Chapter 1: EXTERNAL BALLISTIC FACTORS

2 crucial Ballistic factors in Long Range Shooting/Sharpshooting/Sniping:

1. BULLET DROP

Bullet’s going down due to 2 external forces which are Gravity & Drag/Air resistence.

Gravity is causing it to drop from the line of departure & Drag/Air Resistance is slowing down the velocity

Bullet Drop is always affected by: 

a. RANGE

The farther your target, the bigger your bullet drop! Distance will increase the bullet drop so range your target before shooting! How to range target:

• Laser ranging → using laser rangefinder (the easiest & most accurate way)
  

Vector 21b laser range finder

• Stadiametric ranging → using  telescopic instrument
  

• Mildot ranging → using your scope reticle’s mil dots 

        Ranging Formula using mildot reticle:

               Target actual height (in Meter) x 1000         = target Range

      Target height on the scope (number of Mil-dots)

        example: 

                               Target = 5 mil dots        Target = 4 mil dots       Target = 1,8 mil dots
                                Height = 1,83 m             Height = 1,68 m           Height = 0,38 m
                                 Range = 366 m               Range = 420 m            Range = 211 m  

b. ANGLE OF FIRING (Uphill/Downhill firing)

For a bullet to strike a target at a Slant Range (R_S) and an incline of α , the rifle sight must be adjusted as if the shooter were aiming at a horizontal target at a range of R_H = R_S cos (α) where Slant range x Angle = Horizontal Range.

So when shooting uphill/downhill, you must adjust your scope at horizontal range not the slant range

Under 15°, it doesn’t matter! Above 15°, it matters! Aim at Horizontal range not Slant Range!

Here’s the quick adjustment: 

• 15° → adjust as if aiming at a 95% Slant Range
• 20° → adjust as if aiming at a 93% Slant Range
• 25° → adjust as if aiming at a 90% Slant Range
• 30° → adjust as if aiming at a 86% Slant Range
• 40° → adjust as if aiming at a 76% Slant Range
• 45° → adjust as if aiming at a 70% Slant Range
• 55° → adjust as if aiming at a 57% Slant Range
• 65° → adjust as if aiming at a 42% Slant Range

if you don't know how much your shooting angle is, you can calculate the horizontal distance using the Pythagoras Theorem 

C₂: Slant Range

B₂: Horizontal Range

A₂: Altitude difference (Shooter Altitude – Target Altitude)

c. AIR TEMPERATURE

Higher Temperature actually decreases the Air Density, and therefore decreases the drag so resulting in less Bullet Drop. Lower Temperature actually increases the Air Density, and therefore increases the drag so resulting in more Bullet Drop

d. AIR PRESSURE

Lower Air Pressure actually decreases the Air Density, and therefore decreases the drag so resulting in less Bullet Drop. Higher Air Pressure actually increases the Air Density, and therefore increases the drag so resulting in more Bullet Drop.

e. ALTITUDE

Higher Altitude actually decreases the Air Density, and therefore decreases the drag so resulting in less Bullet Drop. Lower Altitude actually increases the Air Density, and therefore increases the drag so resulting in more Bullet Drop.

f. HUMIDITY

Higher Humidity actually decreases the air density, and therefore decreases the drag so resulting in less Bullet Drop. Lower Humidity actually increases the air density, and therefore increases the drag so resulting in more Bullet Drop.

g. EARTH ROTATION

When shooting east, the bullet drop decreases! When shooting west, bullet drop increases

2. WIND DEFLECTION/SIDEWAY DRIFT

Wind always makes the bullet deviate from its trajectory. In other words, bullet’s drifting to the left or right (sideways drift). Your bullet will drift in the direction of the wind. To compensate for this, you must aim into the wind, to the right or left.

ex: Wind comes from the left pushing the bullet to right so we must aim to left!

Wind deflection Affected by:

a. WIND SPEED

    Measure it with windmeter (Kestrel)

    or by observing the angle of heat waves/Mirage

b. WIND DIRECTION

    Wind Direction will affect the mount of side drift! the angle of the wind determines the wind value. In other words, Wind Direction affects wind speed value.

