## What is the maximum altitude that a bullet will attain

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As with many other subjects that one comes across in forensic firearms examinations, this has little real relevance in everyday case examinations. There was an occasion, however, when a commercial airliner which had been flying in the air space above Northern Ireland was found, on landing, to have a 7.62 mm calibre hole in one side of the tailfin. Unfortunately, the airline concerned was unwilling to have the tailfin dismantled and taken apart due to the costs involved, and it was not possible to determine the exact calibre of weapon used.

The question was, therefore, what weapon could have fired a bullet with sufficient velocity to reach the altitude of 9000 ft at which the airliner was flying.

In 1909, Major Hardcastle fired a number of rounds vertically into the air and shortly after World War I, Julian S. Hatcher carried out a similar set of experiments using the 30-06 rifle round.

A very simple rule of thumb to calculate the maximum altitude that a bullet will reach is that it will be approximately f the maximum horizontal range.

The results of some actual test firings are tabulated as follows (Table 3.6):

The above table indicates, from the limited data available, that only the 30-06 or 0.303 rounds would have sufficient initial velocity to reach an airliner flying at 9000 feet. There are, however, a vast number of hunting cartridges which would be equally capable of reaching this altitude.

Terminal velocity. The terminal velocity of a missile is obviously much more relevant to the investigator as any bullet fired vertically into the air will come down with potential wounding capability. The ability to calculate the actual terminal velocity of a missile could, therefore, be critical to the investigation.

When any object falls through the atmosphere, eventually, the retarding force of drag will balance with gravity, and the object's terminal velocity will be reached. It is easy to calculate this terminal velocity if the drag coefficient is known.

When the forces are balanced,

Mm2v2 = Mg

Table 3.6 Maximum altitude attained by various rounds.

Calibre

Bullet weight (gr)

Velocity (fps)

Maximum height (ft)

40

1257

3868

0.25 ACP

50

751

2287

0.44 Mag

240

1280

4518

5.56 mm. SS109

50

3200

2650

7.62 NATO

150

2756

7874

30-06 M2

150

2851

9331

0.303

175

2785

9420

30-06

180

2400

10 105

12B

No. 2 shot (US)

1312

330

12B

No. 4 (US)

1312

286

12B

No. 6 (US)

1312

242

12B

No. 7\ (US)

1312

209

12B

No. 8 (US)

1312

M = mass of object; m2 = ballistic coeficient; g = gravity; v = velocity.

The mass of the bullet (M) drops out of the equation, which at first may seem strange, since mass clearly should have an effect on terminal velocity. Actually, the ballistic coeficient itself depends on mass (among several other things, e.g. bullet shape, air density and cross- sectional area), so M dropping out of the above equation is merely illusionary.

Because air resistance depends largely on surface area whilst weight depends on volume, larger bullets will drop faster than smaller bullets.

Small bullets will start to tumble, and come down relatively slowly, whereas larger bullets can maintain their stabilizing rotation and come down much faster.

Some examples of the terminal velocity of everyday articles follow: Raindrop = 15miles/h = 22fps Baseball = 95miles/h = 139 fps Golf ball = 90miles/h = 131fps

These figures are well within the penetration limit for skin showing that a falling bullet does have the potential to wound (Table 3.7).

 Calibre Bullet Weight (gr) Initial velocity (ft/s) Terminal velocity (ft/s) 0.22 LR 40 1257 197 240 1280 250 30-06 150 2756 325

Other factors affecting maximum range. Bullet shape also has a pronounced effect; with sharply pointed bullets and those with a streamlined base (boat -tailed) having a far greater range than a round ball. As can be reasonably expected, the higher the velocity, the greater the range.

Journee's formula and the ballistics of shotgun pellets and round balls. The formula most often quoted for maximum range of shot is known as Journee -s Formula, which states simply that the maximum range in yards is equal to 2200 times the diameter of the shot in inches. Thus, a no. 7 shot, which is 0.10" in diameter, should fly 2200 x 0.10" or 220 yd. This formula is so simple that it is sometimes dismissed as too crude to be useful.

