The 'How To' of shooting on an incline.

[308Nut]

A special thanks to Amanda for allowing me to post this article. Thank you!

 

It seems like the topic of shooting up or down a hill is a hot topic. A few of us have always covered the principals of bullets shooting high when fired on an incline but we have yet to explain how to set up for an accurate shot when angles are encountered. This article covers the ‘how to’ basics of accurate compensation. It also seems like some hunters here want to know only the how and others the how and why. So, without the frustration of a debate and trying to explain the function while being tired from a long day’s work and the distraction of a 21 month old tugging on me which all leads to incomplete explanations and gross mistakes, I have put together a how to article. I have also included the why. The first part is the how. When you finish reading the ‘how to’, you can choose to stop there or continue to the why.

 

Before we get started, I understand than many members here don’t want to carry a ballistic calculator in the field. When reading the ‘how to’ below, it will seem very lengthy and complicated. Not to worry. Once we get through the how to, there will be some example pictures that will help you see how easy it is to apply the practical application of calculating a corrected bullet drop due to a sloped shot.

 

First the how to:

 

The following calculation is provided by Sierra Bullets. The reference is taken from the Sierra Reloading Manual 4th addition.

 

The correct way to compensate for the angle is to take the ‘baseline reference’ (this will be defined shortly) bullet drop and multiply by the cosine of the angle. Then that value gets deducted from the bullet drop value at the desired range from your rifle’s zero. If the range to your animal happens to be your zero range, then you deduct the calculated value from 0. You will get a negative number. This will be the inch value that you will want to dial. Instead of dialing up as usual, you would dial down.

 

The baseline reference is the bullet drop at the desired range from your rifle when fired from a perfectly level bore or 0 degrees. For example your 200 yard zero = +/- 0” at 200 where the drop from a level bore (using an average load) at 200 yards = 9.5”. It is this ‘baseline’ that ALL other trajectory corrections are based upon, including angle compensation.

 

Compensation value = ((bullet drop from zero at the desired range) – (baseline bullet drop * reverse cosine of the angle)). The reverse cosine of the angle is 1- cosine. For example, 1-.866 = .134.

 

For example using your 200 yard zero when setting up for a 400 yard shot at 30 degrees of angle, you will need to know 3 things. 1: baseline bullet drop at 400 yards (41.75”). 2: Corrected bullet drop at 400 yards from your 200 yard zero (21.5”). 3: Cosine value of 30 degrees (.134).

 

The calculation is as follows:

 

((21.5)” – (41.75 * .134)) or (21.5 – 5.55) = 15.45”. You will dial your scope for 15.5” instead of 21.5”.

 

This is quite different from the advanced rifleman method. The advanced rifleman method calculations are as follows:

 

21.5” * .866 (cosine) = 18.6” While it would be close enough for a clean kill, 400 yards at 30 degrees angle would be near the threshold for most rifle/load combinations. Any further than that or at steeper angles, the advanced rifleman method will shoot high every time. In this case it is about 3” high because you are compensating for 18.6” where only 15.5” are needed.

 

It sounds complicated but with a drop chart that includes the baseline bullet drop and a list of cosine values and even just a little practice, it is accomplished easily and fairly quickly. Another thing you can do to speed things up is to print a drop chart that includes bullet drops on a level surface and in 5 degree increments. If you would like an excel spreadsheet that will create a drop chart that you can print with angle compensation automatically, PM me and I will email you one. All you have to do is enter your velocity, bullet weight, zero range, temperature, altitude, ballistic coefficient, scope height, wind speed and direction and you will get a drop chart to print.

 

Now the easy application of angle compensation:

 

1 option: PM me for a free calculator in excel that will print you a couple of different range cards (PLEASE include your email address as I cannot send you one without it. Also, this offer is only for established members. Please dont flood this site with new memberships just so you can PM me unless you wish to contribute to this forum.) There are a couple of samples below:

 

 

 

Another sample:

 

 

2: Print your own drop charts using your favorite ballistic calculator which will need to include a baseline bullet drop as well as a corrected path for your zero along with a list of cosine values. This baseline and path will be referred to as something else for other software.

 

Now if you would like to know the why, scroll down. If all you want to know is the how to, then stop reading.

