Horus Vision - FOR INFORMATION OR SALES · 2020-04-16 · appointment of Mr. Davis as Engineering Project Manager for Colt Firearms Division of Colt Industries, in Hartford, Connecticut

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Horus Vision LLC

FAX: 650-589-4569 Phone: 650-583-5471 Phone: 650-589-6066

E-mail: [email protected]

Web site: www.horusvision.com

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Dickinson Buell

Phone: 650-583-5471 Phone: 1-800-99buell


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Wes Harris 14802 N. Coral Gables Dr.

Phoenix, AZ 85020

Phone: 602-997-5370 Cellular Phone: 602-432-2871

FAX: 602-942-5327


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VOLUME II

DISCLAIMER ..................................................................................................................................... 6

FOREWORD ....................................................................................................................................... 7

A BRIEF COURSE IN BALLISTICS................................................................................................. 8 EFFECT OF BAROMETRIC PRESSURE ON THE BULLET’S FLIGHT ........................................................ 9 EFFECT OF AIR TEMPERATURE ON THE BULLET’S FLIGHT .............................................................. 10 EFFECT OF RELATIVE HUMIDITY (RH) ON THE BULLET’S FLIGHT.................................................. 11 EFFECT OF THE EARTH’S ROTATION ON THE BULLET’S FLIGHT...................................................... 12 EFFECT OF WIND ON THE BULLET’S FLIGHT ................................................................................... 13 EFFECTS OF SHOOTING UPHILL OR DOWNHILL ............................................................................... 14 EFFECT OF AMMUNITION TEMPERATURE ON MUZZLE VELOCITY................................................... 15 EFFECTS OF BALLISTIC COEFFICIENT ON THE BULLET’S FLIGHT .................................................... 16 LEAD............................................................................................................................................... 18 EFFECT OF DRIFT ON THE BULLET’S FLIGHT................................................................................... 19 THE ELEMENTS OF DISPERSION ...................................................................................................... 20 WEATHER STANDARDS ................................................................................................................... 22

TRAG1S5 -- AIMING POINT SOFTWARE.................................................................................... 23 WHAT IS TRAG1S5 – AIMING POINT SOFTWARE ............................................................................ 24 WHAT DOES TRAG1S5 ALLOW YOU TO DO (DESKTOPS AND LAPTOPS)......................................... 25 THE HORUS RIFLESCOPE WITH THE HORUS RETICLE ..................................................................... 28 RIFLESCOPE THAT USE ADJUSTMENT KNOBS (CLICKING) FOR ELEVATION AND WINDAGE ........... 29 ENVIRONMENTAL DATA ................................................................................................................. 34

A COMPLETE EXAMPLE BASIC SET-UP FOR A RANGE CARD........................................... 35 GETTING STARTED.......................................................................................................................... 36 HORUSVISION DATA SHEET............................................................................................................ 37

See worksheet section for masters of Horus data sheet for photocopying. ............................... 38 PROGRAM ....................................................................................................................................... 39

1. Set-up ................................................................................................................................. 39 2. Add/Edit Guns ................................................................................................................... 40 3. Atmospheric Conditions .................................................................................................... 43 4. Final Firing Position .......................................................................................................... 44

1) Wind Speed:................................................................................................................... 44 2) Wind from (o’clock) ...................................................................................................... 44 3) Leading a Moving Target............................................................................................... 46 4) Target Range:................................................................................................................. 50 5) Uphill/Downhill Angle: ................................................................................................. 50

THE FINAL RESULT -- YOUR RANGE CARD............................................................................ 51

VISUAL RANGE CARD.................................................................................................................. 52

PERSONAL DIGITAL ASSISTANT A QUICK OVERVIEW ....................................................... 55

WORKSHEETS FOR THE HORUS RETICLE MASTERS FOR PHOTOCOPYING................... 56 HORUSVISION DATA SHEET............................................................................................................ 58 PROGRAM ....................................................................................................................................... 60

CONVERSION TABLES.................................................................................................................. 67 Temperature Conversion............................................................................................................ 67 Barometric Pressure ................................................................................................................... 67 Speed.......................................................................................................................................... 67 Length ........................................................................................................................................ 67 Temperature Considerations (at sea level)................................................................................. 68 Field Use .................................................................................................................................... 68 Trigonometry ............................................................................................................................. 68 Speed of Sound .......................................................................................................................... 69

INFORMATION................................................................................................................................ 70 U.S.M.C. Milliradian (Mils) ...................................................................................................... 70 U.S. Army Milliradian ............................................................................................................... 70 (True) Minute of Angle (MOA)................................................................................................. 70 (Shooters) Minute of Angle (MOA) .......................................................................................... 70

TROUBLE SHOOTING.................................................................................................................... 71

REFERENCES .................................................................................................................................. 72

DISCLAIMER Please be careful when using firearms. A mistake in judgment, a lapse of attention, a malfunction of any kind can result in serious injury or death. Bad things sometimes happen to good people. The information in this manual, while believed to be reasonably accurate as of the date of publication, is not warranted or represented to be accurate, correct, or useful for any particular purpose. Use the information in this manual with caution and common sense, and verify the information with respect to your own firearms before use. The author and publishing company accept no responsibility for errors in the information presented herein, or for accidents, injuries, damage, or any other problems which might arise as a result of your use of the information contained in this book, and expressly disclaim all liability for injuries, death, and damages, whether direct, incidental, consequential, punitive, or otherwise. We are also not responsible for tornadoes, earthquakes, firecrackers that go off in your hand, mad cow diseases, floods, failed crops, or El Nino. So be careful!

FOREWORD The TRAG1S5 program was written by William C. Davis of Tioga Engineering Company, Inc. TRAG1S5 is a Ballistic Software Program that has been enhanced to calculate values for the Horus Reticle. William C. Davis has an extensive and illustrious background in the science of ballistics. His work and participation in the shooting sports these past 60 years prepared him well for creating the Aiming Solutions Program or “TRAG1S5” … a Digital Accuracy System. This system is so advanced it puts shooting well into the next millenium. A life member of the National Rifle Association, Mr. Davis acted as a Technical Consultant and Contributing Editor for the publication, “The American Rifleman” … authoring over 50 Engineering and Technical reports for the U.S. Department of Defense pertaining to small arms and ammunition. Participating in many shooting sports, William Davis has earned an impressive list of commendations and awards. Examining and testing firearms and ammunition involved in criminal and civil litigation led to the appointment of Mr. Davis as Engineering Project Manager for Colt Firearms Division of Colt Industries, in Hartford, Connecticut. William Davis is known for an extensive list of published books and periodicals. Kudos for his latest achievement … “TRAGIS1S5”. The TRAG1S5 allows the rifleman with the aid of a computer to factor in actual rifle muzzle velocities and environmental conditions so realistic, accurate distance values for the targeting grid can be computed. The units of measurement are identical on the Horus targeting grid and the computer printout. The computed values for distance, wind, and lead for each horizontal elevation line can then be easily assigned. The combination of the Horus reticle and the computer allows the rifleman to shoot with greater precision at extended ranges. The combination of TRAG1S5 and Horus have taken the mystery out of long range shooting. For the individual rifleman who still uses the “old fashion” clicking style scope, our latest version of TRAG1S5 will also give firing solutions in MOA or clicks. The values computed give the rifleman relative accurate values. You must never forget all values must be confirmed by live fire.

A BRIEF COURSE IN BALLISTICS As a long range rifleman, you should read this material carefully. William Davis, a master of ballistics, explains in simple English a concise, informative explanation on how real time key factors influence bullet performance. After reading this section, you will understand why Aiming Solution software, using the TRAG 1S5 program is a must for extended range shooting.

