Jacob Koster 4/6/16 Mrs. Peterson Sighting in a rifle scope For my project I sighted in my scope to calibrate the sight of the scope with the shot placement of my rifle. In the application of sighting in my scope I set up a target downrange of my shooting position and took 5 shots at 50 yards, 100 yards, and 150 yards, for a total of 15 shots. The shooting distances were in order starting with 50yards then 100 yards, and finally the 150 yard distance. The rifle that I was shooting was my Remington model 700 and it is chambered to shoot a.308 bullet. The specific bullets that I was shooting that day were.308 caliber 150 grain bullets. The grain of the bullet is the measurement of the projectiles weight. This is very important when considering bullet drop, which I will explain later. When I was shooting I placed my gun in a shooting vise to keep the gun still and to eliminate human error when shooting. This is also very important because the calculations that you do to will be thrown off if the rifle keeps moving. The calculations and terms that I used include bullet drop, minute of angle, horizontal and vertical clicks, windage, heat mirage, angel shooting, and external ballistics, I will also feature Gaspard- Gustave de Coriolis, a French mathematician who was heavily involved in the study of projectiles. Before I can tell you how and why I used these terms and calculations to my project, I will first need to explain them 9n order to eliminate confusion.
Bullet Drop Bullet Drop is defined as the vertical distance of the projectile before the line of departure from the bore (Wiki, external ballistics). So when a powered projectile travels downrange, it arcs below the line of departure as it is being dropped down by gravity. In this case when the firing pin strikes the ignition of the bullet, an explosion is set off with great force and this is what sends the bullet flying through the air. The explosion from the bullet shell can only send a bullet so far and so fast. A bullet cannot travel forever. With that being said, the limited power of the cartridge combined with the weight of the bullet (or grains) will cause the bullet to start to slow down and drop at a declining angle. Once the bullet leaves the muzzle of the gun the bullet will fly straight through the air for about 50 yards, then after that bullet drop will start to take effect. In my case I was shooting 150 grain.308 bullets, which is considered a fairly heavy round. These grain of bullets will fall with a bullet drop of about a ¼ of an inch every 12.5 yards. In order to hit the targets bullseye to sight in my scope properly I needed to compensate for this bullet drop by adjusting my scope. The next calculation I will talk about is minute of angle. Minuet of Angle Minute of Angle is a standard shooting term of measurement. A circle has 360 degrees, and each degree has 60 minutes (www.rifleaccuracyreports.com). For example the calculated distance at a target at 100 yards is 1.04 inches or one-minute. The number is just over one inch. Most shooters when using minute of angle round this number of 1.o4 inches to 1 inch,
To make calculations simpler. If a shooter can shoot 5 bullets and have them all land in a one inch group on the target at 100 yards. In simple terms a minute of angle is just the term used by hunters and shooters alike to classify the group of their shots on a target and how to use this grouping to make their next shots more accurate. The next term I will explain is horizontal and vertical clicks. Horizontal and Vertical clicks Horizontal and vertical clicks are calibrating clicks that are positioned on a scope. The vertical click is called the elevation knob. The elevation is is the dial on the scope that brings the crosshairs from where your bullet struck to the bullseye in a vertical motion. This elevation adjusts your scope from whatever threw your bullet off. The shot may not be hitting the bullseye for a number of reasons. It may be because it may be because of bullet drop or heat mirage or anything really. The elevation dial will put your crosshair on the bullseye to compensate for the faulty shot, whether a shooter needs to go up or down to meet that bullseye. The Horizontal click or horizontal knob does the same thing as the elevation knob but instead of going up and down the horizontal knob will move the vision of the crosshairs from left to right. Both the elevation and the horizontal knob has clicks. These clicks are units of measurement, of how far up or down or right or left a shooter needs their crosshairs to go. On my scope at 100 yards, 1 click will move the crosshairs a ¼ of an inch on the target. So for
example, if I was sighting in my rifle and took my first shot at 50 yards and my bullet landed 2 inches below and 1 inch to the left of the bullseye, then I would bring my horizontal knob 2 clicks to the right (1 click at 100 yards= ¼ inch) and (1/4 inch times 4= 1inch to the right at 100 yards) divided by (2) = (1 inch at 50 yards). Then I would rotate my elevation knob 8 clicks up (1/4 inch times 8 = 2 inches at 100 yards) divided by (2) = 2 inches at 50 yards to meet the bullseye. Windage Windage is exactly how it sounds. It s the horizontal it s the horizontal distance that your bullet is thrown off because of the wind or breeze. The lighter caliber (or smaller size) of the bullet a shooter is using, he more susceptible the bullet is going to be towards the wind. When I was talking about bullet drop, I mentioned that an explosion from the cartridge can only make a bullet go so fast and so far before it starts to slow down. Well this same concept also applies to windage. A bullet no matter what the size, is not going to be effected by windage right out of the muzzle of the gun. But once the bullet starts to gain range then it loses power and starts to slow down, and this is when windage will start to throw off your shot, usually to a declining left or right angle, depending on wind direction. This is especially true with very small caliber bullets such as.22s or.22 mags. To compensate for this shooters will aim at their target a little to the left or right depending on the wind direction and strength. This practice in called Kentucky windage (Azodudes YouTube). For example if a shooter was shooting a.22 caliber rifle in a windspeed of 5mph that is blowing to the right, then the shooter can use Kentucky windage for
