Group

Manual ballistics

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The FM outlines our core skills, policies and guides to ensure every member stands ready for the mission ahead.

Manual ballistics, as opposed to assisted ballistics, is precision shooting without using various tools and gadgets (like the ATragMX) where the shooter is required to manually account for the various effects affecting the ballistic path of a bullet.

During its flight from muzzle to target, our bullet interacts with many forces - some seeming commonplace, with others appearing quite technical. Gravity, the spin of the planet, air density, firing angle and much more all alter the pathway of our bullets. When learning to navigate the many variables of a ballistic solution, care should be taken to remember that marksmanship is a goal-oriented practice. In other words, effects on target are the sole metric that determine how to best approach a situation.

Squad designated marksmen, who engage at moderate distances and are afforded follow up shots without consequence will find much more utility in rapid corrective shots than solving for the Coriolis effect. SF sniper teams, who must be able to guarantee an impact on a mission-critical target, will find solving for the finest of variables a necessity. Learning to navigate these ballistic variables in a practical and field expedient fashion, regardless of marksmanship application, is the distinguishing mark between a textbook ballistician and the highest echelon of effective marksmen.

Ballistic Components

Looking towards application purposes, the components of a thorough and complete ballistic solution can effectively be divided into three categories:

• Primary components affect bullet flight path so greatly that they must be accounted for by all, from SF sniper teams to riflemen.
• Secondary components become a necessity to solve for at extended distance, and are a mainstay of all sniper teams.
• Tertiary components only have a small effect on flight path, but become critical when shots must be guaranteed.

All components of a ballistic solution supported by UNITAF are listed below, grouped by category, and sorted from greatest effect to least:

*Indicates a component that only needs to be solved for under specific conditions.

Realism Where It Matters

It should be noted that the topics to be explored in Manual Ballistics only address the core needs of assembling ballistic solutions accurate enough for the listed applications of marksmanship. Most of these ballistic solution components have been simplified to the greatest extent possible, and where compounding considerations and peripheral concerns could be ignored, they have been intentionally excluded entirely. Looking towards the most rigorous applications of marksmanship available in UNITAF, most of these variables can be accounted for with even greater precision and reliability, should it be a topic of further interest.

Manual Ballistics can quickly paint itself as a complicated topic when presented with all components of a ballistic solution and all options to achieve them. Care should be taken to remember that marksmanship is a goal-oriented practice - in other words; effects on target are the metric by which our task is measured, not the method used to achieve them.

Whatever method is used to solve for the needed components of a ballistic solution, it is critical that that the method provides thorough, reliable and repeatable effects. Throughout this field manual group, we will be offering three methods to achieve the same goal, each with advantages, and each more attractive to a different audience.

Range card

Where sniper teams have existing data available to work off of (such as with a range card), this information can be used to make quick adjustments within the bounds of the data provided.. This method saves the need for more involved calculations and the time required for assembling custom D.O.P.E. - making for an easily accessible option.

It should be noted that although use of the provided range card is an attractive option, it cannot by itself accommodate for all aspects of a flight path, requiring use of D.O.P.E. or calculations to compliment the provided data where necessary. More critically, the data provided on the base range card is not accurate in all scenarios - maps with very high base invalidating all information provided entirely. As a final note, although range card use as a primary means where practical will avoid long commitments with preparation time or in-game calculation, it comes in no lead of its own - being neither the fastest option in operation, or the least cumbersome in preparation.

Calculation

Almost all variables in a bullets' flight path can indeed be accounted for with the use of formulas and calculations, many of which are far more simple than one would anticipate. Using calculations to assemble a ballistics solution is without comparison the most universal method available - there will never be a situation in which a ballistics solution can't be assembled with great reliability. This method is also the most repeatable, with no uncertainty in any component.

With great advantages in hand, it should be noted that calculation is frequently the slowest option available to spotters, most components of a flight path requiring an individual calculation. Although many of the formulas are surprisingly simple, some also turn away from the method before exploring the topic.

D.O.P.E.

Data On Previous Engagements, or D.O.P.E., provides the most hands-on option for individuals not inclined towards calculations. Gathering and recording targeted information on bullet impact provides a tremendously accurate picture of how a bullet will behave under different conditions and at varying distances. This method eliminates the need to account for (most) individual variables in a flight path, allowing spotters to record end products and repeat them with the greatest speed possible… under identical conditions.

D.O.P.E. as a method offers the most strength in precision and speed, however this method also comes with considerable preparation time, requiring spotters to shoot and record a complete set of information under the same atmospheric conditions anticipated in operation. Should these atmospheric parameters change, such as with another operation in a colder climate, the assembled D.O.P.E. can no longer be called upon for reliable and repeatable effects.

The range card provides ready access to some of the most frequently required information for placing measured shots at distance. The first and largest variable to account for in all ballistic solutions is bullet drop, or the effect of gravity on a bullet in flight over time. Auto-populated for your unique combination of rifle and optic in hand, the range card dedicates a majority of its data to accurately accommodating this first variable in a ballistic solution.

Using a range card

The coloured columns under the range card’s “Bullet Drop” section display different sets of adjustments to accommodate the effects of temperature on bullet drop. As temperature affects both muzzle velocity and air resistance, the differences between cold and warm climates can have a significant effect on how far a bullet will fall due to gravity at any given range. Be sure to have a rough estimate of the temperature in hand to help decide which temperature column to read.

With an appropriate temperature column picked out, all of the below values will display how far your bullet will drop for the given “Target Range”, found on the far left side of the sheet. These drop values are measured in milliradians, or MRAD. For example, a value of “-4.5” (reading the 15°C temperature column at a distance of 500m) describes that your bullet will fall 4.5 milliradians below your crosshairs at that distance. To counteract that negative drop value, we need to either hold the crosshairs 4.5 MRADs above the target, or dial our scope up 4.5 MRADs to bring the bullet impact back up to our crosshair level.

Advanced considerations

In a similar fashion, the range card also provides information for use with wind accommodation, engaging moving targets, and for calculations requiring general equipment information. This data, however, is seldom required in the opening marksmanship roles where simplicity encourages speed, and speed is our most valuable asset.

