Re: Cosine Angle Chart?
sent a pm to MitchinOR with power point presentation given at the army marksmanship unit,don't know if i attached it correctly, here's the text version...hope it helps as an introduction aide
EXPLAIN ITS JUST A DOWN AND DIRTY CLASS, AND IS NOT SET UP FOR MAKING THEM EXPERTS. This class is set up to explain the basic things you need to know for taking a shot at an angle.
When we consider target engagements there are a lot of factors that need to be considered when taking the shot. After the classes that you have already heard you have come to realize that there are many considerations to shooting accurately. You have been taught and/or refreshed on the fundamentals, your more versed in ballistics, and have a grasp of the environmental effects. In addition to these necessities you are now going to get a brief introduction to how angles effect ballistics and your abilities to kill the enemy.
All of us here have experience at some level of shooting on level flat ranges. Many of us have engaged targets in various environments, to include the mountains. Few of us have an understanding of what effects angles have on ballistics and how the effects of gravity are different as we increase or decrease the angle to the target.
FACTORS THAT DETERMINE DISTANCE FOR ANGLE SHOOTING
1. Range Estimation
– Straight Line Distance
– Flat Ground Distance
2. Target Angle (up or down)
The ability to accurately estimate the range to the target is one of the most important considerations for engagement
Straight line distance: is the actual distance from you to the target (i.e. laser range finder) The strait line distance to the target is the distance that will be used for your wind formula and time of flight formulas, because that’s the distance the bullet will travel
Flat ground distance: is the distance that a bullet is effected by gravity, and is the distance you will have to use for your zero or elevation adjustments.
Since we are talking only on how angles effect the flight of the projectile. The only thing that we really need to understand is how do we compensate for gravities effect. We simply need to understand the flat ground distance to the target from our firing position. That is it. Then we need to utilize that flat ground distance to determine our elevation adjustments..
To make it as simple as possible, gravities effect on a projectile is only equal to the “flat ground” distance that the bullet travels. For example: If I was to take a shot from the top of this building to the sidewalk immediately below, what elevation setting would I need? If you think back to the ballistics class you understand that as the distance to the target increases so does the bore line to the sight line. This in turn compensates for gravities effect.
If the “straight line” distance from the top of the building to the bottom was 400 yards and I used a 400 yard zero to engage would I hit the target. NO. My impact would be above my point of aim. I would actually need to use zero elevation adjustments as gravity is pulling the bullet straight down, in effect eliminating the effect of gravity all together. If the target moved farther away from the building than I would need to make incremental adjustments to compensate for the increased but still limited effect of gravity.
To simplify it even further. Staying with the football analogy, would I need to throw the football in a high arcing pass or simply drop the ball.
Since we are talking only on how angles effect the flight of the projectile. The only thing that we really need to understand is how do we compensate for gravities effect. We simply need to understand the flat ground distance to the target from our firing position. That is it. Then we need to utilize that flat ground distance to determine our elevation adjustments. To determine the flat ground distance we will discuss a few techniques and a couple of formulas.
It is important to understand that as the angle to the target increases the effect of gravity decreases
Before we get to the formulas and techniques if you only get one thing out of this class it is:________. With the exception of a laser range finder with the capability to compensate for angles all of these methods are time consuming and realistically should be used in a “range card” environment. To engage a target with straight line distance elevation will cause the bullet to impact higher as the angle increases.
Simply stated: With a 500 yard target and a 500 yard zero the bullet will impact point of aim/point of impact on a flat range. Increase the angle to the target to 28 degrees and your bullet will impact approximately 3 moa high or 15 inches. Enough to miss the target. You actually would have needed 440 yard data to achieve poa/poi
Techniques and Formulas
• Map Relation
• Cosine Formula
• Vertical MIL Reading Formula
• Pythagorean Theorem
• Protractor Formula
• These are the formulas and techniques. All of these deal with a way of determining the actual or “flat ground” distance.
Map Relation
• The most simple to use
• Determine your location and the targets location
• Plot both locations on a map
• Measure the distance between points
• This is your “flat ground” distance
COSINE FORMULA
• Straight Line Distance
• Target Angle
• Cosine Chart
• Distance X Cosine = Actual Distance
In order to determine the actual or flat ground distance utilizing the Cosine formula you need three things. The straight line distance can be determined many ways but the most effective is with a laser range finder. There are a couple of ways to determine the target angle and I will discuss them in a second. Once you determine the target angle you compare that angle to the cosine chart and determine your cosine, multiply that by your straight line distance and you will get your actual /Flat Ground Distance.
BASIC METHODS TO FIND THE ANGLE
• Clinometers / Ranger Silva Compass
• Standard Map Protractor
• Laser Range finder
Clinometers are instruments specifically made to measure angles
The Ranger Silva Compass has a built in clinometers inside of it. How to use it is simply put the flat edged base of the compass on the hand guard of the rifle while pointing at the target or target area, and read the angle where the north seeking pivot arm resets.
Standard map protractor. First in the center of the protractor install a piece of string with a weight to act as a angle reading line. Then lay the protractor on the barrel or scope with 90 degrees in the direction of the target. Aim at the target and read the angle from the string.
Once the angle is obtained refer to the angle cosine chart.
COSINE CHART
SILVA COMPASS
Example: Lets say you know the distance to the target is 500 yards strait line distance. By using the built in clinometer in the Silva compass you’ve determined that you are at a 26 degree angle to the target. Refer to the cosine chart, the cosine for a 26 degree angle is 0.89. Now you simply take the strait line distance of 500 yards and multiply it by .89 and you are left with a flat ground distance of 445 yards.
Protractor Method
Example: If you determine the straight line distance to your target is 600 yds. And get an angle from your protractor of 27 degrees. The cosine for a 27 degree angle is 0.89.
600 yds x 0.89 = 534 yds.
Note that there is not that big of a difference now notice the difference as the angle increases.
45 degree = .70 cosine.
600 yds x .70 = 420 yds
PROTRACTOR METHOD
Finding flat ground distance with a protractor should be your last resort. This technique is used in the case there is no way to get the cosine of the angle from either a cosine sheet or calculator. This method does work and is accurate only if the measurements are exact. That’s the biggest disadvantage due to its so difficult to get accurate measurements. This technique is designed to get a accurate as possible flat ground distance rather than just guessing in the case cosines are not available.
STEPS:
1. Range estimation.
2. Find the angle
3. Draw a strait line vertically such as line A
4. Place the center of the protractor on point 1 and draw a line of the angle, such as the line from point 1 past point 2
5. Mark the actual distance from point 1 to point 2
6. Now measure the distance from point 2 to point 3
7. This will give the flat ground distance for elevation settings.
_________________________
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