Long & Ultra Long Range Ballistics of the .22 Long Rifle Cartridge

As can be seen from the last column of the table, the real angle of elevation up to 100 yards is only 8 to 16% greater than that in a vacuum. So we can say that when shooting a .22 Long Rifle at up to 100 yards, the bullet behaves only a bit worse than it would do in a vacuum. But at longer ranges, the effect of drag increases progressively until at the ultra long distances (for this cartridge) of 400, 500 and 600 yards, the angle of elevation reaches nearly twice what it would be in a vacuum. As the range increases, the trajectory becomes more curved, and its height increases. At 500 yards, the trajectory reaches its apex at about 250 yards down range, where its height over the line of sight is about 16 feet (whereas in a vacuum, it would be about 7.5 feet).

This information can most easily be expressed in a Ballistic Table, which essentially provides you with the remaining velocity, time of flight, angles of elevation and fall and wind deflection at each distance down the range. It is of enormous practical value in determining where to set your sights initially and what action to take when things go wrong.

In your handouts are sets of Ballistic Tables for the .22 Long Rifle bullet fired at the two muzzle velocities of 1075 and 1125 ft/s. You will note that the time of flight to 500 yards is approximately 1.84 seconds. If the bullet had been fired in a vacuum, it would only have taken 1.36 seconds to complete its journey of 500 yards. That time interval can be calculated purely from the muzzle velocity and range; it is not influenced by the bullet characteristics or weather conditions. But the real time of flight is dependent on the bullet weight and shape, air temperature, pressure and humidity as well as the muzzle velocity and range. In this sense, the time of flight is a composite measure of all the factors which determine the ballistic performance of the projectile in question.

The ballistic tables indicate that if fired at a muzzle velocity of 1100 ft/s and an angle of elevation of 139 minutes (just over 2 degrees), the 40 grain bullet would travel 550 yards in 2.09 seconds, with a remaining velocity of 598 ft/s. As I said in my introduction, it was the remaining velocity which initially grabbed my attention. After 2.09 seconds in flight, it still retains 54% of its muzzle velocity. By comparison, a Sierra 190 fired at 2725 ft/s only retains about 41% of its muzzle velocity after the same 2.09 seconds in flight.

Why does the snub nosed, flat based .22 bullet appear to retain its velocity better than the sharp nosed, boat tailed Sierra bullet? The answer is the drag coefficient it experiences. I am not going to talk about Mayevski projectiles or functions, Ingalls Tables, Powley equations or Ballistic coefficients. To me, the aerodynamic drag coefficient is what is important. The drag coefficient (Cd) is the ratio of the frontal force actually experienced by the bullet to the pressure calculated by Bernouilli’s equation (p=0.5dV2) acting on a disc of the full bullet diameter. The Match Rifle bullet is fired at about 2.4 times the speed of sound (M=2.4) and its velocity decays down range to about the speed of sound (M=1.0) at a distance of 1200 yards. For most of its flight (as far as 900 yards), it encounters a rising drag coefficient. At M=2.4, Cd is about 0.28, whereas at M=1.25, Cd reaches a maximum of about 0.41. It then falls again, back to 0.28 at M=1.0, where it reaches 1200 yards. It would go on falling if the bullet were allowed to become fully subsonic, reaching a constant minimum of about 0.13 below M=0.8, but this would only occur at 1500 yards down range.

By contrast, the .22LR bullet is fired at M=1.0 or less, where its Cd is about 0.35 to 0.4. Throughout its flight from the moment it exits the barrel, it encounters a falling drag coefficient, reaching a constant minimum of about 0.21 below M=0.9, at 150 yards down range. The falling drag coefficient means that it loses velocity, percentage wise, slower than the MR bullet. All of its flight at long and ultra-long range takes place at a constant subsonic drag coefficient.

Approximate Elevation Table for .22 LR Ammunition

It is very useful to memorise how to construct the approximate elevation table, so as to be able to carry out on-range adjustments as necessary. The table is set out below. It is not exact, but it is close enough to enable you to hit near the middle of the target.

At 100 yards or less, the “rise” is a constant 4 minutes per 25 yards of range, whereas beyond that, the rise for each 100 yards increases by 4 minutes. The reason, as discussed earlier, is that up to 100 yards, the reduction in velocity caused by drag is barely sufficient to cause a noticeable increase in the required elevation; whereas between 100 and 600 yards, drag effects cause a fairly constant increase in elevation beyond that required to cover the range itself. I try to remember that the rise from 100 to 200 yards is 20 minutes, and work from there, adding or subtracting 4 minutes for each 100 yards of range.

