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November 25th, 2021, 09:17 AM  #41  


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target size has nothing to do with it, other than larger being easier to hit. just consider the target being a 1" rock, it's a 1" target at whatever angle you're viewing it and at whatever angle it may be "bladed." gravity has an effect over the HORIZONTAL distance to the target, not the true distance which will be longer when the target is at an angle uphill or downhill from the shooter.


November 25th, 2021, 09:22 AM  #42  


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November 25th, 2021, 10:05 AM  #43  


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The basis for all of this is the Pythagorean theorem. If you first think of the target as a matter of exact horizontal distance (leg 'b' of the triangle), THEN change the angle (modifying leg 'a' length), then yes, the lineofsight distance (leg 'c') does increase. If we elevate the target by 10o at 1000 yards, then our distance is *divided* by our cosine (.985), and our line of sight distance is actually 1000/.985=1015 yards. Note that while we DID increase our lineofsight distance as you correctly suggest, our bullet drop is still what it would be at 1000 yards even, the actual horizontal distance. As a side note, unless distances are huge, we would usually disregard a mere 10o angle. In our 1,000 yard example, the increase is only 15 yards... Conversely, as in our examples under discussion, we are first given our lineofsight distance (the larger figure) as we would have derived from our laser or optical/reticle ranging, and converting to horizontal distance reduces that figure. There, the formula becomes lineofsight distance *multiplied* by the cosine. Quote:
Think for a moment how your vertical trajectory (relative to your reticle) will not curve at all if the shot if fired straight down...effectively limiting the horizontal distance, and apparent drop, to "zero", no matter the lineofsight distance. Anything between "level" (max gravitational effect on vertical) and "straight down" (min gravitational effect on vertical) is going to be a gradient and some number in between max drop and no drop. We use cosine to quantify this gradient. Steeper angles have smaller cosines, approaching 'zero' (straight down), while flatter angles have larger cosines, approaching 1.0 (perfectly perpendicular to gravity). If shooting lineofsight distance (leg 'c' of the triangle) up/down at 45o, the cosine of 45o describes the actual horizontal distance (leg 'b' of the triangle). The cosine for 45o is .707. If our lineofsight distance is 1,000 yards and departure angle is 45o, gravity only gets to act on the bullet for 707 yards (1,000 x .707=707), as opposed to it's entire flight path. This causes an apparent reduction in drop that corresponds to moving the target in closer to 707 yards, a substantial change. Because the bullet DOES travel the entire line of sight distance, wind must be calculated for the entire flight path, which is the 1,000 yard line of sight distance, even if shooting straight down. To simply apply the cosine to distance is a traditional method called the 'Rifleman's Rule' and is a good approximation for ethical hunting distances and 'average' combat engagement distances. The error developed at very long ranges with any sort of substantial angle can cause misses if this method is used. At true long range, errors emerge as a result of this *approximation* and we would shift to the 'scope offset method' for a much more exact solution. The scope offset method more considers actual trajectory and the important fact that the scope is not looking at the target from the same vantage point as the rifle bore. Shooting long range matches in steep terrain, like the Allegheny Sniper Challenge, I got into the habit of exclusively using the scope offset method, wanting to tune our any error I could control. Then my misses are just a result of blowing the shot vs losing the bullet to an approximation before the trigger is pressed.
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November 25th, 2021, 10:19 AM  #44  


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November 25th, 2021, 10:22 AM  #45  


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"Scope offset method"  is there a book or web page. Google / Duckduckgo is not helpful.
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November 25th, 2021, 10:22 AM  #46  


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November 25th, 2021, 10:40 AM  #47  


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I'm not the best shot out there, but stayed at the holiday Inn express. Unless conditions aligned perfectly, id likely never take a shot at 600 yards on a deer. And I shoot 1k+ rounds a year at 600 yards while holding 98% of those shots(NRA high master) at a 6" group. Side note, Eds explanations of things are top notch. Makes me want to dive into the PRS/unknown distance stuff hard. We all have lots to learn in the shooting world and expanding our disciplines. 

November 25th, 2021, 11:54 AM  #48  


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1) Rifleman's Rule: We apply the cosine to the lineofsight distance as discussed above, resulting in correction of distance, but overlooks nonlinearity in trajectory. 2) ComeUp Method: We apply the cosine to the actual comeup data, which addresses the nonlinearity and is probably 'close enough' for 99% of applications. 3) Scope Offset Method: We use the comeup value, add in the distance between the scope and bore, apply the cosine correction, then take the scope offset back out. This tunes out the last factor we can account for, the scope offset, and delivers the most precise solution. Scope Offset Method: a) Take lineofsight range and find your comeup value for that distance. b) Add the distance between the scope axis and bore axis (offset). c) Apply cosine correction. d) Subtract the offset  this is your corrected comeup. Example: .308/175 M118LR equivalent with 100 yard zero Scope height over bore 2" Corrections in MOA Atmospheric condition equivalent to sea level Target at 750 yards (flat ground comeup = 24.1 MOA) Departure angle 30o (cos=.866): 1) Rifleman's Rule: 750 x .866 = 650 yards comeup for 650 yards = 18.8 MOA 2) Comeup Method: 750 yard comeup = 24.1 MOA 24.1 MOA x .866 = 20.9 MOA 3) Scope Offset Method: 750 yard comeup = 24.1 MOA 2" height over bore = 2" / 1.047 = 1.9 MOA 1.9 MOA + 24.1 MOA = 26 MOA 26 MOA x .866 = 22.5 MOA 22.5 MOA  1.9 (offset) = 20.6 MOA This method will match up to most ballistics software solutions when parameters match up. 20.6 MOA  18.8 MOA = 1.8 MOA 1.8 MOA x 7.9" (1 MOA at 750) = 14.2" error generated using the Rifleman's Rule this far away. A low miss...
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November 25th, 2021, 12:04 PM  #49  


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