At the highest level of marksmanship roles, it should be noted that the populated BDA information is limited to temperature and equipment considerations only. Displayed drop values do not account for changes in altitude, pressure or humidity variables, as default Arma values are assumed. This under extreme conditions may compromise all drop, wind and moving target information, requiring manual data collection or calculation.

Accounting for bullet drop with Data On Previous Engagements (D.O.P.E.) provides options for field expedient and remarkably accurate adjustments to be made when the in game range card is rendered obsolete, or when shots must be taken at extended distances. Gathering the information required is a time consuming investment, however, those inclined towards this hands-on method are at an advantage as the details gathered will precisely account for the effects of temperature and air density, removing the need to independently account for these variables altogether.

Data collection

To assemble D.O.P.E. for bullet drop, targets must be placed at known distances. Shots should be taken at these preplaced targets, and the vertical adjustment that is needed to counteract bullet drop due to gravity should be recorded for the respective distances. This vertical adjustment is the information that will be used in operation to impact targets at distance.Note: even with no wind present, the bullet will drift increasingly to the left or right with distance - this drift is the product of spin drift and horizontal Coriolis working together. This information may easily be recorded alongside gathering D.O.P.E. for bullet drop.

Target Range	*Vertical Deflection*	Horizontal Deflection
400m	-2.6	0.1 R
450m	-3.1	0.1 R
500m	-3.7	0.1 R
550m	-4.4	0.1 R
600m	-4.9	0.1 R
650m	-5.5	0.1 R
700m	-6.5	0.2 R
750m	-7.3	0.2 R
800m	-8.0	0.2 R
850m	-8.9	0.3 R
900m	-9.8	0.3 R
950m	-10.8	0.4 R
1000m	-11.7	0.5 R

D.O.P.E. assembled by a sniper team using an M24 SWS

When collecting D.O.P.E. of any kind, it is critical that collection atmospherics match the operation atmospherics. In the case of measuring accurate vertical deflection, we will need a range environment with:

• The same bullets, rifle and scope that will be used in operation
• Wind turned off
• Weather matching operation conditions
• Altitude matching operation conditions
• Using a level firing range
• Shots only being taken facing directly north or south (to avoid Eötvös deflection)

These conditions can be easily achieved by collecting data on the map in use by the operation, by matching the date and time in the editor to the values set on the mission file, and ensuring wind is turned off. To obtain the date and time in use by the mission file, communication with the senior game master is required.

D.O.P.E. example

Sgt McShooty is deployed as a Spotter (Manual) on a Honeybadger. He ranges a priority target at 900m and has prepared D.O.P.E. for his engagements:

Target Range	Vertical Deflection	Horizontal Deflection
900m	-9.8	0.3 R

He recorded that he needed to adjust 9.8 mils up to impact at 900m, so he gives the sniper a vertical adjustment of 9.8 up, accounting for the effects of gravity, temperature and altitude simultaneously.

D.O.P.E. limitations

As with all instances of D.O.P.E., the data assembled is only accurate for the atmospherics in which it was recorded. When these factors change, such as with changes in temperature, altitude or humidity; our recorded information becomes increasingly inaccurate. With small atmospheric changes, such as with normal temperature fluctuations that are seen over the course of a 2 hour operation - adjustments to recorded data can be estimated with success. When larger changes occur, such as with an entirely different set of atmospherics on a separate operation entirely, adjustments to recorded data can no longer be reasonably inferred, and new D.O.P.E. must be assembled.

• Look up the vertical deviation caused by gravity using the range to target and a range card
• Integrate the calculated value into the final ballistics solution

Wind deflection is by a wide lead the most challenging topic in marksmanship, both to navigate conceptually and to accurately account for in field. While most variables in a ballistic solution can be corrected for with certainty and consistency, by nature wind is a dynamic force, making this topic the least predictable aspect of any long range shot. 

Accurate accounting of wind deflection requires not only an understanding of wind direction and speed at the firing position, but also an understanding of wind behavior at the target location and everywhere in between. Accounting for the effects of wind on our bullets trajectory is where science meets art - even ballistic computers fall very short of reliable when considering the full spectrum of wind variables on the path from rifle to target. Fortunately, UNITAF's environmental settings do not reproduce all variables present in real life wind, permitting the topic to be accessible and more predictable for the highest levels of marksmanship.

Variables

Direction and speed are the primary two variables to consider when factoring for wind. Although wind speed affects a bullet in a straightforward fashion (faster wind produces more deflection), wind direction has more complicated effects on the path of a bullet:

A wind from the left pushes the bullet to the right.

A wind from the right pushes the bullet to the left.

A wind from directly behind (tailwind) raises point of impact.

A wind from directly ahead (headwind) lowers point of impact.

These principles can be combined if the wind comes at a quartering angle; meaning a wind that blows from both behind and to the left can shift point of impact higher and to the right simultaneously.

The direction of wind will also influence how much of a winds “pushing power” is used to push a bullet left or right, and how much is used to raise or lower point of impact. For example;

A 4mps wind from 3 o'clock may deflect a bullet 2 mils to the left.

A 4mps wind from 4 o'clock may only deflect a bullet 1 mil to the right, but will also raise point of impact.

As a dynamic force

The variables of direction and speed are the only practical aspects of wind that can deflect a bullet at any given time. Accounting for these variables holistically is exceedingly difficult, however, as:

Wind speed may change at distance when obstructions are present.

Both wind speed and direction may change sporadically.

The most thorough and accurate wind solutions will include:

• Measuring and accounting for wind at the firing position
• Accounting for wind obstructions at all points in a flight path.

Relevance

Wind makes itself a relevant factor in all applications of marksmanship, the force having a much greater effect on a bullets trajectory than intuition would hold. Even wind speeds not yet fast enough to be felt on our faces can produce a point of impact shift large enough to produce an outright miss at distance. Especially when placed in the context of human targets, which are much less forgiving horizontally than they are vertically, wind must be accounted for by all - from SF Sniper teams engaging an HVT to riflemen on a conventional battlefield. The level of care that must be applied to account for all variables present in wind deflection, however, depends heavily on the application of marksmanship.

Although wind must be accounted for by anyone firing a rifle, the level of detail required when compensating varies by role.

