Angle Shooting Simplified..

[JLA]

Recent i have been chatting with JUNKKING about thinking in MOA, and trying to help him grasp the concept.. Last night we were doing mental conversion exercises in the chatroom, He and I and H-D. H-D is very well versed in thinking in MOA, so he was a huge help.

But all that conversion exercise got me to thinking about finding an easier way to calculate hold over for shooting over angles. (angles as in aiming at a distant deer on top of a large hill or mountain side while you are on the low ground)..

I was pouring thru a bunch of my HS math notes (Yeah I know Im a dork, I keep stuff like that) and I came across some of my old geometry and trigonometry notes. And I found something that seemed to work.. So I did an internet search and came across the NASA website that lists the cosine for angles from 0.0 degrees thru 90.0 degrees. which ill get to in a moment..

If your were taught to shoot by your dad or grandad or in the boyscouts you were taught that when you aim at a target thats elevated from your postion, or you are elevated from its poition you always aim low, other wise the bullet will soar over the top of the target right.. Thats the way my grandad taught me..

The reason is becasue the line of sight, being the hypotenuse of the triangle (long side) is longer than the distance the bullet is effected by gravity, which is the base of the triangle (adjacent).. Normally you would laser the line of sight, record that figure and use and estimated angle from your line of sight to the target to calculate holdover which works, but it takes too damn long. Other method is to just hold low and hope the bullet strikes the target which works good a short ranges but is hit and miss at longer ranges.

I figured a way to figure the hold over using the cosine and the lasered straightline distance to the target. in about 10 seconds on your cell phone calculator, or in your head if youre quick at math..

Its simple and its dead accurate. simply multiply the straight line distance by the cosine of the angle youre shooting over. You can estimate the angle or if you have a fancy shooters angle use it.

Heres an example.. You have a whitetail deer at a lasered 700 yds up on the side of a large hill. you ar at the base of the hill in some cover and have a clear line of sight. the angle youre shooting over is roughly 40 degrees. The cosine for a 40 degree angle is .7760 so your holdover distance is 700X.7760 or 77.6% of the full value. 700X.7760 is 543.2, so you would calculate ballistics for 543.2 yards and take the shot.

Another example. You are varmint hunting and have your rest set up over a small cliff overlooking a gopher infestation. the heart of the colony is a lasered 228 yds from your muzzle. so you have a 228 yd line of sight shooting down hill at a measured 45 degree angle. the cosine of a 45 degree angle is .7071. so again you would multiply your line of sight, 228 yds by .7071.. 228X.7071= 161.218 so you would aim at those unlucky gophers like they were a hair over 161 yds away.

It simpl eand its quick. and all you need to do is get good at estimating angles, or buy a shooters level and print the cosine chart from the NASA webpage here..
http://www.grc.nasa.gov/WWW/k-12/airplane/tablcos.html

Enjoy fellas. I know I will..

[langenc]

Would never shoot at a 700 yard deer or anything else..

[dons2346]

I think my head hurts.

[goofy]

Ah What? ok Ah Ah? Boy am I glad my farthest shot is 150 yards.Just to much thinking.But I do have a question. JLA it looks like you spent alot of time on this and i am sure this could help me at my land so if I am in my stand(its 25 feet up) I am on a hill 1st looking down the hill (aprox.35 degree hill) with a 150 yard shot do I shoot high or low as per you numbers and is it opposite looking up the hill? How much different then shooting on leval ground. And is this different for different loads(shotgun,rifle) I'M SOOO confused...GOOFY

[permafrost]

I cosined for my daughter's car once. Big mistake!

[carver]

Another geek here who loves math, but I have a simpler way. I live in the pineywoods, with lots of honeysuckle thickets, so I have never had the opertunity to make long range shots. That simpler way is to invite you to come along if I ever win the lottery, and get the chance to hunt those long range critters! Isn't that simple?

[Juker]

Here I been thinkin' JLA was a good ol' boy, and darn if it don't turn out he's a mathematizzical genius as well.



I live back in the woods, you see
A woman and the kids, and the cats and me
I got a shotgun rifle and a cosine chart
And a country boy can surviiiiiiiive
Country folks can survive

[rcairflr]

Knowing the math for this is kind of neat, but I think for the vast majority of us it would never be used unless your doing some kind of long range shooting contest that includes shooting up or down pretty extreme angles. The vast majority of us would typically not shoot a deer or other game at 700 yards and also if we did we probably wouldn't be doing it at a 40 degree angle (a 700 yard shot up a 40 degree angle would be at an altitude 1350 feet higher than where you are standing).

Now lets take a more reasonable example, but still pretty extreme for most hunting situations. Lets say the deer is at 300 yards and higher at an angle of 25 degrees (now the deer would be 380 feet higher than where you are standing). Now your balistics would be 271.8 yards (using the calculation given by the forum opener). If you were shooting a 270 winchester that was sighted in at 200 yards. The difference in your aimpoint/ impact point at 300 yards vs 272 yards is less than 3 inches.