 

 

************************************************************************

 

 

Now the why:

 

Most shooters understand the principal of the right angle triangle and it’s hypotenuse. For example if you have a triangle with a 6” line at a 60 degree angle, the line at 90 degrees is half the length which is 3”. This can be found by taking 6” * the cosine value of 60 degrees which is 0.5. (6” * 0.5) = 3.0”. Basically, 600 yards line of sight at 60 degrees, is 300 yards on a level plane. Gravity affects objects straight down. A bullet’s ‘baseline’ drop when fired at an angle other than 0 degrees is based on gravity’s effects 90 degrees straight down. The reason that we don’t correct using our drop chart is because of the fact that we have introduced other angles to compensate for the baseline bullet drop. The rifle barrel has to be aimed up above the target to get the bullet to come up past the line of sight to be able to drop into the target due to gravity. The closer you launch a bullet to 90 degrees up, the longer the bullet follows the line of departure. When fired at 90 degrees up, it will follow the line of departure until it stops due to velocity loss which is due to air density and gravity’s influence. When shooting up or down a hill, the principal of gravity affecting the bullet’s path is always straight down. When you launch a bullet while aiming at 60 degrees up a hill, the rifle barrel is NOT 60 degrees. This is why bullets will ALWAYS strike high when using the rifleman method. You must use to baseline bullet drop as a reference because this drop is based on gravity affecting the perfect horizontal line of the bullet. This reference does NOT include to angle of the bore in relation to the target. You always take the baseline drop and multiply it by the cosine value before you incorporate the bullet drop from zero. We can use basic math to validate this theory.

 

Let’s use the worst case scenario. A 90 degree uphill shot at 1000 yards using the rifleman method. 1000 * 0 = 0 yards where the rifle is zeroed at 1000 yards. If you aim for zero yards by compensation, the bullet will never even be close to the target. To get a rifle zeroed at 0 yards the angle of the barrel would have to be so steep to get the bullet to cross the line of sight at zero yards that the bullet would be so high over the target it isn’t even funny. You can argue and use the reverse cosine (1) which is what we should be using, where 0 is at 0 degrees and .5 is at 60 degrees and 1 is at 90 degrees, 1000 yards * 1 = 1000 yards. If you aim for 1000 yards which is where your rifle is zeroed, your bullet will be ‘high’ because while the scope is lined up with the target, the barrel is…….you guessed it, angled away from the target. Mathematically, it would be ‘high’ by the same amount as it would be low at 1000 yards at 0 degrees when fired level. In other words, the baseline bullet drop and the amount you would be high would be equal. Using the average baseline drop at 1000 yards it would be 375” high Now if you apply the correct calculation of ((bullet drop at target * cosine of angle) – bullet drop at zero), the math works out perfectly. In this case, our rifle is zeroed at 1000 yards so you take (0” – 375” * 1.0 cosine = -375”). Now you see that if you come down 375”, your bullet will depart at 90 degrees straight up and hit the target. No matter the angle between 0 and 90 degrees, point blank to as far as your bullets stay stable and have forward motion, the calculation of (bullet drop at target – baseline bullet drop at that range * cosine value = true inches of drop every time.

 

Below is a picture that illustrates the ‘why’.

 

I hope that helps!!

 

M

 

PS: Now the debate can continue!

 

[COOSEFAN]

Great thread, thanks for posting it 308Nut!

 

I got a question tho, what tool or device do you use or reccomend for acquiring the angle of the shot in the first place?

 

 

[308Nut]

Great thread, thanks for posting it 308Nut!

 

I got a question tho, what tool or device do you use or reccomend for acquiring the angle of the shot in the first place?

 

http://www.google.com/products/catalog?q=m...ed=0CFQQ8wIwAA#

 

http://nightforceoptics.com/nightforcescop...ountsadimtL.jpg

 

http://www.horusvision.com/asli.php

[COOSEFAN]

Thanks for those links, I really like the one from Horus Vision because of the Cant Level that is built in. One thing I don't have on either of my long distance rifles is a level and I've noticed the importance of it through trial and error! I'm gonna get a couple of those for sure!

 

A friend of mine is an absolute long range shooting fanatic, he's a retired mathematical engineer also so you can probably understand how the two go together! He tried out a bunch of the different tools out there to figure out which angle calculating device was the most accurate. He even proved that the Leupold Rangefinder w/ angle compensating capabilities was not accurate and he called them out on it! They agreed that it wasn't as accurate as they claimed and said they were "working" on improvements!

 

That same friend settled on the Suunto Clinometer and swears it's the best tool out there. I'm sure the others work fine, but my buddy is very picky so take it for what it's worth. I've got the same Suunto as him and have used it multiple times proving it's value and we've made shots using it that otherwise would've been sure misses!

 

Here's a link: http://www.suunto.com/en/Products/Precisio...to--PM-5/#Story

 

 

[stanley]

Uh...... I can see that I have a LOT to learn about shooting!!! I thought that you just figured that the distance to target needed to be measured 'as the crow flys', ignorning eleveation.....

 

S.