An obvious problem is the large range of adjustment needed on the sights. I am fortunate in owning a 12x Leupold scope, which has just enough internal adjustment to cover 100 to 400 yards if set up at the right forward angle. My iron sight is an old Parker Hale 5B, specially mounted on a bracket, and this has enough adjustment to go from 150 to 500 yards. To reach 600 yards, I have to use a cut down blade element and a framing aim on the target. Other competitors use removable blocks to insert under the rearsight as the range increases. Ingenuity and, I’m afraid, expense are necessary to solve this problem in practical ways.

Wind Deflection

The classic formula for determining the wind deflection experienced by a projectile as it moves down range demonstrates how the time of flight provides a complete picture of the ballistic performance of a given bullet. The formula is devastating in its simplicity, but you have to use consistent units – feet and seconds :

Let: D = the sideways deflection in feet

W= the cross wind velocity in ft/s

T = the time of flight in seconds (i.e the “real” time of flight)

R = the range in feet

V= the muzzle velocity in ft/s

Then D =  W (T - R/V)

e.g. for the .22LR fired at 1100 ft/s, according to the tables, the time of flight is 1.39 seconds at 400 yards. Thus the wind deflection in feet at 400 yards (1200 feet) due to a cross wind of 20 m.p.h. (29.333 ft/s) would be

29.333  x  (1.39  -  1200/1100)  =  8.77 feet  or 105.2 inches.

Divide this by 4 x 1.0472 and you get 25.1 minutes of angle, which is what is observed in practice. The expression (T - R/V) is generally referred to as the “delay time” - the amount of time by which the bullet is delayed by the air from reaching the target, beyond the time it would have taken in a vacuum. Clearly, the wind deflection is the product of the wind speed and the delay time.

Taking the argument to its extreme, it is apparent that a bullet which does not slow down at all (i.e. has zero delay time, or putting it another way, has a time of flight in air equal to that in vacuum) will not experience any wind deflection. This would be despite the fact that it had an appreciable (not zero) time of flight. But how would one make such a bullet? Either it would have zero drag coefficient, which in practice would mean zero cross-sectional area, or it would have infinite mass. Both are impossible, but we can see these ideals being approached either by very slender projectiles with sharp points, or by very heavy ones such as heavy artillery shells. The latter are barely deflected by the wind at distances considered long for rifle shooting. The reason is that, being much longer and heavier than rifle bullets, shells have a much greater sectional density than bullets. They therefore slow down at a lower rate, and their time of flight is shorter than that of a bullet fired at the same velocity. In consequence, their delay time is reduced and thus, they are blown sideways to a lesser extent. For example the 5 ft 4 inch (1.625m) long, 1-ton shell fired from a 16-inch naval gun at 2,650 ft/s (much the same velocity as our match rifles – and I have checked these statistics in a military reference book) would require less than half a minute of wind allowance in a 20mph (Force 5) cross wind at 1200 yards. Of course, 1200 yards is a very short range for a big naval gun, but even at 24,000 yards the shell would only be deflected 12.5 minutes in that wind.

The ballistic table indicates that at 100 yards, the wind deflection in a 20mph cross wind is about 6 minutes, which is about the same figure as for a 7.62mm TR at 450 yards. At 300 yards the .22LR bullet requires a wind allowance of 19 minutes, not dissimilar to a 7.62mm MR at 1100 yards. This is why I suggest that “short”, “long” and “ultra-long” range with the .22LR can be thought of as one quarter of the equivalent distances for full bore Target or Match Rifle.

The falling drag coefficient during the first 150 yards or so of the bullet’s flight produces the counter-intuitive result that the wind deflection is reduced if the muzzle velocity is reduced – but only up to a point. This was noticed by international 50 metre competitors and to take advantage of it, they sometimes tried out pistol ammunition (which is about 50 ft/s slower than rifle) to see if they could find a good batch. Running the computer program with the drag coefficient correctly set up confirms this result. The muzzle velocity which produces the lowest wind deflection at 50m and 100 yards is about 950 to 1000 ft/s. At longer ranges of up to 500 yards, it is about 1000 to 1050 ft/s. So you might think that using standard velocity ammunition (1075 ft/s) would be better than RWS R100 at 1125 ft/s.

However, at long and ultra long range, just as with the Match Rifle at 1200 yards, the most important factor in consistently hitting the bullseye is a tight group. This can only be achieved with good velocity control. Low velocity may give you a little less wind deflection, but it increases the inconsistency of ignition and the result is greater dispersion. For this reason, I am now fairly certain that RWS R100, with its 50 ft/s extra muzzle velocity, shoots better at the longest distances.