But again, I appreciate the time and effort it took into figuring it out and I did have some fun playing with it.

Just out of curiosity, surely the military snipers who do have to make some of these extreme shots. How do they calculate this?

[carver]

All the snipers today use calculators set up for this purpose. They just enter the required #'s, and get set to make the shot. These durn things automatically adjust for wind, temp, the curvature of the earth, barometric pressure, and humidity.

[JLA]

yup. all the thinkin has been done for todays markmen using modern equipment. and all the examples I gave here just hypthetical off the top of my head to show the numbers work. Id never shoot at a deer that was that far up hill. Cuz that means my big ass has gotta hike up there and get him.. No way jose..

I like to play with math like this. it keeps my mind from going numb. For the longest when I thougth about angle shooting I would play in my head figuring out the hold over by estimating the angle, and using the straight line distance to reverse pythagoras theorem to find the adjacent, which is the hold over distance. Screw all that finding square roots BS. I like math but I havent a clue what the square root of 364 yards is..

But i recalled using sine, cosine, and tangents in Geometry and later in trigonometry graphing triangles. so i dug out all my old notes to find what i was remembering form 11-12 years ago and there it was. so i ran it a dozen times thru a dozen different variables and it yielded spot on results every time.

I dont think ill use this knowledge but maybe one time ever in a hunting situation if Im lucky, but you can bet your biscuits itll be in my range bag..

[JLA]

Originally Posted by goofy

Ah What? ok Ah Ah? Boy am I glad my farthest shot is 150 yards.Just to much thinking.But I do have a question. JLA it looks like you spent alot of time on this and i am sure this could help me at my land so if I am in my stand(its 25 feet up) I am on a hill 1st looking down the hill (aprox.35 degree hill) with a 150 yard shot do I shoot high or low as per you numbers and is it opposite looking up the hill? How much different then shooting on leval ground. And is this different for different loads(shotgun,rifle) I'M SOOO confused...GOOFY

shooting up or down hill is irrelevant. you will always aim low as the adjacent distance is always going to be less than the hypotenuse distance.

You are shooting a 150 yds line of sight at a 35 degree angle.. the cosine for 35 degrees is .8191 so multply 150X.8191 and you get your hold over.. 122.9 yds.. which is 82% of the full 150 yds (.8191 = 81.91% or 82%, just move the decimal) If its easier for you to think in percentages you can do it here, it works the same since were dealing with parts of a whole no matter how you look at it..

[todd51]

This is really interesting but I am too old for all that figur'n. Think I'll just hold low bout hmmmm, that much. Oh darn it I still shot over him.

[JLA]

sorry guys. i love playing with math like this almost as much as i like shooting and reloading and fixin guns..

[wyoredot]

I'm a math retard but this is a very good thing to be knowin. I'll study.... and apply. Thanks JLA and crew

[todd51]

We just like yanking your chain.

[Jim Hauff]

Does this apply to trap shooting?

[JLA]

IT does indeed but the difference isnt enough to worry about..

[American Leader]

goofy & permafrost should be ashamed of themselves pickin on poor josh that way. We all should be proud of him qualifying for the space program! Oops, that program's been discontinued cause nobody would cosign

[Jim K]

Nope. Try running that by a math or physics prof at your local college.

Jim

[goofy]

JLA I do not know how but I understandGess that the few days i did go to school i learned something. Yes i see how up or down hill does not matter COOLVery interesting THANKS.......GOOFY

[Airdale]

You all prolly know about this but if you don't and you have a mildot scope this would really help with these kind of calculations.
http://www.midwayusa.com/viewProduct...tNumber=131691

[JLA]

Originally Posted by Jim K

Nope. Try running that by a math or physics prof at your local college.

Jim

Ima busy man.. would you care to elaborate a bit? If theres an unforseen hole in my logic I would like to have it pointed out to me so I can learn the correction. I have run the numbers backward and forward and fail to see how it wont work, afterall a triangle is a triangle whether its graphed on paper or 3 points between you, the base of a hill and the deer on the hill.. Save me the time of seeking a college prof and wasting his time. Hes got kids to teach..

[Jim K]

Nevermind, I am too busy to even think about all the false assumptions, but try this one. How does your system deal with the various trajectories for different ammunition?

Jim

[JLA]

it doesnt. it simply defines the distance the bullet is affected by gravity, the trajectory of a given round calculation is still made using the ballistics of the cartridge you are shooting.

Multiplying the line of sight by the cosine of the angle only gives you the hold over distance. It is up to you to adjust your optics for the holdover distance with the information on your range card for your rifle and ammo.

Therefore the this method of calculating holdover is viable for any shooting system in any caliber.

[JLA]

It would be exceptionally useful shooting squirrels out of trees from a sitting bench with a .22LR. so long as you have your .22 range card handy and know its trajectory out to say 150 yds, you can use this system to determine the adjacent and make better shots on the more distant tree rats.