TTAG

For years now I’ve been a long distance shooter. For much of that time I’ve been missing targets at long distances. There isn’t any shame in missing. Most of you have missed more shots than you’ve made, except that one time you lucked out and actually hit that pop can that somebody else left on the target rail on the 300 yard line of your local range. That time, you had everything just right. So, as the title says, how does one go about figuring things out with only five shots? I’ll tell you one thing . . .

You won’t need a chronograph or a dope card. Let’s face it: you’ll never be so operator that your drop chart matches the one in Guerrilla Sniper. So what do us normal guys who don’t try out fifty handloads in one sitting do? Can we really live without pissing off everyone else at the range while we set up a chronograph and force them all to hold fire so we can stand in front of the line? Yes. Yes you can. And you can do it in only a few shots.

Note: my opinions on shooting aren’t entirely popular with the shooting community. (Notoriously enough, I do most of my shooting and hunting with a 13.5” .308.) What I’m about to say will bunch a lot of shorts in a lot of places. Here goes: velocity isn’t important.

For my example, I will be using data from my .308 load of choice, which is a 168gr Hornady HPBT, Lapua brass, CCI 200 primer, and 43gr of Varget. That load produces 2400fps from a 13.5” barrel. What? 2400? Is that bullet even moving? Yes actually and I’ll elaborate on how to figure that out in a minute . . .

Considering that a bullet from a Marine M40A5 is only seven grains heavier and a paltry 100fps faster coming out of a 24” barrel, I’d say we’re doing just fine with the shorter barrel. It’s all relative, people. The bullet is what’s true. But why shoot a little gun like that when you could shoot another one? Stop it. There’s no practical difference at all. So let’s just go forward with this example.

Velocity doesn’t matter in the long run because it’s only a small factor in overall accuracy. You can have a super-fast load and have it be not-so-great. What should come first: consistency.

You should always pick the load that gives you the best results. Something totally and boringly predictable. If that’s a fast load, then good for you. I’ve found that speed isn’t key to accuracy at practical ranges. At 2400fps, my bullet makes one hole at 100m and .1 mil accuracy out to 1000m. (That’s 10cm at 1000m for those of you that measure in Freedom Units only.) The gun shoots, period.

Once you have your super-consistent load, zero it at 100yds/m. Make sure it’s actually zeroed, because you will need it to be precise for the next part. When you have it zeroed, find the longest distance you can possibly fire at. If that’s only 300 yards, that’s fine, but it won’t be as precise as longer distances. Five hundred meters? Even better. That happens to be the longest distance at my local range. If you haven’t picked up on it already, I’m a mil man.

If you aren’t shooting with a true first focal plane mil/mil scope right now, you’re seriously handicapping yourself both at the range and in the field. The benefits offered by a that kind of scope are literally too many to list. You should say ‘f—k it’ and go buy one today. Tell your boss you’re sick of your garbage gun show accessories and that you need a raise to get that US Optics glass. He’ll understand when you tell him how productive it will make you.

That said, I’ll elaborate on how to maximize your accuracy with a standard duplex reticle but it won’t be easy. Or will it?

Don’t touch your elevation knob no matter what range you’re shooting. Leave it. Use only your reticle, which should have real mils on it. The best and easiest way to do this involves shooting at dirt and steel and then at cardboard. Tape or glue a bunch of cardboard together and secure it to a berm somehow. Use your imagination. The cardboard should be about six feet high and three feet wide. Draw a dot in the middle.

Now line up and fire at the dirt in the berm next to it. Watch for splash and impacts. Since you’re shooting with mils, make note of the impact. It looks like that first shot may have been down 4.5 mils.

Okay, so now you have that. Check shot one.

Move your reticle over to your target and hold the nearest round mil onto the dot in the middle of your target. Since we saw the impact at 4.5 or so, we hold the 4 mil line on your target center. Fire again twice. Or more. (I said five shots is in the title, but you can shoot more if you want.) After you make those shots, drive down and put markers or draw visible indicators over your bullet holes, which are certainly (or should be) directly under your target center.

Go back to the line and look through your scope. Align the 4 mil line with the center and observe where your impacts are. For me, they are at 5.1 mils low of a 100m zero at 500m. Save that information.

