Zak Smith
Member
This is Part II of a three-part series:
article | Practical Long-Range Rifle Shooting, Part I - Rifle & Equipment
article | Practical Long-Range Rifle Shooting, Part II - Optics
article | Practical Long-Range Rifle Shooting, Part III - Shooting
OPTICS FOR PRACTICAL LONG RANGE RIFLE SHOOTING
(C) Copyright 2005 Zak Smith All Rights Reserved
Reproduction or Republication by express written permission only
(Schmidt & Bender PMII scope with 13 mils elevation, 0.1mil clicks, on a Remington PSS rifle.)
What is Practical Precision / Long Range Rifle Shooting?
Practical precision rifle shooting involves engaging small and/or distant targets at the limit of
weapon, ammunition, and shooter capability under time pressure in field settings.
Applications include but are not limited to: very small targets 1/4"-1" at 100 to 200 yards,
so-called "cold bore" shots, arbitrary unknown distance targets, shooter/spotter communication, and
combinations of all of those under time constraints.
Generally, these include everything a rifleman is likely to find in any "sniper", "tactical", or
"field" rifle match. The typical platform is a bolt action rifle, though an autoloader of
sufficient accuracy and appropriate caliber can do the job with some tradeoffs.
For our purposes, consider "long range" to mean within a few hundreds yards of the load's
trans-sonic boundary (the point at which the bullet slows to the speed of sound, Mach 1). For
example, with typical 308 loads and rifles, we are interested in ranges from 25 yards out to about
700-1000 yards.
Ballistics Background
Some understanding of bullet trajectory and the physical factors affecting bullet flight is needed
as background before discussing optics.
In the simplest case, take an accurate rifle with sights zeroed at 100 yards shooting one type of
ammunition. In the absence of wind or shooter error, the bullet will impact the point of aim (POA)
when the target distance is 100 yards-- hence its "zero" is at 100 yards.
The "line of aim" is a line straight from the shooter's eye, through the sighting device, to the
target. The bullet starts off below the LOA by the distance between the center of the sighting
device and the center of the bore. This is called the "sight over bore" distance. The axis of the
bore is not parallel to the LOA-- the bore is angled slightly upwards. This causes the bullet to
start off with some "upward" velocity. As it flies down-range, it rises to meet the point of aim
(POA) which is where the LOA intersects with the target.
Depending on the bullet's velocity, the bullet might keep rising above the LOA and again intersect
with it a second time as it falls. Alternatively, it may rise just enough to meet the LOA and then
start to fall again.
In this graph, two loads are displayed. The green trajectory is a 308 load zeroed at 100 yards. It
starts 2" low, rises to the LOA at 100 yards, and then drops off, ending around 11.5" low at 300
yards.
The red trajectory is the same load zeroed at 200 yards. It starts 2" low, intersects with the LOA
the first time at about 40 yards. At 120 yards, it's about 1.6" above the LOA, then drops,
intersecting the LOA again at 200 yards. This is the second, or primary, zero. At 300 yards, it's
about 7" low.
Looking at the graph with the 200 yard zero, the point of impact (POI) at 100 yards would be about
1.6" above the point of aim (POA). At 240, the POI will be 2" below the POA. At 300, the POI will
be 7.5" below the POA. Thus, to hit a small target at 300 yards, the shooter would have to hold 7"
above the target. The bullet continues to fall relative to the line of aim as target range is
increased.
A table can be constructed which relates the drop distance for every range out to the maximum
engagement range. An abbreviated table might look like this, for a rifle with a 100 yard zero. (An
actual table would have intermediate distances like 120, 140, etc.)
This is helpful, but the shooter is left with the problem of how to aim 47" higher than the target
when the distance is 500 yards. There won't be a 47" yardstick sticking out above the target.
Aiming the cross-hairs at a point imagined to be 47" above the target is difficult and very error
prone.
Angular measurements
Instead of measuring hold-over in terms of linear distance (inches or cm), it would be helpful to
translate those linear distances into units of angular measure. The concept of angular measure is
that an angle of 1 degree demarcates 1.7 yards at 100 yards, or 3.5 yards at 200 yards. Everyone
with a basic understanding of geometry should understand how angles work.
There are two units of angular measurement commonly used in rifle scopes. The first is the "minute
of angle." Dividing a circle into 360 degrees, then each degree contains 60 minutes. One MOA
demarcates 1.0472" per 100 yards of distance.
