How to Calculate Point Blank Range Using 7.62X39 Ammo. By Mike Lee mm-industries.com
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1 1 How to Calculate Point Blank Range Using 7.62X39 Ammo By Mike Lee mm-industries.com
2 On-line Ballistic calculator Point-Blank Range and the 7.62X39 Cartridge 2 Most folks consider the 7.62X39 cartridge a medium range cartridge. Designed to be effective on man-sized targets out to 300 meters (about 328 yards) it has a much shorter effective range for hunting and most target-shooting, because hunting and target-shooting both generally involve smaller target zones. Here is where the concept of point-blank range becomes very useful. Point-blank range is a term most often tossed around at least in popular media to suggest extremely close range, but the reality is very different. The concept is, in fact, a way of calculating the greatest range at which a shooter can take a shot without regard for hold-over (the technique of aiming above a target, so that the bullet is still on-target at the end of its trajectory, when it has already begin falling below the point of aim). The concept of point-blank range works to maximize practical shooting distances with a given firearm, and for that reason it is most useful when shooting cartridges with short to medium range potential, like the 7.62X39. Before going further, it s important to make a few things clear about calculating point-blank range for different firearms. First, readers need to understand that the numbers we will generate here as examples are going to be approximations, not absolutes. That s because some of the variables used in calculating point-blank range vary from firearm to firearm, and between different examples of the same cartridge. This includes variables like bullet weight, bullet shape, the speed of the projectile out of a particular firearm, and even the height (above the bore) of the sights on the firearm.
3 That means, while someone can get a rough idea from reading a document like this one, the figures used here will be only that: A rough idea if your data happens to match what we use here. Otherwise, it s only example of how to use point-blank range data generated for your specific load. For that reason, we ll touch on ways to get a much more precise calculation of point-blank range for a particular load in a particular firearm later on in this discussion. It should also be understood by the reader that point-blank range data is really best applied in practical shooting situations at various and especially at mixed or unknown ranges. That kind of situation comes up often in hunting, and sometimes in silhouette shooting, and other situations where the shooter is successful or unsuccessful based on hit or miss, rather than by group size, or scores based on how close to the bull s-eye a shot or a string of shots are. That kind of job, shooting for score according to the distance of each hit from a bull s-eye, is better done with precise ballistics charts. 3 With that caveat covered, a solid understanding of point-blank range will help shooters set up their rifles to hit various targets at various distances without a great deal of calculation and thought on each shot. It s a way of knowing off the top of your head whether a target is in range for shooting directly at the target, or if hold-over (or hold-under ) is needed. It will help with snap-shooting targets of opportunity within a given maximum range, and for knowing when to choose to stalk in a little closer in hunting. It s also a way of knowing whether a particular rifle is going to be useful for a particular shooting course, or in a particular hunting environment, and a way of setting up the rifle you have for a particular job or environment.
4 Characteristics of the 7.62X39 cartridge This discussion of point-blank range is focused on the 7.62X39 cartridge. The limitations of this cartridge arise from two factors. First and foremost, it is a relatively slow round by modern standards, throwing bullets generally under 2400 feet per second (compared for example, to the 5.56 NATO round which throws a smaller bullet in the ballpark of 3,000 feet per second out of similar length barrels). Second, the projectiles used in this cartridge are not particularly efficient in terms of ballistics. In other words, the air resistance tends to slow them down relatively rapidly over distance, as compared to bigger cartridges which shoot heavier bullets of about the same diameter. Many factors come in to play, and it can be a complex discussion in and of its self, but a bullet s ballistic coefficient value is how we compare different bullets on their ability to cut through the air and how much it will be slowed by that air. The bullets used in the 7.62X39 don t have particularly high ballistic coefficient values, largely due to the relatively light weight of the bullet for the caliber. Typically, the ballistic coefficient for bullets used in this cartridge range from around.225 for lighter bullets, to.325 for those at the heavy end of the spectrum (don t worry about what that number really represents at this point. Just be aware that in ballistic coefficient numbers, higher is better.) By comparison, the.308 Winchester launches similar-diameter, but heavier bullets, and typical ballistic coefficients for spitzer (pointed shape, as opposed to round nosed) bullets run from around.325 up to over.400 or so. That means that the.308 Winchester bullets (which generally start out going much faster anyway) lose much less speed over the first couple hundred yards than the 7.62X39 bullets. 4