For guys who don’t have first focal plane mil/mil scopes, the going is a bit tougher because you have no clear demarcations on your crosshairs and no ability to easily gather information. You may not have mils, but you do have a Sharpie. Here’s where it gets interesting.

If you’re really careful, you can actually take that permanent marker and draw mils on your glass. No wait. Don’t do that. I was kidding. Do not do that. But do get that marker and a measuring tape or meter stick. Those centimeters are what you want.

MOA is kind of a bitch system since there are various MOA versions. Is it actual MOA, like 1.06” at 100 yards or is it 1”? Lord, that .06 is gonna kill us. Quick! Get out that barely-relevant copy of The Ultimate Sniper and hope that it holds the answers. Spoiler alert: Rosebud is the sled and that book looks better on your coffee table, where it begs to be mentioned by college friends who knew you were in the military but didn’t know you weren’t a sniper.

Take that meter stick and make lines on your target. Yes, just like in school. If you are shooting at 500m, make the lines 5cm apart. That’s .1 mil at that distance, which makes 1 mil equal to 50cm. It’s all broken down into tens. If you’re shooting at 849 yards, .1 mil is equal to 8.49cm and so on. Take your standard duplex, zeroed at 100m, and hold it dead center. Actually look down your crosshair and see where the mil lines are. Make note of this.

Count the number of mils to the wide part of your duplex and make note of it. Let’s say it works out to be 3 mils at full magnification. It will change, so leave it on one setting for this procedure.

Now that you know that’s 3 mils, hold those 3 above the target and off to the side. Fire. Watch where it impacts next to the target. You already know that you have 3 mils to the dot. You are good at drawing and drew an additional 4 mils on cardboard. The bullet hits next to the 2 line. You make note of it, hold with the start of the duplex, so 3 mils, on the target center and fire a few more times. Then you drove down and check. Sure enough, you have holes at 2.1 mils. 5.1 again, but the hard way.

Now you know you have a bullet that impacts 5.1 mils low at 500m. Good for you, bruh, because it’s party time. Better put on your shades while reading this because your future is about to get bright.

Okay, so technically your gun now has two known zero points. Since I’m struggling as it is to keep this whole yards and meters thing straight, I’m just going to go full metric.

I know what you’re thinking. Never go full metric. Worry not, friend, I won’t come out empty-handed. Based on the fact that there aren’t too many velocities that will get your given bullet from A to B and put them all in the same place, you are then able to do the last and most critical part of this whole process. Data entry. Also, Microsoft Paint.

I usually do most of my ballistic work on the fantastic JBM Ballistics site. I don’t know what the hell JBM stands for, but it works and is probably the best thing you can use next to the Applied Ballistics app or the ATRAG stuff. You can use those programs the same way. Data stays the same. Anyways, go to jbmballistics.com and begin punching numbers. I select the Litz version of the Hornady 168 HPBT on the scroll menu. Don’t bother with the other inputs in that section.

ballistic1

Skip down to the third column inputs. Muzzle velocity changes to an estimated amount of fps. Because we don’t know it is 2400 yet, we enter 2500 first. Distance to Chronograph needs to be 0.0 since we aren’t using one.

In the next set of inputs, don’t really mess with most of that. Sight height isn’t that critical, unless you eat nails for breakfast and mount your ACOG on your carry handle. Just give it a good estimate and call it good. I do 1.75”

Shut up! I hear you F-Class guys and this isn’t for you! You eat your own food over there. None of that cant garbage needs to be worried about in real life. Make sure you don’t skip the sections for twist rate and twist direction. The second one isn’t super critical, but just get it correct.

TTAG

Ignore wind speed for this time. Make sure target angle is set at 90 degrees. Next enter min and max range. Set max as your actual max, so 500m for me. Enter 100m as zero distance. Go to the next section and enter atmospherics. I’m in West Michigan, so my typical elevation is about 670 feet above sea level. Enter the actual temperature of the day. We can change that later. Humidity can be simply set at 50 percent.

Big secret: humidity has no valid bearing on real shooting. Every fanboy seems to want to throw in humidity and Coriolis like they’re trying to impress someone, but it matters so little in real life at realistic ranges that it’s just safe to set it at 50 percent all the time.

Pressure isn’t as critical as people think, either. I’d just look it up and average it for your area. Mine is averaged at 29.92. Skip down and change the units to mil in the first column and to centimeters @100m in the second one. You’re good to go after checking ‘range in meters’, so press calculate.