EFFECT OF BAROMETRIC PRESSURE ON THE BULLET’S FLIGHT Barometric pressure affects the down-range performance of a bullet because it affects the density of the air through which the bullet must travel. The barometric pressure depends primarily on altitude, and to a much smaller extent on the constantly occurring changes in the atmosphere that produce the barometric "highs" and "lows" that we hear about in weather reports. The barometric pressures given in weather reports are not actual pressures; they have been adjusted to eliminate the effect of altitude. The adjusted pressures given in weather reports everywhere are typically between 29 and 31 inches of mercury, although the actual barometric pressure in Denver (which is above 5000 feet) is typically about five inches less than the pressure in a coastal city such as New York. Adjusted pressures are more suitable than actual pressures for weather forecasting, and users of barometers are generally advised to adjust their barometers to the pressure being reported in a local radio or television broadcast. This adjustment makes their readings comparable to the readings of other barometers used for weather forecasting, but the readings are then unsuitable for use in determining the atmospheric density. The shooter who wishes to use a barometer for determining atmospheric density should take it to a facility where an accurate barometric reading is available, such as an airport control tower or a science laboratory at a college or university. He should explain clearly that the information he requests is the current actual barometric pressure and not the pressure after the adjustment for altitude has been applied. He should adjust his instrument on the spot to that actual pressure, and henceforth the readings obtained from that instrument will reflect not only the effect of altitude, but also the effect of weather-related fluctuations in pressure, wherever the instrument may be. It is this actual barometric pressure that is called for when the user elects to input the barometric pressure explicitly in the computer program that accompanies the SAMMUT/HORUS sighting system. Of course the user of the SAMMUT/HORUS computer program may alternatively choose to input the altitude (as obtained from a topographic map, for example) rather than to input the barometric pressure explicitly. In that case, the program will calculate the air density, with only slightly less accuracy, based on the inputs of altitude and temperature in which the barometric pressure is implicit.

EFFECT OF AIR TEMPERATURE ON THE BULLET’S FLIGHT The temperature of the air affects the aerodynamic drag ("air resistance") encountered by the bullet in its flight. There are two reasons for this. The first and more important reason is that cold air is more dense than warmer air, under conditions that are otherwise the same. The second reason is that the speed of sound is lower in cold air than it is in warmer air. The first reason is the more easily understood. Most people probably know that almost every substance contracts and becomes more dense as it is cooled, and therefore that cold air is more dense than warmer air. They also know that water is much more dense than air, and almost everyone has noticed that much more effort is required to wade through deep water than would be required to walk along at the same speed surrounded only by the air. The more dense the medium through which a body passes, the more energy is expended (and the more velocity is lost) by the body as it passes through. The second reason is not intuitively obvious, but it is a fact that cold air offers greater resistance to the passage of a bullet - especially a supersonic bullet - because the speed of sound is lower in cold air than it is in warmer air. A full explanation of this phenomenon would be too lengthy to include here, but it is a fact that the force of aerodynamic drag on a fast-moving body depends upon the so-called "Mach ratio" which is the ratio of the speed of the moving body to the speed of sound. Because the speed of sound is lower in cold air, the Mach ratio for a bullet at any particular velocity is correspondingly higher in cold air, and the force of aerodynamic drag is therefore greater.

EFFECT OF RELATIVE HUMIDITY (RH) ON THE BULLET’S FLIGHT The relative humidity affects the down-range performance of a bullet because it affects the density of the air through which the bullet flies. Contrary to what many people suppose, humid air is less dense than dry air under the same conditions of temperature and barometric pressure, because the molecular weight of water is less than the molecular weights of the principal gases (nitrogen and oxygen) that comprise our atmosphere. The effect of humidity on the down-range performance of bullets is small in comparison to other factors that affect the downrange performance. The relative humidity has greater effect on air density at high temperature than at low temperature, but even at 90o F. the difference in density between completely dry air and completely saturated air is only about 1/10th of one percent. For a typical .30-caliber 150-grain bullet having a ballistic coefficient of C1=.400 and a muzzle velocity of 2800 fps, the difference in remaining velocity at 1000 yards is about 14 fps, and the difference in drop is about six inches.

EFFECT OF THE EARTH’S ROTATION ON THE BULLET’S FLIGHT The Coriolis effect on the path of a projectile is a consequence of the rotation of the earth, and the fact that the surface of the earth is curved (spherical) rather than flat as we generally assume it to be for the solution of problems in exterior ballistics. The magnitude and direction of the Coriolis effect depends on the location of the gun (its latitude) and the horizontal direction (azimuth) in which the gun is pointed. The Coriolis effect is so small in comparison to other effects on the projectile's path that it is not ordinarily considered except in the case of long-range artillery fire, but of course it does actually have some effect on all projectiles. A somewhat simplified way to visualize the problem is to consider that, because of the earth's rotation, a "stationary" target is not truly motionless as we normally assume it to be, but is constantly moving. Consequently, the point on the target at which the projectile was directed when it left the muzzle will have moved some small distance (relative to the gun) during the time the projectile is in flight. In this sense, the correction for the Coriolis effect is similar to the "lead" required to hit a moving target. The Coriolis effect on projectiles fired either due north or due south is entirely horizontal, and the Coriolis effect (on a vertical target) on projectiles fired either due east or due west is entirely vertical. The effect on projectiles fired in any other direction is both horizontal and vertical, the amount of each depending upon the horizontal direction (azimuth) in which the gun was pointed.

EFFECT OF WIND ON THE BULLET’S FLIGHT The most important effect of wind on the bullet's flight is to change its direction horizontally. In the language of gunnery, angles in the horizontal plane are called angles of deflection, and so the effect of a cross-wind on the bullet's path is correctly called wind deflection effect although the term "wind drift" is often used, rather loosely, instead. To hit targets at long range, riflemen must learn to estimate the cross-component of the wind velocity. The speed and direction of the wind can be measured by suitable instruments, or estimated by experienced observers from signs such as the motion of leaves and grass, and the appearance of "mirage" which is the wavy pattern of distortion that is seen through a powerful telescope, caused by refraction of light passing through waves of heated air as they rise from the ground. Wind flags and other indicators are placed downrange during some types of rifle competition to aid in estimating wind effects. Wind deflection depends upon the cross-component of the wind velocity. A 10-mph wind blowing from 3 o'clock or 9 o'clock has a cross-component of 10 mph. Ten-mph winds from 2, 4, 8 or 10 o'clock have a cross-component of about 8.7 mph, while winds from 1, 5, 7 or 11 o'clock have a cross-component of 5.0 mph. Winds blowing from 6 or 12 o'clock have no cross-component. Wind speed and direction are practically never uniform over the whole distance from the gun to the target, and so the rifleman estimating the allowance for wind must decide whether to concentrate his attention on the wind nearer the gun or on that nearer the target. The answer is that the wind conditions near the gun have much greater effect than the conditions near the target. Two hypothetical examples will illustrate this point. For both examples, assume that the rifleman fires a 150-grain .30-caliber bullet having a ballistic coefficient of C1=.400 at a muzzle velocity of 2800 fps, toward a target 500 yards away. For the first example, suppose that a perfectly uniform 10-mph wind blows from 9 o'clock across the first 100 yards of range, and that there is no wind whatsoever over the remainder of the range from 100 yards to 500 yards. Consider now the situation when the bullet has reached 100 yards. We see that the wind deflection is about 0.8 inch, which means that the bullet is now 0.8 inch to the right of the line from muzzle to target, but also that its path is curved toward the right at an angle of about 1.6 moa. With no further influence from the wind over the remaining 400-yard distance, the bullet's path in the horizontal plane will be straight, but the horizontal angle of 1.6 moa that it had already aquired at 100 yards will carry it 6.4 inches farther to the right of the gun-target line, for a total wind-deflection effect of 7.2 inches at 500 yards. For the second example, suppose that conditions from the muzzle to 400 yards are perfectly calm, but the 10-mph wind from 9 o'clock blows across the range between 400 and 500 yards. The horizontal direction of the bullet remains directly toward the target in the calm air out to 400 yards, where its remaining velocity is about 1959 fps, when it suddenly encounters the 10-mph crosswind. The bullet's flight between 400 and 500 yards will be the same as that of a bullet of the same kind fired toward a 100-yard target at a muzzle velocity of 1959 fps, for which we find that the wind deflection would be about 1.3 inches.