5 Every cartridge has its limitations, and these characteristics of the 7.62X39 round do not suggest that the cartridge is not a good choice. In fact, there are many distinct advantages to the 7.62X39 cartridge, not least of which is the current plenitude of surplus and inexpensive loadings for the cartridge. While it is less powerful than the.308 Winchester, 7.62X51 NATO, or 7.62X54 cartridges, the recoil is also much less, and the weight of the rifle tends to be much less, while still being much more comfortable to shoot. It is also true that there are many rifles offered in 7.62X39 that are less expensive to buy than most rifles chambered in most of the other.30 caliber cartridges, and on the used market, the 7.62X39 chambering is far more common than anything else for inexpensive semi-automatic rifles like the AKM and the SKS. There are actually more rifles in existence around the world today chambered in 7.62X39 than any other cartridge available, including.22 Long Rifle, which has long been the most prolific in the United States. While the 7.62X39 cartridge is considered a medium range cartridge, it also has a great inherent potential for accuracy, and is quite capable of shooting one inch groups at 100 yards, and three inch groups at 300 yards. Most accuracy complaints about the 7.62X39 stem more from the limitations of the rifle it is fired from than from the cartridge itself. However, not all brands and manufacturers of this cartridge are equal, and some (usually cheaper) brands are not loaded to the same exacting specifications as some of the better brands. To make good use of point-blank range in maximizing range, quality ammunition is a necessary ingredient. 5
6 A Word about Bullet Trajectory A basic understanding of bullet trajectory is necessary in order to understand how point-blank range is such a useful concept. Many readers will already be familiar with this, but I find a surprising number of shooters who are not, both beginning shooters, and more experienced shooters. We ll cover a few things that are useful to know, and those who are already familiar with these things can skip to the next section. First, it s necessary to understand that bullets do not travel a straight path to the target. Ever. Any firearm that has been sighted-in for practical shooting at any range begins by shooting the bullet at a slight angle up. That is to say, the bullet leaves the barrel and gains elevation for a time, before reaching an apogee (a peak in the trajectory of the bullet) and beginning to fall, while at the same time it is traveling forward at a much greater rate than it is gaining elevation until very late in the trajectory path. Once the bullet starts falling faster than it moves forward, you are near the end of the path where the bullet hits the ground. This initial gain in elevation is necessary; otherwise a bullet would never strike exactly on target, because rifle sights are always mounted above the bore of the firearm. They might simply be mounted on the outside of the barrel, a bare quarter inch above the bore, or they might be two inches or a bit more above the bore. If the bullet didn t travel up as it began its flight, the best you could do by aiming at the center of a target is to hit a quarter inch or more below the center of the target. 6
7 This upward travel in the trajectory is the critical factor that limits the range for which a firearm can be sighted-in and still be effective at a shorter ranged. At some point, the gain in elevation that the bullet goes through can take the path of the bullet above the maximum height of the intended target, and when that happens the shooter suddenly has to pay attention to range, and hold under the center of the target in order to be sure of hitting targets closer than the range the firearm is sighted-in for. This is one reason point-blank range is so useful. It takes a lot of practice to know when you have to hold over a target, and to be able to guesstimate how much. Holding under the target at close ranges just adds to that learning curve, and under pressure, it s much less instinctive to remember to calculate for that. Although it tends to be much easier to estimate distances close-in than further out, proper use of point-blank range calculations can eliminate or at least minimize that aspect of the equation. 7
8 Just for fun 8 At this point, just for fun, take a moment and consider this scenario: Let s say you are going to take your rifle chambered in 7.62X39 and hunt whitetail deer in a mixed area of dense brush and small open areas. You ve got a couple of tree stands that let you shoot over the brush in places, so you have some lines of sight that extend a quarter mile or better in several directions. Other lines of sight are shorter, and some are very short, say, fifty yards. You don t know yet which places tend to be hot for deer year after year, so you want to be prepared for as wide a variety of shots as possible. Now, how will you sight your rifle in for that hunt? Decide on that, and then we ll go back to pointblank range.