TTAG

So, you have results. Your point A is 100m, but your 500m point B isn’t your expected 5.1. It’s at 4.6, so a half mil high. Too fast.

TTAG

Just to be a problem, I’ll do 2300fps. Go back and change that variable. We’re at 5.6, so too slow.

TTAG

Ah, 2400. Just right. 5 mils of drop. Wait. What about that .1? What about it? If you’ve paid attention, that is 5cm at 500m, also known as one click on a mil/mil scope with .1 clicks. Close enough for what we’re doing. There will be some variance, but we can work with that. Don’t worry too much about being so precise. You will waste ammunition and by definition time and money. Keep it simple.

TTAG

Next is the fun part: proof of concept.

Do not touch that elevation dial. Go back to the range or set your cell phone down and set up a target at a random distance…300 yards…900…whatever. Use your new-found muzzle velocity to predict a trajectory to your target. To get to 300m, I need hold 2 mil below my 100m zero. Line up and fire. I like to shoot at steel for this part. It’s reactive and gives instant feedback. Do that at any range you have and then print off your data.

You now have a range card that you can go in and edit at will tailored to your individual rifle. Play around with temps and such. You’ll discover that you will certainly want a temp-stable powder like Varget. The website will also let you include a zero at Point Blank Range, which is great for guys with the duplex reticles.

There you have it. Doing this saves you having to goof around firing at every individual range. Keep it consistent and you’re golden.

Remember, it isn’t about speed or barrel length. It’s about how uniform all your gear is. Get the very best gear you can afford and make the most out of each shot. Why waste 200 rounds when you can do it in just a few? Consistency builds confidence and confidence builds consistency. Aim small, miss small. Kneel before Zod. You get the drill.

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41 Responses to Calculating Muzzle Velocity and Trajectory With Five Shots (Or So)

  1. Thanks. I appreciate and use the JBM site regularly as well. This article led me to looking into temperature sensitivity of powders. I had not thought much about that before. I may try switching to H4350 where I was using H414.

  2. Excellent write-up. I’ve done similar work before with the JBM site. Before that, I’d interpolate ballistics tables in the back of reloading books.

  3. Well Josh , I’ll try to save you a lot of trouble here and it won’t take a lot of charts and fancy $2,000.00 scopes and any math . If your memory is a little off you may take a pencil and a notebook but leave your calculator at home .
    What you’ll need is ;
    1. A large target , painted flat white rigid cardboard or plywood , about 4′ x 8′ .
    2. A comfortable solid platform .
    3. A decent scope that you learn thoroughly , I prefer a Quantum VX -2 4-12×50 on my long range rifle .
    4. A decent high power rifle with a quality barrel , I enjoy my Noreen BN 36 for 500 yarders .
    5. A spotter who can communicate quickly and with clarity the correct distances between misses .
    6. Quality consistent ammo that your rifle has already eaten well .
    7. A private range .
    Breath deep , exhale , and walk em in and write em down . I have mine memorized at 300 , 500 and 800 yards and can do a 10 inch gong in 3 shots almost every time .
    Don’t under estimate the importance of #7 .
    Something about lots of spectators makes my finger jump .
    I love the long range stuff too .
    Enjoyed your enthusiasm .

    • Well, I hate to break it to you, but math is shooting and a calculator is more important than nearly any tool at our disposal these days, right behind a progressive mindset. There’s a reason that computer guided optics are becoming a thing these days. There will be a day when even a FFP mil/mil is obsolete, but we’re not there yet. In fact, math is in virtually every angle of shooting. You can’t avoid it. You literally cannot avoid it.

      For the record, my complete rifle is about $3000, which isn’t much these days. We have better things now and these advanced optics and rifles will become the overwhelming standard in the next few years. The future and the technology in it isn’t scary. It’s just uncomfortable for people who live in the past. Simple is not always better and when it comes to making hits and winning matches, I don’t ever want to walk rounds on. All these ‘fancy’ things are there to make that first shot and every shot better. Removing margin of error is preferable to claiming superiority based on simplicity.

      Trust me when I say that I’ve been teaching people for years and this method is what I use to instruct at the range. I don’t trust chronographs but I do trust math. Math is irrefutable and forces you to accept facts. Fact is, my method works and offers the flexibility that modern people need when shooting for score or in the field.