EFFECTS OF SHOOTING UPHILL OR DOWNHILL The vertical drop of a bullet below its line of departure is practically the same whether the target is uphill, downhill or at the same level as the gun. That does not imply, however, that the sight adjustment or the allowance in aiming required to hit a target at any range is unaffected by the slope of the gun-target line. The reason for this apparent contradiction is that the effects of an aiming allowance or an elevation adjustment of the sight are in a plane perpendicular to the line of sight, which, in the case of uphill or downhill firing, is not the same as the vertical plane in which the bullet drop is measured. The reason we must take account of the slope of the gun-target line is illustrated in the following examples. Suppose we are firing a .30-caliber 180-grain bullet having a ballistic coefficient of C1=.450 and a muzzle velocity of 2600 fps, under standard sea-level atmospheric conditions, and that we have sighted-in the rifle at 200 yards. Suppose further that we wish to shoot at a bullseye on a tall vertical target 700 yards away on the same level as the gun. We can calculate that, if we were to fire with the sight adjusted for the sight-in range of 200 yards, the bullet would strike about 147 inches low on the vertical target. Therefore, to hit the bullseye we must either (1) aim 147 inches high or (2) make an elevation adjustment of about 21 moa (147/7) on our sight. Now suppose that all the conditions are the same as those described above except that the tall vertical target is on higher ground at an uphill angle of 30 degrees. Since the vertical drop of the bullet is the same as before, the bullet would strike the vertical target at a point 147 inches below the bullseye if we fired with the sight adjusted for the sight-in range. However, as we look upward at a 30-degree angle toward the target, the vertical line between the bullet hole and the center of the bullseye would appear to be less that 147 inches long because of the angle from which we are viewing it. We can calculate by trigonometry that a vertical line 147 inches long would appear to be only about 127 inches (147*cos 30o) when viewed from a location 30 degrees below. Therefore, we could hit the bullseye by (1) aiming 127 inches high or (2) by making an elevation adjustment of about 18 moa (127/7)) on our sight. By reasoning similarly, we can see that a 147-inch vertical line would appear to be about 127 inches long when viewed from 30 degrees above the target as well as from 30 degrees below, and therefore the same allowance in elevation must be made in either case.

EFFECT OF AMMUNITION TEMPERATURE ON MUZZLE VELOCITY As almost everyone knows, the muzzle velocity of a bullet is a factor of fundamental importance in determining the bullet's path. Therefore, the rifleman must have some knowledge of the expected muzzle velocity in order to decide where to aim or how to adjust his sight. The best estimate of the expected muzzle velocity is obtained from carefully conducted velocity testing of the ammunition to be used in the field, fired from the rifle to be used in the field, and preferably with the ammunition at approximately the same temperature that it will be in the field. There are two kinds of factors, random and systematic, that determine the muzzle velocity of any particular shot. Some degree of random shot-to-shot variation in muzzle velocity is inevitable, and its affect on any particular shot is inherently unpredictable. The rifleman can minimize the random variation by choosing ammunition that has demonstrated consistently good uniformity in carefully controlled velocity testing. The ammunition temperature is the principal source of systematic variation in the muzzle velocity, assuming that the ammunition is being fired in the same rifle with which the basic muzzle velocity was established. Unfortunately, the effect of temperature on the muzzle velocity varies widely from one load to another. The rifleman minimizes the systematic effect of ammunition temperature on muzzle velocity by measuring the muzzle velocity with the ammunition at approximately the same temperature that it will be in the field. A Memorandum Report written by Barbara Wagoner of the U.S. Army Ballistic Research Laboratory contains an analysis of a great many velocity tests of ammunition ranging in caliber from 5.56mm to 30mm, loaded with both single-base and double-base powders, and fired at various temperatures from -65o F. to +165o F. The effect of temperature varied quite widely from one load to another, as was undoubtedly expected from previous experience. If all the various ammunition types are lumped together, however, the data indicate a typical velocity change of approximately 0.4 percent for a change of 10o F. in ammunition temperature. This implies, for example, that a load which produces an average muzzle velocity of 3000 fps at +70o F. would be expected to average approximately 3024 fps at +90o F. and approximately 2976 fps at +40o F. These differences are significant if targets are to be engaged at very long range, and that fact underscores the desirability of having reliable muzzle-velocity data for the ammunition at a temperature reasonably close to the temperature at which it will be in the field.

EFFECTS OF BALLISTIC COEFFICIENT ON THE BULLET’S FLIGHT The ballistic coefficient of a bullet is the measure of its ability to move through the air with minimum resistance. This resistance is called aerodynamic drag, and its most significant effect is to reduce the velocity of the bullet en route to the target and thereby to increase the bullet's time of flight. An increase in time of flight increases the vertical drop of the bullet away from its original line of departure, and therefore it also increases the vertical aiming allowance or sight adjustment required to hit targets at different ranges. Aerodynamic drag also reduces the striking velocity of the bullet at the target, and it may thereby reduce the bullet's terminal effectiveness, depending on the nature of the target. Another important result of aerodynamic drag is that it makes the bullet susceptible to wind deflection, which is the horizontal change in direction of the bullet's path, caused by wind blowing across the gun-target line. Contrary to what many people suppose, the effect of cross-wind on the bullet's path does not depend primarily upon the bullet's time of flight, but upon the length of time that the bullet is delayed en route to the target by aerodynamic drag. Any increase in the ballistic coefficient of the bullet tends to reduce this delay time, and it may do so even though the gain in ballistic coefficient is achieved at the expense of a lower muzzle velocity and a longer time of flight. The following example will illustrate this point. Consider first a .308 Win load that consists of a 150-grain bullet having a ballistic coefficient of C1=.400, fired at a muzzle velocity of 2850 fps. We can calculate that its time of flight to 700 yards, for example, would be about 1.027 seconds, and that its wind deflection in a 10-mph crosswind would be about 51 inches. Now compare this .308 Win load to another one using a 180-grain bullet of similar shape, which would have a ballistic coefficient of about C1=.480. The muzzle velocity attainable with the heavier bullet at comparable chamber pressures would be only about 2600 fps, and the time of flight to 700 yards would be increased to 1.070 seconds. Nevertheless, the wind deflection would actually be reduced by about ten percent, from 51 inches to 46 inches at 700 yards, owing to the higher ballistic coefficient of the 180-grain bullet. The ballistic coefficients of commercial sporting bullets in the U.S.A. are almost invariably based on comparison with the "G1 Standard Projectile" which has a specified diameter and weight, and a particular shape. A ballistic coefficient based on the G1 projectile shape is properly identified as "C1" to distinguish it from other possible ballistic coefficients such as "C5," "C6," "C7," "C8," etc. that were once widely used in military sources referring to projectiles of various different shapes. References to "the" ballistic coefficient (or sometimes "the B.C.") of a commercial sporting bullet in the U.S.A. should be taken to mean the C1 ballistic coefficient unless the source gives specific notice to the contrary. Most manufacturers of commercial sporting rifle bullets will provide values of the (C1) ballistic coefficients of their bullets upon request, and several manufacturers include that information in the reloading handbooks that they publish. One manufacturer, Sierra Bullets, lists several different C1 ballistic coefficients for each bullet, each ballistic coefficient being intended to apply to a different velocity range. For Sierra bullets fired at a muzzle velocity of at least 2500 fps, the ballistic coefficient listed by Sierra for a velocity of 2500 fps will generally produce satisfactory results

using the SAMMUT/HORUS computer program, over the ranges of practical interest to the rifleman.

LEAD The actual lead required also depends upon some factors that are determined by the actions of the shooter in firing the shot, and therefore cannot be predicted. These include the particular shooter’s human “reaction time” (time between the instant he decides to pull the trigger and the instant that the trigger is actually pulled), and also the “lock time” (time between sear release and firing-pin impact on the primer) of the particular rifle and the “action time”(time between firing-pin impact on the primer and exit of the bullet from the muzzle) of the load. The errors introduced by these unpredictable variables are minimized if the shooter uses the “sustained lead” technique of shooting at moving targets, and maintains a consistent “follow through”; the errors are maximized if the shooter attempts to “spot shoot” the target by taking aim at a fixed point ahead of the target and then pulling the trigger.