This. A.22 caliber bullet weighs 20 grains, and the wind will blow a 10 grain bullet off range up to ½ inch at 100 yards per mph of wind speed. If the intended target was at 100 yards using the example above but the shooter was shooting a.22 caliber bullet that weighed 20 grains, then the shooter would compensate with Kentucky windage by aim about a ¼ inch to the right of his target. The shooter will only aim a ¼ of an inch because his bullet is 20 grains of weight and is twice as heavy as the above examples 10 grain bullet. In my case I did not have to use windage because the time I was shooting I did not experience any wind at all, and even if there was wind. It would have to be blowing very hard for windage to effect the massive size of my bullet. Heat Mirage Heat mirage is a visual illusion that effects the optics of a scope, when the weather is really hot. Heat mirages can make an object seem as if it is closer, father, or in a completely different location then where it really is. In my case I did not experience heat mirage because I was shooting in the morning when the weather was still fairly cool. The fact that we are still in spring may be another reason why I did not experience heat mirage. Although heat mirages have occurred during spring time weather, they are unlikely during this time. Heat mirage usually happens when the temperature is 90 degrees and above and are most commonly experienced during summer. The next calculation I used was figuring out angle shooting.
Angle shooting Angle shooting is when a shooter is on an elevated position shooting at a downwards angle at a target, or shooting at a target that is at an above angle from the shooter. Shooting long distances at angles can throw a shooter off tremendously. For example a shooter will think they are at a distance they are shooting at a distance 150 yards but they are on a hill that is elevated from their target at 7 feet. The shooter will dial there scope in at 150 yards and will mostly likely miss the target in this case. This is because the shooter miscalculated the true distance away from their target, which in fact is not 150 yards away. The pathagorem theorem can be used to explain this concept, but after I did a little research I found out another formula that many shooters used to fix this problem. The formula reads, the (straight line distance away from target) times (the cosine of the angle) = corrected shooting distance (Www.loadoutroom.com). Before I used this formula I took my first 2 shots that were way off, but after I calculated this my last 3 shots all hit bullseyes. The next term in my project is external ballistics. External Ballistics External Ballistics is the behavior of the projectile while it is in flight. External Ballistics has to do with the flight of a non- powered projectile that is in flight. In the case of a bullet, it is only powered with the first ignition of the cartridge. Once the bullet leaves the muzzle of the gun, it is no longer being powered by any source of energy (Wiki Exterminating frame Ballistics). External ballistics are well known to be a part of shooting but it also is found in fields such as
archery, rocket flight, as well as other projectiles such as shells, rocket assisted projectiles, as well as balls in certain sporting events. Gaspard-Gustave de Coriolis was well influenced with Projectiles and external ballistics. A French mathematician, engineer, and phisist Coriolis was born in 1792 and died in 1843. He was known for his work on supplementary forces that are detected in a rotating frame of reference, leading to the Coriolis Effect. He was the first to coin the term work as being the transfer of energy by a force though distance (Wiki). Now that I have explained the terms and calculations that I have used in this project, now I am going to show you how I applied them. 50 yard distances The first distance I started at was 50 yards. When sighting in a scope 50 yards is a well-chosen starting point, because it is close enough to the target that the chances of your first shot hitting the target are very great and from there it s just a matter of working your shot placement towards the bullseye. In my case my first shot hit the target about 3 inches below and an inch to the right of the bullseye. I did not do any measurements in-between shots, only after I was done shooting. (I should have, it would have saved me a lot of time). I guessed I was only about an inch below the target, so I used my elevation knob to adjust my crosshairs 2 clicks up. This
put my 2 nd shot about 2 inches below the bullseye and was still an inch to the right. After this I adjusted my horizontal knob 2 clicks to the left which put my 3 rd shot just a little to the left of The bullseye and was still about 2 inches below it. So I adjusted my horizontal knob half of a click which put my 4 th shot directly in line with the bullseye and still 2 inches below it. Now that my horizontal knob was dialed in for this distance, I adjusted the elevation knob 4 clicks up and sure enough my 5 th shot hit the bullseye. (The bullseye on these targets are depicted as the capital A, see picture below.
