Mathematics and the Long-Range Shot

[sscoyote]

Had a very rewarding experience happened to a buddy and I yesterday. He'd gotten a gun back from his friend he'd sold to him years ago--an unusually accurate Parker-Hale 243. But the scope on it was now a 3-9X B&L 3000. He wanted to get it up and running again for coyotes. But we were in the field with no range around for testing etc. So I thought to see what we could come up with. He had some old Rem. 80 gr. PSP factory rounds that his buddy gave him too. So we thought to zero it on a rock on a tepee butte at 200 yds.-3 rounds and it was done. So I wanted to see what the plex reticle's post tip subtended so we could match it to a ballistics program for an improvised long-range 1-stadia ballistic reticle. I lasered a cactus then at 100 yds. and at 9X noted as precisely as possible where the post tip lined up on the cactus. I took a tape measure then and measured it at 4" or 4 MOA. I figured it would be close to maybe 350 yds. and when he shot, noted it was just a couple inches high. We then set up at 400 and it was dead on.

So I then got to thinking let's crank the scope to whatever magnification would net us the 7 MOA the ballistics program called for for 500 yds. Since magnification is inversely proportional to subtension, the equation is 9/7 x 4 = 5X (honestly, I couldn't remember that at the time but after several attempts manipulating the numbers, 5 power was the only feasible solution). So buddy Mitch cranked the scope to 5X and we walked over to the edge of a hill and looked for a likely 500-yd. victim in the prairie dog town we were going to shoot our 22's in to test the system on. I found one in the open that was perfect. He shot once and was just a bit off, so I told him to turn the power to the left edge of the 5 number since he was just a bit high and aim about .1 "plex unit" into the wind and see what would happen. The next shot nailed the PD and we were both happy shooting campers.

I then looked at what 3X would net just for fun. I knew that that would be 3 times the 9X 4 MOA subtension or 12 MOA = 650 according to the ballistics program. He took a shot then at a grass clump then on another tepee butte and was just a bit short so we figured maybe 625 yds. or so.

We didn't get any coyotes yesterday but it sure was fun playing the math game for long-range shooting. Buddy Mitch now has a 500-yd. system if he chooses to use the rest of the 80 PSP's for coyotes this year.

 

[powderbrake]

The path of the bullet is pretty well defined, and Brian Litz has made a career of it. Working the data and making the hit is a lot of fun.

I was on a prairie dog hunt, and the guide asked my about my ballistics program and how it worked. I said, "watch this". I ranged a prairie dog at 450 yards, checked the wind with my wind meter, put the data into my iPhone running Applied Ballistics, adjusted the elevation and windage, held the dot on the dog, squeezed, and dog down. He was amazed...… I was very happy. While I expect it to work, I know the winds are different along the flight path, and I will take whatever good fortune comes my way.

 

[sscoyote]

Pretty good sir! Great story! Love it. Once years ago before our beloved ballistics programs and cell phones (yeah I love 'em too) I had an Eddystone-actioned 25-06 with a 29" bull-barreled rig with a gouged out pine (or something) stock that had a 20X Unertl 2" Target on it. If nothing else it sure looked badass. Found it in a Baltimore pawn shop and it actually shot really good-luckily. This was back around 1985. I used to carry it in a gun rack out to Western MD. from Glen Burnie, just to show it off when I was young, dumb, and full of ...whatever. The truckers would hit their air horns whenever they passed me--it was great. Once I asked a farmer for permission to shoot chucks, and pulled it out. Can't remember if he was impressed or not, but he walked over to where we could see his planted field and there was a chuck out feeding quite a ways out, and he said if I could shoot that chuck he'd let me shoot on his place. I got setup prone and guessed a yardage and "holdover" solution for whatever I thought it was-can't remember now, and shot. I was pretty sure I got the sucker but the farmer questioned it, so I walked out and sure enough it was dead in it's hole 75 gr. Hornady HP as I remember. I could just imagine the look on the farmer's face as he saw me lift it up through binocs. Got a new farm that day. It was great!

 

[Frankr]

Good story. well 30 years ago we used a 4-12x40 leupold duplex and a 270 win with a 130 at 3,100 FPS and we knew 6" at 300, 18" at 400 and 29" at 500 and we used the top of the duplex was 300, just down was 400 and down a bit more was 500 and we just remembered where to hold on the plex from experience and out to 500 yards we were around 90% effective. out further we just had to guess more and would hit less. I shot a white tail doe at a guess ta mated 750 yards one day with that set up. later it was ranged with a range finder and 750 it was. we were quite good at it but then I put 500 round a summer threw it shooting ground hogs...Now I am crippled with out my range finder and my dial on my scope anything past 300 is a hail marry.

 

[hogpatrol]

Always fun to play with the numbers. I just wish all scope manufacturers would list the subtensions on BDC scopes. Leupold is notorious for not doing it.

 

[fredo]

Enjoyed the post, Steve!
Fond memories of discussing this type of stuff with you (and others) years back on that other site...
Course now we have all kindza graduated FFP reticles that render having to understand inversely proportionate subtensions for SFPs obsolete, but it's still good to know! Heck, if ever one of the framers I know stop over to shoot, they're usually rocking a simple duplex. So, to get them in on some steel safari fun, we gotta do it "old school", as you so nicely described above...

One things for sure, seeing the look on their face when they successfully impact target at beyond 'point blank' range with their own rifle, is worth the effort...

Good shooting!

 

[sscoyote]

Jeez, can't believe I didn't notice the comments. Gawd getting old is for the birds...? thanks guys love the comments. My fascination for the math has been a big part of my shooting career, and understanding/researching it has helped me some through the years. Once I was able to calculate the size of a target at 1000 yds. to within .3" of it's true measurement, by manipulating the "mil-ranging" equation to calculate a subtension at a different (higher-powered) magnification, on a target of known dimension at 500 yds. then remilling the 1000 yd. target and then reverse-milling the target size. It was SO REWARDING, can't even tell you.

Another thing that understanding the math does is it lets you know when your calcs were just lucky or truly accurate/precise.

Have even applied some of this math to iron-sighted handguns to calc. MOA of front sight vs. sight radius to match to a ballistics program and rangefinding and it works!! Even archery sight pins--that works too.

Fredo, your comment drives it home really well. If you can bring a smile to the face of a farmer/rancher by applying such a system, chances are you'll be in like Flint on their property, huh?