The constant drag coefficient of the .22LR bullet, once it has passed 150 yards, has another interesting result. The wind deflection in minutes is almost exactly proportional to the distance. So for a 20mph cross wind from 3 or 9 o’clock, the wind deflections at 100, 200, 300, 400 and 500 yards are near enough 6, 12, 18, 24 and 30 minutes. This is because the delay time increases at a constant rate.

Variation of Vertical Point of Impact and Velocity Control

We have seen from discussion of the theoretical and the real trajectories that the necessary angle of elevation (for small angles less than 1 or 2 degrees, which is the case in our context) is proportional to the range and inversely proportional to the square of the muzzle velocity. So for a given range, a higher velocity will require a smaller angle of elevation and vice versa. The practical result of this is that when shooting at a given distance, variations in muzzle velocity produce vertical dispersion at the target – high velocity shots strike high and low velocity shots strike low. It is important to examine the magnitude of this effect.

Looking again at the ballistic tables, we can see that at long range, the vertical point of impact is very sensitive to variations in velocity, whereas at short range it is remarkably insensitive. At 50 yards, there is only a half minute change of elevation between the nominal muzzle velocities of 1075 and 1125 ft/s. But at 500 yards, those 50 ft/s cause a difference in elevation of 6.9 minutes, so to reduce the dispersion to one minute, one would require the velocity to be controlled to within 50 / 6.9 = 7.25 ft/s, or to within 2 ft/s for a quarter minute. Clearly there is a need for uniformity of muzzle velocity to achieve acceptable results at long range.

Obviously you cannot hand load .22LR cartridges and anyway, there is only about 1.2 grains of powder in each cartridge. I have not yet done any chronograph testing on .22LR ammunition, but what I have done is to check variations in the overall weight of individual rounds. Not surprisingly, the expensive brands are more consistent in weight than the cheap ones. In my tests, Lapua X-Act (which is the most expensive brand) came out best in this respect, with every single round in a box of 50 weighing the same to within 0.1 grain in an overall weight of about 51 grains. RWS R50, R100 and Eley Tenex are nearly as good, with almost every round within 0.2 grains. Cheap brands such as Eley Club and SK Rifle Match vary by as much as 0.6 to 1 grain.

Variation in powder charges is not the only factor which can cause large groups - the dimensional quality and weight consistency of the bullet is also very important. Thus you can see how important it is to use the best quality ammunition. Even so, I usually take the trouble to overall weigh my ammunition and shoot it in order of weight. This can only benefit its ability to group well at the longest ranges.

Atmospheric Effects

As we have seen, the difference between the theoretical trajectory in vacuum and the real one in air is due to the aerodynamic drag which the air causes. The drag is primarily due to the density of the air and you will not be surprised to hear that variations in air density cause variations in the vertical point of impact. The effects of these variations are much greater at long range than at short.

The density of the air is affected primarily by the barometric pressure and temperature. It is also affected by variations in humidity, but not greatly, the reason being that water vapour is much lighter than air. You may find this surprising but water vapour has a molecular weight of 18 whereas air, consisting of approximately 75% nitrogen and 25% oxygen, has an average molecular weight of about 29. Humidity cannot be very easily measured so I will not mention it further.

The range of variations in atmospheric pressure and temperature likely to be experienced when shooting outdoors in the UK is quite wide. Atmospheric pressure varies between about 28.5 and 31.5 in.Hg, or 960 to 1070 mb – by more than 11%. Atmospheric temperatures likely to be experienced will generally lie between 5 and 35 Deg.C, i.e. 278 to 308 Deg.K – again a range of about 11%. The extremes of pressure and temperature are unlikely to occur at the same time, but nevertheless one might expect an overall range of air density varying by up to 15%. The ballistic tables I have issued gives an idea of the corrections in elevation needed to allow for these atmospheric variations. Such variations are enough to result in the angle of elevation at 300 yards to vary by as much as 5 minutes between the most favourable and the most unfavourable days. From the point of view of the air density, the “favourable” days would be low pressure and high temperature – stormy days in the summer. The “unfavourable” days would be high pressure and low temperature – fine, calm days in winter. However, I suspect the lack of wind on the “unfavourable” days would tend to compensate (in terms of the resulting score) for the extra elevation needed and the lower remaining velocity at the target.

The wind, when blowing from in front or behind, can also affect the elevation. A strong head wind slows the bullet down and a corresponding increase in elevation is required to maintain the vertical point of impact. Conversely, a tail wind speeds the bullet up slightly and will cause it to strike high unless some elevation is taken off. Although the effects are not that great (a 20 m.p.h. head or tail wind only causes an elevation change of 1.2 minutes at 300 yards), it is enough to push you up or down into the inner from a central bullseye. The effect is at its most damaging when the wind is changing in direction and small elevation changes are needed as well as windage adjustments.