Wind indicator

The in-game wind display can be activated with the default key bind: Shift + K. The indicator will appear in the top left of the screen and display information for both wind direction and wind speed. In a similar fashion to a soldier experiencing wind without any devices to precisely measure velocity and bearing - this indicator does not provide precise values or directions, only estimations. With an understanding of the systems and methods in use to display these estimates, information precise enough for marksmanship may be gathered for use.

Direction values

The wind indicator displays wind direction with an arrow, pointing towards the blow of the wind. The direction of the arrow, however, does not track very precisely - only updating the indicator once every 30°. Although a 30° margin of error is relevant considering how severely a moderate wind can deflect a bullet, the 30° direction brackets create 12 even display directions, making range card use with the wind indicator a simple task alongside the clock method.

Looking towards a more precise answer for long range marksmanship, we can find the exact values for wind direction by understanding the angle values at which the wind direction indicator changes. These values at which the arrow changes directions can be used to determine an exact wind bearing, for use with calculations.

Precise values attached to the wind indicator are diagramed below:

Above: A diagram of the wind indicator displaying precise values for direction shifts.

Wind indicator

The in-game wind display can be activated with the default key bind: Shift + K. The indicator will appear in the top left of the screen and display information for both wind direction and wind speed. In a similar fashion to a soldier experiencing wind without any devices to precisely measure velocity and bearing - this indicator does not provide precise values or directions, only estimations. With an understanding of the systems and methods in use to display these estimates, information precise enough for marksmanship may be gathered for use.

Beaufort scale

The in-game wind indicator displays wind speed using wind “force” levels of the Beaufort scale. The force levels are represented with corresponding numbers of dots under the direction indicator, alongside color changes for each force level. The wind speeds corresponding to the Beaufort force levels (in meters per second) are detailed below:

Limitations

Measurements using the Beaufort scale come with a very relevant degree of error when applied to marksmanship. In the instance of two dots, or a Beaufort wind force of two, the difference between 1.5mps and 3.2mps can produce a miss by a wide margin at distance. This degree of uncertainty makes wind the largest challenge to accurately accommodate in manual marksmanship, and in many instances, will determine which shots can no longer be guaranteed.

Although this inherent error cannot be mitigated without instruments capable of providing a precise reading, we may better understand where precisely the wind speed falls after observing the degree of shot deflection. Should a “discovery” shot not me permissible, such as in the case of an SF Sniper Team, hit probability may be increased with error-accommodating techniques such as Four Corners or engaging with multiple weapon systems.

Above: The wind indictor displaying a 9 o'clock wind at 1.5 - 3.2mps

Method

Obtaining a precise horizontal wind adjustment from our range card requires a two step process:

1. Scaling the range card wind values to match the current wind speed
2. Adjusting the scaled wind values for the wind direction

This simplistic take on wind deflection comes with notable limitations, but in hand with simplified UNITAF server settings, serves very well as a baseline method.

Adjusting for wind speed

The range card provides deflection values for wind speeds of 4 meters per second. As the degree of wind deflection experience is affected by temperature, three temperature columns are populated:

Target Range	Bullet Drop (MRADs)									*4mps Wind (MRADs)*
(in meters)	-15°C	-5°C	5°C	10°C	15°C	20°C	25°C	30°C	35°C	-15°C	10°C	30°C
400m	-3.0	-3.0	-2.9	-2.8	-2.7	-2.6	-2.5	-2.4	-2.3	1.1	1.0	0.8
450m	-3.7	-3.6	-3.5	-3.4	-3.4	-3.3	-3.1	-3.0	-2.9	1.3	1.1	1.0
500m	-4.5	-4.4	-4.2	-4.1	-4.0	-3.9	-3.8	-3.6	-3.5	1.4	1.3	1.1
550m	-5.3	-5.2	-5.0	-4.9	-4.8	-4.6	-4.5	-4.3	-4.1	1.6	1.4	1.2
600m	-6.2	-6.0	-5.8	-5.7	-5.6	-5.4	-5.2	-5.0	-4.8	1.8	1.6	1.4
650m	-7.2	-7.0	-6.7	-6.6	-6.4	-6.2	-6.0	-5.8	-5.5	2.0	1.8	1.5
700m	-8.3	-8.0	-7.7	-7.5	-7.3	-7.1	-6.9	-6.6	-6.3	2.3	2.0	1.7

An in-game range card excerpt using an M24 SWS

If wind conditions in operation are greater or smaller than the 4mps benchmark, we will need to scale the deflection values accordingly. Because wind deflection scales linearly, adjusting values to match target wind speeds is a simple task.

Operation Wind Speed	Range Card Value Multiplier
1mps	x0.25
2mps	x0.5
3mps	x0.75
4mps	x1 (no adjustment needed)
6mps	x1.5
8mps	x2

Adjustments for range card wind values using linear scaling.

Adjusting for wind direction

Wind direction will also affect how far our bullet is deflected by the wind. A 90° crosswind permits the full force of the wind to deflect our bullet path horizontally, while quartering winds deflect our bullets less - even with wind velocity unchanged. The range card lists deflection values for a full crosswind, so these values must be reduced for wind directions other than 3 and 9 o'clock:

Direction	Deflection Multiplier
12 o'clock	x0 (no horizontal deflection)
1 or 11 o'clock	x0.5
2 or 10 o'clock	x0.87
3 or 9 o'clock	x1 (no adjustment needed)
4 or 8 o'clock	x0.87
5 or 7 o'clock	x0.5
6 o'clock	x0 (no horizontal deflection)

Adjustments for determined wind values using trigonometric scaling.

Example

Sgt McShooty is deployed as a Spotter (Manual) on a Honeybadger. He ranges a priority target at 700m. The wind is blowing from 2 o'clock at a speed of two dots (1.5~3.2mps). He uses the 10°C column on his range card to find his starting wind value:

Range Card: a 4mps wind @ 700m = 2.0 MRADs

• Wind Speed: 2.0 MRADs x0.5 = 1.0 MRADs 
• Direction: 1.0 MRADs x0.87 = 0.9 MRADs

Because the wind is from the 2 o'clock direction, the bullet will deflect 0.9 MRADs to the left due to wind deflection.