EFFECT OF DRIFT ON THE BULLET’S FLIGHT Drift is one of the phenomena that contribute to the horizontal deviation of a spin-stabilized projectile from the vertical plane containing its line of departure. Drift is an incidental consequence of gyroscopic precession, which itself is otherwise essential for the satisfactory performance of spin-stabilized projectiles. It is precession that forces the axis of a spin-stabilized bullet or artillery projectile to change its direction constantly as the trajectory curves downward, so that the projectile flies point-forward with its axis nearly parallel to the direction in which it is moving. The angle between the axis of a projectile and the direction in which it is moving is called yaw. After a spin-stabilized projectile has recovered from the effects of certain disturbances that it encountered during launching, it settles into an attitude of relatively small yaw that is called the yaw of repose. At the yaw of repose, the axis is inclined slightly upward and toward the right for projectiles fired from a barrel having right-hand twist of rifling, or upward and toward the left for projectiles fired from a barrel having left-hand twist. It is the horizontal component of the yaw of repose that causes drift. For projectile fired from a barrel rifled with right-hand twist, the horizontal component of the yaw of repose is toward the right, which causes the air pressure on the left side of the projectile to be greater than the air pressure on the right side, thereby forcing the projectile to drift toward the right. The horizontal component of the yaw of repose tends to increase as the trajectory curves more steeply downward, and therefore the drift increases ever more rapidly with increasing range. The horizontal directions are reversed, of course, for projectiles fired from a barrel rifled with left-hand twist. The calculation of drift is relatively complicated, and to calculate it very accurately requires detailed information about the projectile that is not available for small–arms projectiles except for a few that have military applications at very long range. The drift calculations incorporated in the Horus reticle and the corresponding computer program are based on typical values for a class of bullets generally used for long-range rifle fire. Specifically, long-pointed boattail bullets of low-drag configuration such as the U.S. military 173-grain 7.62 mm M118 Match and the 650-grain Caliber .50 M33 Ball. Because the whole contribution of drift to the horizontal deviation of the trajectory is relatively small, the lack of detailed information specific to each of the many different bullets that might be used for long-range rifle fire will not detract seriously from the practical accuracy of the results.

THE ELEMENTS OF DISPERSION In reference to shots fired at a target, dispersion refers to the scattering of the shots around the center of impact. Small dispersion is synonymous with what is commonly called good accuracy, and large dispersion is synonymous with what is commonly called poor accuracy. The causes of dispersion are sometimes divided into two classes. The first, which can be called aiming error, refers to errors in the direction in which the gun is pointed when it is fired. The second, which can be called ballistic dispersion, refers to deviations of the bullet from its intended path toward the target after it has left the muzzle. In the most restricted sense, the term aiming error may refer to the degree of accuracy with which the shooter has aligned the sight on his chosen aiming point at the instant of firing. In a more general sense, however, the aiming error includes also the shooter’s error in choosing the point at which to aim. Thus, for example, if the range to the target is much greater than the range at which the rifle has been sighted-in, and the shooter fails to adjust his aiming point or his sight so as to make proper allowance for this difference in range, then the mistake in elevation angle so introduced becomes a part of his total aiming error irrespective of the steadiness with which he aims the rifle. The ballistic dispersion depends primarily upon the quality of the rifle and the ammunition. If the shooter can make satisfactorily small shot groups at short ranges such as 100 yards or 100 meters, he has established the quality of the rifle and most of the properties that determine the quality of the ammunition. The accuracy of the rifle/ammunition system at long ranges cannot be inferred reliably from small groups fired at short ranges, however, because the vertical dispersion at long ranges depends very heavily upon the shot-to-shot variation of muzzle velocity, whereas the short-range accuracy is often quite insensitive to variations in muzzle velocity. Whereas the ballistic dispersion depends upon the quality of the rifle and ammunition, the aiming error depends upon the skill of the shooter and the capabilities of the sighting system. It is assumed that serious users of the SAMMUT/HORUS sighting system will already have acquired the necessary skills in marksmanship. The SAMMUT/HORUS reticle, and the related computer program, are intended to reduce the total aiming error by helping the shooter to select the correct aiming point (or the correct sight adjustment) based on the conditions under which the shot is to be made. The information about the prevailing conditions must be provided by the shooter or by his coach or observer. The various elements of this information are more or less important, depending upon the range to the target and the relative magnitude of each element’s effect on the bullet’s path. The muzzle velocity, the ballistic coefficient, the range, the wind conditions and the target speed (in the case of a moving target) have relatively large effects on the bullet’s path relative to the gun-target line and therefore must be most accurately known. Moderate differences in the uphill and downhill slope of the gun-target line have only moderate effects on the bullet’s path, and therefore reasonable estimates of the uphill/downhill angle will generally be satisfactory. The drift (which is caused by the gyroscopic precession of the bullet) and the Coriolis effects (which is caused by the rotation and sphericity of the earth) have relatively trivial effects on the bullet’s path, and they are not often considered in calculation of the relatively flat trajectories that are characteristic of rifle fire. Nevertheless, provision is made for taking

account of all these factors in the SAMMUT/HORUS system because all of them make at least some small contribution to the total aiming error which the system seeks to reduce insofar as is practicable. It must be recognized, however, that neither the aiming error nor the ballistic dispersion can ever be reduced to zero, and therefore whether or not a target will be hit by any particular shot is a question of probabilities, depending on the size of the target, the proficiency of the rifleman, the accuracy of the information about the conditions under which the shot will be made, and the ballistic dispersion of the gun/ammunition system. The rifleman should learn by experience and recognize realistically the outer limits of the ranges at which various types of targets can be engaged with a reasonable probability of success.

WEATHER STANDARDS Atmospheric Conditions Used in Calculating Firing Solutions A. The TRAG1S2 program offers three choices for atmospheric conditions. The first two

choices define “Standard Atmosphere”.

A “Standard Atmosphere” defines the atmospheric conditions for which the “standard” firing tables and other tables giving “standard ballistics” are computed. In the solution of actual gunnery problems, the corrections for the prevailing atmospheric conditions are made on the basis of the agreed standard atmosphere.

1. The ARMY STANDARD METRO atmosphere was established at the U.S. Army

Aberdeen Proving Ground and was used for many years by the U.S. Army as the atmosphere for which all standard firing tables were computed. This standard atmosphere was also adopted by the manufacturers of commercial ammunition, and it is still in use by the major manufacturers of commercial ammunition and bullets. In the Army Standard Metro, the atmosphere at sea-level has a temperature of 59 degrees F., a barometric pressure of about 29.53 inches of mercury, and a relative humidity of 78 percent. The atmospheric density under these conditions is about .0751 pounds per cubic foot.

2. The “ICAO STANDARD ATMOSPHERE” was defined by the International Civil

Aviation Organization during the early 1950’s, and it was adopted in the late 1950’s as the standard atmosphere for all of the U.S. armed forces. In the ICAO standard atmosphere, the atmosphere at sea-level has a temperature of 59 degrees F., a barometric pressure of about 29.92 inches of mercury, and a relative humidity of zero. The atmospheric density under these conditions is about .0765 pounds per cubic foot.

B. The Horus Vision System offers the rifleman two choices to factor weather data.

1. Altitude and temperature choice is recommended when computing a range table. This table is usually attached to the stock of your rifle.

2. Real time barometric pressure, temperature, and relative humidity choice of field

data to help calculate a very accurate firing solution. Recommended when long range precision is a must.

TRAG1S5 -- AIMING POINT SOFTWARE What is TRAG1S5 software. What does TRAG1S5 allow you to do. (desktop and laptop computers) Riflescopes with Horus Reticle Riflescopes that use adjustment knobs (clicking) Teaching aid Preparation for accurately employing Horus Vision’s Aiming Solution Software The Horus riflescope with the Horus reticle Riflescopes that use clicking (adjustment knobs) for elevation and windage Environmental data A complete example – basic set-up for a range card.

WHAT IS TRAG1S5 – AIMING POINT SOFTWARE Our software program helps the rifleman hit targets at extended ranges. Versions on the software can run on desktop, laptop or hand held computers. The program requires the rifleman to enter fixed data about their rifle and ammo. In addition, environmental data (temperature and barometric pressure) is also required. Factors such as wind speed and direction, and the speed of moving targets can also be included. Once all data is entered, the computer will calculate the proper line to hold on.

WHAT DOES TRAG1S5 ALLOW YOU TO DO (DESKTOPS AND LAPTOPS) Based on the gun, ammo and environmental data you input, Horus Vision’s TRAG1S5 Aiming Point software will allow you, the rifleman, to do the following. For riflescopes with the Horus Reticle, you can print a range card that assigns range/distance values for each horizontal line of the Horus targeting grid. In addition, wind and lead values are given for each line. Example:

For scopes that rely on adjustment knobs (clicking) to correct for holdover, windage and lead, you can print a range card. Example:

For use as a teaching aid to demonstrate the influence of environmental and gun/ammo factors, a Horus Reticle calibrated in U.S.M.C. Mils is used as a reference to show final firing solutions. You can easily change any simple factor used to calculate your original firing solution. Immediately, you can visually observe the change of a single or combination of factors on the Horus Reticle. This teaching aid is also a valuable tool for the rifleman. He can simulate conditions on his computer to match field conditions. This allows the rifleman to visually reaffirm holdover and windage corrections or change ammo to meet his desired goals. Note: Please review “A Brief Course in Ballistics”. Example:

THE HORUS RIFLESCOPE WITH THE HORUS RETICLE

Preparation for Accurately Employing HorusVision Aiming Solutions Software

A. Your Rifle

1. Make sure your rifle is in good operational condition. If you are not sure, have a competent gunsmith check your rifle.

