Advanced Marksmanship Angled shooting

[JFComfort]

Angled Shooting | Sin City Precision

I wanted to share what I have learned about angled shooting. When the guys and I started out, we would constantly push ourselves to learn more. We covered things like range estimation, moving targets and angles. Before I really started researching I would hear different things, from different people. Some folks said, you would impact differently depending if the shot was up hill or downhill (that is not true). The riflemen’s rule was complicated and took me awhile to decipher it. The math wasn’t something I was going to be able to do quickly out on the range or in the desert.

After some time and practice we figured out how to account for angled shots. We found we preferred using the modified rifleman rule. When you have an angled shot think back to your days in geometry glass. The pythagorean theorem is a way to solve the problem if you have the correct variables. The Pythagorean theorem demonstrates the different between the line of sight range and the actual horizontal range. The line of sight range will be greater than the actual horizontal range. This will cause you to shoot over your target regardless if the shot is up hill or downhill. The severity of the angle will exacerbate the effect.

The easiest way to correct for an angled shot is to measure the angle, use a cheat sheet to find the correct cosine, once you know the cosine take your DOPE for the line of sight range and multiply that by the angle cosine. (A cosine is a way to express an angle in decimal form)

Example:

Line of sight range = 600 yards

Angle = 25 degrees

Cosine = 0.906

DOPE = 11.5 MOA

11.5 (DOPE) x 0.906 (Angle cosine) = 10.419 MOA , dial 10.5 MOA

To find the cosine I use two methods. The first and simplest is a sextant I made using a protractor, straw, string, key ring and tape. Before shooting I will look down the straw and put the target on the center of the straw. The string is weighted and will hang freely, once the target is in the center I will hold still and pinch the string against the protractor. This will tell me how many degrees to my target. Once I know the angle I use a cheat sheet to get the cosine. Now that I have the variables I am able to do the equation to solve for the correct horizontal range or correct your DOPE.

A faster way to do the same thing is to use an angle cosine indicator. The one I have is made by Sniper Tools Inc. and is mounted to my rifle using a mount from Badger Ordnance. With my scope on zero I put my reticle on the target. While on target I look at the indicator which tells me the cosine for the angle. With that information I can solve for the horizontal range or correct my DOPE.

With these things figured out, I am able to easily correct for angles. Some of the areas we hunt are located in pretty rough country. Having the ability to accurately solve the problem allows me to send accurate rounds down range.

 

[MajorGunHo]

Cool post. I found this to be very interesting, especially since I am just starting out in the LR stuff.

 

[Knight6]

Thanks for this!

 

[Graham]

Angled shooting

Good post. A few comments:

1) The accuracy of your rounds is not affected by the angle of the shot.

2) Elevation data (as opposed to distance to target) divided by cosine is called the improved rifleman's rule.

3) Large angles at short ranges require more compensation for the angle than do shallower angles at longer ranges. And, assuming that you are not shooting in the Khyber pass, longer ranges usually make for shallower angles.

4) Most PDAs use the improved rifleman's rule to give the correct elevation output when the user inputs the angle. Therefore knowing the angle is more important than knowing its cosine.

 

[Mod Adahy]

I agree with most of the above with the exception that uphill or downhill make no difference. Most programs do not account for them because the difference is very little. For instance, 40 degree uphill takes 200.2" at 1k and downhill takes 195.7" at the same 40 degrees. Now that is the exteme edge of the two, but none the less it is 5". That is with my 223 with 90 grain vlds. Normal 308 with 175's is almost 8" difference at the same 1k. So, it is so little that most would overlook it but it is there.

 

[Graham]

Angled shooting

I agree with most of the above with the exception that uphill or downhill make no difference. Most programs do not account for them because the difference is very little.

Programs do not dispense with calculations because "the difference is very little". That's simply not how programs work. Besides, 8" at 1000 yards is not 'very little'.

Why is there this difference that you claim between shooting uphill and shooting downhill: What causes the discrepancy?

 

[Mod Adahy]

Programs do not dispense with calculations because "the difference is very little". That's simply not how programs work. Besides, 8" at 1000 yards is not 'very little'.

Why is there this difference that you claim between shooting uphill and shooting downhill: What causes the discrepancy?

I agree that it is very little. These numbers were amplified due to 40 degree angle and 1000 yards, but it was just to post an exaggerated example. Is a 1000 yard shot at 40 degrees possible, absolutely. Talk to goat hunters in Alaska. Is it ideal, probably not. Is 40 degrees at 600 within most realms?

Applied allows you to input a + or - number to indicate uphill or downhill and covers it real well in his book. But for the most part we can thank gravity. The differences I posted came from the AB app.

 

[Jaeger308]

Field Firing Solution calculates the same solution for positive and negative angles

Patagonia Cold Bore takes affects of gravity into account and will have different solutions for positive and negative angles

 

[smokebomb]

We're splitting hairs at uphill vs downhill...