The second is the "mil". One mil is one part transverse per 1000 parts distance. In units we
understand, 1 mil is 3.6" per 100 yards (ie, 100 yards is 3600", one thousandth of which is 3.6").
Consequently it's also 1 yard at 1000 yards. Alternatively, in metric, 1 mil is 10cm per 100
meters, or 1m at 1000 meters.
Wind
Just like the atmosphere pushes on the bullet as it moves forward, slowing it down, any winds
present in the bullet's path can affect its trajectory. The most common effect is the cross wind. A
10mph cross wind will move a typical 308 bullet about 6" at 300 yards. The following graph
demonstrates the wind deflection as range increases for a left or right 10mph wind.
Just like the drop table, we can generate a wind table, which might look something like this:
Lead
For moving targets, the shooter must aim in front of the target a distance which depends on the
target distance and speed. This is called "lead." We'll generate a table for some standard target
speed and add it to our table.
Both the "drift" and "drop" values in the tables can be translated to use angular measurements (MOA
or mils) instead of linear measurements (inches or cm) to aid utility.
Typical Data Card
The shooter might end up with a data card that looks something like this. The first line describes
the load so he can keep straight what the data-card describes. The second line reminds him what
each column means.
Columns:
1. Range
2. elevation for #1's target distance, in MOA
3. wind for #1's target distance, in MOA
4. lead for #1's target distance, in MOA for a target traveling at 4mph (a medium walking pace)
All the trajectory values can be calculated using one of the modern small-arms ballistics calculator
programs, such as Sierra Ballistic Explorer, Exbal, QuickTarget, Agtrans, etc. Several parameters
are critical to their accuracy: (1) bullet ballistic coefficient (BC) values, (2) accurate measured
muzzle velocity from a chronograph, (3) solid zero distance, and (4) accurate environmental
conditions including station pressure, temperature, or density altitude.
Data Confirmation by Shooting
It is important to verify computed data by actually shooting targets at various distances and
looking at the actual hits (or misses) to determine if the elevation values are correct. Shooting
known-distance targets every 100 yards out to the maximum range is a good way to do this.
Desired Sighting System Capabilities
Let's look at the things we want to accomplish with the rifle sighting system:
1. Precisely specify drop hold-over out to our maximum engagement distance.
2. Precisely specify wind drift out to our maximum engagement distance.
3. Precisely specify target lead for moving targets/shooter.
4. Range targets of known size when Laser Range-finders are not appropriate
5. Observe target area
6. Retain #1-5's capabilities in low light conditions
Optical Considerations
Magnified rifle optics have several salient optical properties which we need to understand before
discussing the capability trade-offs later:
Parallax Error
Parallax is the error in apparent POA vs. actual POA due to misalignment of the shooter's eye
vs. the scope's axis. A scope can be set to be parallax error free at one distance. A scope
either has adjustable or fixed parallax. Fixed parallax means the distance at which there is no
error is fixed to something like 100 or 200 yards from the factory. Most tactical scopes have
adjustable parallax, which means the user can adjust the parallax error free distance on the fly
to reduce parallax error whatever the current target's distance.
First Focal Plane vs. Second Focal Plane Definition
Variable-magnification optics can have a first focal plane (FFP) or second focal plane (SFP) reticle
configuration. A first-focal (FFP) reticle's features always demarcate the same angular
measurement regardless of the scope magnification setting. The reticle will appear to "shrink"
and "grow" with the target area as the magnification is adjusted.
A second focal plane (SFP) reticle demarcates angular distance that depends on the scope
magnification setting. The reticle appears to stay constant as the target area shrinks and grows
as the magnification is adjusted.
A fixed power optic is FFP by definition.
(continued)
article | Practical Long-Range Rifle Shooting, Part I - Rifle & Equipment
article | Practical Long-Range Rifle Shooting, Part II - Optics
article | Practical Long-Range Rifle Shooting, Part III - Shooting
OPTICS FOR PRACTICAL LONG RANGE RIFLE SHOOTING
(C) Copyright 2005 Zak Smith All Rights Reserved
Reproduction or Republication by express written permission only
(Schmidt & Bender PMII scope with 13 mils elevation, 0.1mil clicks, on a Remington PSS rifle.)
What is Practical Precision / Long Range Rifle Shooting?
Practical precision rifle shooting involves engaging small and/or distant targets at the limit of
weapon, ammunition, and shooter capability under time pressure in field settings.