2. Select the ammo that consistently shoots 1 MOA or less (preferably ½ MOA) at 100

yards (or meters).

3. Obtain an accurate muzzle velocity value for your gun firing the ammo you selected. Muzzle velocity values are extremely important when shooting at extended ranges.

4. Zero your rifle.

B. Your Scope (with the Horus Reticle)

1. Your variable power scope is in the first focal plane (objective plane), all elevation and windage adjustments on the Horus rangefinder and targeting grid are valid and true regardless of the power setting. Your point of impact will not change as power is changed.

C. Range Work

1. Using your rifle, your ammo, your scope, check and confirm via live fire your zero at exactly 100 yards. It’s noteworthy to mention that many riflemen use a 2 or 300 yard zero.

Note: Using a 100 yard zero as an example to insure maximum accuracy, I strongly recommend you take a steel tape and confirm the distance is exactly 100 yards from rifle to target. Always check. Many rifle ranges are not measured to precisely 100 yards.

RIFLESCOPE THAT USE ADJUSTMENT KNOBS (CLICKING) FOR ELEVATION AND WINDAGE

Preparation for Accurately Employing HorusVision Aiming Solutions Software

A. Your Rifle

1. Make sure your rifle is in good operational condition. If you are not sure, have a competent gunsmith check your rifle.

2. Select the ammo that consistently shoots 1 MOA or less (preferably ½ MOA) at 100

yards (or meters).

3. Obtain accurate muzzle velocity value for your gun firing the ammo you selected. Muzzle velocity values are extremely important when shooting at extended ranges.

4. Zero your rifle.

B. Your Scope

1. Determine the calibrated value for the elevation and windage adjustment knobs. Is the value:

a. True minute of angle (where 1 MOA subtends 1/60 of a degree or exactly 1 inch

@ 95.5 yards).

b. Shooters minute of angle (where 1 MOA subtends exactly 1 inch @ 100 yards).

Warning: If you fail to identify the correct calibration (true minute of angle or shooters minute of angle) for your riflescope, you may have a 4.6 % error in your elevation. At extended ranges, the elevation error becomes significant. You will probably miss the target.

2. How many clicks are required to move the elevation and windage crosshair 1 MOA?

a. Most scopes require 4 clicks to move 1 MOA. b. Some scopes require from 2 to 8 clicks to move 1 MOA.

25 3. Variable Power Scopes

There are two basic types, they are first focal plane and second focal plane:

a. If your variable power scopes is in the first focal plane (objective plane), all elevation and windage adjustment clicks are valid regardless of the power setting and point of impact will not change.

Note: Most European and a few American scopes are in the first plane. A first plane scope can usually be identified by looking through the scope while changing the power. If the reticle changes size, the scope is in the first plane (objective plane).

b. If your variable power scope is in the second plane (ocular plane), the values

of your elevation and windage adjustment are not valid for all powers of your variable scope. When shooting at different powers, your point of impact will most likely change. To find the exact power setting where the calibration values of the adjustment knobs are valid and true, you must read your scope instruction manual, call the manufacturer, check the catalog, etc. The exact power setting is extremely important.

If your scope has Mil-DOTS, that exact power setting is extremely important when using Mil-DOTS to determine range. A wrong power setting will yield an incorrect answer for range. Warning: When long range shots are to be taken after the proper number of clicks have been dialed in for elevation and windage, you must be sure your vari-power adjustment is set to the correct power. Failure to use the correct power means your bullet could miss the target.

4. Fixed Power Scopes

All elevation and windage values are valid (simplest of all to use).

C. Range Work

1. Using your rifle, your ammo, your scope, check and confirm via live fire your zero at exactly 100 yards. It’s noteworthy to mention that many riflemen use a 2 or 300 yard zero. Once your zero is confirmed, set your elevation and windage adjustment knobs to zero. Note: Using a 100 yard zero as an example to insure maximum accuracy, I strongly recommend you take a steel tape and confirm the distance is exactly 100 yards from rifle to target. Always check. Many rifle ranges are not measured to precisely 100 yards.

2. Using live fire to check the accuracy of your riflescope by employing a predetermined series of elevation and windage adjustments in combination with live fire. a. For a target, find a piece of stiff cardboard approximately

24”x 24”. Place a small removable sticky dot at the center.

b. Your rifle, if possible, should be on a bench rest exactly 50 yards from the

target at approximately the same height. Measure the distance. Do not guess!

The example I am using will be for a riflescope that requires 4 clicks to move 1 MOA.

c. Shooting as accurately as you can. Shoot at the dot on the target. Since your gun is sighted in at 100 yards, your shot will be high, that is O.K. Label the impact point #1. Remove the sticky dot from the cardboard. From that point you must use the impact point of your first bullet to sight on as your target.

Dial --- 28 clicks up --- shoot --- Label #2 Dial --- 28 clicks right -- shoot ---- Label #3 Dial --- 28 clicks down -- shoot- --- Label #4 Dial --- 28 clicks left ---- shoot --- Label #5 (should be in hole #1) Dial --- 28 clicks left --- shoot --- Label #6 Dial --- 28 clicks down -- shoot --- Label #7 Dial --- 28 clicks right --- shoot --- Label #8 Dial --- 28 clicks up ----- shoot --- Label #9 (should be in hole #1)

Repeat the sequence above using 56 clicks.

d. Examine the target.

Remember, we are shooting at 50 yards (1/2 value for distance 1 MOA subtends). 1-2 9-10 2-3 10-11 3-4 11-12 4-5 should be 3 ½ inches 12-13 should be 7 inches 5-6 apart 13-14 apart 6-7 14-15 7-8 15-16 8-9 16-17

You should have fair neat squares if your scope is in proper calibration and functioning properly. e. Special Ultra Long Range

If you intend to engage targets beyond 800 yards, you should perform this test. Take a 1”x 8”x 8 foot board and draw a heavy line approximately ¾” wide down the length of the board in the center. 1) Place this target board in a vertical position exactly 100 yards from

the rifle that should be on a bench rest. Be sure you confirm the 100 yard distance by measuring. Use a level or plumb bob to insure the heavy line is perpendicular to the ground.

2) Approximately 1 foot from the bottom of the target board carefully

draw a thin horizontal line which can be easily seen in your rifle scope.

3) From the horizontal line upward, mark in a very light pencil the

following points 10-20-30-40 and 50 inch. You should not be able to view these horizontal lines in your scope.

4) Live fire – use three rounds for each point. Assume with your scope

that four clicks move vertical crosshair 1 MOA.

Using the intersection the vertical and horizontal lines as your target, fire three shots.

5) On Target

Dial 40 clicks up Total 40 clicks up Fire 3 shots = 10 inches Dial 40 clicks up Total 80 clicks up Fire 3 shots = 20 inches Dial 40 clicks up Total 120 clicks up Fire 3 shots = 30 inches Dial 40 clicks up Total 160 clicks up Fire 3 shots = 40 inches Dial 40 clicks up Total 200 clicks up Fire 3 shots = 50 inches

6) Check your target. Did your scope subtend the distance properly? You are ready for ultra long range shooting if your rifle and scope performed in an acceptable manner?

ENVIRONMENTAL DATA

1. The Aiming Solutions program offers two choices:

a. Altitude and temperature. Enough data for accurate shooting to 500 yards.

b. Barometric pressure, temperature and relative humidity. You have the highest probability of a first round hit with real time input of these weather perimeters.

2. Wind speed and direction.

You need real time accurate measurements for extended range shooting. Note: Weather perimeters can easily be measured by pocket style weather stations by Kestrel, Brunton, and others. In addition, there are a variety of wristwatches that are modestly priced that give weather data. The tooth fairy and California guesswork about weather perimeters and measurement does not cut it. Garbage in, garbage out.

D. Shooting Skills.

Practice, practice, practice.

A COMPLETE EXAMPLE

BASIC SET-UP FOR A RANGE CARD

GETTING STARTED

In order to achieve a high probability of long range hits with your first (1st) shot, the TRAG1S5 Aiming Point Program requires an accurate input of data from you about your gun/ammo, environmental conditions, etc. The first order of business is to fill out the Horus Vision Data Sheet. To help you input the data sheet information, I have put reference notations in this section. These notations should help answer questions you might encounter. I suggest you file this data sheet as a future reference along with computer printouts. Finally, I have included “a complete example” of how to … You can follow the entire procedure step by step. Warning: When the rifleman fails to input correct data and relies on Kentucky guesswork, the accuracy potential of the Horus Reticle decreases.