9 Using Point-Blank Range There are a few values details about the load and rifle we are using that we need to know before we can put point-blank range into use. These include factors about the cartridge and load to be used, but also, we have to know what the dimensions of the target(s) are. In this case, the dimensions of the target does not necessarily mean the whole size of whatever we are shooting at. Instead, it s the size of a vital zone within the target, where a hit anywhere within that zone constitutes a successful shot. For example, if a hunter is intending to shoot deer, the animal itself is madeup of much more area than it is humane to shoot at. Ethical hunters know that there is a vital zone which includes heart and lung shots, which will generally result in a rapid, humane kill, and there are a lot of areas which, if hit, will result in a wounded animal running away, too far and too fast, to suffer and perhaps die without ever being recovered by the hunter, or harvested. In this case, the target is not the whole animal, but a zone within the chest area of the animal that yields the humane kill. If we specify that the hunter is hunting whitetail deer, and the average deer in the area run about 125 pounds, a diligent hunter might take a look at a diagram of the heart/lung area for that animal and come up with a vital zone target circle of about ten inches diameter. That is to say, out of perhaps 18 inches, top to bottom, and perhaps inches from nose to tail, there is a circle about 10 inches in diameter that constitutes the real target zone the hunter is aiming at. Properly locating this zone on the animal, the hunter who shoots at the center of this target can now hit up to five inches high or five inches low and still strike the critical target he is striving for. Point-blank range calculations will tell us how far the maximum distance is that our hunter can be sure that, if he executes a good shot, aiming directly at the center of this zone, he can be confident of making his shot and harvesting the animal humanely. 9
10 Now we ll sort out the values we need to know about the rifle and cartridge we are using: 10 Muzzle Velocity: This is simply the velocity at which the bullet leaves the barrel. Most of time, manufacturers publish this information as a figure which is an average of bullets fired from a test barrel, and that information is usually available on the Internet. Purists will buy or borrow a chronograph and test fire their own rifle with the ammunition they intend to use. There will be some variation, so averaging the values across a sample of a dozen bullets is a good idea, when using a chronograph. If you use published figures, instead of test-firing the ammunition out of your own rifle, there will be some variation because every rifle is different. In that case, check your figures by shooting at various ranges, and make any adjustments, as necessary. For this example, we re going to assume we have a velocity of 2400 feet per second, which is a good average for 7.62X39 cartridges in the 123 grain bullet range.
11 Ballistic Coefficient: 11 This information is also published, or sometimes calculated for popular bullet options by third-parties. The formula for ballistic coefficient is complex by most of our standards, and looks like this: Fortunately, we won t have to mess with that formula ourselves. The information will be available somewhere on-line, or can be estimated by comparing similar bullets. For this example, we ll use data I pulled from Gundata.org, which gives the BC of a 123 grain bullet from a 7.62X39 cartridge as.225, although they listed the muzzle velocity slightly lower than our 2400 fps, at 2349 fps (we ll assume our gun has a smoother bore or a better length, which could easily generate that 50 fps difference.)
12 Sight Height: 12 This is a measurement of how high the sights sit above the bore of the rifle. For this figure, I ll take a typical AK sight-height and round it off to two inches above the bore. I measured one at 1.97 inches by dial caliper, but yours may be slightly, or even significantly, different. Measure from the center of the bore to the top of the front post, with iron sights, or the center of the scope for optical sights. Target Zone: We covered this in the lead up, but let s mention it again. For this first example, we are using a 10-inch target zone, to represent the vital zone of a whitetail deer.