Limitations

This method of wind accommodation only accounts for wind conditions at the firing position. Although wind direction is persistent across the entire map with UNITAFs server settings, wind speed may be altered down range due to obstructions and terrain features, decreasing horizontal deflection.

As with all methods that rely on the range card, any conditions that invalidate the populated data on the range card, such as maps with very high base altitudes, will also invalidate the wind deflection information.

• Calculate the horizontal deviation caused by the wind using the Beaufort scale and range card values or comparable methods
• Integrate the calculated value into the final ballistics solution

Introduction

A moving target poses one of the largest challenges available for placing accurate and reliable shots on target, frequently determining which shots are possible, and which are not. The presence of a moving target not only requires all typical components of a ballistic solution to be addressed with accuracy, but it also requires n precise target lead - which can frequently be a very large value at typical distances, leaving little room for error. In addition to the need to solve for target lead, the limited exposure of a moving target means that all considerations must be put in place on a time limit. For these reasons, accurately and deliberately accounting for moving targets marks a core 

Fortunately, humanoid targets move at a small number of set speeds in Arma 3, allowing the informed marksman to turn educated guesswork into precision solutions capable of first round impacts.

Variables

From the perspective of a marksman, the largest considerations for moving targets are target speed and time available. A sniper team who is given plenty of time at an FFP will find much more success and speed with pre-calculating moving target holds than a sniper team who is surprised by a moving target and needs to act quickly. On the other hand, a sniper team who is preparing to ambush a convoy without a known speed will not be able to calculate a precision hold and will have to rely on alternative methods.

Understanding your targets and environment will inform the best method for addressing moving targets

Relevance

The very large adjustments needed for accurate shot placement requires that moving targets must be accounted for by all - from SF sniper teams engaging an HVT to rifleman shooting at short distances. The level of care that must be applied to selecting a method appropriate for the engagment range, however, depends heavily on the application of marksmanship.

Although moving targets must be accounted for by anyone firing a rifle, the appropriate methods vary by role.

Method

When the opportunity to calculate moving target holds ahead of time is not available to a sniper team, when the speed of a target is unknown, or when moving targets present spontaneously, the speed of deliberate estimation becomes a necessity. 

To obtain a reliable and repeatable hold value, we only need to know our time of flight. With our bullets travel time in hand, we can measure how many MRADs our target travels within the flight time, and hold over by the measured amount.

Data collection

Time of flight can be found in the ATragMX under the “RC” button in the top right of the screen or derived in an online ballistics program. As the ATragMX suite is not available in situations where manual ballistics are relevant, time of flight information should be recorded prior to operation start.

Example

Sgt McShooty is deployed as an Spotter (Manual) on a Honeybadger. Without warning, a moving target presents itself at a known distance of 800m, a shot that will have a time of flight of 1.5s.

He sets a timer to count down from 1.5s, and presses “start” when the target is in the center of his crosshairs:

In those 1.5s, the target traveled 5.6 MRADs from the start point.

Because target is moving from left to right, he tells his sniper to adjust 5.6 MRADs to the right, into the direction of travel.

Limitations

This method has the potential to provide a remarkably accurate hold value for moving targets. It should be noted, however, that the hold values are only as precise as the person employing them. 

For those using timed estimation, it is highly recommended to practice and grow comfortable reading MRAD values on the cue of a timer.

Equation

To manually calculate horizontal hold for moving targets, we will need to know:

• Target distance
• Target speed
• The time of flight for our bullet

(Target Speed / Distance) * Time of Flight * 1000 = Horizontal Lead in MRADs

Data collection

Time of flight can be found in the ATragMX under the “RC” button in the top right of the screen or derived in an online ballistics program. As the ATragMX suite is not available in situations where manual ballistics are relevant, time of flight information should be recorded prior to operation start.

Human targets in Arma 3 only have a few predetermined movement speeds to utilize. Common speeds for human targets are listed below:

Calculation example

Sgt McShooty is deployed as a Spotter (Manual) on a Honeybadger. He ranges a priority target at 800m, a shot that will have a time of flight of 1.5s. The target is moving in Combat Pace with his gun up.

(3 / 800m) * 1.5s * 1000 = 5.6 MRADs

Because target is moving from left to right, he tells his sniper to adjust 5.6 MRADs to the right, into the direction of travel.

Equation limitations

This equation only provides a pinpoint accurate solution for targets that are moving perfectly perpendicular to the shooter. When a target moves at an angle, its horizontal velocity is in effect decreased, meaning the listed values will overestimate the target lead. 

When targets do not move perpendicular to the shooter, decrease the output of this equation.

It should also be noted that although this equation provides great accuracy for leading moving targets, working through the math will only be practical when sniper teams have the opportunity to prepare hold values for moving targets ahead of time, to be utilized when targets present themselves. It should also be noted that when the target speed is unknown, this method cannot be utilized.

When values for moving targets cannot be calculated ahead of time, use a method of deliberate estimation.

• Use timed estimation to determine horizontal lead values to accurately engage moving targets, or calculate using an appropriate method.
• Integrate the calculated value into the final ballistics solution

When flying towards a target, our oblong bullets spin at nearly 300,000 rotations per minute to resist tumbling through the air and remain stable on its axis of flight. Although this tremendously fast spin is necessary to make precise and accurate shots at distance, this rotation complicates a bullets trajectory downrange, making spin drift one of the most complex topics to accurately represent in marksmanship. This stabilizing spin not only keeps our bullet stable, it elevates the nose of our bullet away from our rifle bore and above its flight arc, it creates differences of pressure on all sides of our bullet, and it even alters the direction our bullet points in flight towards its direction of spin. This final point, the change in bullet direction on account of its spin, is known as gyroscopic drift, or more commonly as spin drift. Spin drift creates substantial horizontal deflection at distance and becomes a key component of an accurate ballistics solution beyond the opening applications of marksmanship.

Variables

The direction of deflection on account of spin drift is dependent on direction of the barrel rifiling. Most barrels use a right hand twist, creating a significant deflection to the right at distance. In the uncommon scenario in which a rifle utilizes left hand twist rifiling, an equal degree of deflection on account of spin drift would be witnessed to the left.

Although atmospheric conditions do play a small factor in the degree of spin deflection, these are negligible for most manual ballistics scenarios, leaving time of flight and distance as our only other variables to consider.

Relevance

Spin drift is best classified as a secondary variable, producing a much smaller effect than bullet drop due to gravity or (typically) horizontal deflection due to wind. Beyond these two primary variables, spin drift produces our next largest deflection, and should be an integral part of all ballistics solutions in the context of sniper teams. If left unaccounted for, spin drift may produce a miss beyond 800m on its own and earlier if compounded with inaccuracies in other variables.

Above: A diagram detailing an altered bullet angle as a product of rotation - the primary cause of spin drift

Equation

To manually calculate spin drift, we only need to know the distance of our shot and how long our bullet will be in flight.

((SG * Time of Flight ^ 1.83) / Distance) * 1000 = Spin Drift in MRADs

The variable “SG” is the stability factor of our projectile, considering many details of rifle and bullet construction. This information will be provided for commonly used rifle and bullet combinations in a chart below.

Data collection

Time of flight can be found in the ATragMX under the “RC” button in the top right of the screen or derived in an online ballistics program. As the ATragMX suite is not available in situations where manual ballistics are relevant, time of flight information should be recorded prior to operation start.

SG or Stability Factor is provided below for common combinations of rifles and projectiles for campaigns that utilize manual ballistics. Note that the following SG values have been further modified to simplify the initial equation:

Calculation example

Sgt McShooty is deployed as a Spotter (Manual) on a Honeybadger. He ranges a priority target at 900m, a shot that will have a time of flight of 1.8s. His sniper is using M118LR ammunition for this shot.

((.0759 * 1.8 ^ 1.83) / 900) * 1000 = .25 MRADs

Because the rifiling of the M24 SWS barrel twists to the right, the bullet will deflect .25 MRADs to the right due to spin drift.

Equation limitations

This equation serves tremendously in almost all circumstances, with very little inherent error included in the calculations, even within extended operating ranges.

It should be noted that the "Modified SG" values provided do include atmospherics as a part of the calculations as air resistance does affect spin drift deflection over distance. When these provided values were assembled, default Arma 3 values of 15°C & 1013 milibars of pressure were assumed. Only when operations require the effects of a single shot to be guaranteed, and when atmospheric conditions deviate from default values significantly, a new modified SG value should be assembled.

If the effects of a shot must be guaranteed and atmospherics vary greatly from default values, a new modified SG value should be assembled.

Accounting for spin drift with D.O.P.E. is the most simplistic method available and by far the fastest to make use of in operation. Gathering the information required is indeed a more time consuming investment than preparing calculations, however, those inclined towards this hands-on method are at an advantage as the details gathered account for both horizontal spin drift and horizontal Coriolis simultaneously - eliminating the need to consider both individually when assembling a ballistic solution.

Data collection

To assemble D.O.P.E. for spin drift deflection (and horizontal Coriolis), targets must be placed at known distances. A vertical adjustment should be applied to allow shots impact the center of the targets, but no horizontal adjustment should be used initially. With no horizontal adjustment applied, the bullet will stray increasingly to the left or right of the target center with distance, even with a well placed shot. This horizontal deflection is the end product of spin drift and horizontal Coriolis working together, and by how far our bullets stray for the target distance is the information we will use in operation.

Target Range	Vertical Deflection	*Horizontal Deflection*
400m	-2.6	0.1 R
450m	-3.1	0.1 R
500m	-3.7	0.1 R
550m	-4.4	0.1 R
600m	-4.9	0.1 R
650m	-5.5	0.1 R
700m	-6.5	0.2 R
750m	-7.3	0.2 R
800m	-8.0	0.2 R
850m	-8.9	0.3 R
900m	-9.8	0.3 R
950m	-10.8	0.4 R
1000m	-11.7	0.5 R

D.O.P.E. assembled by a sniper team using an M24 SWS

When collecting D.O.P.E. of any kind, it is critical that collection atmospherics match the operation atmospherics. In the case of measuring accurate horizontal deflection, we will need a range environment with:

• Latitude matching the operation map used
• Altitude matching the operation map used
• Weather matching operation conditions
• Wind turned off
• The same bullets, rifle and scope that will be used in operation

These conditions can be easily achieved by collecting data on the map in use by the operation, by matching the date and time in the editor to the values set on the mission file, and ensuring wind is turned off. To obtain the date and time in use by the mission file, communication with the senior game master is required.

D.O.P.E. example

Sgt McShooty is deployed as a Spotter (Manual) on a Honeybadger. He ranges a priority target at 900m and has prepared D.O.P.E. for his engagements:

Target Range	Vertical Deflection	Horizontal Deflection
900m	-9.8	0.3 R

He recorded that his bullet hit 0.3 mils to the right at 900m, so he gives the sniper a horizontal adjustment of 0.3 to the left, accounting for the effects of both spin drift and horizontal Coriolis.

D.O.P.E. limitations

As with all instances of D.O.P.E., the data assembled is only accurate for the atmospherics in which it was recorded. When these factors change, such as with changes in temperature, altitude or humidity; our recorded information becomes increasingly inaccurate. With small atmospheric changes, such as with normal temperature fluctuations that are seen over the course of a 2 hour operation - adjustments to recorded data can be estimated with success. When larger changes occur, such as with an entirely different set of atmospherics on a separate operation entirely, adjustments to recorded data can no longer be reasonably inferred, and new D.O.P.E. must be assembled.

• Use observed correlation and/or recorded data to estimate the horizontal deviation caused by spin drift, or calculate using an appropriate method
• Integrate the calculated value into the final ballistics solution

Shooting at an angle introduces another factor to a ballistic trajectory: gravity's subtle defiance.

Contrary to a novice expectation, an angled shot at a target both above or below the shooter will always impact high.

Inclined shooting matters because the angle of the shot alters gravity's influence on the bullet. When shooting uphill or downhill, gravity's pull splits into a horizontal and a vertical component, causing the bullet trajectory to deviate from one shot level. This happens because gravity acts perpendicular to the Earth's surface towards the centre, not simply into, e.g. a mountainside. Therefore, a shot aimed high or low will have gravity ‘pull’ more on the velocity of the projectile (i.e. from the tip or tail of a bullet) rather than the path (i.e. down the side of the bullet). 