It should be noted that this only relates to shotgun ammunition and round balls and has no relevance at all to conventional bullets.

The work of Gen. Journee, a French officer, was actually much more sophisticated than his simple formula for maximum range would seem to imply. In experiments that he began in 1888, Journee actually measured the times of flight of shot, fired from shotguns, at various ranges from about 3-65 yd. From these observations, he deduced the aerodynamic properties of small shot with surprising accuracy and used these aerodynamic data to calculate trajectories.

Considering the relatively primitive instrumentation then available, Journee's work was quite remarkable. His omission of the muzzle velocity in his formula for maximum range was not a matter of ignorance of its effect, but recognition that it makes no important difference, within the practicable levels of shot shell velocities, as can be seen in Table 3.8.

The ballistic properties of large spherical projectiles were also studied intensively in the years before the twentieth century, because cannon in those days were mostly smooth-bores, firing round shot and shell.

 Maximum range (yd) Shot size 2 00 Buck MV = 210 303 561 1200 ft/s MV = 1500 ft/s 219 317 591 650

Accurate artillery fire is an important factor in winning wars, and a knowledge of exterior ballistics is essential to the science of gunnery. The aerodynamics of cannon balls was, therefore, a matter of national importance, and it received the attention of such distinguished scientists and engineers as Benjamin Robins, Sir Isaac Newton and Professor Bashforth in England, Mayevski in Russia, Didion in France, Col. Ingalls in the United States, and many others.

Later investigators in the US Army Ballistics Research Laboratories and elsewhere have extended the base of information by measuring the aerodynamic drag characteristics of smaller spheres, using more modern methods and equipment. A technical report prepared in 1979 by Donald G. Miller in the Lawrence Livermore Laboratory of the University of California brought together much of the information from previous experiments on the drag of spheres.

Miller's report contains information from which the trajectories of small spherical projectiles can be computed accurately by the methods commonly used for other types of small arms projectiles.

Unfortunately, the modern experimental data on spheres does not include those as small as birdshot. The Livermore Laboratory report deals specifically with spheres from 1.0" down to 0.3" in diameter, the smallest being the size of no. 1 buckshot.

It is known that cannon balls from 2 to 8" in diameter, fired in earlier experiments, do not have quite the same aerodynamic properties as small spheres, especially at velocities below the speed of sound. No great difference is found, however, in the aerodynamics of spheres between 1.0 and 0.3" in diameter, and it is probably not greatly in error to apply the same characteristics to smaller shot.

Table 3.9 includes the maximum ranges for various lead shot sizes, computed by Journee's Formula.

A muzzle velocity of 1200 fps was assumed for all shot sizes to afford a direct comparison with shots of different sizes. As can be seen in Table 3.8, the exact muzzle velocity makes little difference in the maximum range.

 Shot size (lead shot) Diameter (in.) Maximum range Striking velocity (ft/s) 12 0.050 110 63 9 0.080 176 79 8 0.090 198 82 7* 0.095 209 85 6 0.110 242 89 5 0.120 264 94 4 0.130 286 96 2 0.150 330 99 BB 0.180 396 107 4 Buck 0.240 528 125 1 Buck 0.300 660 135 00 Buck 0.330 726 139
 Shot size Return velocity (ft/s) 12 63 9 79 8 63 7"2 75 6 7 1 5 75 4 78 2 1 05 BB 1 15 No. 4 buckshot 132 No. 1 buckshot 147 No. 00 buckshot 154

Table 3.8 illustrates that no great error is introduced by neglecting the effect of muzzle velocity on the maximum range of small shot. This results from the poor ballistic shape of spheres which causes the aerodynamic drag to be very high at supersonic velocities. However, small shots soon drop to the velocity of sound, irrespective of the velocity at which they are launched.

For example, a no. 7-2 shot fired at a muzzle velocity of 2400 fps, twice that of a normal target load, would have its velocity reduced to 1120 fps, the speed of sound, within about the first 26 yd of flight. Doubling the velocity would increase the maximum range by only about 26 yd.

