Exterior Ballistics for Hunters

In this article I will try to unravel some mysteries of exterior ballistics as to just how they pertain to hunting rifles and how bullets fly.  Here we will delve into different calibers and or bullet weights along with their trajectory as pertaining to different types of hunting.

Exterior ballistics covers everything that happens during a bullet's flight between the muzzle of the rifle, and the target.

Have you ever wondered why rifles have that name?  The early muzzle loaders used a smoothbore.  Accuracy suffered at any distance.  It was found that if there was grooves cut internally in the bore that rotated, that this gave the bullet rotational stabilization.  These grooves are called rifling.  Look at a football quarterback when he is making a pass, the ball is thrown so that it is spiraling.  However if the ball is simply thrown and wobbles or goes end over end it does not go as far even with the same amount of effort in the throwing.  The same applies to bullets.   These shallow rifling in barrels are cut in a specific rotation depending on the diameter & weight of the bullet being used.  A rate of twist of 1 turn in 14" will not stabilize a heavy bullet that may need a 1-10 ratio.

One Gun Fits All ? ;   At times one gun does not fit all uses, sure some may come close, and I may somewhat contradict myself below, but a short range 150 yard firearm greatly handicaps a hunter who is trying to pit it against a hunter who has a gun that will reach out 300 yards beyond his capability.  And the other way around, a Mule deer hunter of Wyoming would be totally out of his elements in the brush of western Washington or Oregon where his bipod and 4.5X14 scope would be about useless.  You may find a compromise gun that fits many needs, but will be lacking on both ends of the spectrum.

The guy who is a armchair hunter, reads, watches TV is no match for the hunter who has "been there done that", and learned by experience.  Some of this experience is expensive in both dollars and time involved.  This type of experience is not easily forgotten.  Books and TV programs are a great information sharing thing, but are normally made for someone to make a profit, therefore there is usually a financial motive in there somewhere.  Sure some of those neat things shown on the TV outdoor show may be helpful, but do they really fit into your style of hunting?

Our Goal As a Hunter ; The goal is for a hunter to be able to hit an animal at what ever range that it presents its self OR YOU deem possible.  You may be able to make a stalk which puts you closer for a better chance of making a humane kill.  Let's pick a few calibers and different bullet weights for a comparison to see where it leads us.

Lighter bullets will be going faster, but will not have the penetrating power.  Lighter bullet loadings are many times been referred to as varmint rounds.  Most varmint bullets are made with a thinner outer jacket so they WILL explode at a longer range.  This is not wanted for game hunting bullets that need to penetrate, expand, creating knock down power.  So you will need to decide the animal you will be hunting, select the caliber and bullet accordingly.   What I am really saying here, is just because a ammunition manufacturer makes ammo with loadings from light to heavy like a 30-06 comes in bullets from 110 gr. to 220 gr.  neither are desirable for deer hunting.  Whereas a bullet from 150 to 180 gr. may be fit the bill better.  Some calibers you will find an intermediate bullet weight that is a compromise and will work surprisingly well in some cases.

In the chart below you will notice the different bullet weights, muzzle velocity, kinetic energy in foot pounds and bullet trajectory for each bullet.  Heavier bullets will drop faster at longer ranges.  Any bullet as it reaches longer ranges slows down and therefore also looses energy.  Energy in this case equals knock down power. 

This chart was taken from the Remington sales pamphlet.  In order to be comparative, some of the data was captured from other sources in order to get a 200 yard zero for all.  You will also note that all of these velocities were taken off a test barrel of 24" when in reality some hunting rifles are 22" like the Remington 742/760 or even 20" like for Winchester model 94 30-30.  With a shorter barrel the velocity will be lower than this advertised data AND also the trajectory will also suffer.  In reality, when a hunter chooses Weatherby rifles, many times they opt for a 26" barrel. The common rule of thumb is velocity drops 100 FPS for every 1" shorter than the published data.

In developing a load for any cartridge, the manufacturer (or reloader) uses powder to try to match the cartridge case and firearm design which all meet SAMME specifications for safe loads.  Some powders burn faster than others.  It has been found that efficiency of powder is best when burn rates of powder match the cartridge case when it is nearly full.  Therefore faster powder is used in smaller capacity cases to achieve the desired safe end result.   You will notice on the chart below that the bullet diameter/bullet weight is smaller/lighter for smaller capacity cases.  Bullet energy is also less for these lighter bullets.  Bullet energy equates to knock down power at the target.  The reason barrel length makes a difference in velocity is that as the powder burns it creates energy, generally the longer time the bullet is inside the barrel allowing the powder to burn more completely, the more velocity is achieved on the bullet.  Barrel length may be a compromise between powder efficiency & the hunters ability to carry around a rifle all day.

