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Is a FoV formula available?

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Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: January/13/2010 at 08:06
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I asked something similar about FoV for a 3-9 scope set at 6x with a FoV of 39'-13.5- and got this response:
 
************************************************
 
No, roughly speaking, the FOV at 6X would be half of what it is at 3X and 1.5 times what it is at 9X. However, there is rarely an exact progression from the low to the high end. If you divide 39 in half (39 * 6/3), you get 19.5 and if you multiply 13.5 X 1.5 (13.5 * 9/6) you get 20.25. It might be reasonable to average those two values (19.875) and consider the scope to have about a 20' FOV @ 6X.

If my math is right, a 3-9 scope would typically show half of its FOV (.e.g 26.25) around 4.5X.
************************************************
 
This formula doesn't seem to work on my Redfield 3-9x40 that lists a FoV of 42.5 - 10.9'  At 6x for example, 1/2 of 42.5' = 21.25' and 1 1/2 times 10.9' is 16.35'.  That's a difference of 4.9' compared to the .75' in the above example. Do I still average those numbers or have I messed up somewhere?  I was wanting to figure the various settings on my 2-7x32 which lists 57.78' - 18.34' and wondering if there's a formula to figure FoV at every power setting?    Thanks. 
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: January/13/2010 at 08:51
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The field of view is determined by the size of the field stop ring.
This is a general formula:
True field of view = eyepiece field stop diameter ÷ telescope focal length x 57.3
 This will give you field of view in degrees, which can be converted to MOA and to feet.
 
So you need to know the field stop diameter of your telescope . Only the manufacturers will have that info (or break it open and measure it!!!)
You then need your focal length, which changes through the zoom of your power settings. So for each setting say 3X and 6X and 9X you will need the exact focal legth. It is rather technical stuff, which scope manufacturers seem to keep to themselves.
 
Far easier to sit at a 100yd range and see how much you can see left and right. Get someone to knock in pegs and measure it with a tape measure.


Edited by 8shots - January/13/2010 at 08:59
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: January/13/2010 at 09:17
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"Far easier to sit at a 100yd range and see how much you can see left and right. Get someone to knock in pegs and measure it with a tape measure"
 
+1 on that "8", actually a pretty good idea.
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: January/13/2010 at 12:23
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Originally posted by tpcollins tpcollins wrote:

I asked something similar about FoV for a 3-9 scope set at 6x with a FoV of 39'-13.5- and got this response:
 
************************************************
 
No, roughly speaking, the FOV at 6X would be half of what it is at 3X and 1.5 times what it is at 9X. However, there is rarely an exact progression from the low to the high end. If you divide 39 in half (39 * 6/3), you get 19.5 and if you multiply 13.5 X 1.5 (13.5 * 9/6) you get 20.25. It might be reasonable to average those two values (19.875) and consider the scope to have about a 20' FOV @ 6X.

If my math is right, a 3-9 scope would typically show half of its FOV (.e.g 26.25) around 4.5X.
************************************************
 
This formula doesn't seem to work on my Redfield 3-9x40 that lists a FoV of 42.5 - 10.9'  At 6x for example, 1/2 of 42.5' = 21.25' and 1 1/2 times 10.9' is 16.35'.  That's a difference of 4.9' compared to the .75' in the above example. Do I still average those numbers or have I messed up somewhere?  I was wanting to figure the various settings on my 2-7x32 which lists 57.78' - 18.34' and wondering if there's a formula to figure FoV at every power setting?    Thanks. 

You will get closer number if you start with the higher magnification FOV and work off of that.

For example,  for the Redfield, the field of view at 9x is 10.9 ft@100yards.  It is probably pretty safe to assume that at 4.5x, it is double that (21.8ft@100yards) or very close that.  At lower magnifications other factors come into play, so the change in FOV is not always linear.  However, for the top 70% or so of the magnification range, it is pretty linear.

ILya
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: January/13/2010 at 12:49
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Set your rifle, unloaded, in a rest, look through the scope and then go out to where the edges of view are and measure,  Easier than all that math and you won't have a headache!
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: January/14/2010 at 08:03
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Subtract the high end magnification form low end magnification.  42.5-10.9=31.6  Divide 31.6 by the difference of low to high pwer 9-3=6   31.6/6=5.27 (rounded).  Starting at 3x subtract 5.27 from 42.5
 
3x=42.5
4x=42.50-5.27=37.23
5x=37.23-5.27=31.96
6x=31.96-5.27=26.69
7x=26.69-5.27=21.42
8x=21.42-5.27=16.15
9x=16.15-5.27=10.88
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: January/14/2010 at 12:23
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Originally posted by magshooter1 magshooter1 wrote:

Subtract the high end magnification form low end magnification.  42.5-10.9=31.6  Divide 31.6 by the difference of low to high pwer 9-3=6   31.6/6=5.27 (rounded).  Starting at 3x subtract 5.27 from 42.5
 
3x=42.5
4x=42.50-5.27=37.23
5x=37.23-5.27=31.96
6x=31.96-5.27=26.69
7x=26.69-5.27=21.42
8x=21.42-5.27=16.15
9x=16.15-5.27=10.88

Unfortunately, that does not work for most scopes, since there is non-linear field of view constriction at low magnifications.

ILya
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: January/14/2010 at 15:26
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"Unfortunately, that does not work for most scopes, since there is non-linear field of view constriction at low magnifications."
 
 
So if you were looking at a drawing of how the field of view goets smaller from low to high power it would resemble the bottom of an hourglass?
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: January/14/2010 at 15:39
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I mean something like this (very hypothetical and not drawn to scale):


Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: January/15/2010 at 12:29
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That's kinda what I figured it would be like after reading about the non-linear constriction. 
 
So it would actually be closer to correct if you added the derived number (5.27) to the high end FoV and worked your way down in magnification.
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: January/15/2010 at 12:34
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Originally posted by magshooter1 magshooter1 wrote:

That's kinda what I figured it would be like after reading about the non-linear constriction. 
 
So it would actually be closer to correct if you added the derived number (5.27) to the high end FoV and worked your way down in magnification.

Not really, no.

Your 5.27 number is derived assuming linear change in FoV.  

ILya
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: January/15/2010 at 15:02
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So while you cannot get an exact number for FoV you can get a number that will in actuallity (sp?) be a liitle bit less than the actual FoV?
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: January/15/2010 at 15:30
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Originally posted by magshooter1 magshooter1 wrote:

So while you cannot get an exact number for FoV you can get a number that will in actuallity (sp?) be a liitle bit less than the actual FoV?

The closest would probably be to just take the FoV at the highest magnification (9x, for example).  At half the magnification, you can assume that the field of view will be double that.  At magnifications between 4.5x and 9x, it will be pretty linear.  At lower magnifications, you just do not know for sure.

ILya
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: January/16/2010 at 08:14
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Thanks Koshkin, actually it's the mid and upper powers that I was interested in. When sitting on stand deer hunting, I keep my 3-9 or 2-7 set at about 4.5 - 5 power and don't recall ever changing it to make a shot except one time. I think compensating for the extra shake at higher powers while hunting is counter productive.  Actually I think a scope with something like 4-7 variable power would be better suited than what's offered now. 
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: January/18/2010 at 07:22
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I have a spreadsheet that does a pretty good job of predicting the FOV of a scope throughout the range based on the FOV at the minimum and maximum magnifications. If you want to compare the FOV of several scopes within the same magnification range you enter the data, and then integrate the equation for the predicted line across the desired magnification range and the one giving the greatest area under the curve will have the greatest average FOV throughout the selected limits.

Edited by TwoLaneBlackTop - January/18/2010 at 07:35
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