# Long Range Incline and Declined Angle Shots

Discussion in 'Long Range Hunting & Shooting' started by CA48, Jan 22, 2011.

1. ### CA48Well-Known Member

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I need a little help from you angle shooters out there. I have been playing around with my 338 edge for a while now out to 1,965 yds on a regular basis and still have a lot of learning to do. I understand the effects of weather conditions, spin drift, and the lesser effects from Coriolis, ect... But all of my shooting has been from for the most part level ground. I may have a new shooting spot but there is going to be a lot of inclined angle shots. So how does this work figuring in with your regular drop. Do you get your angle while your aimed at your target before adjusting for drop with something like a protractor with a level. Then get the cosine for that angle and times it by the ranged distance to get your new distance or am I way off here?

2. ### trebarkWell-Known Member

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You pretty much have it down.

Measure the angle (up or down), determine the cosine of the angle, then multiply your dope by the cosine for a final elevation value.

You can get a angle cosine indicator from several different companies.

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4. ### brentcWell-Known Member

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This reminds me of a show I was watching last weekend with Gunwerks Mike Davidson on a goat hunt. Anyway, he ranged a goat at around 600 yards, and then he proceeded to say that they woud need to float the yardage to "doable" 700 to compensate for the angle.

Lol! I just had to laugh. Good luck hitting that goat!

5. ### Michael EicheleWell-Known Member

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The how to of shooting on an incline.

The following calculation and methods are provided by Sierra Bullets. The reference is taken from the Sierra Reloading Manual 4th addition. The verbage is mine.

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.

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

6. ### SBruceWell-Known Member

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Thanks Michael, great post.

7. ### CA48Well-Known Member

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Thanks for the replys and thanks Michael for the detailed post. So what about ACI devices how accurate are they +-1 degree, how precisely can you get a reading from them. I hear good things about them, see a few articles, but I would like to hear from you guys who use them often. Are they worth the \$150 or am i Going to get more accurate readings from something like a protractor.

8. ### SBruceWell-Known Member

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CA48,

A protractor with plumb bob hanging from it does work, but kinda hard to point it exactly at your target and still read the numbers on the side.

IMO, the rifle mounted system with angle or cosine indicator is the way to go. When mounting it, we can ensure the rifle is plumb level and that the indicator reads 0 at the same time.

Some rangefinders now give the shot angle too, which is a great idea I think.

Least accurate method is to use the cosine times the "line of sight" distance, as Michaels post illustrates.

Last edited: Jan 25, 2011
9. ### sp6x6Well-Known Member

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I have the ACI, which is cosine tool,OR angle tool,They do the same thing. It just depends how you input your math.I dont have PDA YET, so cosine is easier for me. IT reads on dial0,99,98,96,94,91 etc for cosine,BUt these are also all 5 degree increments down the dial, you just have to keep that in mind,I marked mine w/dremel on one side so I HAVE BOTH.

10. ### SBruceWell-Known Member

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Not trying to start an argument here, but I have a real life experience that happened about 15 years ago, that made me realize the standard "shoot to distance" or normal cosine type of calculation is not as precise as needed sometimes.

Shooting rockchucks high up on a cliff. Laying flat on my back on basically level ground. Had my rifle proped up on 36" tall shooting sticks that were only about a foot and 1/2 from my armpit..........it was steep, and the line of sight distance was almost 400 yds. "Shoot to distance" would have been like 280 yds or something...............long story short, I held for the shoot to distance and was shooting way high. I had to come down another 3" (relative to the rockchuck) to make the hits.

At 280 flat ground I was dead on, but at the angle I was shootin those chucks; I had to hold about 3" below them........dead on wasn't enough.

Last edited: Jan 25, 2011
11. ### rscott5028Well-Known Member

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You don't reckon the radical change in shooting position had anything to do with the movement of the barrel during recoil what with you being flat on your back against the ground and all that?

I'm certain that it happened just as you say it did and that you did some fine shooting. I just don't think that particular situation is a case for anyone to doubt geometry although it certainly points out that you have to be prepared to adapt to radical shooting situations.

Regards,
Richard

12. ### sp6x6Well-Known Member

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Sbruce, As Micheal explained, there are three general methods, you still need to know angle or cosine, it is in how the cosine is applied, Method one, which is simple triangle method , still helps in closer to 400 yrd on big game, but the least accurate, of the three. In my post I was also relating that the ACI, reads the angle too,

Last edited: Jan 24, 2011
13. ### SBruceWell-Known Member

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rscott5028,

Yes, I suppose that shooting position had some effect on muzzle rise, but that can't really be calculated. I think we should use the most accurate calculations possible because things (just like you mentioned) can and do happen. I don't doubt geometry or trigonometry. In fact; I use both very extensively every day........it's my job Oil companies pay me pretty decent \$\$'s to hit their targets that are 2 or 3 miles away.

sp6X6,

We actually don't need to know the angle if we know the line of sight distance and the horizontal distance. That's how the cosine value is calculated.

Try this: 282.8 yds (horizontal distance) divided by 400 yds (line of sight distance) and we get .707 not coincidence, .707 is also the cosine of 45 degrees (the angle)..............The shoot to distance (pythagorean theorem) or using the cosine of the line of sight distance both give the same result.

The other method, (which Sierra and NF ballistic programs use) results in a different answer. It is only a couple inches in the rockchuck example, but at least 2 out of my 3" error was due to the simpler and more recognized "cosine of the angle times the distance" method.

When your indicator reads 96, how is that supposed to be used? Are you supposed to dial 96% of your normal dope?.........I've never used one like that.

I see now, the 96 is actually .96 or the approximate Cosine of 15 degrees, .94 being Cosine of 20 degrees, .99 being Cosine of 5 degrees............now I can visualize what you're getting at.
gun)

Last edited: Jan 25, 2011
14. ### sp6x6Well-Known Member

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SBruce, Not trying to debate it with you. Your first point, for me as I sit on moutain, I only get line of site with my lazer, so I have to use my cos. dial on rifle to get any more info. And I DONT HAVE a pda type devise,yet.IF I did, that is most accurate, with either cos. or angle as it has inputs for either. And it sound like you are in surveying or some type of area that relates. I BUILD multi mill. homes and have watched the surveyors stake in for me on steep or tight lots. OR I do it myself for easier sites.I did note that triangle method is least accurate. I am forced to use the second which is use your cos. for your drops worked out previous as you noted, and I am taking notes on Micheals , which I think is a more accurate variation.I also want to know how to do sytem w/cos. an simple calc. as I AM trying to cut pack in weight. Thanks for your posts