Remaining energy at 500 yards (last column) is an enlightening observation.  Just how much is needed to effectively kill a deer at that yardage?   I am no ballistics expert, but I would guess that possibly 800 foot pounds would be a desired minimum.  IF you estimated your range correctly AND had a good rest, AND your rifle was sighted in correctly, AND the deer was in an open area enough that you could see it and the surrounding area after the shot AND you were lucky, a 500 FP bullet COULD put it down.  However just because it was a good lung shot, does not mean the deer will lie down then wait for you to find it, but then by the time you got to it, it would have probably have bled to death (if you can find him).

As in many things there is also a happy medium on bullets.  A light fast bullet does not retain velocity well, just as a heavy slow one does not.  Somewhere in between there is a point where one bullet is more efficient than others.  Bullet design will also enter into this equation.  There has to be a middle ground between bullet weight/velocity/ bullet drop for long range shooting.  You can not have it all and still have a safely designed firearm that you can pack around.  Also for longer range shooting a boat tail bullet will carry up slightly better in that it having a slight taper on the rear as compared to a flat base, this boat tail will create less disturbance behind the bullet, increasing it's efficiency.

This chart may or may not depict recommended sight in for deer hunting, but shows differences in different calibers and their trajectory all using a 200 yard sight in zero.  The bullets selected here are all pointed so as to make a more equal comparison, except the rounded nosed required for tubular magazines like the 30-30.  You will notice that as the bullet weight goes up so does the energy.  Also as the muzzle velocity goes up so does the energy.  Pointed bullets retain more velocity at longer ranges than blunt bullets, (better Ballistic Coefficients). 

If it were possible to push a 200 gr. 30 caliber bullet at 3600 FPS, we could have a all around perfect gun.  This is not possible because of pressures involved and needed barrel length, or the weight it would have to be when finished.

There are 2 of these loadings that deviate from the 200 yard zero, one at 300 and the other at 100, simply because of the bullet weight and velocity of these 2 along with the usual intended distance shot.

The 22 LR is shown just for a comparison and with it sighted in for 50 yards.

Caliber Bullet
Muzzle Energy 100 yd. 200 yd. 300 yd. 400 yd. 500 yd. Remaining Energy
22 LR

  40 gr.

22" 1255 140 -3.0"          
223 Rem   55 gr. 24" 3240 1282 +1.9" 0.0 -8.5" -26." -59.6" 197
22-250   55 gr. 24" 3680 1654 +2.3" +1.9 0.0 -3.4" -15.9" 272
243 Win   80 gr.   24" 3250 1953 +1.2" 0.0 -5.8" -17.1" -35.2" 495
"  100 gr. 24" 2960 1995 +1.9" 0.0 -7.8" -22.6" -46.3" 708
270 Win  130 gr. 24" 3060 2702 +1.8" 0.0 -7.4" -21.6" -42.0" 1801
"  150 gr. 24" 2850 2705 +2.3" 0.0 -9.7" -29.2" -62.2" 1385
30-30  150 gr. 24" 2390 1902 +1.8" 0.0 -24.6" -65.3" -134.9" 316
"  170 gr. 24" 2200 1827 +2.0" 0.0 -25.1" -63.6" -126.7" 425
308 Win  150 gr. 24" 2820 2648 +2.3" 0.0 -9.1" -26.9" -55.6" 810
"  165 gr. 24" 2700 2670 +2.5" 0.0 -9.7" -28.5" -58.8" 881
"  180 gr. 24" 2620 2743 +2.6" 0.0 -9.9" -28.9" -58.8" 1028
30-06  150 gr. 24" 2910 2820 +2.1" 0.0 -8.5" -25.0" -51.8" 876
"  165 gr. 24" 2800 2872 +2.3" 0.0 -9.0" -26.3" -54.1" 1047
"  180 gr. 24" 2700 2913 +2.4" 0.0 -9.3" -27.0" -54.9" 1105
7mm Rem Mag  150 gr. 24" 3110 3221 +1.7" 0.0 -2.8" -20.5" -42.1" 1160
"  175 gr. 24" 2860 3178 +2.0" 0.0 -3.2" -22.7" -45.8" 1372
300 WBY Mag   180 gr. 24" 3200 4092 +2.6" 0.0 -3.3" -14.4" -32.4" 1663
"   220 gr. 24" 2850 3967 +2.3" 0.0 -6.8" -20.2" -42.8" 1117
340 WBY Mag   220 gr. 24" 3040 4053 -1.6 0.0 -7.1 -20.9 -42.9 1350
"   250 gr. 24" 2784 4330 +1.8" 0.0 -7.9" -23.1" -46.8" 1262
45-70 Govt.   405gr.   24" 1330 1590 0.0 -24.6" -80.3" -172.4" -305.9" 679