Applications include but are not limited to: very small targets 1/4"-1" at 100 to 200 yards,
so-called "cold bore" shots, arbitrary unknown distance targets, shooter/spotter communication, and
combinations of all of those under time constraints.
Generally, these include everything a rifleman is likely to find in any "sniper", "tactical", or
"field" rifle match. The typical platform is a bolt action rifle, though an autoloader of
sufficient accuracy and appropriate caliber can do the job with some tradeoffs.
For our purposes, consider "long range" to mean within a few hundreds yards of the load's
trans-sonic boundary (the point at which the bullet slows to the speed of sound, Mach 1). For
example, with typical 308 loads and rifles, we are interested in ranges from 25 yards out to about
700-1000 yards.
Ballistics Background
Some understanding of bullet trajectory and the physical factors affecting bullet flight is needed
as background before discussing optics.
In the simplest case, take an accurate rifle with sights zeroed at 100 yards shooting one type of
ammunition. In the absence of wind or shooter error, the bullet will impact the point of aim (POA)
when the target distance is 100 yards-- hence its "zero" is at 100 yards.
The "line of aim" is a line straight from the shooter's eye, through the sighting device, to the
target. The bullet starts off below the LOA by the distance between the center of the sighting
device and the center of the bore. This is called the "sight over bore" distance. The axis of the
bore is not parallel to the LOA-- the bore is angled slightly upwards. This causes the bullet to
start off with some "upward" velocity. As it flies down-range, it rises to meet the point of aim
(POA) which is where the LOA intersects with the target.
Depending on the bullet's velocity, the bullet might keep rising above the LOA and again intersect
with it a second time as it falls. Alternatively, it may rise just enough to meet the LOA and then
start to fall again.
In this graph, two loads are displayed. The green trajectory is a 308 load zeroed at 100 yards. It
starts 2" low, rises to the LOA at 100 yards, and then drops off, ending around 11.5" low at 300
yards.
The red trajectory is the same load zeroed at 200 yards. It starts 2" low, intersects with the LOA
the first time at about 40 yards. At 120 yards, it's about 1.6" above the LOA, then drops,
intersecting the LOA again at 200 yards. This is the second, or primary, zero. At 300 yards, it's
about 7" low.
Looking at the graph with the 200 yard zero, the point of impact (POI) at 100 yards would be about
1.6" above the point of aim (POA). At 240, the POI will be 2" below the POA. At 300, the POI will
be 7.5" below the POA. Thus, to hit a small target at 300 yards, the shooter would have to hold 7"
above the target. The bullet continues to fall relative to the line of aim as target range is
increased.
A table can be constructed which relates the drop distance for every range out to the maximum
engagement range. An abbreviated table might look like this, for a rifle with a 100 yard zero. (An
actual table would have intermediate distances like 120, 140, etc.)
Code:
RANGE DROP
100 0"
200 2.87"
300 11.2"
400 25.6"
500 46.9"
600 76.0"
700 114.9"
800 161.7"
when the distance is 500 yards. There won't be a 47" yardstick sticking out above the target.
Aiming the cross-hairs at a point imagined to be 47" above the target is difficult and very error
prone.
Angular measurements
Instead of measuring hold-over in terms of linear distance (inches or cm), it would be helpful to
translate those linear distances into units of angular measure. The concept of angular measure is
that an angle of 1 degree demarcates 1.7 yards at 100 yards, or 3.5 yards at 200 yards. Everyone
with a basic understanding of geometry should understand how angles work.
There are two units of angular measurement commonly used in rifle scopes. The first is the "minute
of angle." Dividing a circle into 360 degrees, then each degree contains 60 minutes. One MOA
demarcates 1.0472" per 100 yards of distance.
The second is the "mil". One mil is one part transverse per 1000 parts distance. In units we
understand, 1 mil is 3.6" per 100 yards (ie, 100 yards is 3600", one thousandth of which is 3.6").
Consequently it's also 1 yard at 1000 yards. Alternatively, in metric, 1 mil is 10cm per 100
meters, or 1m at 1000 meters.
Wind
Just like the atmosphere pushes on the bullet as it moves forward, slowing it down, any winds
present in the bullet's path can affect its trajectory. The most common effect is the cross wind. A
10mph cross wind will move a typical 308 bullet about 6" at 300 yards. The following graph
demonstrates the wind deflection as range increases for a left or right 10mph wind.