Former and Existing Competitions for Long Range .22LR

Around 100 years ago, competitions for the .22LR at up to 200 yards were included in the July NRA Meeting, and in fact the Donegall, at 200 yards, was open to .22 rifles until 1967. After the Second World War, Col Turbutt of Derbyshire presented a series of cups for shooting with the .22LR at 200, 300 and 500 yards. These trophies still exist and are competed for annually in a meeting, held at Thorpe Cloud range in the Peak District, at the end of September. I have competed at this meeting for the last two years and very good fun it was too. Here at Bisley, Surrey Smallbore Rifle Association runs the Leslie Williams at 200 yards and a long range shoot at 300 yards every spring. In April 2013, the NRA held an inaugural Long Range .22 Trial, which attracted 20 entries, and they are repeating this on Sunday 27 April this year. The course of fire will be 10 shots at 100, 200 and 300 yards in the morning, and 15 shots at 400 and 500 yards after lunch.

Summary

• • As the .22LR has a muzzle energy of less than 150 Joules, open ranges of up to 500 yards restricted to the use of this cartridge should enjoy much smaller (or possibly no) danger areas, perhaps opening the way for some existing closed ranges to be re-opened for this purpose as well as for new ranges to be established – maybe alongside golf courses.  Obviously range development would require a lot of commitment and effort on the part of the governing bodies

• The wind has the same order of effect on the .22LR at 100 to 300 yards as on a 7.62mm bullet at the full Bisley distances of 300 to 1200 yards.  Long Range .22 can thus be regarded as a genuine simulation of fullbore long range shooting.  Schools remote from military ranges could be encouraged to practise with their No 8s at 50 to 200 yards (possibly within their own grounds) as a supplement or an alternative to shooting TR at 300, 500 and 600 yards

• Firing .22LR out of doors generates comparatively little noise, to the benefit of firers, markers, spectators and the general population nearby

• It has a low environmental impact, since only 40 grains of lead is discharged per shot, compared with 155 to 200 grains per full bore shot.  Pollution due to the products of combustion is very low too, as a .22LR cartridge only contains about 1.2 grains of explosive (compared with 40 to 50 grains for full bore cartridges)

• Round for round, .22LR ammunition costs less than 25% that of 7.62mm.  RWS R50 is currently 15.6p a round and Club ammo is obtainable for less than 10p (overall weight selection can make it shoot better)

• .22 LR barrels wear at a very slow rate.  I believe that they frequently reach 50 to 100,000 rounds without appreciable deterioration in accuracy

• There is virtually no recoil, making it comfortable for the firer, especially newcomers, youngsters and those getting less fit with age

• Such a discipline could provide useful common ground between the NRA and the NSRA – possibly resulting in joint ventures for the purpose of range construction

• A knowledge of the theory of ballistics in a vacuum is useful to establish the minimum angle of elevation at a given muzzle velocity and range.  The trajectory at short ranges up to 100 yards is very similar to that in a vacuum

• The real trajectory in air becomes more curved than the vacuum trajectory as the range increases.  The remaining velocity is still more than half the muzzle velocity by the time the bullet reaches 600 yards.  The angles of elevation at the longest distances of up to 600 yards are nearly double what they would be in a vacuum

• The time of flight is a composite measure of all the ballistic characteristics of the projectile in question and can be used, with the vacuum angle of elevation, to determine the real angle of elevation

• It is useful to memorise how to construct the approximate elevation table to enable on range adjustments to be made

• The wind deflection is the product of the cross wind velocity and the delay time

• The best quality ammunition is essential for good results.  Weight sorting of individual rounds will assist the control of velocity variations, especially at 300 yards and over, where the angle of elevation is very sensitive to the muzzle velocity

• Barometric pressure, air temperature and head or tail winds can have significant effects on the required angle of elevation, and more so at long range.

Thus as well as continuing to promote traditional TR and MR, I believe the NRA should consider encouraging the use of the .22 LR cartridge for competitive outdoor shooting, as practised in the Bisley style, at distances of up to 400 or 500 yards. Given appropriate support by the NRA and NSRA, there are grounds to believe that such a development at a number of locations around the country could encourage the participation of new competitors, many of whom may have found it difficult to make a start hitherto. That difficulty probably stems from the cost of transport to remote ranges as well as from the high cost of 7.62mm ammunition. Such participants would naturally be attracted to marksmanship as an interesting challenge, but would welcome the benefits of a similar amount of fun, at much lower cost and more favourable environmental impact, inherent in this alternative approach.