To take advantage of this, say you are using a 30-06  165 gr. bullet and anticipate that your maximum range to be 300 yards.  Using known trajectory charts, you may want to adjust your sights so you are hitting slightly over 2" high at 100 yards, which will put you about dead on at 200 yards then about 9" low at 300 yards.  Using this sight in, for a deer sized animal, your "dead on hold" will be out to about 250 yards, but you may have to hold higher like possibly to the top of the back at 300 yards.  Here 250 yards is called Maximum Point Blank Range.  The real secret here is range estimation on your part when you get beyond that 250 yard mark.

The bullet path above the line of sight is known as Mid Range Rise.  With True Zero at the intersecting point of the bullet path & line of sight.

Trajectory of a hunting rifle
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A rifle sighted for this a specific bullet weight of ammo will NOT hit the same place of impact as with a lighter or heavier bullet.  Even changing brands of ammo while still using the same weight of bullet or for the reloader using a different powder may make for different impact points.   It seems to be the vibrations of the barrel that effect this.  Each load needs to be sighted separately, unless you have an exceptional rifle.

In picking a compromise big game hunting caliber and bullet, after looking over the chart, compare a 308 Win. and a 30-06 165 gr. loading out to 300 yards.  The only real difference is that the 308 being a slightly smaller case produces about 200 FPS slower.  Out to 300 yards, there is no appreciable difference in the two calibers.  But we start to see some minor differences beyond that but range estimation at those ranges can counteract this.   Both will kill a deer even at the longer range.

If you really want to get into where your gun is shooting, you will probably become a handloader.  There are many reloading books published by many different bullet and powder manufacturers.  Read them thoroughly AND understand what you read (this may take a while for the uninitiated).  Here a chronograph will come in handy to verify bullet velocity, in your own firearm, which in turn relates to better understanding YOUR trajectory.

How Does Wind Effect Your Bullet ?   Gravity drop of the bullet is only the first of many effects that we need to compensate for, in order to shoot precisely at long range.  The second, and probably the most difficult to compensate for is wind deflection.   Unfortunately, wind deflection is not quite as easy to calculate as gravity drop.

For those of you who hunt in brushy areas with a 200 yard shot is at your outer limits, wind will probably not be an issue for you.  However when you get out to the 400 yard range in open country, it could be very important.   Wind acts upon every bullet.  There is no wind that will allow you to send your bullet happily on its way without something happening.   The bullet drift will be effected in proportion to the wind.  The lighter the bullet, the more the wind will effect it.  Wind drift is something that the average hunter may not even be aware of.  Wind is funny in that there may be no wind where you are, but a gust between you and your target.  Anything your bullet passes thru will effect it's flight.  Look for tree tops moving, grass etc. for any indication.

A wind of possibly less than 10 MPH out to 300 or even 400 yards may not be that great of a threat with the average deer rifle, but when it doubles that speed, at the longer ranges you may even miss an animal.

OK, here is a example that may help explain.  In 1985 on a Alaskan Dahl sheep hunt, I was packing a 35 Whelen.  Partly because I was familiar with it, understood it's trajectory and 2nd we were in Grizzly country.  After chasing these wily critters for 3 days, on the last day, we finally spotted a nice ram near the top of a rocky ridge.  There was no possible way we could get near him from that side of the ridge.  We circled around then climbed the back side of the ridge.  As we broke over the top it became obvious that a storm was moving in very fast from the west.  We were facing gusts quartering us in the 25 MPH plus range.  Breaking over the top, there he was bedded down about 1/4 of the way down (about 350 yards) from the top in a steep (45 degrees) shale slide.  He was in a rock gorge with large boulders on both sides of him that we could not see past between us and him either way.  We were lucky to have popped over this ridge exactly where we did.

