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Cosine Indicator

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Unread 12-09-2004, 01:37 PM
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Re: Cosine Indicator

Correcting for the effects of gravity – “Angle Shooting”

There is a physical ballistic problem encountered when shooting on angles that causes the bullets point of impact to hit high.

Shooting on angles is what every hunter experiences while hunting in mountainous terrain. Sheep hunters and deer hunters alike know all to well, that if their target is up or down on an angle, that they must aim low because the bullet will impact high. The reason for this has to do with gravity and the adjusted site height above the bore of the barrel.

When we zero in our rifle at 100 yards, we are shooting on a flat plane with the full force of gravity pushing down on the bullet. In order to zero properly and get the bullet to strike the bulls-eye, we need to adjust the sight height above the bore of the barrel for this particular condition, (shooting on a flat plane) so that when the bullet leaves the bore of the barrel it arcs up into the full force of gravity, and then drops down onto the bulls-eye.

However, when we shoot on an incline or decline (up or down on an angle) the force and effect of gravity is less on the bullet; but the sight height above the bore of the barrel remains the same, or adjusted for shooting on a flat plane.

Because of this, the bullet will have a flatter trajectory and strike the target higher than where our intended point of aim was. It is imperative that when we are shooting up or down on an angle that we eliminate the guesswork, and correct the straight line distance to the target or “sloped distance,” to the, corrected for gravity, distance to target.

Now, this is an easy adjustment; a simple equation that will put you very close to right on target, if not dead on. However there are two ways to obtain this and one is a little more accurate than the other.

The first method is called the “field expedient” method. As an example, when a surveyor is shooting a mountain top for mapping purposes, he uses an instrument called a theodolite. The theodolite tells the surveyor the angle of his aim. His/her goal is to obtain the base of the triangle distance, or flat line trajectory. Hence, simple geometry comes into play. The surveyor notes the angle that he is holding at, then goes to his data book and obtains a cosine number of that angle, which he then multiplies to the sloped distance.

Figure 2

In figure 2, you can see the sloped distance to target equals 500 yards and the angle that the hunter is holding on is 30 degrees (cosine number of .87). To obtain the bottom leg of the triangle, you would multiply the cosine number of .87 to the 500 yards. (.87 X 500 yds. = 435 yds.) This gives you the corrected distance as if you were shooting on a flat plane, with the full force of gravity affecting the bullets path of flight.

Referencing a .300 Remington Ultra Mag, utilizing a flat shooting 180 grain Nosler Partition bullet, with a velocity of 3250 feet per second, the uncorrected for gravity distance of 500 yards to target would cause the bullet’s point of impact (under the field expedient method) to hit approximately 13.2 inches high; or 1.75 minute of angle. You can verify this by utilizing "Exbal" Ballistic Targeting Software.

To the average hunter, these trajectories, at first, may not appear to be significant, but as an experienced hunter you know that they are; and the angle that you will be holding on demands a correction. As an example, let’s say that your rifle shoots an average group size of one inch at 100 yards (large for a pro-grade rifle). At three hundred yards the group size will open to three inches; at five hundred yards, five inches. So, if you are going to be thirteen inches high at 500 yards if uncorrected for gravity, then you can add an additional five inches to that, theoretically, in any direction. This is not difficult to see; math is math and science is science and when the math is done correctly, one round will put one animal down.

The U.S. Military as well as other Government agencies, train all of their Precision Marksmen on how to obtain the corrected for gravity distance to target. The original method of approach was to utilize a Protractor, string and paper-clip. The string was tied to the center of the protractor and weighted with the paper-clip. When the Marksman was aiming at his target, the protractor was held in place with the weighted string along the side of the receiver inline with the barrel. The Marksmen would then carefully grab the protractor and string, and obtain the angle that he was holding on. Then, the Marksman would go to his data book and obtain the cosine number, then do the math; very simple and very straight forward. Only today there is an easier, faster and more dependable method of obtaining the cosine number; and that is by using an “Angle Cosine Indicator” manufactured by “Sniper Tools Design Company.”

The Angle Cosine Indicator, (ACI) pictured in figure 4, is a widely excepted method of obtaining the cosine number of the angle that the hunter is holding on, by all Branches of the U.S. Military and militaries throughout the world.

Figure 4

It is a simple tool for hunters who hunt in mountainous terrain and is a vault solid precision instrument. It is manufactured from aircraft grade aluminum and anodized a flat black color. It fastens onto your rifle or your scope; either by a standard Weaver Base scope ring, or as seen in figure 4, by “Badger Ordnance’s” military specific picantinny rail mount. When the rifle is held on target, the “ACI” indicates the cosine number of that angle by means of a highly visible index mark; in addition, the cosine numbers transverse the body in five degree increments. The ACI is easily zeroed to your rifles bore by simply loosening the side screw and rotating the body until the zero cosine number sits inline of the index mark.

To install the Angle Cosine Indicator you will first need to decide on your method of mounting; either a Weaver base scope ring or a Badger Ordnance’s Picantinny rail mount. Once that is decided, you will level the bore of your barrel by placing a spirit bubble level on the inside rail of your receiver, which is where your bolt lugs ride on. Once the bore is level, install and zero the ACI, insuring that it is indeed level with the bore of the barrel and the zero cosine number is sitting ontop of the index mark. Once that is accomplished, you are ready to hunt. The following is the procedure for utilizing the ACI while in the field.

1) You spot your target. 2) Range / obtain the distance to your target by either utilizing a laser range finder or a ranging reticle. 3) Aim at your target and then look off to the side of your rifle at the Angle Cosine Indicator and obtain the indicated Cosine number. 4) Multiply the cosine number to the distance to your target, which will give you your corrected for gravity distance. Now, look at your data card to obtain your hold for the corrected target distance, and adjust your turrets as specified. Pretty simple and quick; but best of all, the ACI will assist you in eliminating the guesswork of where to hold, and increase your first round hits.

In the second method of obtaining the corrected for gravity distance to target, the ACI still plays its role, however the cosine number is inputted into “Exbal” Ballistic Targeting Software. “Exbal” is written by Gerald Perry of “Perry-Systems,” and is ported to run on three different platforms; 1) Mobile Windows based Pocket PC; 2) Windows PC desk top and 3) Palm Pilot PDA. The Windows based Pocket PC such as the Dell Axim 30 (624 MHz) is what I strongly recommend.
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Unread 12-12-2004, 04:54 PM
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Join Date: Nov 2004
Location: GF Montana
Posts: 467
It\'s a SIN to pronounce sin (or cosine) SIN

a mathematical cliché, but it's a dbl <font color="red"> SIN </font> to mis-spel cosine.
"A.C.I." indicates the cosign number
Mathematicians use "cos".
The mathematics is trivial. Ballistics software accounting for pressure, temp, and horizontal component (math speak for cosine), dynamic BC can very accurately account for all these anomalies

I used to think Kenton's Dial a Yardage knobs were the way to go, ( I like to stick to one bullet as they require), but I shoot a too many elevations, temp, etc.
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Unread 12-12-2004, 09:37 PM
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Join Date: Jun 2001
Location: Palmer, Alaska
Posts: 2,539
Re: Cosine Indicator

<font color="red"> Now, this is an easy adjustment; a simple equation that will put you very close to right on target, if not dead on. However there are two ways to obtain this and one is a little more accurate than the other.

I think what Ward is refering to here as being more accurate is the method that is more comonly used, by Sierra and most every ballistic program I've run accross... including Exbal.

1.0 minus the Cosine of the incline/decline angle multiplied by the actual drop from your boreline (not to be confused with bullet path). Subtract this amount from your level fire come-up.

First - It's easiest to do this math in MOA verses inches then converting to MOA.

770 yard shot at a 35 degree angle.
LOS to target is 770 yards, and corrected horizontal range is meaningless here.
35 deg = .819 Cosine
1 - .819 = .181

"Vertical" drop from boreline = 16.32 MOA at 770 yards - (this remains constant, level fire or incline fire)

"Level fire" bullet Path = 10.63 MOA at 770 yards.

16.32 MOA * .181 = 2.954 MOA

10.63 MOA - 2.954 MOA = 7.676 MOA (corrected MOA you'd now dial) My RSI Ballistics Lab program for example predicts the corrected drop to be 7.68 MOA too.

