Author Topic: Trajectory & Sight-In Ballistic Relationships  (Read 79664 times)

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Frisco Pete

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Trajectory & Sight-In Ballistic Relationships
« on: November 20, 2010, 12:42:33 PM »
When sighting in a rifle you should be aware of the relationship between the:
BORE LINE - which is a straight line from the bore of the rifle or pistol.
SIGHT LINE - which is a straight line from the scope, other optic, or iron sights.
BULLET TRAJECTORY - which a parabolic curve that the bullet path takes after it leaves the barrel.

Since the bullet starts to drop from level (barrel) to the earth from the moment it leaves the barrel - in order to have a zero sight-in at some reasonable point downrange we compensate by basically tipping the sight line down through adjustment until it intersects the bullet path at our desired zero yardage, whether it be 25 yards, 100 yards or 250 yards, it doesn't matter.

The following chart illustrates the relationship of all these concepts:

Another thing to keep in mind that there is a CLOSE ZERO range and a distant ZERO range due to the nature of the straight sight line intersecting the curving bullet trajectory path from it's start from the muzzle located below the sights.  Between these two points the bullet path is actually above the line-of-sight.  Generally we are trying to fine tune the more distant of the two zero ranges, because that is more accurate and is normally the range we say the gun is "ZEROED" or sighted in for.  The bullet path will drop below the line of sight after the furthest zero range where the sight line and bullet path cross, and as gravity and air resistance combined with a slowing of the bullet's velocity take a greater effect, the bullet path will drop radically until it strikes the earth.

The graph below illustrates how a .308 Winchester Federal Gold Match 168-gr Boat-tail Hollow-point load zeroed at a range of 250 yards leaves the barrel of the rifle 1.5 inches below the line-of-sight (a scope in this instance) and crosses the line-of-sight first, or "close zero" at 20 yards, then continues to rise above the line-of-sight until it drops back to coincide with the line-of-sight again at 250 yards or the distance we say the rifle is "zeroed" at.

TWO ZERO RANGE GRAPH - .308 Winchester Federal Gold Match 168-gr Boat-tail Hollow-point Match load

Deciding on the proper zero depends on the cartridge your gun is chambered for and your specific needs.  Some cartridges are considered shorter range rounds (like the .30-30 or 7.62x39mm) while there are very flat shooting Magnums on the other extreme.  
Some people will never take a shot beyond 200 yards, while others may hunt or shoot at longer ranges.  Some may want to stretch their shooting to the longest ranges they can.  Rifle matches require set distance shooting that the rifle must be sighted in for.  This all affects the zero decision.  
A great many choose a compromise zero that keeps the bullet at a reasonable distance above and below the line-of-sight as far, or a little farther then they expect to shoot.  By doing this the bullet will hit the target area, if not dead-center, at least in the target or kill zone.  This is most popular among hunters who encounter game at varied and unknown distances, and works in a military combat setting as well.  
Shooters who shoot at extreme ranges will often use a zero range that is a very distant yardage (500+), and one in which the bullet is a surprising height above the line of sight for quite a distance - in order to be on zero at the desired range, and not have too much drop below the line of sight at target ranges beyond the zero point.  Sometimes scope mounts that are raised excessively in the rear need to be used to achieve this angle relationship at extreme range in order for the scope's internal adjustment not to run out of adjustment range.  We will look at the differences in various zero ranges chosen from the three general areas we just looked at and their effect on bullet path next.

Some ballistic programs illustrate the bullet path.  This ones you see here are from the Oehler Ballistic Explorer  The parameters can be set by the user and you can use the data to figure out what that bullet is doing after it leaves the barrel.  The Oehler Ballistic Explorer allows up to 3 different comparisons at once, which is useful for illustrative purposes like on this post here.  However, it is not free.
Of course you can use other ballistic programs as well.  There are both free Internet programs and ones that you can buy available.  I have listed some of the Internet ballistic program sites at the end of this post.  If you have any favorites, please PM me with the details and I will get it added to the list.
In this particular illustration, the data is for the popular .308 Winchester Federal Gold Match 168-gr Boat-tail Hollow-point load (#GM308M).  This is typical of a match or sniper load shot from one of the popular .308 Tactical rifles.  It utilizes a Sierra 168-grain MatchKing bullet with a ballistic coefficient (BC) of 0.457.

These are some other factors that will affect your bullet path - and I've showed what data I plugged into the ballistic program to achieve my results:
Ballistic Coefficient is a scientific way of quantifying how streamlined a bullet is.  The higher the number - the better the streamlining.

Velocity is 2600 feet-per-second.  The more velocity, the flatter the trajectory.  Chronographing the velocity of YOUR ammo in YOUR rifle gives the most accurate data.

Altitude is set for 2000 feet.  Bullets shoot a little flatter the more altitude you have because of thinner air.

Temperature is set at 70 degrees F.  Temperature is another variable.

Humidity is set at 60%.  Humidity is another variable.

Scope height is set at 1.5 inches above the bore.  This generally assumes a bolt-action rifle with a 40mm objective in medium rings.  This changes the relationship between the bore line and sight line.  While 1.5 inches is typical for a scoped rifle, iron sight are closer to the bore, and optically-sighted AR15s, AKs, FALs and any rifle with a large objective scope, are higher.  These changes from muzzle to (far) zero are graphed further down.

Zero is set for three different yardages.  Trace 1 is 100 yards.  Trace 2 is 250 yards.  Trace 3 is 500 yards.  

ZEROED AT 3 DIFFERENT RANGES GRAPH - .308 Winchester Federal Gold Match 168-gr Boat-tail Hollow-point Match load

You can see that using a 100 yard zero makes you hold over longer range targets a lot more once the bullet crosses past 230 yards or so.  The bullet never rises any significant distance above the line-of-sight but drops alarmingly past 230 yards or so.
The popular 250 yard zero is a good compromise for most common hunting, or even combat, distances with the .308 cartridge where any type of longer range is anticipated.  Rise above line-of-sight is not enough that you would miss a deer, being only about 4-inches or so at 150 yards, and the bullet gains another 90 yards before it drops 7-inches below the line-of-sight.  Zeroing at 100 yards would require the bullet hit 3.5 inches above the point-of-aim (POA) to achieve a 250 yard zero.

The 500 yard zero is an interesting illustration.  This would put you dead-on for shooting a known-distance target in competition at 500 yards.  The obvious drawback to zeroing at such long ranges is for general use, whether combat or hunting is the excessive height of the bullet above the line-on-sight at normal ranges.  At 250 yards it is 23 inches high!  To attain such a zero at a normal 100 yard range, you would have to zero 13-inches higher than the bulleye/POA.

Now let's look at the same graph - only extended out to 1000 yards.  You will be able to see the reason that the .308 Winchester with the common 168-grain Sierra BTHP Match bullet is considered to be an 800 yard sniper round.  Even using the 500 yard zero, the bullet drops about 120 inches, or nearly 10 feet at 800 yards!  Because this graph only goes to a drop of -160 inches (13.33 feet) you can't even see where it crosses 1000 yards.

1000 YARD GRAPH - .308 Winchester Federal Gold Match 168-gr Boat-tail Hollow-point Match load

The general illustration information above is based on a scope height of 1.5 inches.  Your iron sights would be lower and your scope height may be different by more than 1/2 inch - which causes a variation.  If that is the case, the information would be fairly close, but more particulars like exact sight height and perhaps altitude would narrow in down a bit finer.

Checking the FAL in my safe, the iron sight height runs about 2.2".  Further "guestimation" using a scoped AR15 to approximate a scoped AR10 gave a sight height of 3.2"  Running that sight height against the 1.5" (bolt gun 40mm objective medium rings) height used in the graphs gives this difference up close trajectories and variations in the POI at 100 yards to achieve a 250 yard zero with Fed 168-gr Match:
Trace 1 (RED) 1.5 inches
Trace 2 (GREEN) 2.2 inches
Trace 3 (BLUE) 3.2 inches

3 Different Sight Heights Graph - Fed 168-gr GM / T1 +1.5" / T2 +2.2" / T3 +3.2"

Let's take a different view of the target and add a twist - the wind plus the effects of zero and path/drop.  
Illustrated is a head-on view of a target AT 300 yards shot with the above load using the 250 yard zero.  You will see the arc of the bullet path toward the target - striking 4.7 inches low - and you will also see the bullet drift from the effect of a 10-mph wind blowing 90 degrees from the right - that blows the bullet 6.9 inches to the left of aim.  Point of Impact (POI) of the bullet on target is where the "scope crosshair" is at the 8 o'clock position.  The increment numbers on the target rings are a bit confusing so ignore them.

Notice how much a 10 mph wind will affect the bullet!  While you can fairly easily adjust for elevation, judging the wind is another matter entirely and takes practice!
A wind blowing:
At five to eight miles per hour - leaves will rustle in trees and bushes.
At eight to ten miles per hour - small trees and large plants will bend.  This is the amount of wind illustrated above.
Twelve to fifteen miles per hour - is enough wind force to sway large tree limbs and violently disturb small trees and bushes.
If a flagstaff is visible, the angle between the bottom edge of the flag and the pole divided by four will approximate the windís velocity at that point.

Next let's look at the effect of using different weight bullets in the same .308 on trajectory.  We will stick with popular military or target styles again using:

Federal/American Eagle 150-grain FMJ-BT BC 456 - here we have a military 7.62 NATO M80 duplication load with a BC similar to the 168-gr Match bullet, but in a lighter bullet at a higher velocity - 2750 fps.
Federal Gold Match 168-grain BTHP (Sierra MatchKing bullet) BC 457 - the one we have been looking at before in all the graphs.
Federal Gold Match 175-grain BTHP (Sierra MatchKing bullet) BC 483 - this is the newest heavy-bullet sniper .308 load that shoots to the same velocity as the 168-gr Gold Match.  You will be able to see the effect of a bullet with a higher BC at the same velocity.

250 YARD ZERO / 3 DIFFERENT BULLETS - Fed/AE 150-gr FMJ / Fed 168-gr GM / Fed 175-gr GM

The amazing thing here is that all three loads have virtually identical trajectories when zeroed at 250 yards with the flattest trajectory going to the 150-gr FMJ, which, despite it's lower BC, started out faster and never relinquished the slight trajectory edge.  In fact it is about 4 inches flatter shooting at 450 yards.  If you were to extend the range to 1000 yards with this zero, drop would become 10 times what it is at 450 yards, or about 328 inches (27.33 feet)

Okay, now we will try the 500 yard zero for all loads with the range extended to 1000 yards.

500 YARD ZERO / 3 DIFFERENT BULLETS - Fed/AE 150-gr FMJ / Fed 168-gr GM / Fed 175-gr GM

Here we have the "little" 150-gr FMJ still flatter shooting with a drop of around 105 inches (about 8.8 feet) at 1000 yards, while the next best is the 175-gr Match bullet with it's higher BC.  However all are relatively close.  Either way, range estimation becomes critical past 600 yards despite a 500 yard zero due to the steep drop of the projectiles, as the following shows:  
150-gr FMJ = 800 yard drop - 105" / 1000 yard drop - 249"  
168-gr HPBT = 800 yard drop - 120" / 1000 yard drop - 283"  
175-gr HPBT = 800 yard drop - 115" / 1000 yard drop - 270"

1000 YARD WIND DRIFT / 3 DIFFERENT BULLETS - Fed/AE 150-gr FMJ / Fed 168-gr GM / Fed 175-gr GM

This next graph shows the wind drift of all three bullets up to 1000 yards from the effects of a 10-mph sidewind from 90 degrees.  Here we notice a bit different phenomena.  The high ballistic coefficient of the 175-grain match bullet gives improves "wind-bucking" over the 168 match bullet, although it is basically the same as the 150 FMJ-BT M80-type bullet.
At 1000 yards we have the following amount of wind drift for each bullet:
150-gr FMJ = 92"  
168-gr HPBT = 100"    
175-gr HPBT = 92"
So where does the advantage of using the match bullets like the 175-gr lie, ballistically-speaking?  In their accuracy superiority over standard FMJ ball ammo.  Especially using the newer 175-grain Sierra MatchKing load, shooters have an extremely accurate bullet that will mimic the trajectory and wind drift of the cheap 150-gr ball ammo that sights are iron sights regulated for and is inexpensive to practice with.  

What about sighting in with different bullet weights?  You have to remember that each load acts individually on barrel vibrations or harmonics.  Therefore one cannot just blindly assume that even if the loads have a similar trajectory, that they will print to the same POI on paper.  The powder, powder charge weight, bullet weight and length can change vibration patterns.  So always check each different load for POI and zero first.  Often small adjustments may be necessary.  Write these down so you can have the data to dial in your scope when changing to another load.

Next lets have some fun and look at three popular military calibers all zeroed at 200 yards and see how they stack up for bullet path.  We will use the:
.223 Rem. 55-gr FMJ-BT 5.56 M193 duplication load by Winchester.  BC .272
7.62x39mm 122-gr FMJ M43 duplication load by PMC.  BC .292
.308 Win. 150-gr FMJ-BT 7.62x51 NATO M80 duplication load by Fed/AE.  BC .456

3 CALIBER PATH COMPARISON - .223/55, 7.62x39/122, .308/150 all zeroed at 200 yards

The .223/5.56 and .308/7.62 NATO loads are neck and neck in trajectory and much flatter than the slower a 7.62x39mm load.  Even though the .223/5.56 has the lowest BC by far, the initial velocity of 3240 fps, which is much faster than either of it's two rivals, keeps it flat shooting.  The .308 has a nice combination of decent velocity and a very high BC that makes it so ballistically balanced.

3 CALIBER ENERGY COMPARISON - .223/55, 7.62x39/122, .308/150 in foot/pounds

Okay, this ought to make .308 shooter feel a lot better, because it shows why the .223 and 7.62x39mm are considered "medium-power" cartridges and the .308/7.62x51 NATO is a "full-power" cartridge.  It also shows why the military consider both medium-power cartridges 300 meter rounds - when velocity, energy, and drop are considered.

Okay, enough ballistic comparisons.  You could do this all day and dial-ups could never get it loaded!  I hope you understand trajectory, sight-in or zero range, the effect of the wind on bullets, and all the rest of the exterior ballistic stuff and know more about how to apply it for your rifles and cartridges.


If you know of others, please PM me and I will add them to the list.
« Last Edit: November 20, 2010, 03:42:10 PM by Frisco Pete »
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Re: Trajectory & Sight-In Ballistic Relationships
« Reply #1 on: November 20, 2010, 12:46:27 PM »
Talking to Pete I feel like Uma Thurman in "Kill Bill" when she went to train with the master of martial arts guy.
Thanks Pete.
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Re: Trajectory & Sight-In Ballistic Relationships
« Reply #2 on: August 23, 2013, 03:45:38 PM »
Best illustrations and explanations I've seen on the topic, thanks Frisco Pete!
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Re: Trajectory & Sight-In Ballistic Relationships
« Reply #3 on: May 16, 2014, 03:20:36 PM »
What is the height of the sights on a Chinese SKS? Unless I have missed it (which is entirely within the realm of possibility!) I have found no info on this anywhere on the net.
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Re: Trajectory & Sight-In Ballistic Relationships
« Reply #4 on: July 05, 2015, 01:48:24 AM »
If I've measured mine correctly,  I have between 1.370"  and 1.450"   above bore center    depending...... ;-)

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Re: Trajectory & Sight-In Ballistic Relationships
« Reply #5 on: September 26, 2016, 03:34:57 PM »
I feel like I'm back in physics class and I love it. Thanks for the post!
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