He spotted us on the skyline and stood up.  Showdown time.  I shed my day pack, then used it for a rest.  I did not even think of the wind we were facing into because it was either do or die as he was ready to go.   I aimed a tad high for the lung shot and touched one off.   I had no idea whether I had hit him or not because he did not go down but moved out of sight behind the boulders.  The guide ran down the ridge for better visibility, but I hesitated long enough to grab my pack.  I was not going to re-climb that ridge.

When I got to the guide, he said that I had gut shot this sheep.  He could see blood on the rear belly and said that when he got to where he could see the sheep, that the ram was standing holding one rear leg straight back.  The sheep moved angling toward us across this shale slide, when he got at about 150 yards, I shot him again in the lungs.  He went along the shale hillside a short distance, then below a large boulder the size of a house.  We being above him could see all around.  He did not come out the other side, then we heard rocks rolling and saw him rolling down this shale slide to the bottom.

When we got to him, we found that the first shot had castrated him.  That wind had blown that bullet about 24" sideways.  If I would have had a lighter bulleted rifle I would have probably not have even of touched him.

We caped, then quartered him and got back to the base camp tent about the time the storm hit.  Which kept us there for 3 days before the float plane could get into the small lake we were camped on to get us.

Trajectory & Your Gun ;  Now let us get into how this trajectory can relate to your own hunting.  Also we are assuming that you will be hunting in a location near the same elevation as your gun was sighted in at.  If you intend to hunt at a much greater elevation, your gun may shoot higher because of the lighter air. 

 Let us assume you will be using a 30-06 and have picked the middle weight or the 165 gr. bullet for deer (which can also be used for elk, where the 150 gr. would be not heavy enough).  You anticipate you will never shoot over 300 yards.  Your Point Blank Range will be about 250 yards of about 6" total from your high to low point of impact.

 Caliber Bullet  100  yards   200 yards   300 yards  400
 500 yards
30-06 165 gr. +2.3" 0.0" -9.0" -26.3" -54.1"

Now you get the opportunity to hunt Mule deer in Wyoming where the range may be a lot farther.  If you readjust your sight in, you can still use your 30-06 with the same load instead of having to buy a new 300 Ultra Mag long range rifle.  Here you have now extended the practical range by at least 150 yards with a hold over of about 24" instead of 48".     And you still have a Point Blank Range of about 350 yards with about 10" of high to low.  A hit 5" high at either 100 or 200 yards will not really make any difference if you hit a deer in the chest.  Just remember that if an animal is in the 50 yard range, you will need to hold under if you are holding on the head or neck.  And you should have some idea if an animal is out there at 300 + yards, so hold slightly higher than you would at 100 yards.

 Caliber Bullet  100  yards   200  yards   300 yards  400 yards  500  yards
30-06 165 gr. +4.4" +5.2" 0.0"



When you get into hold over, remember that a adult buck Mule deer's chest should be about 18" high so trying to hold over with any reticule 24" or more is simply guessing.  Now if you are using a scope with a Duplex reticule, you might consider doing some practicing by using the heavy bottom post as a aiming point at known longer ranges.

Now all of this looks well and good on paper, BUT 400 and 500 yards is a LONG way out there.  And any shot you may take at these ranges has to be from a steady rest.   In your range shooting off a bench, you should be able keep a easy 2" group, but if you shoot offhand even at that range, I will bet your group will at least double and very likely triple in size.  Now consider if you try to shoot offhand at the 400 yard deer, your 4" group will equal at least 16" at that range.  And what if the deer is 450 yards, that opens up your group even more.  With a deer's chest being 18", your chance of even hitting it becomes a chance.  However, if you can take a rest, that 400 yard group becomes 8", an entirely different but doable situation now. 

And definitely this long range shooting is not conducive to fine accuracy after you have ran a few hundred yards and are huffing and puffing.  Even being able to EXACTLY be able to pinpoint where the animal was standing when you shot from that distance will be a chore, when you go there to look for a blood trail.

