectory that long range hits are next to impossible for other than certain "never miss" gun writers and Uncle Elmer's 600 yard deer. (We'll ignore the silhouette shooters for the time being since that is a specialized activity, usually with optical sights and with equipment that often stretches the definition of "pistol."). While the defensive handgun is designed for use at short ranges (50 yards--and usually much less), don't feel under gunned if your target is at greater ranges (assuming that you know how to shoot!). The following table give the trajectories of typical 9mm 125gr, .357Mag 158gr, and .45ACP 230gr duty ammunition with a 50 yard zero and 3/4" sight height.

 Typical Handgun Ammunition Trajectories

Defensive pistol shooting at long range is not recommended except in dire straits. However, when the goblin is way out there near Fort Mudge and thinks he's out of harms way, if you hold on the head and carefully squeeeeeze one off you'll easily get a chest hit (and ruin his whole day). I once wowed a couple of MPs by getting 5 solid chest hits with 5 shots on an IPSC "option" silhouette at 100 yards using a Detonics pocket .45 from the braced sitting position. If I can do it so can you!

Maximum Distance A Bullet Will Travel

The are actually two "maximum distances to consider.  For the purpose of this page I will refer to them as Maximum Horizontal Range and Absolute Maximum Range to Bullet Freefall.

Maximum Horizontal Range
Maximum horizontal range is defined as the maximum distance a projectile will travel over level ground.  This distance depends upon muzzle velocity, barrel elevation, distance of the muzzle above ground level, and bullet design.   For computational purposes the  distance is computed at the line of sight as at the typical distances of a barrel above ground level the difference at the actual ground would be slight.

In a vacuum a firearm would achieve its absolute maximum range at an elevation of 45°.  However, with typical small arms projectiles the effect of air resistance is so great that maximum range is usually obtained at a departure angle of between 29° and 35°. The table below gives the calculated approximate absolute maximum ranges for some common rounds  using modern drag modeling techniques at standard sea level conditions, and a not so common projectile.  It may differ from some previously published data based on older methods of computation.  The data indicated by "#" is from government firing tables.  

Note that all this data assumes point forward flight during the entire trajectory and is based upon "standard" conditions.  However, this may in fact not be the case--see the article on vertically fired projectiles, above--except for the M829 "dart" which is fin stabilized.  While this data is sound one should not consider the data to hold for all cases and conditions--especially when considering range safety implications.  Changes in projectile stability, elevation above sea level, temperature, barometric pressure, humidity, and wind speed and direction at both ground level and at altitude can contribute to wide variances (10 to 15 percent in either direction).  

For round shot pellets, similar complicated formulas can be used, but a close enough answer is given by Journee's Rule, which states that the maximum level ground distance is  approximately 2200 times diameter of the shot in inches for typical shotgun velocities.  Velocity is not considered in this formula because at typical shotgun velocities the drag is fairly consistent.  The rule holds fairly closely when compared to actual firing tests giving slightly shorter ranges for small shot sizes and longer ranges for buck shot.  As an example the calculated level fire max range for 00 buck using the Gs drag model is about 540 yads

Absolute Maximum Range  to Bullet Freefall
There is also another "maximum distance" which is the range at which the bullet starts to fall straight down with no "forward" velocity, as if fired from a tall mountain or an aircraft.  While pretty much an impractical solution, this is the absolute maximum range that is possible for the projectile to achieve.

In the graphic below the projectile has a level ground maximum rage of 5084 yards.  However, if fired from an aircraft flying at some 27,000 feet above ground the bullet would reach vertical free fall after traveling 6180 yards (dropping 321316 inches (8925 yards) below the line of sight).

Huh?

So what can we learn from all of the above? Know your rifle and ammo! It is more important to use/develop a load that shoots accurately and consistently in your rifle than to worry about getting the last foot-second or quarter inch of trajectory or group size and spending countless hours or dollars in a quest for the Holy Grail. Use your time and resources to load good ammunition and then practice your shooting and learn where your chosen load(s) shoot at various ranges. You'll be much better off than some guy with a Remingchester .392 Super-blotto Magnum with the Mk7 Laser-dazer zippo sight who can't shoot and who has no idea where his bullets are going.

To quote Robert Heinlein, "There are no deadly weapons, only deadly men."

Job Aids

With a proper zero one really doesn't have to worry to much about trajectory until one gets past 300 yards unless you can really shoot and are going for eyeball shots and require pin-point precision. However, if you would like to have the data handy, nicely made and laminated pocket sized cards containing trajectory information, wind drift, and lead data for various commercial and hand loads are available from:

Ballisticard Systems
P.O. Box 74
Atascadero, CA 93423
805.461.3954
ballistic(at)tcsn(dot)net
http://www.ballisticards.com

Please mention this site if you contact them.

I hope all this information has been of some help and that you've learned not to sweat the small stuff. The other thing I hope you have gotten out of all this is that for truly accurate results you need to test your stuff where you use it. (By the way, does anyone know where Ft. Mudge really is???)*

* See the very end of this page for the answer.

To email me click here

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Disclaimer

As far as I know all the information presented above is correct and I have attempted to insure that it is. However, I am not responsible for any errors, omissions, or damages resulting from the use or misuse of this information, nor for you doing something stupid with it. (Don't you hate these disclaimers? So do I, but there are people out there who refuse to be responsible for their own actions and who will sue anybody to make a buck.)

Ft. Mudge? Ft. Mudge was first mentioned in the Pogo comic strip. It is located in the Okefenokee Swamp near Miggles store. This fact was first brought to my attention by Steve Munden 1/99.  However, I was recently informed that Ft. Mudge really does exist.  It is located in Brantley County in Georgia off of Rt 1 (Jacksonville Highway).  Fort Mudge is described as a wilderness fort, having been built about the same time as the U.S. Revolutionary War. The local town is named for it.

I am assuming that the "out past Ft. Mudge" expression came about as an off-hand reference to its distances from the "civilized" world of the time.

Updated 2013-10-12