Table 3.10 shows the remaining velocity for no. 6 shot at its maximum range of 237 yd, achieved at a firing elevation of 22

For all shots from No. 12 up to 00 buckshot, the maximum range is achieved at firing elevations of about 20 °-25 °. It is important to note, however, that a firing elevation of only 10 ° produces nearly 90% of maximum range.

Whilst the striking velocity of about 80 fps for these small shots would not be fatal in itself, a pellet in the eye could cause serious injury from which death could result. In the case of no. 2 or BB shot, the maximum range exceeds 300 yd and the striking velocity is about 100 fps. This would produce a much more serious injury.

Many shooters want to know the velocity of shot returning to earth after it has been fired upward at very steep angles. The answer is that the returning velocities are not much different from those shown in Table 3.9 for shot fired at its maximum horizontal range.

This is illustrated by Table 3.11, which shows the returning velocity of shot fired vertically upward.

There is, for any body falling through the atmosphere, some velocity at which the force of aerodynamic drag equals the weight of the body. When that velocity is reached, the body ceases to accelerate under the influence of gravity and falls

 Firing elevation Distance to Angle of fall Time of Impact (degrees) impact (ft) (degrees) flight (s) velocity (ft/s) 0 0 0 0 1200 1 119 2.6 0.75 224 5 187 18.8 2.28 100 10 212 37.8 3.53 83 15 231 51.1 4.48 82 20 236 59.5 5.23 89 25 236 64.8 5.82 92 30 231 69.0 0.27 95 35 222 71.2 6.63 97 40 209 73.0 6.78 97 45 193 74.0 6.84 96

All figures are for no. 6 shot fired at a velocity of 1200 ft/s.

All figures are for no. 6 shot fired at a velocity of 1200 ft/s.

at constant velocity, sometimes called the 'terminal velocity of return', regardless of how far the body falls.

It should also be mentioned that other factors not considered in the calculations can affect the maximum range of shot.

A strong wind could, since the time of flight is several seconds, materially affect the maximum horizontal range.

Deformation of the individual pellets will generally shorten the maximum range.

It is also possible for several pellets to be fused together if hot propellant gases leak past the obturating wad into the shot charge. This is far less likely now, due to efficient plastic obturating wads, than it was with felt and card wads. However, when this does happen, the clusters of shot can travel considerably farther than individual pellets in the charge.

Maximum effective range. As can be seen from the chapter on Bullet Performance and 'Wounding Capabilities', the amount of energy needed to be 'effective' on a given target is an extremely difficult thing to quantify.

The 'maximum effective range ' is probably even more difficult to quantify due to the number of variables which come into play, that is, bullet weight, bullet design, velocity, bullet diameter, bullet placement, weapon accuracy, and so on. Each and every situation must, therefore, be taken on its own merit.

It has been stated that the ' maximum effective range is the greatest distance that a weapon may be expected to fire accurately and inflict casualties or damage'.

Another source, somewhat nebulously, states it is 'the range at which a competent and trained individual has the ability to hit the target sixty to 80% of the time'.

The US Military states ' the maximum effective range is the maximum range within which a weapon is effective against its intended target,' and calls for ' a delivery of between 35 and 270 ft/lbs to be effective'. A somewhat rather large spread of values.

To complicate matters further, the US Army defines the maximum effective range of a 0.308 as 800 m. The US Marine Corps defines the effective range as 1000 m. The US Army also states that bullets are no longer effective once they become subsonic, which happens at around 1000 m with a 0.308. Why this velocity is chosen is not stated.

According to tests undertaken by Browning at the beginning of the century and recently by L.C. Haag, 'the bullet velocity required for skin penetration is between 147 and 196 ft/sec which is within the velocity range of falling bullets.'

This wide range of opinions is indicative of the difference in specifications and ideas on the subject.

It could be considered, and in fact English law takes this opinion, that any missile with sufficient velocity to penetrate skin is capable of inflicting a potentially lethal wound. Thus, virtually any missile at its extreme range could be considered as ' effective against the target'.

Of course, skin penetration is not required in order to cause serious or fatal injury; a serious bruise on an elderly person could cause death by shock alone.