The easiest thing that I have done to help simplify these calculations in the field was to ask Jim Ristow at RSI ( www.shootingsoftware.com ) to modify the drop from boreline results in his program to read in MOA, not just inches etc... thanks Jim!.

What you can now see by having the DROP and PATH column results "both" in MOA is the exact MOA "difference" between the two.

The reason this becomes important is that in the field we use our bullet path - not the drop from our bore line, which is what we now find is needed for these calculations to be ACCURATE.

If you compare bore line DROP and bullet PATH MOA, you'll notice that there might be an average of 4.0 MOA difference between the two from 300 yards to 1200 yards, or something like that... maybe it's 3.75, 5.5 MOA or some other number. The important thing is to know "what number" it IS to add to the bullet PATH numbers you have commited to memory already so you know the bore line DROP in an instant also.

This eliminates the need to carry or memorize a bore line DROP chart also... the point of this whole thing, it eliminates a step in the math involved with virtually no loss of accuracy of the firing solution.

If my PATH requires 10 MOA correction at 750 yards, and a 35 degree incline is encountered, I add my "set" 4 MOA to the 10 MOA for 14 MOA, then multiply by .181 for 2.5 MOA to subtract from the original 10 MOA.... so I dial 7.5 MOA.

Pretty simple really, but very ACCURATE.

Another method, much more accurate than the "Slant Range converted to Horizontal Range" method (which our military has embraced), but still lacking for accuracy is where you multiply the bullet PATH MOA correction by the cosine of the incline angle and simply dial this new MOA solution.

Sierra explains this all much better than I can on their site here. http://www.exteriorballistics.com/eb.../article1.html

They also explain in detail WHY, and WHAT is going on that effects incline fire.

Hope that helps and I didn't confuse.

Here's another discussion from last year too.
Brent Moffitt
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Unread 12-13-2004, 12:29 AM
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Re: Cosine Indicator

B1g_B0re: You may beleive that it is a sin to mispell "Cosine." However, here is the correct spelling and Webster's definition.

co·sine ( P ) Pronunciation Key (ksn)
n. Abbr. cos
In a right triangle, the ratio of the length of the side adjacent to an acute angle to the length of the hypotenuse.
The abscissa at the endpoint of an arc of a unit circle centered at the origin of a Cartesian coordinate system, the arc being of length x and measured counterclockwise from the point (1, 0) if x is positive or clockwise if x is negative.

Simply put,


n : ratio of the adjacent side to the hypotenuse of a right-angled triangle [syn: cos]

In addition, in regards to angle shooting and the difference between MOA and inches of drop; they do not work the same. Inches of drop is not an angular method of measurement whereas both MOA and MIL-Rad's are. If the Shooter holds over for inches of drop while shooting on an angle, they will almost for certain, miss.

Brent: Thanks for the additional input. I have heard of one person in particular who multiplies the cosine to the MOA hold depicted on his drop chart. That person recently took an Elk at 1080 yards this way.
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Unread 12-13-2004, 08:50 AM
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Join Date: Jul 2003
Location: Orofino, ID
Posts: 165
Re: Cosine Indicator

W, if you are referring to David Power's son it was not an elk. It was a Mule deer at 1020 yds.
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Unread 12-13-2004, 09:51 AM
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Join Date: Sep 2004
Location: Southwestern Montana
Posts: 294
Re: Cosine Indicator

If we are taking into account time of flight differences between angled measure and flat line measure, shouldn't we take into account the effect on time of flight if the angle were up or down? Wouldn't up hill have a deceleration effect while down would cause an acceleration (just like your car)? This would cause time of flight to be different although minute. maybe the ballistics programs need to be tweaked a little more? Maybe I'm out to lunch and don't have a clue. The range difference is an easy concept to grasp but I think there are other factors to consider if we want the real number. I think for now I have to be content on a close enough for a kill shot number or put a palm pilot on my hunting equipment list. [img]/ubbthreads/images/graemlins/crazy.gif[/img]
If you're gonna be dumb you better be tough.
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Unread 12-13-2004, 12:46 PM
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Re: Cosine Indicator

Hunter66654::: Thank you for setting me straight on that. The story had begun to loose it's direction a bit... I am getting older...

Cowboy ~ Put a Del Axim 30 and Exbal on your List.
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