Rifle Scopes ;  Scopes optics have come a long way.  There is documentation of military snipers during the American Civil War of making 1000 yard kill.  WWII era American scopes were pitiful by today's standards.  The German military scopes of that time were way superior to the US.  Technology improved after WWII and American manufacturers have now designed very good scopes.  In the early years there were about 3 scope companies, Weaver, Lyman and Stith.  Redfield later took over the old Stith line.  Most of the early scopes either had just a heavy post or a fine cross hair as a reticule.  They did not have self-centering reticules and as there were very few rifles that were drilled and tapped for scopes in those days.   Some gunsmiths in drilling the older guns did not have precise means to align the newly drilled holes precisely centered on the receiver, making the scope reticules possibly off center. 

They were not waterproof either.  I remember my first used scope in about 1956 that was a Weaver K2.5.  It helped my shooting to be more accurate, but was woefully short of identifying small horns even at 100 yards.  And it had the habit of fogging up if the mornings were cooler if I got out of a warm pickup truck.  I would have to unscrew the rear lens, let the temperature equalize inside the scope, then reinstall this lens before I could start a hunt.  Later scopes were nitrogen filled and better seals were developed.  This nitrogen is a dry gas that when sealed inside a scope helps prevent "Fogging" because of differences of inner/outer temperatures.

As time went on all scopes had self centering reticules and the reticule themselves mostly became the duplex crosshair where the center sections were thinner.  There were some reticules that had a 2nd wire below the main crosshair which helped in estimating range of an animal.  If I recall correctly Bushnell was the first to come out with their Scopechief VI  BDC, a (Bullet Drop Compensator) elevation adjustment.  This had a replaceable internally splined ring to fit different calibers in 100 yard increments that went inside and under the elevation cap.  There was a small clear plastic window at the rear of this turret tower.  Once you set this ring for your sight-in, you then slid the ring onto the splines with the 100 yard number showing at the alignment mark in the window, then all you had to do was dial your anticipated range & the reticule would raise to match that trajectory.   The bad thing is that IF the dial had gotten moved and you did not notice, you may be shooting over your anticipated range.

Japanese made scopes entered the market about 1965 or so.  Bushnell was one of these main brands, followed by Tasco.  One brand, Swift was the only Japanese brand that sold only direct to the retail sporting goods stores.  Many off name Japanese scopes hit the market before long.  Some quite economical and many made using lots of plastic parts which did not hold up to much usage.  There were many different models, with the economical ones sometimes not worth what you paid for them.  The more expensive top of the line ones were made quite well however.

Redfield scopes used a 2nd crosswire below the main reticule and this could be used as a rangefinder in that it represented 18" which correlated to the chest height of a adult Mule deer.  By adjusting the power setting so that a deer was bracketed within these wires, there was a numbered post that dropped down inside the top of the scope, giving you the range.

I have done basically the same with my Leupold 2.5X8.  I have looked at many known size targets at different ranges and have concluded that by adjusting my power setting to 5X the crosswire to the top of the bottom heavy duplex equals this 18" distance, which as said before is about the distance of a deer's chest height.  I then multiply how many of these segments to get my estimated target's range.  Knowing this I can then use the top of the bottom duplex for a long range aiming point at about 450 yards with my rifle.

Now we get to more modern reticules / rangefinders.  The new Bushnell DOA (Dead On Accurate) uses differently spaced partial lower wires with small dots at their intersections.  These wires are longer nearer the main crosshair.  On these wires near the ends are small short vertical wires.  This system is twofold in that it acts as a rangefinder also.  Since the bulk of game hunting is at deer sized animals, these crosswires equal a deer's ear width.  Mature Whitetail ears will extend horizontally the width of the wires INSIDE the small upright wires at 100 yards when the deer is looking at you.  Mule deer's ears are wider and extend to the ends of these crosswires.  So if you bracket the ears equaling these crosswires by adjusting your power setting, you can now pick the matching aiming point at that intersection.  In the photo below on the left, this Whitetail would be 300 yards.

Of course Bushnell has this reticule patented and only available on their more expensive Elite or Trophy model scopes.  For a link to Bushnell's technical information for general scope definitions  CLICK HERE.