13 With that information in place, we are ready to calculate point-blank range for this example. Just as we did for the BC numbers, we won t calculate point-blank range by hand. We ll let the Internet do the work, turning to software to do the job for us. For this example, I ll return to Gundata.org, and run ballistic charts, entering the information for our assumed bullet, and varying the sight-in range until I find one that approaches, but never crosses significantly above the five-inch apogee limit that our ten-inch target zone allows for, and then I ll look at the down-range numbers to see how far out the bullet goes before it crosses below the five-inch limit for bullet drop. That will be our maximum point-blank range for this example. As I run the numbers initially, I ll start with 10-yard increments, sighted-in for 100 yards. That yields a chart that looks like this: 13
14 (Note that the name of the cartridge, given at the bottom of the chart, is NOT 7.62X39. That s because that entry isn t one of my choices when generating the chart, but no matter; While I had to pick something off their list for that field, I then entered the proper values in the software, so the chart is accurate in the trajectory for the bullet we are working with, NOT for the bullet/load named on the chart.) 14
15 Some software packages will do this calculation for you much more simply than this one requires for custom data entry. My personal favorite is the ballistic software from Sierra.com, which will calculate point-blank range with one click, after you enter the proper values. Doing it this way, by trial and error takes a bit longer, but yields results using on-line software, without purchasing anything else. It s FREE, and available to all on the Internet, so we used it for this example. My thanks to the people at GunData.Org for making it available! 15
16 Reading the Chart 16 Looking at the chart, you can see that this is a representation of the bullet s trajectory. The line goes from left to right, graphing the path of the bullet, based on the values we entered. The numbers on the left side show the rise and fall of the bullet above in inches above or below zero, which is the line of sight from the sights on the rifle. The numbers across the bottom show how far the bullet has travelled from the muzzle of the rifle in yards. You see that I don t use anywhere near the five-inch rise I have allowed for the target-zone, and I m five-inches low at about 185 yards. By 190 yards, I ve fallen outside my target zone, and would have had to hold-over to make the kill shot I want on the deer we have described. Now I start to narrow-down my range, and after entering a 200 yard zero, I find I m still not up to my five-inch height limit, but at a 250 yard zero, I go OVER the five-inch limit (those charts are not copied here to save space.) I ve got a zone to work within, now, and it s just a matter of plugging in numbers until I get the result I m after. Looking at my results, I know that if I zero the rifle somewhere between 200 and 250 yards, I ll hit my maximum 5-inch rise, and then I can see on that chart where the bullet falls below my maximum 5-inch drop. Shortly, I hit upon a zero of 230 yards, and here s what that looks like.
17 (Again, note that the label is NOT the cartridge we are considering, and the data is NOT correct for that cartridge!) 17
18 This looks pretty good. Examining the numerical values that accompany this chart on the website, I see that I wind up less than an tenth of an inch over my five-inch height limit at the maximum (at around 140 yards,) and now I don t fall below my five-inch limit until somewhere around 270 yards. That s about as good as it s going to get with this method of calculation, so I look now to see how this rifle is actually sighted-in to get this results. Looking at the chart, I m going to say that it appears to be sighted about 4.5 inches high at 100 yards, so if I sight my rifle for that, I ll be very close to my limits shooting out to 270 yards at whitetail deer. Past that, I ll have to hold high, but anything from zero yards to 270, I can just aim at the center of my vital zone, and take the shot (the actual value when I checked the numbers after writing this was inches high at 100 yards.) Because I m using estimates, instead of testing muzzle velocity with a chronograph, and shooting test groups, I might decide to limit my range to 260 yards, at least until I have tested a shot at distance, but in theory, I m on pretty solid ground out to (Once more for clarity, I simply chose the label at the bottom of each chart at random, from the list of options on the website, but the values I entered represent the fictional bullet we are using for an example. This is NOT accurate for the cartridge mentioned on the chart s label; it IS accurate for a.30 caliber, 123g bullet with a BC of.225, fired out of a rifle at 2400 fps, with sights 2 inches above the bore, and sighted in at 230 yards for zero. I considered blanking out that label before pasting the image in to this document, but in the end, I left it because that s how it appears on the website I used, and that s how it will look for anyone who works up a load in 7.62X39 on that site.)
19 What this example of using the concept of point-blank range shows is that for hunting, the range of a 7.62X39 rifle would be a good choice for whitetail deer out to 270 yards (in a rifle that is reasonably accurate to that distance,) and to maximize the chances on a fast-shot scenario, that rifle should be sighted for four and a half to four point six inches high at 100 yards. I could go further with this information, and check out my hunting area to make sure that I know the ranges from my deer stand, or across open areas, so that I have that 270 yard limit firmly in my mind. I can pick out landmarks, or even place markers if I m doing the survey well in advance of my hunt. 19 What this data does NOT show is how the bullet will perform when it hits the target. That is a whole different topic. Suffice to say, there are MANY different brands, bullets, manufacturers for the 7.62X39 cartridge. Not all are suitable for hunting, and not all to the maximum distance the weapon can be sited to shoot. An ethical hunter knows this, and does some homework to make sure the ammunition chosen is suitable for the task at hand.