Everyone has his or her own opinion as to the maximum effective range of a cartridge and, for illustrative purposes only, a list of published figures from various sources follows (Table 3.12).

Use of sight to compensate for bullet drop. To compensate for the bullet drop due to gravity, the sights are raised to give the barrel sufficient elevation that the bullet will strike the target at a set distance. For handguns, this is generally 10 yd; for a 0.22" rifle, 25 yd and for full-bore rifles, generally 200 yd (Figure 3.2).

 Cartridge M aximum effective range 9 mm. PB <230 ft 0.45 ACP <164 ft 5.56 x 45 mm <1800 ft 7.62 x 51 mm (Rifle) <2700f 7.6 x 51 mm (M60 GPMG) <3600 ft 7.62 x 54 mm. R <3300 0.300 Winchester Magnum <3950 ft 0.338 Lapua Magnum <5248 ft 0.50 BMG/12.7 x 107 mm <6550 ft 14.5 x 114 mm <6232 ft

GPMG, General purpose machine gun, PB, Parabellum, ACP, Automatic colt pistol.

GPMG, General purpose machine gun, PB, Parabellum, ACP, Automatic colt pistol.

With the rear sight so elevated, the sight line would be parallel to the ground and the sight line along the barrel axis considerably elevated above the target. Thus, the bullet leaves the barrel below the sight line but along the barrel axis. At some point from the barrel, it passes through the sight axis line, describes a trajectory between the barrel axis and sight line eventually striking the target at the point of aim.

Other influencing factors. In addition to air resistance and gravity, there are other forces which influence the flight of the bullet.

Wind will cause the bullet to drift with it in proportion to the wind direction and velocity.

Thus, a wind blowing from the right of the bullet will cause it to drift to the left. Rear winds will have an increasing effect on the velocity and nose winds a decreasing effect. The amount of wind drift, when striking the bullet at 90 can be calculated by the following:

D = deflection of bullet by wind; R = range; V = muzzle velocity; T = time of flight; W = cross wind speed.

Drift is caused by the rifling of the bullet. This is a result of the gyrostatic properties of the rifling-induced spin of a bullet. This effect gives bullets with a right-hand spin a drift to the right and left-hand spinning bullets a drift to the left. It is hardly of any significance in rifles and virtually none at all in handguns.

With a 0.303" rifle, the drift will be approximately 13 i n. to the right at a range of 1000 yd.

Yaw is something which only has real relevance to rifle ammunition. This is due to a slight destabilization of the bullet as it leaves the barrel and is probably the result of excessive spin on the bullet. This causes the bullet to describe an air spiral whilst at the same time having a spin round its own tail axis. At close ranges, this results in a larger target group than would be expected. As the range becomes greater, the effect disappears and the target groups return to their expected dimensions. The effect is very similar to that of a spinning top which wobbles slightly before settling down into a stable spinning condition.

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### Responses

• Roger Yates
What maximum altitude can a 3006 bullet attain?
9 years ago
• kidane
What is the max height of the bullet?
9 years ago
What is the max height of a 3006?
9 years ago
• dolores
How far will a 0.338 laupa penetrate an earthen berm?
7 years ago
• tarja
What difference does elevation do to a bullet?
7 years ago
• Welde
What altitude can a .45 acp reach?
6 years ago
• Eglantine Hogpen
How much does altitude affect ballistics of 5.56?
4 years ago
• aston
What is the maximum altitude for a .22 LR fired from the ground?
2 years ago
• joseph
How high will a .303 bullet go fired vertically?
2 years ago
• rasmus
How much height can a bullet atain?
2 years ago
• Isengrin
How to calculate the height of a bullet fired straight up?
5 months ago
• alfio
How to figure maximum height of a bullet's trajectory?
3 months ago
• Lamorac
What difference does elevation mean to bullet balistics?
3 months ago
• asmarina
Is there a table to determine the most effective altitude to fly at?
2 months ago
• Weldon Gauna
How to calculate the maximum height a bullet can reach?
14 days ago