 

[308Nut]

Another danger of using corrected yardage instead of actual drop inches is that line of sight still applies for MIL, MOA and click values at the line of sight range

 

Example:

 

By using the rifleman method of a 600 yards shot and shooting for 300 yards (600 * 0.5 COSINE). If you look at your drop chart and find that your 300 yard drop is 1 Mil from your 100 yard zero, and hold for 1 mil at 600 yards even though your drop chart at 300 yards says 1 Mil, it compounds the problem because 1 mil at 300 yards = 10.8 inches where 1 mil at 600 yards = 21.6 inches. If there is a bullet drop value of 79" at 600 yards from a 100 yard zero on a 0 degree shot, and you take 1/2 of that which is 39.5" and IF this method worked, holding for 1 mil which is the 300 yard holdover, an 18" mistake will occur. This is because 1 Mil at 600 yards = 21.6". You would be shooting for 21.6" where the rifleman method told you 300 yards or 1/2 the drop inch value which would be 39.5". 39.5 rifleman method drop - 21.6 1 mil holdover = 17.9" error. In other words, using a yardage cut of 300 yards will lead you astray because your drop chart says 1 Mil for 300 yards where you need a 1.8 mil hold for the shot.

 

This is all of course based on the riflemans method which you all know I dont agree with and is for illustration purposes.

 

 

Forget yardage cuts and go with drop inches. When the new drop inch is determined you will convert inches to MOA or Mils or clicks.

[Red Rabbit]

M,

How close is the improved rifleman's method (cosine x moa adjustment) to your program?

[308Nut]

M,

How close is the improved rifleman's method (cosine x moa adjustment) to your program?

 

It depends on alot of factors but for MOST practical huntting conditions, the improved rifleman method is fairly close. Obviously, the further out and steeper the incline the further apart they become.

 

For example, I shot a dall ram at 763 yards in 2002. He was at 4500', temp was 58 degrees and the incline was 17 degrees. The standard drop would have been 17.75 MOA. The corrected MOA was 16.5MOA. Using the rifleman method, (17.75 * .956) = 16.9MOA or about 4" of error which isnt too bad. For this example, it works out pretty good.

 

On the flip side, in 2008, I shot another dall ram at 702 yards at 38 degrees incline which normally would work out to 15 MOA at 5400' and 52 degrees F. Add the incline and it works out to 10.25MOA. Using the RMM, (15 * .788) = 11.8 for an 11 inch mistake (11.8 - 10.25) * 7.02 = 11". Granted, this was a very long shot and a very steep incline. Most hunters will never encounter a shot like that. However, I know alot of you are sheep fanatics and you may just find yourself in that position or worse someday.

 

One thing is FOR SURE! That is that the riflemans method works MANY times better when using MOA values instead of yardage.

 

For the record, if you check my calculator against any other calculator out there including RSI, Exbal, JBM (online), Berger, Sierra etc.....the numbers are within anywhere from fractions of an inch to 2" at 1000 yards. You will see those variances in all programs when comparing them side by side.

 

M

[Dan]

Thanks for all the great info !!!!

[Verndog]

Great information!!!!!!!!!!!!!! Thanks a ton for posting it and explaining it at the same time! I also see that I need to put more thought into my shots. Thanks again. Verndog

[JLB]

Somewhere around 2003 or 2004, I marketed a very simple device that you could put in your pack (weighs almost nothing and came with a cosine chart ) and would give you a pretty good idea of the angle to the target. When the laser rangefinders came out with angle compensation, I pretty much stopped selling my device. I have given away a lot of these through Amanda and this website. I have a few more left if anyone is interested. I am not trying to sell them, just give them away. Send me a message if you are interested in getting one.

[cosninocanines]

It's going to take me some time to work through this I just purchased the Leica 1600B rangefinder which has a ballistics program and bullet compensation built in. I was under the impression the hold over would be different shooting uphill vs downhill, is that the case? Thank You for this post I have an awfull lot of learning ahead of me.

[Coues Sniper]

It's going to take me some time to work through this I just purchased the Leica 1600B rangefinder which has a ballistics program and bullet compensation built in. I was under the impression the hold over would be different shooting uphill vs downhill, is that the case? Thank You for this post I have an awfull lot of learning ahead of me.

No, the "hold over" is the same shoting uphill vs. downhill at the same angle and distance. The horizontal distance is the same, so therefore the drop is equal also.

[azmetalman]

Watch this!!! Ryan Cleckner has many excellent videos that are produced by the National Shooting Sports Foundation. Here is one that takes the mystery out of up and downhill shooting. He was a sniper, really knows his stuff and is a good teacher.

 

[azgutpile]

Watch this!!! Ryan Cleckner has many excellent videos that are produced by the National Shooting Sports Foundation. Here is one that takes the mystery out of up and downhill shooting. He was a sniper, really knows his stuff and is a good teacher.

 

His technique will get you close, but it isn't perfect. What it doesn't take into effect is that the bullet still has to travel thru the air the entire unadjusted distance which means it is effected by drag. He would be better off taking his MOA adjustment (12 MOA) and multiplying it by the cosine making the adjustment 9.24 MOA.

 

Again, his technique should work fine when shooting out to <500 yards.