100 yard distance When I was sighting in my scope at 100 yards, my 1st shot landed about 2 inches to the left and about 4 inches below the bullseye. From my distance I guessed that I was about an inch below the bullseye. So I went 4 clicks up and 4 clicks to the left, which put my 2 nd shot an inch to the left and 3 inches below the bullseye. At this point I walked over to the target and measured my
shot placement with the bullseye, and found out that I was still way off. My 2 nd shot was still an inch to the left and 3 inches below the bullseye. So I did 12 clicks up on my elevation and 4 clicks to the right on my horizontal knob and took my 3 rd shot. Although I made progress and got my shot closer to the bullseye, this 3 rd shot was still very low and a little to the right. This 3 rd shot landed low because of bullet drop. So at this point I left the elevation and horizontal knobs alone and aimed my crosshairs just a little to the left and about 2 inches above the bullseye. This action did not put me on the bullseye but it did give me progress. My 4 th shot was just slightly to the left of the bullseye and an inch below it. So I adjusted my elevation and horizontal knobs and hit the bullseye with my 5 th shot. For this shot placement it put my total minute of angle at a total of a 12 inch area. (See picture)
150 yard distance On my 150 yard distance I was shooting at a downwards angle. I was about 15 feet elevated from my target. My 1 st shot was extremely low, but the horizontal positioning was directly in line with the bullseye. The first shot landed 6 inches below the bullseye. Then I raised my crosshairs about 6 inches above the target, thinking I was dealing with a case of bullet drop.
Then I took my 2 nd shot and it was a little higher but still very low, and hardly any progress from my 1 st shot. So after I did a little research I found out the reason for my low shots was because of angle shooting, and I found a formula that would fix this. The formula is the (actual straight line distance) times cosine of the angle = corrected shooting distance. In my case my straight line distance = 150 yards and my cosine of the angle was 15 feet. So the calculation went as 150 times cos (15) = 144.8 yards. This made sense why my 1 st and 2 nd shots were so off. When I adjusted my elevation knob for this compensation, I hit the bullseye with my 3 rd, 4 th, and 5 th shots. After that I had a little fun and shot the rest of my ammo at the target (see picture).
In conclusion, I learned a lot from this project, and I found it to be really fun. I learned a lot about the step by step aspects of sighting in my scope with my rifle. The Application process taught me a lot when I did elevation and horizontal clicks, bullet drop compensation, angle shooting, minute of angle, and external ballistics. The research part of the project was extremely long, but at the same time enjoyable, because I learned a great deal of knowledge. I
also found Gaspard-Gustave de Coriolis to be extremely interesting, and how he researched and worked a great deal with projectiles.
Works Cited https://en.wikipedia.org/wiki/external_ballistics 26, March 2016 10:30 a.m. http://www.rifle-accuracy-reports.com/minuteofangle.html http://www.hornady.com/ballistics-resource/ballistic-chart 9 September 2009 https://www.google.com/search?q=kentucky+windage&oq=kentucky+windage&aqs=ch rome..69i57j0l5.4023j0j4&sourceid=chrome&es_sm=0&ie=utf- 8#q=kentucky+windage&tbm=vid http://loadoutroom.com/11744/how-to-high-angle-shooting/ https://en.wikipedia.org/wiki/gaspard-gustave_de_coriolis 30, March 2016