The Nikon BDC reticule allows hunters to hold “dead-on” at ranges exceeding those previously thought possible.  The BDC’s unique see-through ballistic circles offer an incredible advantage for long range shooting—yet allow a normal sight picture for shorter-range shots where the crosshair itself is the aiming point.   This reticule uses aiming points very similar to the Bushnell and Burris, however it gives you no range estimation that I can find, just point of aim at apparent known ranges.  I have not been able to find any printed bullet drop figures on their internet site, I guess they want you to buy their product before they tell you the important data.  They brag it up but publish to statistics. 

Leupold has redesigned their product line and offers a wider range of scopes.  They offer probably a greater selection of reticules than most manufacturers, with at least 3 versions of Duplex, a Boone and Crocket reticule along with one they call the LR version.

Bushnell Dead On Accurate Nikon Bullet Drop Compensator

Most scope manufacturers now offer a "Mil Dot" for scopes that could be used on tactical rifles.  This is very similar but more complex than the Nikon BDC, & the Burris Ballistic Plex as shown below.    They are usually designed for the 223 or 308 which are basically military calibers.  You will notice by the chart above & the illustrated reticule below, that both of these calibers, even though they use bullets of vastly different weights, the trajectory is very close.

One of Burris's reticules that works great is the Ballistic Plex as shown below.  In the actual scope it does not show the yardage, just the reference marks.  The width of this horizontal opening on the 3 X 9 X 32 scopes equal 6.5" at the higher power and 18" at the lower power at 100 yards.   In using this reticule, it appears that you would sight it dead on at 100 yards and then calculate the distance by what-ever means, then use the aiming reference point as a aiming point, not using a normal hold over as being say 2" high at the 100 yards. 

However for me personally, I still sight my standard rifles (243 with 100 gr bullets and 30-06 using 165 gr) in for 2" high at 100 yards if the intended range may not exceed 250 yards, then will use the magnum side for my aiming point reference at longer ranges.  This may not be exact, but I can then do actual firing at the known ranges to double check for the actual bullet drop.

Burris Ballistic Plex

Other scope manufacturers have reticules that have thin, increasing  size circles below and to the sides of the bottom vertical wire,  These are of known diameters equaling a deer's chest cavity.  Horizontal lines run thru these circles.  This gives you a good range estimation method and corresponding aiming point.

However if, I intend to hunt Montana with my grandson, where the range could be longer, I sight it in for 3" high at 100 yards, which puts me 1.5" high at 200, right on at 250, 4.5" low at 300 and 18.5" low at 400 yards.   Using a rangefinder is practical at that distance as animals will not normally be skitterish at that range.  The 400 yard drop would be about the same as the body height would be, so if I have a good rest and hold 6" to 8" over their back, i should be good for a lung shot.

Check Your Eye Focus ; One thing you need to do with any scope is to focus the eyepiece to fit your eye.  Adjust it by loosening the smaller lock ring and rotating the eyepiece by turning it either in or out until the reticule becomes clear.  The target should also be clear and in focus.  Now close your eyes for a minute or so, look through the scope again.  Look through the scope again, is it still clear?  When you really concentrate, your eye may adjust for better vision.  You want to have the same vision as if you just pulled the gun up and needed to fire a quick shot, not taking a lot of time and forcing your eye to see better.  If not, re-focus and try again.

This above happened on a trip I was on with a friend of mine in Montana for deer and antelope.  His son found out we were going and wanted to go along.  The boy had not hunted for possibly 30 years, but was using his gun that had killed a nice bull elk, years before when he was in high school.  When we got at the uncles ranch, the boy targeted his old rife in.  Impact was still centered where he wanted it at 100 yards.  BUT the next week, I witnessed him missing a decent Mule deer buck at about 150 yards on an open hillside, using a rest off a boulder the size of a Volkswagen.  A few days later, I directed him down a hidden draw and up a small rise upon a small band of bedded down Antelope, which he rested again over a small rock the size of a wheelbarrow and at again about 200 yards, missed a bedded down buck Antelope.  He finally got a doe Mule deer at about 30 yards that about ran him down while he was sitting along a fencerow.

It took a while for me to realize what was happening.  He had not picked up his old rifle for 30 years and his eyesight had changed.  In sighting in the gun, he could spend all the time needed to fire a shot, but when hunting, he was seeing the animal in the scope, but the reticule was probably so far out of focus that he was not even seeing it and did not realize the situation, thereby simply pointing in that direction.

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Originated 11-26-2010,  Last updated 01-02-2016
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