Types of wind:

1. HeadWind & TailWind (12 o’clock & 6 o’clock/0°) don’t matter too much so Wind Speed x 0
2. CrossWind does matter coz it has the strongest effect on horizontal path of the bullet! types of Crosswind:

• 9 o’clock & 3 o’clock wind (90°) give full effect so Wind Speed x 1
• 11 o’clock, 1 o’clock, 5 o’clock, & 7 o’clock (30°) give little effect so Wind Speed x 0.5
• 10 o’clock, 2 o’clock, 4 o’clock, & 8 o’clock (60°) give almost full effect so Wind Speed x 0.86
• 45° wind give little effect so Wind Speed x 0.7

c. SPIN DRIFT/GYROSCOPIC EFFECT

Even in completely calm air, with no sideways wind at all, a spin-stabilized projectile will experience a spin-induced sideways component. For a right hand (clockwise) direction of rotation this component will always be to the right. For a left hand (counterclockwise) direction of rotation this component will always be to the left. At extreme long range (beyond 1000 m), spin drift increases significantly.

______________________________________________________________________________

Chapter 2: SCOPE 

A sniper scope is basically a specialized telescope containing a targeting reticle (crosshairs) over the amplified image. Beside for magnification purpose, scope helps us compensate for external balistic factor. Inside the scope, there’s a reticle or crosshair that will enlarge as the scope magnifies. 

Here some example of a scope:

here's the view inside a scope:

25x Scope in a Sniping Simulation called “Sniper Spirit"

here some scope magnification:

         10x magnification                                           

            16x magnification

            

          

        25x magnification

Note: as the scope magnifies, both of the target (red box) & the reticle enlarge at the same time. The reticle remains in the same visual proportion to the target across the scope entire magnification range. As you can see, there are some mil dots on the center of the crosshair.

Because of external ballistic factors (Bullet Drop & Wind Deflection), point of aim (where you are aiming) is not going to be point of impact (where the bullet lands) so you always have to compensate for it using your scope (reticle). 

There are 2 ways to compensate for the external ballistic factors:

a. HOLDOVER

To compensate for Bullet Drop, you can hold your reticle over the target. Just place your reticle above the target so the bullet will drop directly onto the target. In other words, the shooter is aiming higher than the target's position in the sight to allow for the bullet's drop during travel rather than adjusting the scope.This method is usually called Arkansas Elevation.

To compensate for Wind Drift, you can aim into the direction of the wind. You can aim to left or right, depending on which way the wind comes from. If the wind blows from the right, you aim to right. If the wind blows from the left, you aim to left. In other words, the shooter is aiming at a point horizontal to the target's position in the sight rather than adjusting the sight to compensate. This method is usually called Kentucky Windage

b. SCOPE DOPING / SCOPE ADJUSTMENT

Because of external ballistic factors (Bullet Drop & Wind Deflection), point of aim (where you are aiming) is not going to be point of impact (where the bullet lands). Ideally, snipers want point of aim and point of impact to be exactly the same. So They line up these points by adjusting the scope (after external ballistic factors been factored into the shot).

Basically, scope adjustment is almost the same thing with Holdover! But instead of placing the reticle above the target & aiming into the wind, you actually adjust your scope optic so the optic lines up the point of aim & point of impact, as if you're aiming right at the target whilst you're actually doing a holdover. in other words, the scope helps you holdover the target. 

To overcome those 2 external ballistic factors you need Scope Adjustment/Correction to be dialed in on your scope! There are 2 types of adjustment (correlating with those 2 ballistic factors):

1. ELEVATION ADJUSTMENT

Elevation Knob (the turret above your scope) → to increase MoA, rotate it clockwise! to decrease MoA, rotate it counterclockwise!)

to see what Elevation Adjustment is, watch this video! 

watch the Elevation adjustment part at 0:55

    2.   WINDAGE ADJUSTMENT

Windage Knob (the turret on the right side of your scope) → to increase MoA, rotate it clockwise! to decrease MoA, rotate it counterclockwise!)

If the wind comes from the right, MoA value will be positive (+)

If the wind comes from the left, MoA value will be negative (-)

to see what Windage Adjustment is, watch this video!

watch the Windage adjustment part at 2:08

To operate the scope adjustment, we must use Minute of Angle & Miliradian as our angular measurement! Minute of Angle (Moa) & Miliradian (Mil) are the units of measurement being used in sniping/sharpshooting! We always use MoA & Mil because they’re so much better in measurement than degrees, thus more precise. It is extremely important to understand those 2 things!