  4. Unlike other chris, my eyes glazed over. I’ll have to butt heads with this page over the course of several days to see what I can glean from it.

    • Yeah, but you get much more use out of high quality glass than a chronograph that will wind up shot, sooner rather than later. (And the former gets you much more street cred.)

    • Yeah, this method is sort of a way to reverse-engineer your velocity. Chronographs can be had for around $100 and they definitely have their place.

      • I’m loading 308 for AR-10 and 30-06 for a bolt.

        RL-19 for the 30-06 and IMR 4064 for the 308… no Varget I have been able to find around here.

        I’ve seen a lot of conflicting advice regarding crimping for the AR-10, both as to whether or not it’s really necessary and if it really affects accuracy…

        Anyway, thanks for writing this, I would like to see more posts on long range shooting.

  5. Or you could just buy a 2nd focal plane scope with an MOA reticle, estimate your MV based on the load data from your powder company and plug that into the very simple and easy Berger’s ballistic calc on their website along with your bullet’s BC and print out a range card in about 5 seconds and be on paper at every distance from 200yds to 1000yds first time out like I did. Mils are stoopid.

  6. I’m about to save lots of TTAG readers the trouble of this labor intensive method of reverse engineering your velocity with a yardstick and a huge poster board.

    Buy Strelok. It allows you to estimate velocity based on your current zero and the amount of drop at another chosen range, say 300 yards. Input the ballistic parameters of your bullet, shoot at chosen yardage, and measure the difference in drop in inches, minutes, or mrads, and hit a button.

    Velocity estimated.

  7. Glad to see another 308-ophile! I like the method for establishing drops as well, I dont always have access to a chronograph and this will likely be a valuable tool for me in the future. Now for some constructive criticism.

    “Here goes: velocity isn’t important”

    Generally a good idea to avoid speaking in absolutes, on top of that, categorically stating that velocity “doesnt matter” is a bit misleading. If you are chasing that last 25-50fps out of a given rifle/load at the expense of dangerous pressures, decreased brass life , and especially when that extra velocity might take you off the accuracy node of your barrel, then yes velocity doesn’t matter. When you start talking about 200-400fps though, yes, velocity absolutely matters. So it comes down to what you want to do. I push 2815 fps with a similar load to the one you mentioned out of my 26″ 308 (disclaimer on that in a second). That carries ~400fps over your 13.5″ configuration. The folks at Precision Rifle Blog did a “How much does it matter?” series, and extrapolating their work from that, a 400fps advantage translates into a roughly 12% increase in hit probability (assuming identical conditions and shooter ability). That’s not “nothing”. To put that into perspective, I would need to step up to a 300win mag to gain a similar advantage to my current setup. As I learned at Pecos this year, a 10% difference in score is the difference between placing where Tyler placed (in the top 10) and where I placed (somewhere a good bit lower than top 10).

    (Here’s that disclaimer I promised) I will be the first to admit that a 26″ barrel is pointless on a 308, but thats how my rifle came from the factory, and to the extent I have hand loaded for it so far it shoots lights out so I am inclined to leave it be. It carries no practical penalty for me because I mainly bring it out when I will be hunting from a fixed location. If I was having a rifle built it would wear a 22″ barrel, and experience shows I would still be carrying a nearly 300fps advantage over a 13.5″ barrel. If 22″ barrel is still too big for maneuvering, I have far more appropriate tools at my disposal.

    Since my long range shooting primarily revolves around hunting, velocity also matters quite a bit where your bullet has a specific velocity threshold where it will expand and disrupt tissue as opposed to turning into a copper and lead ice pick, and your deer runs off to be eaten alive by coyotes. Using my pet load with a 165gr Nosler ballistic tip (min expansion @ ~1800fps) over 45grains of Varget (thats a full grain below max charge) pushed to 2815fps puts my maximum expansion threshold at 550yds or so. Now, if I drop muzzle velocity to 2400fps that brings minimum expansion range all the way in to ~325 yds. So what? Big deal right? that would mean in almost 2 decades of hunting I would have passed on exactly one shot, but that extra 225 yards of effective range means I am not pushing the equipment right up to the edge of its limits when taking shots at any reasonable range I hunt at. Thats a 40% decrease in effective range.

    I have been fortunate, for the two main loads I shoot in this rifle I have found good accuracy nodes on the higher end of velocities, but without having to run at max charges or push pressures.

    YMMV

    • The guys at PRB are good, but they get real stale with their presentation and ideas on philosophy of use. They are about like guys in F Class. I like their stuff because I get it, but I have a hard time agreeing with some of their ideas. They are focused on PRS competition, which is fine, but there so few actual competitors in that that they may just write it up on Olympic biathlon. Unless you’re in a competition like that, the 6XC and like calibers don’t hold up against things like the .308 for real use on game

      I never hunt with regular hunting bullets. I’ve been hunting with Hornady 168 HPBT match bullets for years and I’ve never had an issue. I don’t ever worry about expansion rates and such. I’ve been on enough hunts to know it doesn’t really matter in real life. Deer, pigs, and coyotes all drop just the same from 100m to 500m+.

      • That’s good to know, I haven’t hunted with the hornady hpbt bullets ever, but I am working on loads for a 168gr and 185gr Berger bullet which are holding promise. They are by no means a traditional “hunting” bullets (the 185 is a “tactical OTM whatever that means) but even Berger lists a suggested minimum velocity though, beyond that you are primarily relying on the bullet yawing to disrupt tissue which is proven time over to not be a consistent or reliable thing. I wasn’t sitting with you when you took your shots so I will take your word for it though.

  8. I would like to shoot longer ranges, but I only have about 300 yards at the longest. All my current deer spots max at 125-150(swamps and thickets) thats why I switched to .300 blackout exclusively. Using holdover I was able to figure out to aim 11 inches high with a Ruger semi auto .44 mag @ 200 yards, talk about slow velocity, fire gun, 1 wecond silence and then whap.

    Great read, where in West Michigan is there a 500 meter range?

  9. Man, we hear you, we hear u buddy velocity aint no important. I really love what my stubby barrels are doing for me. By the way to prolong the service life of you brain by preventing overheating just buy MagnetoSpeed

  10. Thanks for the article. Just curious how well you’re .308 setup does at 800, 1000, 1200, etc. What would you consider the max hunting / target range of your platform?

    I like the consistency of the .308 myself, but it definitely peters out at long range. The 175 grain Eagle Eye loads I use do 2,620 out of my 20″ LTR. If I’m not mistaken, Travis Haley has shot the 300 BLK out to 1,000 yards. Not sure how well he did but he’s got some amazing skills.

    • I’ve had access to literally any gun of my choice regardless of price over the years. There isn’t anything a 13″ .308 can’t do. I’ve shot in competition, hunted successfully out to 500m+ and have never worried about it. It drops a bit at 1K+, but if you use your data, the hits come as regularly as with any caliber. I actually don’t like shooting past 500m these days. I find I get my best prone and offhand done at that distance.

    • I forgot to mention that I also have shot .300 BLK out to long ranges and found the hits to be easy to make. Just accounting for drop and firing.

      The .308 doesn’t peter out at long range. It all depends on what you consider long range to be. I consider long range in the field to be 500m and out. Long range on the target line starts at 600m. Impractical range begins at 1000. Its fun to see, but isn’t practical.

      The .308 is good to a mile. Don’t believe me? Go buy Magpul’s Art of the Precision Rifle. You will learn more than I have time to write on this page.

  11. I’d like to add a couple of things to what Josh said here:

    “velocity isn’t important.”

    Mostly true. You need to pay attention to velocity in two aspects, and they are:
    a) do your rounds go trans-sonic on the way to the target?
    b) how consistent is your muzzle velocity?

    When your rounds go trans-sonic (ie, from super-sonic to sub-sonic) on the way to the target, they can become upset and unstable, depending on bullet weight, form, etc. Your group sizes can open up.

    Inconsistent muzzle velocity results in vertical stringing.

    “I’ve found that speed isn’t key to accuracy at practical ranges.”

    Or at any range.

    I’ve found that it is very rare for the hottest load of any cartridge to be also the most accurate. If you buy a Lyman reloading manual, you’ll see that they call out an accuracy load as well as a maximum load in their tables. You’ll NB if you read these tables what I’m saying is true – it is very infrequent for the hottest load that Lyman has tested to also be the most accurate.

    Getting one’s load standard deviation down into single digits of fps is challenging, but it can be done.

  12. I guess I am going to be the guy that gets bunched up on your velocity/caliber claim. The factual truth is that velocity & BC do matter. The real variable in long range shooting is wind, nothing helps you negate its effects better than a high BC bullet with good speed. Your 308 load moves approx 46″ more at 1000 yards than my .260 load in a 10 mph wind. Tell me thats not important.

    • I will tell you that it’s not important. It just isn’t. 1000 is an imaginary landmark in rifle accuracy. As detailed in other articles I’ve written, most people never shoot beyond 300. That 46 inches is nothing in real life. It can be accounted for by simple calculation in a mil/mil system. Plus, I’d never shoot an animal at that range and on targets it doesn’t matter. It’s a game when it’s on paper for score, not life and death. The only thing that matters is your philosophy of use and how you apply it to your gear. I have a real-world rifle for real-world uses and it still does .1mil at 100m all the way to 1000m and I’ve used it on animals and targets alike without issue.

      That said, this article isn’t about my rifle. It’s about building a range card based on data.

      • 1000 is an imaginary landmark… 46″ @1000 is nothing and easily accounted for….

        Man, you are pushing it.

        I agree with your short&thick=rigidity=PRECISION. But precision is not equal to accuracy.

        Lemme give you one practical application for 1000+ shooting: killing govt goons when the 2A is finally applied into real use, which is why we own guns in the first place. Dissing long range just because it’s impractical for hunting or target shooting is not a valid reason to dismiss the need for sufficient velocity.

        No amount of calculation is completely accurate. Wind is different across the entire trajectory’s height and range yet we can only eyeball the mirage and get one data point at the kestrel. Pressure and temperature is different when the max ord is dozens of yards above sight line and this is assuming you are not shooting across a valley. All of these will lead to inaccuracy in the ballistics solution and the best way to compensate right off the bat is more velocity.

        Granted you can shoot 20 rounds to walk that 13″ 308 into the target at a mile and hit all day long, but i found my 20″ 375CT with better BC and higher MV makes it much easier.

        • Comments like this are why people don’t like this community.
          You’ve just proven your immaturity to every sane person reading this. I’m sad that people like you are part of the community. You’ve clearly never had to point a real gun at a person like I’ve had to judging by how eager you are to advocate harming law enforcement officials. My best friend wears a badge and I used to wear chevrons. I know people like you and you wouldn’t last a minute against those you call goons. I have a responsibility to this site to tell the truth about guns, and sir, the truth is I won’t write what I truly feel about you because I won’t stoop to the strata you occupy. Arguing ballistics in regard to killing our own people is disgusting and irreverent tobthose who died in the line of duty.

        • Dude calm down aint nobody’s advocating killing american LE and MIL when there is not a revolution going on.

          And even when there is, the vast majority of cops and servicemen will stand with us, not some politician like king obama.

          But, if you refuse to acknowledge our 2A is put in there against tyranny, which exactly means when the gobbermint use goons in blue and green who do not know better to oppress the citizenry, i dunno what truth about guns you have to offer. Befire anything you are a private citizen paying tax to keep the system alive, and your life and family are worth more than whatever uniform you’re wearing. Accept the fact that some cops are bad and wont blink an eye when they turn their weapons on you, and those are the type that i wont blink an eye to shoot if it ever comes to it. No apologies, and you’re welcome.

          I know probably during your career you’ve only run into the type that would trade their lives for mine, but that by no means indicate the totality of the situation.

  13. Ahh, the science of walking it in and then running calculations backward. You still don’t know jack at the end of the procedure. Change barometric pressure or temperature and all that work is for naught. Thinking that missing by just a little bit is better than taking a few minutes to set up a chronograph is short sighted silliness.

    This is just the sort of guy that’d buy an RV and then bitch about the cost of gas.

    • False. Data points can be expanded on by altering variables from a constant. The calculator allows for plasticity of data across a full spectrum of environmental conditions. Once a baseline is established, you can alter it at will to match your conditions. Pure math, man.

      I’ve tested a variety of chronos and they are seldom fully accurate. Look it up.

      • This whole concept just proves to me one thing . I HATE MATH !!!!!!!
        I don’t doubt you Josh , it just doesn’t appeal to me and I’ve been a reloader for 25 years .
        I printed it out just the same .
        Thanks for the work .

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