20 The Real Value of Using Point-Blank Range Over Other Methods Compare the result we obtained to the more common methods of sighting a deer rifle in. Most of the folks I ve hunted with over the years use one of two methods. The most common method is to sight the rifle in an inch high or two inches high at 100 yards, depending on personal preference. The other method I ve seen frequently is sighting in dead-on at a flat 200 yards. Neither of these is a bad method. But neither of these maximizes the range of the rifle for deer-sized targets. Most hunters I ve been in the field with don t really have any solid idea of the true trajectory of their rounds, but say that they generally have good luck with one of these two sighting methods. Taking the example of sighting in at 200 yards, what you will see with a 7.62X39 rifle and load as I described above is that the bullet falls below the 5-inch line at 235 yards. By calculating point-blank range, we push that out an extra 35 yards, to 270, and we still know that any shot under 270 yards is in the target zone. That s almost 13% further. Someone who chooses to sight in two inches high at a hundred, doesn t even do that well, because a 200 yard zero on the rifle we described for the example is more than five inches high at 100 yards; acceptable for combat soldiers, taught to aim at center mass, but not for a hunter. That hunter may be dead-on at 200, but a quick shot taken at 100 yards could miss the vital zone we are looking for. Again, this would be less important with a higher velocity, longer-range rifle, because the arc of the bullet trajectory would be less severe but if I choose to hunt with my 7.62X39, this is how to maximize the range I can shoot with confidence. 20
21 What Calculating Point-blank Range Won t Do For You It s important to point out that setting a rifle up for point-blank range has no bearing on factors other than range. Wind-drift and group size are not improved. In fact, if anything, wind-drift could become a bigger problem, because you may find yourself shooting at longer distances than you have previously. And group-size can be a significant issue with many of the semi-automatic rifles in 7.62X39. It becomes a bigger issue as range increases. The point here is that while point-blank range can maximize the range you can hit a target zone without hold-over, it doesn t improve the accuracy of the rifle itself. In the example we discussed above, we talked about a ten-inch target at 270 yards. If the rifle or the shooter is incapable of shooting a teninch group at that distance (a little more than three and a half MOA) then it is irresponsible to shoot at game at that distance. A little drift to the left or the right could result in a gut-shot animal, one that will run away and perhaps die over a series of days. Point-blank range gives you the theoretical maximum range to shoot without hold-over or hold-under, but the limits of the range a particular hunter should shoot at still come down to the ability and ethics of each individual shooter. 21
22 Point-blank Range on a Practical Shooting Course While in the recent past, civilian non-hunting shooting sports used to focus almost entirely on shooting bull s-eye targets for score, the current trend is towards more practical applications generally, shooting courses designed to simulate combat, or training for self-defense. In fact, there is an explosion of new training schools and new competitive events at all levels that expand the boundaries of the shooting sports in many different directions. Some of these are prime applications for applying the concept of point-blank range, and putting it to good use. A quick review of YouTube clips for various rifles chambered in 7.62X39 indicates that a lot of ammunition in this chambering is expended on silhouette targets that represent enemy combatants. These are frequently very similar to the standard military E and F targets. The E target is a half silhouette which represents the upper-half of a standing soldier, from the beltline up. The F target is shorter, representing the upper chest, shoulders, and head of a prone enemy combatant. 22 Suppose you intend to shoot a course of several of these targets, at unknown ranges, out to a maximum range of 300 yards. The course is scored as hit or miss, meaning there are no extra points for headshots or center shots; it s strictly a did the shooter ring the target? system. How do we use point-blank range to set the rifle up for this course?
23 We begin with the ballistic information for the load we are shooting, and the sight-height of the rifle, just as we did in the previous exercise. We ll use the same values here as we did above. The next step is to figure the size of the target zone, and in this case, we have more than one size. And, for this exercise, we ll stipulate that we don t know which size targets will be at what distance. All we can do is take the dimensions of the smallest target and work with that. The smaller target is the F target, the one which represents a prone man. After looking up a few examples on-line, it seems these targets tend to run to a maximum top-to-bottom dimension of 19 inches, but we haven t seen the actual targets, so we ll shave an inch off to be safe, and call it an 18 inch target zone. We now have a maximum dimension to work with, and we can start calculating point-blank range, and see how we should sight the rifle in for this course. In this case, what we want is a chart that shows the bullet drop to be half the height dimension of the target zone at 300 yards, the furthest distance we will shoot. But we also want to be sure that the bullet never travels above 9 inches OVER the line of sight. Our previous chart, zeroed at 230 yards for whitetail hunting, shows that at 300 yards, we are around 11 inches low, so we know we are going to try to zero the rifle past 230 yards, right away. Let s try a 250 yard zero. 23
24 (Here, I ve lined-through the random cartridge name) 24
25 Here we see the results (this time with a line through the random label I selected in the software, because again that label is meaningless, so long as we input the correct data.) Note that at 300 yards, we re a little over 8 inches low, and the peak path of the bullet never rises above 7 inches. This is well within our parameters, and wouldn t be a bad setting to use for the course we just described. When I checked the tables that accompany this chart on the website, it shows that at 100 yards, the bullet is inches high, so if I sight my rifle in 5 and ½ inches high (or a smidge higher) at 100 yards, I m very close to this trajectory. As far as elevation, I should be able to put my sights on the middle of the target and score a hit at all ranges within this course. There is the added benefit that the furthest targets will be struck low, below the head shot zone and well into the shoulders/chest area, where the target is wider. I can shoot the whole course without regard for hold-over or hold under, just aiming at the center of the target. If I want to hold a little high at the furthest ranges, I can elevate the shot three or four inches, say, if I had to clear some tall grass, shooting from a prone position. But if I forget to do that on a given target, I m still in the hit zone. 25
26 Maximum Point Blank Range 26 Determining the maximum point-blank range for a given rifle, cartridge and target size using this method is simply an exercise of entering longer zero-ranges until you see the bullet trajectory crosses above the upper limit of half the target size. We see in the last chart that point-blank range for the 7.62X39 rifle we have been working with, shooting at F -type targets, is greater than 300 yards. We didn t find out the maximum because, in this exercise we were postulating a particular shooting course with a known maximum range of 300 yard targets. But now, you re equipped to do the calculation yourself, for your own rifle and load. Decide what the target (or vital zone) is going to be, and take half the height dimension of that. Then, enter the values until you see the trajectory cross the upper limits. When you find that, look to see what range the bullet is at when it crosses below the aim point a distance of half that height dimension. That s the maximum pointblank range. Finally, see what the bullet height is at the 100 yard mark, and sight your rifle in for that height at 100 yards. The trajectory will be very close to what the chart gives you all the way, assuming you have entered the proper data. You have now maximized point-blank range for that rifle on that target.
27 Conclusions 27 I stated previously that a high-powered, longer-range rifle reduces the need for using point-blank range, and that s true as far as shooting any set range goes. However, I should also point out that long-range rifles actually benefit more from the same calculations. It s just the case that, at medium ranges, it s generally less critical to squeeze every bit of range out of them, because they have a longer zone to work with from the start. Likewise, very short range cartridges are not often used in situations that require this kind of careful consideration. For example, point-blank range for a 9mm Luger on human sized targets (head and chest shots) is actually well in excess of 100 yards; far beyond what most people ever attempt with a handgun, and really at about the limit of what most folks would ask of a small carbine chambered in 9mm Luger. But the principles outlined here apply to all cartridges, and if a shooter is capable of holding a good sight picture while squeezing off a round at long distances, point-blank range will help to maximize the potential for hits by eliminating or reducing the need for calculating elevation as a part of everything the shooter has to keep in mind while making that shot.
28 When I first learned to use point-blank range, I was shooting prairie dogs with an old Remington 788 chambered in.223 Remington. It s still a good rifle, and I still have it, but I went from dead-eye at 300 yards and 50/50 at about 350 yards, to very reliable one-shot hits anywhere up to about 375 yards, and 50/50 between 400 and about 430 yards over the course of that summer. It wasn t a night and day difference, or the determining factor in having fun verses wasting ammo. But I hit a lot more prairie dogs, and won more than a few bets, when someone would pick out a p-dog at the limits of my range, and challenge me to hit it without putting the range-finder on it first. It s a little bit of work, learning to use point-blank range for a lot of different scenarios. It takes a bit of strategic thinking, sometimes, to use it to the best advantage. But an extra ten percent of range is worth a little extra work, when dinner (and bragging rights) is on the table, verses running away through the brush. 28
29 29 As a thank you for reading our e-book, please click here to get a 15% off coupon on one of our AK accessories. We would also love to hear your thoughts about this e-book and any ideas you may have to suggest for future e- books. Let us know at info@mm-industries.com. 2016, by Michael Anthony Lee All rights reserved
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