HORUSVISION DATA SHEET By: ____ ________ Date:___

My 300 WIN MAG Set-up for NorthernTerritory, Australia

Rifle ID: 1. Cartridge Identification 2. Atmospheric Information

a. 1) Altitude ------------------------------------------- ___ 2) Temperature--------------------------------------- ______

b. 1) Barometric Pressure ----------------------------- _______ 2) Temperature -------------------------------------- _______ 3) Relative Humidity ------------------------------- _______

c. Wind

1) Effective Cross Wind ----------------------------- _________2) Wind Direction from Firing Lane --------------- ________ (use the

3

3. Gun and Bullet Information

a. Muzzle Velocity ----------------------------------------- ____

b. Bullet Weight --------------------------------------------- _____

c. Ballistic Coefficient -------------------------------------- _____

d. Height of Scope ------------------------------------------ _____ 4. Lead

(No entry necessary if you are shooting at non-moving targets ex a. Target Speed ---------------------------------------------- _____ 4

(Moving 90º from line of fire)

_______Dennis

_____ Time:_____ 0

_

__

___

___cl

cl

_

X012345

8/21/

_________

__________ ______9

___________________________

_________________1

ock system)

_________

________

______

________

usively)

_________

11:00

_____

_ feet
_____1500 _ F __
_ in Hg _ ° F _ %

mph
_
_ ft/sec
_____2942
__ gr
____190
__
______0.533
inches
____1.9
_ mph
__

5. Targeting Grid Values in Yards or Meters (Circle One) 6. What is your Sight in Range (zero) --------------------- ___________________ 100

7. What is the Maximal Range You Intend to Shoot --- ___________________ 1500

OPTIONAL (For calculating values for Horus targeting grid for standard, hot and cold temperatures.) What is the coldest (average) temperature you intend to shoot your rifle?______ º F What is the muzzle velocity (average) of your bullets at that cold temperature?-----------------------------------------------------------______ ft/sec What is the hottest (average) temperature you intend to shoot your rifle? --------------------------------------------------------------------- _______ º F What is the muzzle velocity (average) of your bullets at that hot temperature? ---------------------------------------------------------- _____ ft/sec See worksheet section for masters of Horus data sheet for photocopying.

PROGRAM 1. Set-up

Illustrative example: my 300 Win Mag set-up for Australia’s Northern Territory. Computer Screen Shows:

Distance Display Results English ______________ Horus Reticle _____________ Metric ______________ Shooters MOA _____________

X X

True MOA _____________ Clicks _____________ Temperature C __________ Print Scope ______________ F __________ Print Range Card ___________ X X Print Number of copies __________ 4

Save Cancel Reference Notations: If you were developing a range card for your clicking scope that requires you to turn elevation and windage knobs for adjustment, you would enter a different set of perimeters in “Display Results”. Display Results Horus Reticle ____________

Shooters MOA ___________

* True MOA ______________ X

Clicks __________________ 4

* This is a graphic example – the entry depends on the perimeters of your scope.

2. Add/Edit Guns Computer screen shows: Name _________________________________________

Bullet Weight _________________________________________

Bore Ht. _________________________________________

300 WIN MAG FED GOLD

190

1.9

CI Bal Coef. _________________________________________

Sight in Range _________________________________________

Muzzle Velocity _________________________________________

.533

100 ds yar2942

Reference Notations: Gun and Bullet Information Muzzle Velocity is the velocity (speed) of the bullet as it leaves the barrel. It is also one of the most important pieces of data in the computation of the ballistic table which is a key to assigning real values to the Horus targeting grid. Personal chronograph work is the best way to obtain an accurate muzzle velocity number. All velocity measurement must be taken using the rifle you intend to use the Horus reticle with. The same rifle and bullet combination can produce different muzzle velocities. Temperature is the main culprit. Generally speaking, as the temperature increases the muzzle velocity increases.

An excellent resource for ballistics coefficients and standard muzzle velocities is a book called Ammo and Ballistics written by Bob Forker published by Safari Press Inc., phone number (714) 894-9080.

Height or Sight above Bore (ins)? The height of sight above bore is the exact measured distance between dead center of the rifle bore to dead center of the mounted rifle scope. The TRAG 1S5 Aiming Point program requires the unit of measure to be in inches.

For the illustrative example, I used the following data to demonstrate the simplicity and ease of use. 1. 1.9 inches Your sight in range? This is your choice. Select any sight in range (zero), you are comfortable working with. For the illustrative example, I used the following data to demonstrate the simplicity and ease of use.

1. 100 Note: For most cartridges, I recommend a 100 yard zero (or 100 meters). The rifleman must

locate a place to shoot safely whether at an established shooting range or an open space area. With my own steel tape, I personally measured the 100 yard distance to plus or minus ½ inch.

The primary step in setting-up the Horus reticle is a precise 100 yard zero (or 100 meters) with a group of 3 to 5 shots in a group of less than one inch.

If you are shooting magnum ammo or wildcat cartridges, the Horus Reticle can Accommodate any zero desired (i.e. 200, 300, 500, etc.).

3. Atmospheric Conditions Computer screen shows (right side center):

Calc. Method A B a. Altitude (feet) __________

Temperature (F) ____ ___

b. Temperature (F) __________ Barometric Press (in) __________ Relative Humidity __________ Reference Notations: Since I am calculating a range card for my 300 Wmethod A. “Method A” represents the average conditions I w Note: If you are not sure of the conditions, siconditions you might expect. The altitude of 1500 was taken from a Topo Map The temperature of 95˚ is based on my data from p Note: “Calc. Method B” is used exclusively when thesolution in the field. In the field, the rifleman Kestrel 4000 and a Palm hand computer loaded w The combination of the Horus riflescope, accuTRAG1S5 given the long range specialist real tim

1500
______________________
______________________
___95
______________________ ______________________ ______________________

in Mag for use in the Northern Territory, I used

ould expect to encounter during normal shooting.

mply print several Range Cards to reflect those

of the area I intend to shoot.

revious experience of hunting in that area.

rifleman needs to calculate a very precise firing must use a small weather station device like the ith TRAG1S5 software.

rate weather data, correct slope angle, etc., and e precise firing solutions.

4. Final Firing Position

Computer Screen Shows (right side – lower): Final Firing Position Wind Speed (mph) __________________________ 10

Wind from (o’clock) __________________________

Uphill/Downhill angle __________________________

Target Speed __________________________

Target Range __________________________

3

0

4

1500

Reference Notations: To develop a user friendly range card that is quick and easy to use, we enter the following: 1) Wind Speed:

We use 10 mph which is a simple number to calculate wind “hold points” for any of the 13 elevation line of the Horus Targeting Grid. For a 20 mph wind, I simply double the value of the calculated “hold point” at 10 mph. If the wind is blowing at 15 mph, I simply use a multiply of 1.5.

To make proper use of the range card in the field, I personally use a small battery powered meter to determine wind speed and a piece of survey ribbon to determine direction. The rifleman must have accurate information so he can determine the proper hold-off. Some experienced riflemen can read the wind visually quite accurately. Kentucky guesswork doesn’t cut mustard at extended ranges.

2) Wind from (o’clock)

We use 3 o’clock which is the full wind value. If the wind is from a “half value direction” simply cut the wind speed “hold point” in half. In other words, if the program call for two “hackmarks” to the left for a full value wind, move only one hackmark to the left for a wind of the same strength but blowing from a “half value” direction. If a 20 mph wind is blowing from a “half-value” direction, just use the calculated 10 mph wind hold point.

Clock System Courtesy of U.S. Army

What side of the Horus Reticle is used to correct for wind direction? - Wind from the left to the right – hold on the right. - Wind from the right to the left – hold on the left.

3) Leading a Moving Target

Lead When the target is moving, the rifleman must aim ahead of the target. The Theoretical Lead is a specific intercept point where the fired bullet will meet the moving target. The TRAG1S5 Ballistic Software Program in combination with the Horus Reticle allows the rifleman to easily and accurately plot the theoretical leads. All calculations and plot points are based on targets moving 90 degrees to the rifleman’s position.

The Horus Reticle’s uniform targeting grid allows TRAG1S5 Ballistic Aiming Program to calculate and give the targeting grid plot points for theoretical leads at various ranges. For the most useful information, I have TRAG1S5 aiming program calculate the lead of a target moving 4 mph. For an 8 mph moving target, I simply double the value of the grid plot points. Note: The actual lead required also depends upon some factors that are determined by the

actions of the shooter in firing the shot, and therefore cannot be predicted. These include the particular shooter’s human “reaction time” (time between the instant he decides to pull the trigger and the instant that the trigger is actually pulled), and also the “lock time” (time between sear release and firing-pin impact on the primer) of the particular rifle and the “action time” (time between firing-pin impact on the primer and exit of the bullet from the muzzle) of the load. The errors introduced by these unpredictable variables are minimized if the shooter uses the “sustained lead” technique of shooting at moving targets, and maintains a consistent “follow through”; the errors are maximized if the shooter attempts to “spot shoot” the target by taking aim at a fixed point ahead of the target and then pulling the trigger. *

* Commentary written by William Davis Target Speed or Lead:

We use 4 mph which is the speed of a walking man. I suggest you stick with 4 mph because that value is a good reference to judge speed. The TRAG1S5 Aiming Point Software gives the calculated “hold point” for a 4 mph lead for all 13 elevation lines of the Horus reticle. Target speed “hold points” represent a simple linear relationship. For an 8 mph moving target, we simply double the value of the calculated 4 mph “hold point”.

4) Target Range:

We use 1500 yards. The TRAG1S5 will calculate the elevation values for 13 lines of the Horus Targeting Grid. 1500 yards is a max for computer entry.

5) Uphill/Downhill Angle:

We use zero since we are calculating a range card for general use.

THE FINAL RESULT -- YOUR RANGE CARD

1. Make at least 4 copies.

a. Attach one to stock of rifle. b. One in your backpack. c. One in your front pocket. d. File copy (attach to data sheet)

VISUAL RANGE CARD

For the riflemen who is a visual learner

Many individuals like visual information. Personally, I am a visual person. I prefer information that is more visual than numeric. I find that I can personally shoot faster and more accurately using graphically drawn wind and lead values.

PERSONAL DIGITAL ASSISTANT A QUICK OVERVIEW

A PDA (Personal Digital Assistant) is simply a hand held computer with the same capacity as a desktop computer. It can be carried in your pocket, runs on batteries and can easily be taken into the field. Horus Vision has taken our desktop personal computer software, TRAG1S5 and reprogrammed it to run on a PDA. We call the PDA software ATRAG1 so it will not be confused with TRAG1S5. When precision is a must at long range, the rifleman now has a personal hand held computer with ATRAG1 software for use in the field. This combination allows the rifleman to enter real time environmental and target data. Within a split second the PDA computer is a firing solution for that moment. Data entry into the PDA with the ATRAG1 software is almost exactly the same as data entry for the desktop personal computer. Please review the sections of this manual that reference TRAG1S5. For operational instructions, a user manual is included with each PDA unit.

WORKSHEETS FOR THE HORUS RETICLE MASTERS FOR PHOTOCOPYING

HORUSVISION DATA SHEET By: ___________________ Date:________ Time:_____ Rifle ID: _______________ 1. Cartridge Identification 2. Atmospheric Information

a. 1) Altitude ------------------------------------------- __________________ feet 2) Temperature--------------------------------------- __________________ F

b. 1) Barometric Pressure ----------------------------- __________________ in Hg 2) Temperature -------------------------------------- __________________ ° F 3) Relative Humidity ------------------------------- __________________ %

c. Wind

3) Effective Cross Wind -------------------------------- ____________________ mph 4) Wind Direction from Firing Lane ------------------ ____________________ (use the clock system)

3. Gun and Bullet Information

e. Muzzle Velocity ------------------------------------------ ___________________ ft/sec

f. Bullet Weight --------------------------------------------- ___________________ gr

g. Ballistic Coefficient -------------------------------------- ___________________

h. Height of Scope ------------------------------------------- ___________________ inches

4. Lead (No entry necessary if you are shooting at non-moving targets exclusively) b. Target Speed ---------------------------------------------- __________________ mph

(Moving 90º from line of fire) 5. Targeting Grid Values in Yards or Meters (Circle One) 6. What is your Sight in Range (zero) --------------------- ___________________ 7. What is the Maximal Range You Intend to Shoot --- ___________________ OPTIONAL (For calculating values for Horus targeting grid for standard, hot and cold temperatures.) What is the coldest (average) temperature you intend to shoot your rifle?______ º F What is the muzzle velocity (average) of your bullets at that cold temperature?-----------------------------------------------------------______ ft/sec What is the hottest (average) temperature you intend to shoot your rifle? --------------------------------------------------------------------- _______ º F What is the muzzle velocity (average) of your bullets at that hot temperature? ---------------------------------------------------------- _____ ft/sec

PROGRAM 1. Set-up

Computer Screen Shows: Distance Display Results English ______________ Horus Reticle _____________ Metric ______________ Shooters MOA _____________ True MOA _____________ Clicks _____________ Temperature C __________ Print Scope ______________ F __________ Print Range Card ___________ Print Number of copies __________ Save Cancel Reference Notations: If you were developing a range card for your clicking scope that requires you to turn elevation and windage knobs for adjustment, you would enter a different set of perimeters in “Display Results”. Display Results Horus Reticle ____________ Shooters MOA ___________ * True MOA ______________ Clicks __________________ * This is a graphic example – the entry depends on the perimeters of your scope. 2. Add/Edit Guns

Computer screen shows: Name _________________________________________ Bullet Weight _________________________________________ Bore Ht. _________________________________________ CI Bal Coef. _________________________________________ Sight in Range _________________________________________ Muzzle Velocity _________________________________________ Reference Notations: Gun and Bullet Information Muzzle Velocity is the velocity (speed) of the bullet as it leaves the barrel. It is also one of the most important pieces of data in the computation of the ballistic table which is a key to assigning real values to the Horus targeting grid. Personal chronograph work is the best way to obtain an accurate muzzle velocity number. All velocity measurement must be taken using the rifle you intend to use the Horus reticle with. The same rifle and bullet combination can produce different muzzle velocities. Temperature is the main culprit. Generally speaking, as the temperature increases the muzzle velocity increases. An excellent resource for ballistics coefficients and standard muzzle velocities is a book called Ammo and Ballistics written by Bob Forker published by Safari Press Inc., phone number (714) 894-9080.

3. Atmospheric Conditions Computer screen shows (right side center):

Calc. Method A B a. Altitude (feet) ________________________________ Temperature (F) ________________________________ b. Temperature (F) ________________________________ Barometric Press (in) ________________________________ Relative Humidity ________________________________ Reference Notations: Since I am calculating a range card for my 300 Win Mag for use in the Northern Territory, I used method A. “Method A” represents the average conditions I would expect to encounter during normal shooting. Note: If you are not sure of the conditions, simply print several Range Cards to reflect those conditions you might expect. The altitude of 1500 was taken from a Topo Map of the area I intend to shoot. The temperature of 95˚ is based on my data from previous experience of hunting in that area. Note: “Calc. Method B” is used exclusively when the rifleman needs to calculate a very precise firing solution in the field. In the field, the rifleman must use a small weather station device like the Kestrel 4000 and a Palm hand computer loaded with TRAG1S5 software. The combination of the Horus riflescope, accurate weather data, correct slope angle, etc., and TRAG1S5 given the long range specialist real time precise firing solutions.

4. Final Firing Position

Computer Screen Shows (right side – lower): Final Firing Position Wind Speed (mph) __________________________ Wind from (o’clock) __________________________ Uphill/Downhill angle __________________________ Target Speed __________________________ Target Range __________________________

Reference Notations: To develop a user friendly range card that is quick and easy to use, we enter the following: 1) Wind Speed:

We use 10 mph which is a simple number to calculate wind “hold points” for any of the 13 elevation line of the Horus Targeting Grid. For a 20 mph wind, I simply double the value of the calculated “hold point” at 10 mph. If the wind is blowing at 15 mph, I simply use a multiply of 1.5. To make proper use of the range card in the field, I personally use a small battery powered meter to determine wind speed and a piece of survey ribbon to determine direction. The rifleman must have accurate information so he can determine the proper hold-off. Some experienced riflemen can read the wind visually quite accurately. Kentucky guesswork doesn’t cut mustard at extended ranges.