But, downhill traveling bullets do travel with a very minute assist from gravity while uphill traveling bullets receive more resistance THAN downhill shots from gravity. This "assistance" is in relation to the primary direction of travel. Bullets fired on a flat (+/- 5 deg plane, have far more gravitational effect from trajectoy than either uphill or downhill.

That said, if you are going to split hairs that much then you may also want to account for the differences in pressure. Shooting downhill will go from shooter's pressure to pressure closer to sea level...ie denser air. Opposite for uphill shooting.

So technically simplified: Shooting downhill, the bullet receives SOME velocity retention via assistance from gravity, however since the bullet is going to an area of SLIGHTLY higher air density SOME of that effect is cancelled.

In Michigan, and much of the US, 25-30 deg is near the maximum angle one would encounter that the distance would be over 200 yards.

Multiplying your dope by the cosign of the angle is much more convenient and accurate if you aren't using electronics.

 

[Rob01]

Elevation is only part of the problem. Don't forget about wind. You use the actual range to target to figure your wind hold/dial. Some forget this and use the adjusted range for elevation and wind.

 

[rookie101]

I should keep my mouth shut because I am way to new at this to really offer anything to the conversation. That said, over the years I have collected a number of neat gadgets, most of which I do not have a use for. One such gadget I now have a use for. It is a Suunto clinometer and it has cosine decimals printed on the back. I believe perfect for this application. Rob, thanks for the wind correction education, I would have used corrected distance, but what you say makes sense because the bullet is still traveling for that distance, not corrected distance. Love learning new stuff.

 

[smokebomb]

Very true Rob!

The bullet still covers the same distance, regardless of our elevation requirement.

In our world of gadgets and gizmos, nearly everything (provided accurate data and use) can be accounted for. The biggest factor that makes or breaks the shot at long distance, unfortunately, is the wind. It is the one constantly inconstant variable that nothing can make the final calculation on, save the human eyeball.

Watch a sandy-bedded stream; how the current varies so drastically depending on terrain features. Then remember that a stream has a constant flow rate, and that air flows much easier than water. How rare a truly pure 10 mph wind from 3 o'clock is, if you really think about it.

 

[JFComfort]

Many of you have good points and I appreciate you all posting your input and sharing information regarding the subject. I'm sure this can be broken down to a gnats ass and honestly I only posted it here to see how it was received. I know many here are more experienced than myself, honestly for me angled shooting means putting an animal down cleanly, this allows us to do just that. Areas we hunt are standing on end and knowing your shit is very helpful.

Rob thank you for adding the information about the wind, I forgot to add that when I wrote the article. One of the things we focused on was eliminating anything electronic. We see so many shooters these days that don't know shit without their wiz bang toys. Learning how to make and use a sextant, ACI or even the "fist rule" is MORE effective than a toy with no batteries. The electronics are a great aid and I am thankful for them but I feel it is best to know how to solve the problem with out needing to rely on anything that takes batteries. I was always surprised how few people in this community actually knew how to correct and explain angled shooting.

 

[sled_mack]

JFC - Nice write up.

One thing I would add from a hunting perspective - knowing the animals anatomy. Here we don't have the same type of angled shooting, the angle comes from a tree stand. But people will be 20 ft up a tree, have a deer 10 ft from the base of the stand and use the same aiming point they would use if they were on level ground with the deer. Add to that the scope offset of a 20 ft shot, and it doesn't end well. And the story usually ends with "I'm using a different bullet next year, this bullet didn't work on a deer at 20 ft!"

Most bow hunters that I know (I am not one of them) seem to have a better grasp of the animal's anatomy and also angled shooting since almost all of their hunting is done from a tree stand.

 

[p_pops]

....the "fist rule" is MORE effective than a toy with no batteries.

Alright, I know what the other 2 items are you mentioned (and how to make them) but what is the "fist rule"?

BTW, great post! Very informative!

 

[JFComfort]

Alright, I know what the other 2 items are you mentioned (and how to make them) but what is the "fist rule"?

BTW, great post! Very informative!

Thank you! I appreciate the kind words.

Lenny Bolton of Venom Tactical was explaining it to me... and I honestly do not remember exactly how it is done but you basically use the horizon, fist with your arm extended and eye sight to guess the angle to a target. If I run into Lenny I will have to ask him to explain it to me again.

 

[pizzamanny]

Great post, sticky worthy.

 

[Papa Zero Three]

Thank you! I appreciate the kind words.

Lenny Bolton of Venom Tactical was explaining it to me... and I honestly do not remember exactly how it is done but you basically use the horizon, fist with your arm extended and eye sight to guess the angle to a target. If I run into Lenny I will have to ask him to explain it to me again.

Are you talking about the WORM formula used by forward Observers by chance? The results are typically in mils but could be converted to degrees easily enough. There is also a manual method of determining remaining sunlight using ones fingers for minutes remaining which again can be converted to degrees.

 

[JFComfort]

Papa, that sounds familiar. I apologize that I can not correctly recall what was explained to me.

 

[Sterling Shooter]

BTW, the USAMU has an excellent video on You Tube about angle shooting. I do not know how to link it to this post but with a little googling it will be worth the effort I'm sure.