How would one theoretically rate the increasing difficulty of hitting a standard target as distances increase?

Leaving out the problems of wind.

This is a theoretical question so actual rifle accuracy can be discounted!

I believe it may be expressed using something like the inverse square law but I'm not sure.

For example: (all targets are the same size reguardless of distance)

Moving from 100 to 200 yards does it become twice as difficult or 4 times as difficult. I'd venture it's 4 times as difficult because the errors are propogated in both the horizontal AND vertical direction.

So, in my thinking it can be expressed like this for distances out to 1000 yards using 100 yards as the standard.

200 yards = 4 times the difficulty
300 yards = 9 times more difficult
400 yards = 16 times more difficult
500 yards = 25 times
600 yards = 36 times
700 yards = 49 times
800 yards = 64 times
900 yards = 81 times
1000 yards = 100 times more difficult

These figures seem to be very high in the difficulty factor but,I'm not sure

Figuring the windage factor in, I would place it as the standard amount of 200 yards=2X (2 times the distance) plus 2X(Wind factor) =4 for the wind factor and yardage increase.
Not figuaring anything else in this is what I had figured.

200 yards 4X (2X as difficult plus the 2X for wind)
300 yards 6X (3 times as dificult plus 3X wind factor)
400 yards 8X
500 yards 10X
600 yards 12X
700 yards 14x
800 yards 16x
900 yards 18x
1000 yards 20x

2000 yards 40x
2500 yards 50x

I'm not sure if this is totally correct but, as conversations go at the 1000 yard matches, this is what many say it is.

Wind factor certainly has to be considered plus a MAJOR consideration has to be the velocity decrease in the bullet over the path to the target. Lets say you start out the bullet at 3000 FPS at the muzzle and end up with a velocity of 1000 fps at the 1000 yard target, you have lost 66% of your velocity which is something that MUST be considered. This velocity loss alone will increase the difficulty factor. Light changes may be another factor to be considered?

Possibly my figuares above are too low.

Maybe Warren would have some insight into this one.

I sure is handy having Warren around isn't it. [img]images/icons/grin.gif[/img] [img]images/icons/grin.gif[/img] Kind of reminds me of when I was a kid and needed help, I'd just yell for ma or dad but nowadays it comes out sounding like Warren!!!

Interesting topic. In my limited experiance, 1000yds seems about 10 times more difficult is all with wind around 5mph max, double the wind speed and triple the level of difficulty. I'd say that applies from about 500-1000yds, beyond that, initial velocity, velocity decay rate, scope and WIND vary the difficulty level so much I doubt there could be only one rate, or could there be. I think the graph would show quite a curve upward after 1000yds reguardless and wouldn't be linear at all. Any thoughts?

Yes, it has always been an interesting topic.
With the rapid reduction of velocity downrange, the difficulty level would certanly be more then 10X at 1000 yards as compared to 100 yards.

There are just too many varibles to overcome from at least the 400 to 500 yard mark to 1000 yards and much further . The further out you send the bullet the difficulty level RAPIDLY increases because of the forces at work such as ANY wind and the slowing down of the bullet.

At a 100 yard zero the bullet is on it's upward part of the arc (forces don't effect it that much) and crosses the arc at around 300 yards coming down. When shooting 1000 yards the bullet has been coming down from a bit further then mid range being around 600 yards. The forces have a much better chance to effect the flight of the bullet in this segment of it's downward flight/fall to the target.
Taking everything into consideration, 10X more difficult at 1000 yards as compared to 100 yards would be way low in the difficulty level. Even 20X may be very low.

Understanding, I'm completely out of my league here... (and completely ignoring that wind was to be discounted!)
I would think that the gusting of the wind would be what does you in the most. The amount of deflection @ 1000 yards when the wind gusts +/- 2mph vs the same gusts @ even 500 yards. I ran a quick check and my PCB 18 says that a 240gr MK would be +/- about 1.6" @ 500y with wind variance from 8-12 mph vs the same bullet (3000 fps) @ 1000y where impact would be +/- 12" with the same wind.
I ass-u-me that any thermals that have variance or gusting winds that are traveling up or down a hill between you and your target would have an equally adverse effect on elevation. That alone(over simplified) would make shooting @ 1000y 8x harder to hit the same target or 4x harder to hit one that's optically similar (12" @ 500y and 24" @ 1000y), due to wind variable alone.
Fun Topic!
Coyoter

200 yards = 4 times the difficulty
300 yards = 9 times more difficult
400 yards = 16 times more difficult
500 yards = 25 times
600 yards = 36 times
700 yards = 49 times
800 yards = 64 times
900 yards = 81 times
1000 yards = 100 times more difficult

... are dead on.

Some might have a hard time seeing it, but if you think of a square piece of paper that is 10" on each side, it represents a target that is 100 square inches... but also 100 (rounding the 1.047") square "MOA's". That target at 200yds is only 25 square MOA's, at 500yds = 4 SQ/MOA's, and at 1000yds = 1 SQ/MOA!... so it is 100 times as hard to hit at 1000yds.

CatShooter.

__________________
.
Spring has sprung, da' creek has riz, I wonder where dem kitties is? Here, kitty kitty kitty.