MINUTE OF ANGLE (MoA)

A minute of arc, arcminute, or minute of angle (MoA), is a unit of angular measurement equal to one sixtieth (¹⁄₆₀) of one degree. Because one degree is defined as one three hundred and sixtieth (¹⁄₃₆₀) of a rotation, one minute of angle (MoA) is ¹⁄_21,600 of a rotation.

To understand MoA, look at a circle (360°)! There are 360 degrees in a circle, and each degree (1°) is composed of 60 minutes (60’).

Therefore, there are 360 (degrees) x 60 (minutes) = 21,600 minutes in a circle (21,600’).

1 MoA = ¹⁄₆₀° = .016667°

in simple words, always remember that:

1 MoA @ 100m = 2,9 cm 

1 MoA @ 1000m = 29 cm

Example of MoA usage on scope adjustment:

MILIRADIAN (Mil dots)

Reticle uses miliradian/mil (gap between scope dots)  1 Mil = 3,43 MoA

What is a radian? A radian is a unit of angular measurement. Officially, one radian subtends an arc equal in length to the radius of the circle, “r”. What a radian is it associates an arc length, called a radian arc, which is equal in length to the radius of the circle, with an angle at the center of the circle. The angle the arc created is called a radian. Or, another way, it’s the angle created at the center of a circle by an arc on the circumference of the circle, and that arc length is equal in length to the radius of the circle. Think of it as a piece of pie, that all the sides of the piece of pie are equal.

What is a milliradian? A “mil” is defined as “one thousandth”, or 1/1000. Therefore, a milliradian is 1/1000 of a radian. Take each of the radians that go around a circle and chop it up into a thousand pieces. Since there are 6.2832 radians in a circle, and each radian is chopped up into a thousand pieces, then there are 6.2832 x 1000 = 6,283.2 milliradians in a circle. (Milliradians is usually just shortened to “mils”)

how many degrees are in each milliradian? A circle has 360 degrees, and/or 6,283.2 milliradians that go around it (B above). Therefore: 

There are .0573 degrees per mil (degrees/mil)

Look at the circle below! Make the radius 100 meter! Remember earlier that all the sides of the piece of pie are equal. Therefore, if one side is 100 m, then all sides of the pie are also 100 m . So what is 1/1000 of any of those sides, which would also be 1/1000 of the radian arc? Essentially, what is 1 mil equal to (remember, 1 mil is defined as 1/1000 of a radian)? 100/1000 = 0.1 m. 

So Remember, at 100 m, 1 miliradian = 0,1 m (10 cm)!

_____________________________________________________________________________

Chapter 3: RANGE CARD/BALLISTICS TABLE (aka “CHEAT SHEET”)

Range card is a crucial tool to make a scope adjustment, it helps a sniper determine how much Elevation & Windage correction he has to dial in on his scope. Ideally, specific range card should be prepared for each atmospheric condition. Usually, you’ll get the range card from your firearms manufacturer but you can make your own Range Card using Ballistic Calculator or by testing it yourself in a firing range.

here some Examples of Ballistic tables:

Winchester 70 sniper rifle (with 5.56 x 45 mm bullet) ballistic table

M24 sniper rifle (with 7,62x51 M118LR bullet) ballistic table 

L115A3 sniper rifle (with .338 Lapua Magnum bullet) ballistic table 

Mcmillan Tac 50 (with .50 cal cartridge) ballistic table

Range (meter)	Elevation (MoA)	Wind Drift 1 m/s (MoA)
100	-11,75	0
200	-8,75	0,2
300	-6	0,25
400	-3	0,3
500	0	0,4
550	1,5	0,5
600	3	0,57
650	4,75	0,57
700	6,5	0,57
750	8,5	0,75
800	10,25	0,75
850	12,25	0,75
900	14,50	1
950	16.75	1
1000	19	1
1050	21,25	1,25
1100	23,75	1,25
1150	26,50	1,5
1200	29,25	1,5
1250	32	1,5
1300	35	1,5
1350	38	1,75
1400	41,25	1,75
1450	44,50	2
1500	48	2
1550	51,50	2,25
1600	55,25	2,25
1650	59,25	2,5
1700	63,25	2,5
1750	67,50	2,75
1800	72	3
1850	76,75	3
1900	81,50	3,25
1950	86,75	3,5
2000	92	3,5
2050	97,50	3,75
2100	103,50	4
2150	109,75	4,25
2200	115,75	4,25
2250	122,36	4,5
2300	129,25	4,5
2350	136,50	4,75
2400	144	5

i use this table in "Arma 2" (with ACE mod)

______________________________________________________________________________

Chapter 4: SUMMARY

Sniping/Sharpshooting is not an easy thing! Every shot is a different shot!

CRUCIAL STEPS in Sniping/Sharpshooting:

1. SPOTTING the target

2. Determine the BULLET DROP by:

• RANGE the target
• Know your shooting ANGLE (multiply it with target Range, then you’ll get the actual range that you have to compensate for).
• Measure the AIR & AMMO TEMPERATURE, AIR PRESSURE, & HUMIDITY
• Use your BALLISTIC TABLE/RANGE CARD to calculate how much elevation correction (in MoA) you gotta dial in on your scope
• After knowing how much the elevation corection, you DIAL the number of the elevation (in MoA) into your elevation knob (to increase MoA, rotate it clockwise! To decrease the MoA, rotate it counterclockwise!)

3. Determine the WIND DEFLECTION/SIDEWAY DRIFT by:

• determine the GYROSCOPIC EFFECT/SPIN DRIFT
• Check the WIND SPEED!
• Check the WIND DIRECTION!

          1) if it’s HEADWIND or TAILWIND (12 o’clock or 6 o’clock wind), then Wind Speed x 0 

          2) if it’s CROSSWIND:

             9 o’clock & 3 o’clock wind (90°) then Wind Speed x 1 (full value)

             11 o’clock, 1 o’clock, 7 o’clock, & 5 o’clock wind (30°) then Wind Speed x 0,5 (half value)

             10 o’clock, 2 o’clock, 4 o’clock, & 8 o’clock wind (60°) then Wind Speed x 0,86 (eight-tenths value)

• After getting the final value of the wind, multiply it with the windage MoA on the Ballistic table. After knowing the final windage MoA, you dial that number into the windage knob (to increase MoA, rotate it clockwise! To decrease the MoA, rotate it counterclockwise!) & just remember:

          If the wind comes from the right, MoA value will be positive (+)!

          If the wind comes from the left, MoA value will be negative (-)!

4. After done making scope adjustment/scope doping, AIM AT THE CENTER OF THE TARGET BODY! Put him right in the middle of your reticle!

5. HOLD YOUR BREATH & PULL THE TRIGGER then  BOOOMM!!!!! (i guarantee that it’ll be 100% a BULLSEYE/right on target!!!)

6. HAPPY SNIPING/SHARPSHOOTING! J



______________________________________________________________________________

Chapter 5: PRACTICE / QUIZ

Case 1: 
You’re a British Sniper with L115A3 sniper rifle (.338 Lapua Magnum). You spot a Taliban & you want to shoot him down. Here’s the situation:

Range = 1290 m

Angle = 20°

Temperature = 60°F

Air pressure = 29.53 in hg

2 o’clock Wind = 5 mph

You’re using Schmidt & Bender 3-12x50 LP PM II Scope which has ¼ MoA adjustment so 1 click = 0,25 MoA, with max elevation: 60 MoA & max windage: 15 MoA

Questions: how will you shoot that Taliban at that distance?

Answer:

1. Look at the L115A3 Ballistic Table!
2. Range the target = 1290 m → slant range
3. Find the horizontal range (because of 20° shooting angle):

          Rh = Rs x cos (a)
          Rh = 1290 m x cos 20° = 1290 m x 0,93 = 1200 m  

          That means you have to adjust your elevation at 1200 m!

     4.  For Elevation, use the horizontal range (1200 m)! The ballistic table says that at 1200 m, 60°F, & 29.53 in hg , the Elevation Adjustment you gotta make is = 40 MoA

     5.  Check the wind speed = 5 mph

     6.  Check the wind direction = 2 o’clock (60°) → wind blows from the Right (Positive)

     7.  Determine the wind value:

          2 o’clock (60°) means Wind Speed x 0,86 = 5 mph x 0,86 = 4,3 mph

     8.  For Windage, use the slant range (1290 m)! The ballistic table says that that at 1290 m, the Windage Adjustment you gotta make is = 4,3 x 0,95 = 4,1 MoA

     9.  So you dial in those values on your scope, Elevation (40 MoA) & Windage (4,1 MoA)! Remember your scope has ¼ MoA adjustment so 1 click = 0,25 MoA. Rotate the Elevation knob 160 clicks & Rotate the Windage knob 16 clicks (clockwise).

   10. Finally, just fucking shoot it! BANG & BULLSEYE!!!

Case 2: 
Sgt. Jim Gilliland is an US Army Sniper in Iraq war. He’s using M24 (7,62x51 mm) sniper rifle. He spots a Taliban sniper. Here’s the situation:

Range = 1000 m

Angle = 0°

Temperature = 100°F 
Air pressure = 30 in hg

9 o’clock Wind = 2 mph

He’s using Leupold Mark 4 3.5-10x40mm LR/T M3 scope which has 1/2-MOA windage dials (0,5 MoA per click for Windage) and 1-MOA elevation dials (1 MoA per click for Elevation), with max elevation: 65 MoA & max windage: 65 MoA

Question: how will he shoot that sniper?

Answer:

    1.  Look at the M24 Ballistic Table!
    2.  Range the target = 1000 m
    3.  Find the horizontal range:
         Rh = Rs x cos (a)
         Rh = 1000 m x cos 0° = 1000 m x 1 = 1000 m (no change because it’s  0°)
         That means he has to adjust his scope (elevation & windage) at 1000 m!

    4.  The ballistic table says that at 1000 m, 100°F, & 30 in hg, the Elevation Adjustment he gotta make is = 38,12 MoA
  

    5.  Check the wind speed = 2 mph

   

    6.  Check the wind direction = 9 o’clock (90°) → wind blows from the Left (negative)

    7.  Determine the wind value:

         9 o’clock (90°) means Wind Speed x 1 = 2 mph x 1 = 2 mph

    8.  The ballistic table says at 1000 m, the Windage Adjustment he gotta make is = 2 x -0,93 = -1,86 MoA

    9.  So he dials in those values on his scope, Elevation (38,12 MoA) & Windage (-1,86 MoA)! But remember your scope has 1-MOA elevation dials & 1/2-MOA windage dials. Rotate the Elevation knob 38 clicks (clockwise) & Rotate the Windage knob 4 clicks (counterclockwise).

   10. Finally, just fucking shoot it! BANG & BULLSEYE!!!

Case 3:

You’re a Law Enforcement/Police sniper equipped with Winchester 70 sniper rifle (5.56 x 45 mm). You're facing a hostage crisis. There's a bank robber holding a hostage! you gotta shoot him down without killing the hostage. Here’s the situation:

Range = 200 m

Angle = 10°

Temperature = 60°F

Air pressure = 29.53 in hg

3 o’clock Wind = 10 mph

You’re using Leupold Mark 4 3.5-10x40mm LR/T M3 scope which has 1/2-MOA windage dials (0,5 MoA per click for Windage) and 1-MOA elevation dials (1 MoA per click for Elevation), with max elevation: 65 MoA & max windage: 65 MoA

Questions: how will you shoot that robber at that distance?

Answer:

1. Look at theWinchester 70 Ballistic Table!
2. Range the target = 200 m → slant range
3. Find the horizontal range (because of 10° shooting angle):

          Rh = Rs x cos (a)
          Rh = 200 m x cos 10° = 200 m x 0,98  = 196 m  

          That means you have to adjust your elevation at 196 m!

     4.  For Elevation, use the horizontal range (196 m)! The ballistic table says that at 196 m, 60°F, & 29.53 in hg , the Elevation Adjustment you gotta make is = 2,5 MoA

     5.  Check the wind speed = 10 mph

     6.  Check the wind direction = 3 o’clock (90°) → wind blows from the Right (Positive)

     7.  Determine the wind value:

          3 o’clock (90°) means Wind Speed x 1 = 10 mph x 1 = 10 mph

     8.  For Windage, use the slant range (200 m)! The ballistic table says that that at 200 m, the Windage Adjustment you gotta make is = 10 x 0,22 = 2,2 MoA

     9.  So you dial in those values on your scope, Elevation (2,5 MoA) & Windage (2,2 MoA)! Remember your scope has 1-MOA elevation dials & 1/2-MOA windage dials. Rotate the Elevation knob 2 clicks (clockwise) & Rotate the Windage knob 4 clicks (counterclockwise).

   10. Finally, just fucking shoot it! BANG & BULLSEYE!!! 





Case 4: 
Sgt. Rob Furlong is a Canadian Army Sniper in Afghanistan war. He’s using McMillan Tac 50 (.50 cal BMG). He spots 3 Talibans carrying RPK machine gun. Here’s the situation:

Range = 2580 m

Angle = 20°

Temp & press = static & stable

9 o’clock Wind = 8,8 m/s

All maxed out, Holdover elevation 4 mils & windage 4 mils (13,5 MoA)

He’s using Leupold Mark 4 LR/T 16x40mm scope with ¼ moa adjustment, max elevation 140 MoA, max windage 45 MoA

Question: how will he shoot those Talibans?

Answer:

    1.  Look at the McMillan Tac 50  Ballistic Table!!!

    2.  Range the target = 2580 m → slant range

    3.  Find the horizontal range (because of 20° shooting angle):

         Rh = Rs x cos (a)

         Rh = 1200 m x cos 20° = 2580 m x 0,93 = 2400 m

         That means he has to adjust his Elevation at 2400 m!

    4.  The ballistic table says that at 2400 m, in static & stable air condition, the Elevation Adjustment he gotta make is = 144 MoA

Range (meter)	Elevation (MoA)	Windage (MoA)
2400	144	5

 

    5.  Check the wind speed = 8,8 m/s

    6.  Check the wind direction = 9 o’clock (90°) → wind blows from the Left (negative)

    7.  Determine the wind value:

         9 o’clock (90°) means Wind Speed x 1 = 8,8 m/s x 1 = 8,8 m/s

    8.  For Windage, use the slant range (2580 m)! The ballistic table says that that at 2580 m, the Windage Adjustment he gotta make is = 8,8 x -6,64 = -58,50 MoA

Range (meter)	Elevation (MoA)	Windage (MoA)
2580	180,75	6,64

    
9.  So he dials in those values on his scope, Elevation (144 MoA) & Windage (-58,50 MoA)! Remember your scope has ¼ MoA adjustment so 1 click = 0,25 MoA. Rotate the Elevation knob 576 clicks (clockwise) & Rotate the Windage knob 234 clicks (counterclockwise).

  10.  But wait a minute! Remember that his scope only has max elevation (140 MoA) & max windage (45 MoA)! Whereas he has to make 144 MoA elevation & -58,50 MoA windage. So what he gotta do? First, He has to aim above the target (hold the reticle over the target). This is called Arkansas Elevation! Second, he has to correct for the wind by aiming at a point horizontal to the target's position in the sight rather than by adjusting the sight to compensate This is called Kentucky Windage!

  11.  How does he do the holdover? (Remember that 1 Mil = 3,4 MoA)

        

         For Elevation

The elevation adjustment is maxed out to 140 MoA so he has to holdover: 144 MoA – 140 MoA = 4 MoA

so 4 MoA =  4 ÷ 3,4 = 1,17 Mils

        For Windage

The windage adjustment is maxed out to 45 MoA so he has to holdover: 58,50 MoA – 45 MoA = 13,5 MoA

so 13,5 MoA = 13,5 ÷ 3,4 = 4 mils

Conclusion→ after adjusting the Elevation (maxed out to 140 MoA) & the Windage (-45 MoA), Rob Furlong has to place his reticle 1,1 Mil Dot above his target & 4 Mil Dots in order to hit the target  accurately!

Leupold Mark 4 LR/T 16x40mm scope, 16x Magnification, he already adjusted the Elevation: 140 MoA (maxed) & the Windage: -45 MoA (maxed)