2) Wind from (o’clock)

We use 3 o’clock which is the full wind value. If the wind is from a “half value direction” simply cut the wind speed “hold point” in half. In other words, if the program call for two “hackmarks” to the left for a full value wind, move only one hackmark to the left for a wind of the same strength but blowing from a “half value” direction. If a 20 mph wind is blowing from a “half-value” direction, just use the calculated 10 mph wind hold point.

Clock System Courtesy of U.S. Army

What side of the Horus Reticle is used to correct for wind direction? - Wind from the left to the right – hold on the right. - Wind from the right to the left – hold on the left.

3) Leading a Moving Target

Lead When the target is moving, the rifleman must aim ahead of the target. The Theoretical Lead is a specific intercept point where the fired bullet will meet the moving target. The TRAG1S5 Ballistic Software Program in combination with the Horus Reticle allows the rifleman to easily and accurately plot the theoretical leads. All calculations and plot points are based on targets moving 90 degrees to the rifleman’s position.

The Horus Reticle’s uniform targeting grid allows TRAG1S5 Ballistic Aiming Program to calculate and give the targeting grid plot points for theoretical leads at various ranges. For the most useful information, I have TRAG1S5 aiming program calculate the lead of a target moving 4 mph. For an 8 mph moving target, I simply double the value of the grid plot points. Note: The actual lead required also depends upon some factors that are determined by the

actions of the shooter in firing the shot, and therefore cannot be predicted. These include the particular shooter’s human “reaction time” (time between the instant he decides to pull the trigger and the instant that the trigger is actually pulled), and also the “lock time” (time between sear release and firing-pin impact on the primer) of the particular rifle and the “action time” (time between firing-pin impact on the primer and exit of the bullet from the muzzle) of the load. The errors introduced by these unpredictable variables are minimized if the shooter uses the “sustained lead” technique of shooting at moving targets, and maintains a consistent “follow through”; the errors are maximized if the shooter attempts to “spot shoot” the target by taking aim at a fixed point ahead of the target and then pulling the trigger. *

* Commentary written by William Davis Target Speed or Lead:

We use 4 mph which is the speed of a walking man. I suggest you stick with 4 mph because that value is a good reference to judge speed. The TRAG1S5 Aiming Point Software gives the calculated “hold point” for a 4 mph lead for all 13 elevation lines of the Horus reticle. Target speed “hold points” represent a simple linear relationship. For an 8 mph moving target, we simply double the value of the calculated 4 mph “hold point”.

4) Target Range:

We use 1500 yards. The TRAG1S5 will calculate the elevation values for 13 lines of the Horus Targeting Grid. 1500 yards is a max for computer entry.

5) Uphill/Downhill Angle:

We use zero since we are calculating a range card for general use.

CONVERSION TABLES Temperature Conversion F = (Degrees C)(9) + 32 5 C = Degrees F-32 x 5 9 Barometric Pressure

1 hecto – pascal (hPa) = 1 millibars (mb) Speed Mph = (feet per sec) (0.6818)

Feet per sec = (miles per hour) (1.467) Knots per hour = (miles per hour) (0.8684) Kilometers per hour = (miles per hour) (1.609)

Length Centimeters = (inches) (2.54) Meters = (yards) (0.9144) Yards = (meters) (1.094) Centimeters = (feet) (30.48) Meters = (feet) (0.3048) Kilometers = (feet) (0.0003048) Centimeters = (yards) (91.44)

1 foot = 12 inches 1 yard = 3 feet 1 meter = 39.37 inches 1 yard = 36 inches 1 mile = 5,280 ft or 1,760 yards or 1.609 kilometers 1 nautical mile = 6,076.1155 feet

Temperature Considerations (at sea level) Degrees F Degrees C Boiling point of water 212 100 Very hot weather – heat wave 104 40 Average body temperature 98.6 37 Warm 86 30 Mild spring day 67 20 Warm winter day 50 10 Freezing point of water 32 0 Field Use 1 U.S. Quarter (25c) is approximately 1 inch in diameter 1 U.S. Penny (1c) is approximately ¾ inch in diameter 1 standard business card is approximately 3 ½ inches wide by 2 inches long. Trigonometry

SIN ∆ = X Z COS ∆ = Y Z TAN ∆ = X Y

Speed of Sound v = 1088 1 + c 273

v = velocity of sound c = temperature centrigrade Transonic range = starts at approximately 0.75 mach and extends to 1.20 mach

INFORMATION U.S.M.C. Milliradian (Mils) 6283 Mils = 1 circle 17.5 Mils = 1 degree 1 Mil = 3.438 MOA 1 Mil = covers exactly 3.60 inches @ 100 yards

1 Mil = covers exactly 100 mm @ 100 meters U.S. Army Milliradian 6400 Mils = 1 circle 17.8 Mils = 1 degree 1 Mil = 3.375 MOA 1 Mil = covers exactly 3.53 inches @ 100 yards Note: This is an approximate 2% error between the U.S. Army Mils and the USMC Mils. This

difference can be significant at extended ranges. (True) Minute of Angle (MOA) 1 MOA = 1/60th of a degree 1 MOA = covers or subtends exactly 1.047 inches at 100 yards 1 MOA = subtends 1 inch @ 95.5 yards (Shooters) Minute of Angle (MOA) 1 MOA = covers or subtends exactly 1.00 inch @ 100 yards Inch of Angle (IOA) = (shooters) minute of angle (MOA) 1 IOA = covers or subtends exactly 1.00 inch @ 100 yards Note: I personally use the term Inch of Angle (IOA) to avoid confusion with the term MOA. When using MOA, you must define exactly what an MOA is or you can pick up an error of 4.7%. This error can become significant when you are shooting at extended ranges.

TROUBLE SHOOTING

When you are not achieving the accuracy potential you desire, please check: 1. Zero:

Did you measure the distance from the rifle to the target with a steel tape. You absolutely must have an exact measured distance.

2. Muzzle Velocity:

Did you chronograph your ammo in the rifle you intend to shoot with in the field? Please read “A brief course in ballistics”. - Effect of ammunition temperature on muzzle velocity. - The elements of dispersion.

3. Scope Height:

Did you measure it properly. 4. Ammo:

Did you field test via live fire your ammunition’s ability to group at extended ranges? Because it can group at 100 or 200 yards, does not mean it will hold a group at 500, 700, 1000, etc., yards. If your bullets cannot group, I suggest you find a bullet that will hold a group at extended ranges.

5. Weather Data:

Are you entering real time weather data, or are you employing California guesswork with the help from the tooth fairy? Weather data is extremely important in extended range shooting. Garbage in – Garbage out.

6. Slope:

Are you accurately measuring the slope? When shooting at extended ranges even a small slope angle error can equate to a miss. If you want results don’t guess.

REFERENCES

Brown, Earl B. Basic Optics. New York: Stoeger Arms Corporation Carmichael, Jim. “What You See” Outdoor Life Magazine, Vol. 200, no. 5 (January 1998) Davis, William C. “TRAG1S2 Ballistic Software Program”. Wellsboro, PA Forker, Bob. Ammo & Ballistics. Long Beach, California: Safari Press Inc. Greener, W. W. Sharpshooting for Sport and War. New York: Truslove, Hanson & Comba Gregg, James. The Sportsman’s Eye. New York: Winchester Press. Maor, Eli. Trigonometric Delights. Princeton, N.J.: Princeton University Press. McBride, H.W. A Rifleman Went to War. Mt. Ida, AR: Lancer Militaria Michaelis, Dean. The Complete .50-Caliber Sniper Course. Boulder, CO: Paladin Press. Noblitt, Tony M. and Warren Gabrilska. Dead On. Boulder, CO: Paladin Press. Pejsa, Arthur J. Modern Practical Ballistics. Minneapolis: Kenwood Publishing. Plaster, John L. The Ultimate Sniper. Boulder, CO: Paladin Press. Rinker, Robert A. Understanding Firearm Ballistics. Corydon, IN: Mulberry House Publishing. Smith, T.D. TDS Tri-Factor. Oklahoma City: TDS Tri-Factor. Whelen, Townsend. Telescopic Rifle Sights. Onslow County, N.C.: Small Arms Technical Publishing.

Documents

Horus Vision - FOR INFORMATION OR SALES · 2020-04-16 · appointment of Mr. Davis as Engineering Project Manager for Colt Firearms Division of Colt Industries, in Hartford, Connecticut