In effect, the bullet's trajectory will be shorter in the vertical plane, resulting in a higher point of impact.

This effect starts out subtle, but while you might intuitively ‘just hold down a little’ for small changes in angle at short to medium distances, you must employ more rigorous techniques for success at greater variations.

Rifleman's Rule, aka ‘map distance’

A first step to understanding the problem is to look at a simplified solution.

The Rifleman's Rule states that any shot should be adjusted as if it was the purely horizontal distance to target - like a ruler on the map.

What is the horizontal distance? It's the cosine of the incline multiplied by slant range.

Given a target that is 500 metres away, but at a 20° incline, this distance is the slant range. It discounts the angle, because it's line of sight. A laser rangefinder would show this value.

So, horizontal distance: cos(20°) x 500 m = 469 m

This difference can be significant, so you better account for it.

Problems with the Rifleman's Rule

Out to 500 metres and below 20° inclination, the Rifleman's Rule will get you results. Not pinpoint accurate, but better than nothing.

The trouble is, it ignores all bullet drag.

The further you shoot and the more you angle the gun, the more it breaks down. You'll still hit the vital zone at 500 m and 15°, but take it out to 600 m and 20°, you will likely miss.

A better solution

The follow-up guide FM/BG-455 - Inclined shooting: calculation presents a method several times more accurate with only one additional step. 

Rather than accounting purely for distance, it uses the already known bullet drop adjustments from the range card. The drag factor is inherited from there, then a minor adjustment is made to catch any error.

With it, even out to 1000 m and 50°, you will make centre mass shots look effortless.

Equation

To manually calculate inclination adjustment, we only need to know our typical bullet drop for the target distance and our angle of fire:

BDA * cos(angle°) - (.01 * angle°) = Adjusted vertical hold in MRADs

Where:

• BDA = bullet drop adjustment

Data collection

Angle of fire can be determined by opening the in-game firing angle indicator using Shift+Ctrl+K. Unadjusted bullet drop information can be found on the in game range card or collected prior to operation start as D.O.P.E.

Calculation example

Sgt McShooty is deployed as a Spotter (Manual) on a Honeybadger. He ranges a priority target at 900m with an inclination of 20°. Looking at his range card, he notes he would typically need to adjust 9.8 MRADs up for this range.

9.8 * cos(20°) - (.01 * 20) = 9.0 MRADs

The adjusted vertical hold for 20° of inclination is 9.0 MRADs.

Equation limitations

This equation will serve well under most conditions and the small degree of inherent error will not impede operations in target rich environments or in high value target environments.

• Calculate the vertical deviation caused by the inclination between the firing position and the target value using [the Better-Improved Rifleman’s Rule equation] or comparable methods
• Integrate the calculated value into the final ballistics solution

On its path around the Sun, our planet rotates on its axis at a staggeringly fast constant speed - and all things in contact with the planet spin along with it. A vehicle in motion, a cyclist at rest, even a rooted tree all spin along with the planet as they are in direct contact with the Earth. When an object separates from the planet, such as a ball being tossed into the air, this inherited rotational velocity gradually begins to decrease as the object in flight meets air resistance while no longer being propelled by contact with the spinning Earth. As observed from our constantly rotating rifles, this gradual loss of rotational velocity shows itself when a bullet in flight begins to rotate around the earth slower than our scopes and appear to drift to the left or right on its way to the target. We call this relative motion the Coriolis effect.

Variables

Both the direction and the magnitude of horizontal Coriolis deflection will change according to global position. As we move closer to either the North or South pole (as latitude increases), horizontal Coriolis deflection will also increase, with the most extreme effect being observed directly on either geographic pole. As we move away from the poles and towards the equator (as latitude decreases), horizontal deflection also decreases, with horizontal Coriolis deflection being entirely absent directly over the equator. Direction of deflection is dependent on which hemisphere a projectile is in, deflecting to right in the northern hemisphere and to the left in the southern.

Relevance

The Coriolis effect produces a relatively small effect on our bullets’ trajectory when compared to primary variables such as bullet drop and wind, or even secondary variables like spin drift. In the opening applications of marksmanship where speed is key, Coriolis deflection is well accounted for by a fast and measured follow up shot in response to any misses. In more advanced applications of marksmanship, where precision becomes precedent and greater ranges more common, Coriolis will become a relevant variable to factor into a firing solution - the effect producing tangible point of impact shifts between 800 and 1000m.

Above: A horizontal Coriolis force diagram, detailing both direction and magnitude

Equation

To manually calculate horizontal Coriolis deflection, we only need to know the latitude of our position and how long our bullet will be in flight:

cos(latitude°) * (Time of flight in seconds) * .072 = Horizontal deflection in MRADs

Where:

• positive outputs = right deflection
• negative outputs = left deflection

Data collection

Time of flight can be found in the ATragMX under the “RC” button in the top right of the screen or derived in an online ballistics program. As the ATragMX suite is not available in situations where manual ballistics are relevant, time of flight information should be recorded prior to operation start.

Map latitude in Arma 3 does not always correlate with real word locations, rather this information is manually populated by map makers and is persistent for an entire map. Latitudes for common UNITAF campaigns are listed below:

Calculation example

Sgt McShooty is deployed as a Spotter (Manual) on a Honeybadger. He ranges a priority target at 900m, a shot that will have a time of flight of 1.8s.

cos(35°) * (1.8s) * .072 = .11 MRADs

Because the output is a positive value, the bullet will deflect .11 MRADs to the right due to horizontal Coriolis.

Equation limitations

This equation will serve well under most conditions and the small degree of inherent error will not impede operations in target rich environments.

In high value target environments, or when the effects of a single shot must be guaranteed, it should be noted that this equation does not take into account the complicating factors caused by atmospheric conditions. Under extreme circumstances, this can create a small degree of error which may become relevant when factored alongside other unknowns. In general, this equation overestimates the effects of horizontal Coriolis deflection, between .02 - .04 MRADs at typical distances up to 1000m. This error increases as distance increases.