Just like the drop table, we can generate a wind table, which might look something like this:
Code:
RANGE DRIFT for 10mph cross
100 0.6"
200 2.6"
300 6.0"
400 11.0"
500 17.8"
600 26.5"
700 37.5"
800 50.9"
Lead
For moving targets, the shooter must aim in front of the target a distance which depends on the
target distance and speed. This is called "lead." We'll generate a table for some standard target
speed and add it to our table.
Both the "drift" and "drop" values in the tables can be translated to use angular measurements (MOA
or mils) instead of linear measurements (inches or cm) to aid utility.
Typical Data Card
The shooter might end up with a data card that looks something like this. The first line describes
the load so he can keep straight what the data-card describes. The second line reminds him what
each column means.
Code:
155 LAP: 2825fps 100yd 0'
RANGE elev wind 4mph->(MOA)
25 4.00 0.25 6 moa
50 0.75 0.25 6 moa
75 0.00 0.50 6 moa
100 0.00 0.50 6 moa
125 0.25 0.75 6 moa
150 0.50 1.00 6 moa
175 1.00 1.00 6 moa
200 1.50 1.25 7 moa
225 2.00 1.50 7 moa
250 2.50 1.50 7 moa
275 3.00 1.75 7 moa
300 3.75 2.00 7 moa
325 4.25 2.00 7 moa
350 5.00 2.25 7 moa
375 5.75 2.50 7 moa
400 6.50 2.50 7 moa
425 7.25 2.75 7 moa
450 8.00 3.00 7 moa
475 8.75 3.25 7 moa
500 9.50 3.50 7 moa
525 10.25 3.50 7 moa
550 11.25 3.75 7 moa
575 12.00 4.00 7 moa
600 13.00 4.25 8 moa
625 13.75 4.50 8 moa
650 14.75 4.75 8 moa
675 15.75 5.00 8 moa
700 16.75 5.00 8 moa
725 17.75 5.25 8 moa
750 18.75 5.50 8 moa
775 20.00 5.75 8 moa
800 21.00 6.00 8 moa
Columns:
1. Range
2. elevation for #1's target distance, in MOA
3. wind for #1's target distance, in MOA
4. lead for #1's target distance, in MOA for a target traveling at 4mph (a medium walking pace)
All the trajectory values can be calculated using one of the modern small-arms ballistics calculator
programs, such as Sierra Ballistic Explorer, Exbal, QuickTarget, Agtrans, etc. Several parameters
are critical to their accuracy: (1) bullet ballistic coefficient (BC) values, (2) accurate measured
muzzle velocity from a chronograph, (3) solid zero distance, and (4) accurate environmental
conditions including station pressure, temperature, or density altitude.
Data Confirmation by Shooting
It is important to verify computed data by actually shooting targets at various distances and
looking at the actual hits (or misses) to determine if the elevation values are correct. Shooting
known-distance targets every 100 yards out to the maximum range is a good way to do this.
Desired Sighting System Capabilities
Let's look at the things we want to accomplish with the rifle sighting system:
1. Precisely specify drop hold-over out to our maximum engagement distance.
2. Precisely specify wind drift out to our maximum engagement distance.
3. Precisely specify target lead for moving targets/shooter.
4. Range targets of known size when Laser Range-finders are not appropriate
5. Observe target area
6. Retain #1-5's capabilities in low light conditions
Optical Considerations
Magnified rifle optics have several salient optical properties which we need to understand before
discussing the capability trade-offs later:
Parallax Error
Parallax is the error in apparent POA vs. actual POA due to misalignment of the shooter's eye
vs. the scope's axis. A scope can be set to be parallax error free at one distance. A scope
either has adjustable or fixed parallax. Fixed parallax means the distance at which there is no
error is fixed to something like 100 or 200 yards from the factory. Most tactical scopes have
adjustable parallax, which means the user can adjust the parallax error free distance on the fly
to reduce parallax error whatever the current target's distance.
First Focal Plane vs. Second Focal Plane Definition
Variable-magnification optics can have a first focal plane (FFP) or second focal plane (SFP) reticle
configuration. A first-focal (FFP) reticle's features always demarcate the same angular
measurement regardless of the scope magnification setting. The reticle will appear to "shrink"
and "grow" with the target area as the magnification is adjusted.
A second focal plane (SFP) reticle demarcates angular distance that depends on the scope
magnification setting. The reticle appears to stay constant as the target area shrinks and grows
as the magnification is adjusted.
A fixed power optic is FFP by definition.
(continued)
Last edited: