Mathematical Formula for Optical Illusion ?

[Guest snapper]

Here's one for a full-fledged mathematition : Say you have a yardage marker at 100 yards that measures 2' x 3'...what would the yardage marker sizes be - at 50 yard increments, (out to 600 yards), to make them all "appear" to be the same size ? I'm cutting out a long rifle range on my place and I want to mark it at 50 yard increments with markers that my old eyes can see easily, plus who knows, maybe the buck of a lifetime will walk out on it...it'll make ranging him quick and easy !!

 

 

[2.ooohhh]

At 50 yards 3' is .573 degrees of angle so rounded to the closest whole foot-

 

50 yards- 1'x1.5'

100 yards- 2'x3'

150 yards- 4'x6'

200 yards- 6'x9'

250 yards- 8'x12'

300 yards- 10'x15'

350 yards- 12'x18'

400 yards- 14'x21'

450 yards- 16'x24'

500 yards- 18'x27

550 yards- 20'x30'

600 yards- 22'x33'

Edited October 24, 2013 by 2.ooohhh

[Mechanic_X]

No calculations needed. Similar triangles.

[Guest snapper]

I can't see (or afford) making markers that big, so I think I'll make the 600 yd marker out of a full 4' x 8' peice of treated plywood (or the equivalent of) and take off 3" vertically and 6" horizontally for every 50 yards back, that way I'll end up with a marker 1' x 2'6" at 50 yards, surly I can see those !!

[2.ooohhh]

No calculations needed. Similar triangles.

I really only calculated for the first one, excel did the rest.  :woohoo:

[LngRngShtr]

3" and 6"  every 50 yds won' be very distinct difference

 

Just use different 12" shapes and color combinations

 

orange triangle of every 50 or 1 shape @ 50 2 shapes @ 150 etc.

 

blue square for every 100  2 squares @ 200 3 @ 300  etc.

 

maybe bump to 18" after 350 yds. by way of comparison the 600 yd NRA target for Hipower matches is only a 36" black circle

 

bright enough to see even if you get snowed on

 

quick range estimation and not colors found in nature so should stand out and when the buck walks out to see what 4 blue squares are

 

make your correction (400 yds) and fire :cool:

Edited October 24, 2013 by LngRngShtr

[tnguy]

I really only calculated for the first one, excel did the rest.  :woohoo:

I think Excel may have lied to you :)

[2.ooohhh]

I think Excel may have lied to you :)

Excel rarely makes the mistakes for me, it's far more likely I mis-keyed in either entering the formula or transposing the answers if you found an error. :surrender:

[tnguy]

Double distance should be double linear size, right? Triple distance, triple linear size.

[2.ooohhh]

I think Excel may have lied to you :)

I stand corrected(thanks tnguy!), forgot to fill down after modifying the formula slightly.  :rant: It was initially set up to determine screen size vs projection distance for my projector so it needed some slight modification to work here. Still pretty large markers at the far end.

 

50 yards- 1'x1.5'

100 yards- 2'x3'

150 yards- 3'x4.5'

200 yards- 4'x6'

250 yards- 5'x7.5'

300 yards- 6'x9'

350 yards- 7'x18'

400 yards- 8'x12'

450 yards- 9'x24'

500 yards- 10'x15'

550 yards- 11'x16.5'

600 yards- 12'x18'

Edited October 24, 2013 by 2.ooohhh