If the effects of a shot must be guaranteed, decrease the equation output as distance increases.

Introduction

Accounting for horizontal Coriolis force with D.O.P.E. is the most simplistic method available and by far the fastest to make use of in operation. Gathering the information required is indeed a more time consuming investment than preparing calculations or extrapolations, however, those inclined towards this hands-on method are at an advantage as the details gathered account for both horizontal Coriolis deflection and spin drift simultaneously - eliminating the need to consider both individually when assembling a ballistic solution.

Data collection

To assemble D.O.P.E. for horizontal Coriolis deflection (and spin drift), targets must be placed at known distances. A vertical adjustment should be applied to allow shots impact the center of the targets, but no horizontal adjustment should be used initially. With no horizontal adjustment applied, the bullet will stray increasingly to the left or right of the target center with distance, even with a well placed shot. This horizontal deflection is the end product of horizontal Coriolis and spin drift working together, and by how far our bullets stray for the target distance is the information we will use in operation.

Target Range	Vertical Deflection	*Horizontal Deflection*
400m	-2.6	0.1 R
450m	-3.1	0.1 R
500m	-3.7	0.1 R
550m	-4.4	0.1 R
600m	-4.9	0.1 R
650m	-5.5	0.1 R
700m	-6.5	0.2 R
750m	-7.3	0.2 R
800m	-8.0	0.2 R
850m	-8.9	0.3 R
900m	-9.8	0.3 R
950m	-10.8	0.4 R
1000m	-11.7	0.5 R

D.O.P.E. assembled by a sniper team using an M24 SWS

When collecting D.O.P.E. of any kind, it is critical that collection atmospherics match the operation atmospherics. In the case of measuring accurate horizontal deflection, we will need a range environment with:

• Latitude matching the operation map used
• Altitude matching the operation map used
• Weather matching operation conditions
• Wind turned off
• The same bullets, rifle and scope that will be used in operation

These conditions can be easily achieved by firing and collecting data on the map in use by the operation, by matching the date and time in the editor to the values set on the mission file, and ensuring wind is turned off. To obtain the date and time in use by the mission file, communication with the senior game master is required.

D.O.P.E. example

Sgt McShooty is deployed as a Spotter (Manual) on a Honeybadger. He ranges a priority target at 900m and has prepared D.O.P.E. for his engagements:

Target Range	Vertical Deflection	Horizontal Deflection
900m	-9.8	0.3 R

He recorded that his bullet hit 0.3 mils to the right at 900m, so he gives the sniper a horizontal adjustment of 0.3 to the left, accounting for the effects of both horizontal Coriolis and spin drift.

D.O.P.E. limitations

As with all instances of D.O.P.E., the data assembled is only accurate for the atmospherics in which it was recorded. When these factors change, such as with changes in temperature, altitude or humidity; our recorded information becomes increasingly inaccurate. With small atmospheric changes, such as with normal temperature fluctuations that are seen over the course of a 2 hour operation - adjustments to recorded data can be estimated with success. When larger changes occur, such as with an entirely different set of atmospherics on a separate operation entirely, adjustments to recorded data can no longer be reasonably inferred, and new D.O.P.E. must be assembled.

• Calculate the horizontal deviation caused by the Coriolis effect using [the Horizontal Coriolis Force equation] or comparable methods
• Integrate the calculated value into the final ballistics solution

Our planet rotates on its axis from the West to the East, which as many will recognize, creates horizontal deflection for bullets in flight, known as the Coriolis effect. Under the right conditions, this same rotation can also create a vertical deflection, becoming a relevant component of ballistic solutions assembled for top ranges.

Variables

When accounting for vertical Coriolis deflection (or the Eötvös effect), our latitude will have the same effects on the magnitude of deflection, but now direction will become a relevant variable too:

When firing to the East, our bullet travels in the same direction as the planet spins. Although our projectile will begin to move independently from the rotation of the planet when it leaves our barrel, the target will not, still being firmly rooted to the Earth. As the bullet loses its velocity inherited from the planets’ rotation, but the target does not, the target will begin to move further away and lower (along the curvature of the earth) from our bullet in flight. This relative lowering of the target raises our point of impact.

When firing towards the East, point of impact will be higher

When firing to the West, the opposite is true. As our projectile flies against the rotation of the planet, the target will maintain its Eastward velocity, moving closer and higher (along the curvature of the earth) towards out bullet. This relative raising of the target lowers our point of impact.

When firing towards the West, point of impact will be lower

It should be noted that there will be no vertical deflection when firing directly North or South, as our target is only in relative motion from West to East as a product of global rotation.

When firing either straight North or South, there will be no vertical deflection

Between our Northern & Southern directions where there is no vertical deflection, and our Eastern & Western directions where we experience maximum vertical deflection, we have many scenarios in which our bullet will experience only a portion of the full deviation value.

Relevance

The Eötvös effect may best be classified as a tertiary consideration. Considering that human targets are much taller than they are wide - we are given enough flexibility in target rich environments to still meet great effectiveness without factoring for this additional variable. 

In high value target environments, or when shots are directed mostly to the East or West, the Eotvos effect can become an important variable to consider - potentially displacing a bullet by as much as horizontal Coriolis can at maximum values. In either instance, accounting for Eötvös can allow a greater degree of error in our ranging estimates without producing a miss, increasing hit probability should time permit.

Above: When firing to the west (against the spin of the earth) our target appears to rise along the curvature of the planet, lowering point of impact.

Method

When Eötvös accommodation becomes a practical need (such as with an SF Spotter in a HVT environment), calculation may be avoided in most cases involving human-sized targets without compromising reliable shot placement.

In these instances, estimated corrections are most effectively communicated with hold off values, or designating altered points of aim.

Value estimation

The Eötvös effect is a directional factor that shifts point of impact vertically. Due to its directional nature, no displacement is seen when firing directly north or south. Vertical deflection gradually increases as our direction of fire shifts towards the East or West, with a maximum deflection when shooting straight east or west.

To guide estimation and better determine under which conditions the Eötvös effect becomes relevant, rough values for Eötvös deflection are provided below:

Example 1

Sgt McShooty is deployed as an SF Spotter. He ranges his HVT at 1000m. Needing to guarantee shot placement, he measures the target azimuth at 90°, straight East. Firing towards the East will raise point of impact.

After providing the SF Sniper with a ballistic solution, he designates an altered point of aim to accommodate for the Eötvös effect:

“Aim 6 O’clock, belt buckle"

Example 2

Sgt McShooty is deployed as an SF Spotter. He ranges his HVT at 800m. Needing to guarantee shot placement, he measures the target azimuth at 315°, directly Northwest. Firing towards the West will lower point of impact. Firing to the Northwest decreases this effect.

After providing the SF Sniper with a ballistic solution, he designates an altered point of aim to accommodate for the Eötvös effect:

“Aim 12 O’clock, shirt collar”

Limitations:

The height of human targets (as compared to their width) allows us a margin for error, and permits the relatively small deflection of the Eötvös effect to be estimated with reliable success. Should the height of our target no longer be as forgiving, such as in the case of an obscured target, estimation of the Eötvös effect will no longer be a reliable method for achieving guaranteed shot placement.

The provided values for Eötvös deflection assume an average latitude for all of our campaigns (38.5*) and do not account for atmospheric conditions. A 7.62 NATO cartridge has been assumed for the needed time of flight values. While this method will serve well in most scenarios, it should be noted that map latitudes or bullet times of flight deviating greatly from the data used can produce drastically different effects downrange.

Equation

Calculating vertical Coriolis deflection (or the Eötvös effect) is an almost identical process to calculating for horizontal Coriolis. We will need to know:

• The latitude of our position
• Our compass bearing
• The time of flight for our bullet 

cos(latitude°) * sin(azimuth°) * (Time of flight in seconds) * .072 = Vertical deflection in MRADs

Where:

• positive outputs =  higher point of impact
• negative outputs =  lower point of impact

Data collection

Time of flight can be found in the ATragMX under the “RC” button in the top right of the screen or derived in an online ballistics program. As the ATragMX suite is not available in situations where manual ballistics are relevant, time of flight information should be recorded prior to operation start.

Bearing can be determined by aligning the in-game compass with the target.

Map latitude in Arma 3 does not always correlate with real word locations, rather this information is manually populated by map makers and is persistent for an entire map. Latitudes for common UNITAF campaigns are listed below:

Calculation example

Sgt McShooty is deployed as an SF Spotter on a Honeybadger. He ranges his HVT at 900m, a shot that will have a time of flight of 1.8s. Needing to guarantee shot placement, he measures the target azimuth at 90°:

cos(35°) * (sin(90°) * (1.8s) * .072 = .11 MRADs

Because the output is a negative value, the bullet will impact .11 MRADs higher due to the Eötvös Effect.

Equation limitations

This equation will serve well under all conditions and the very small degree of inherent error will not impede operations in either target rich or high value target environments.

• Use observed correlation and/or recorded data to estimate the vertical deviation caused by Eötvös, or calculate using an appropriate method
• Integrate the calculated value into the final ballistics solution

• When altitude deviates slightly from sea level, estimate vertical deviation due to changes in pressure
• When altitude deviates greatly from sea level, utilize D.O.P.E. for bullet drop values

Preparation

Sgt McShooty is deployed as a Spotter (Manual) on a Honeybadger. He aims for to be able to assemble a ballistic solution in any conditions, so he prepares calculations for the operation.

His sniper is using the M24 SWS and they will only be using the M118 LR bullet. Prior to operation start, he looks at an ATragMX to record time of flight for his given atmospherics.

Target requirements

In operation, Sgt McShooty identifies an OPFOR machine gunner engaging a friendly squad. A follow up shot will not compromise any objectives, so he can disregard most Tertiary Components entirely.

In addition to this, he is presented with fairly typical shot conditions, as:

• There is no wind present
• The target is stationary
• He is not firing at a steep incline

Ballistic solution assembly

Bullet drop

Sgt McShooty ranges his target at 800m according to FM/BG-522 - Milliradians: Mil-relation formula. 

Looking at his range card, he finds a bullet drop adjustment of 9.1 mils.

Spin drift

He uses the Spin Drift formula to calculate horizontal deflection according to FM/BG-558 - Spin drift: calculation:

((SG * Time of Flight ^ 1.83) / Distance) * 1000 = Spin Drift in MRADs

((.0759 * 1.43 ^ 1.83) / 800) * 1000 = .18 MRADs

Because his barrel twist is right hand, his bullet will deflect .18 MRADs to the right.

Coriolis effect

He uses the Horizontal Coriolis Effect formula to calculate horizontal deflection according to FM/BG-553 - Horizontal Coriolis force: calculation:

cos(latitude°) * (Time of flight in seconds) * .072 = Horizontal deflection in MRADs

cos(35°) * (1.43) * .072 = .08 MRADs to the Right

Final ballistic solution

Sgt McShooty adds his two horizontal components together for a total of .26 MRADs to the right.

Because his deflection is low and to the left, he tells his sniper to adjust up and to the right

Final Ballistic Solution: 9.1 mils up, 0.26 mils left

Preparation

Sgt McShooty is deployed as a Spotter (Manual) on a Honeybadger. He aims for to assemble ballistic solutions quickly and easily, so he prepares D.O.P.E. for the operation.

His sniper is using the M24 SWS and they will only be using the M118 LR bullet. He receives the set .pbo date and time from the Senior Game Master, and assembles vertical and horizontal D.O.P.E. according to the Manual Ballistics guides:

Target requirements

In operation, Sgt McShooty identifies an OPFOR machine gunner engaging a friendly squad. A follow up shot will not compromise any objectives, so he can disregard most tertiary components entirely.

In addition to this, he is presented with fairly typical shot conditions, as:

• There is no wind present
• The target is stationary
• He is not firing at a steep incline

Ballistic solution assembly

Sgt McShooty ranges his target at 850m according to https://unitedtaskforce.net/handbook?c=marksmanship-temp&g=FMG83. Looking at his D.O.P.E., he sees his 850m impact was recorded at -9.0 mils low and 0.3 mils to the right. To compensate, for a low and right impact, he has his sniper adjust up and to the left.

Final Ballistic Solution: 9 mils up, 0.3 mils left