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Dumb Question of the Day-FOV calculation

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koshkin View Drop Down
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Post Options Post Options   Thanks (0) Thanks(0)   Quote koshkin Quote  Post ReplyReply Direct Link To This Post Posted: December/27/2014 at 17:49
Originally posted by Trailblazer Trailblazer wrote:

As stated earlier, the FOV on any scope represents a triangle from your scope, to whatever distance we're talking about, be it 100 yards, 200 yards, etc.  There is only one triangle in which base (FOV) doubles when the altitude (distance to target) doubles, and that is  a right isosceles triangle.  Therefore, if that is the ONLY triangle with which the FOV could double as the distance doubles, then every scope would have to have pretty much the same FOV, otherwise, it couldn't be a right isosceles triangle.

Make sense?

That is slightly correct and mostly flat out wrong.

The FOV is an angle.  The projection of it onto a plane a particular distance away from the vertex forms a triangle.  That is typically an isosceles triangle (though not necessarily, since I have seen plenty of scopes with asymetric FOV due to manufacturing tolerances).  However, the angle at the vertex, varies considerably from scope to scope and from magnification to the magnification.

The distance to the target plane is the height of the triangle and for ANY triangle, isosclees or otherwise, the length of the opposite side of the triangle (which is the FOV in this cases), doubles if you double the height of the triangle.

That is VERY basic geometry.

I am guessing that you are confusing isosceles triangle with an equilateral triangle.  In an equilateral triangle, the angle at the vertex is always 60 degrees.

Aside from the geometrical considerations, what does any of this have to do with the diameter of the objective lens?

ILya
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Post Options Post Options   Thanks (0) Thanks(0)   Quote koshkin Quote  Post ReplyReply Direct Link To This Post Posted: December/27/2014 at 17:52
Originally posted by Trailblazer Trailblazer wrote:

..meaning to fit into your theory of the FOV of any scope doubling when the distance doubles, they would all have to have a FOV that represents a right triangle, which would mean they would all have to be the same.

This is obviously not the case, so therefore I believe your theory is flawed.

Once again, right triangle and equilateral triangle are not the same.

And for the record, this is not my personal theory.  This is how geometrical optics works.  I work withoptical instruments for a living and how FOV works is pretty well established.

ILya 
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Post Options Post Options   Thanks (0) Thanks(0)   Quote Trailblazer Quote  Post ReplyReply Direct Link To This Post Posted: December/27/2014 at 19:10
Right...but my point remains the same.   If each scope has a different "base FOV" as you put it, then it's impossible for every scope's FOV to double when the distance doubles as Koshkin suggests.

...or were you referring to something else?
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Post Options Post Options   Thanks (0) Thanks(0)   Quote Trailblazer Quote  Post ReplyReply Direct Link To This Post Posted: December/27/2014 at 19:13
Originally posted by koshkin koshkin wrote:


Once again, right triangle and equilateral triangle are not the same.

And for the record, this is not my personal theory.  This is how geometrical optics works.  I work withoptical instruments for a living and how FOV works is pretty well established.

ILya 


I never said "right triangle".  Re-read my post.  I said "right isosceles" triangle.  BIG difference.

Let's start from scratch.  Do you disagree that a scope's field of view represents an isosceles triangle?
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Post Options Post Options   Thanks (0) Thanks(0)   Quote Trailblazer Quote  Post ReplyReply Direct Link To This Post Posted: December/27/2014 at 19:30
Perhaps this will help.  Click on the link below and tell me where I'm wrong.  Perhaps I'm missing something...

Click on the link below (or copy and paste if you can't click on it)

http://www.mathopenref.com/isosceles.html


Point "A" represents the scope, or perhaps your eyeball, or whatever.  (Yes, I realize that the FOV will never come to a sharp point like the tip of the triangle, but I think this still makes my point).  The distance between "B" and "C" in the illustration represents the FOV.  The "altitude" figure on the left would represent the distance to the target.  There is only ONE case in which the base of the triangle would be double the altitude, and that is when the angle at "A" is 90 degrees.  Drag point "A" down so that the altitude is 18 (Half the base which is 36) to see what I mean.  With the angle at "A" set at 90 degrees, the base would double to 72 (double the original 36) if you doubled the altitude to 36, and it would continue to double as the distance doubled.

ANY other angle at "A" would NOT result in the base doubling as the altitude doubles.  Therefore, it doesn't seem as though the FOV on every scope would double as the distance doubles, unless  the peripheral vision while looking through the scope was not a straight line like the sides of a triangle, but rather a curved line similar to a parabola if the angle was greater than 90 degrees, and a line that curves the opposite way if less than 90 degrees. 

http://www.mathopenref.com/isosceles.html

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Post Options Post Options   Thanks (0) Thanks(0)   Quote Dogger Quote  Post ReplyReply Direct Link To This Post Posted: December/27/2014 at 20:39
I think you had better listen to Ilya on this one otherwise your thread title risks becoming a self fulfilling prophecy.   If you use your triangle calculator you will see how doubling the altitude will double the base as long as you keep the angle at "A" constant.
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Post Options Post Options   Thanks (0) Thanks(0)   Quote billyburl2 Quote  Post ReplyReply Direct Link To This Post Posted: December/27/2014 at 20:48
Originally posted by Dogger Dogger wrote:

I think you had better listen to Ilya on this one otherwise your thread title risks becoming a self fulfilling prophecy.   If you use your triangle calculator you will see how doubling the altitude will double the base as long as you keep the angle at "A" constant.
THIS!
Some scope manufactures even post FOV numbers in degrees. This is the one constant that is fixed by the design of the scope.
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Post Options Post Options   Thanks (0) Thanks(0)   Quote Trailblazer Quote  Post ReplyReply Direct Link To This Post Posted: December/27/2014 at 20:51
Originally posted by Dogger Dogger wrote:

I think you had better listen to Ilya on this one otherwise your thread title risks becoming a self fulfilling prophecy.   If you use your triangle calculator you will see how doubling the altitude will double the base as long as you keep the angle at "A" constant.


You are right!  I concede!
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Post Options Post Options   Thanks (0) Thanks(0)   Quote koshkin Quote  Post ReplyReply Direct Link To This Post Posted: December/27/2014 at 20:52
I am not trying to be mean, but there are a few things you are missing, most notably geometry and optics.

How did you get an idea that the the linear FOV at a particular distance is double the distance to the target? 

There isn't a riflescope in existence for which that is accurate.

Using your terminology, if you double the altitude of the triangle, the distance from B to C, assuming the angles remain the same, will double.

ILya
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Post Options Post Options   Thanks (0) Thanks(0)   Quote Urimaginaryfrnd Quote  Post ReplyReply Direct Link To This Post Posted: December/28/2014 at 00:59
So let me get this straight. Point A times point B may or may not equal point C except on alternate Thursdays when a lunar eclipse occurs at which time the point may become pointless or inversely proportional in clarity to M.U.D. (Miscelaneous Undocumented Devices). Therefore in theory: The closer you are to chit, the less chit you can see, and the farther you are from chit the wider range of chit you can see, which means that an optic on an orbiting satelite can see a world of chit.

Edited by Urimaginaryfrnd - December/28/2014 at 19:46

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Post Options Post Options   Thanks (0) Thanks(0)   Quote Voodoo6 Quote  Post ReplyReply Direct Link To This Post Posted: December/28/2014 at 07:47
I plumb guess I gots ma gizzintus mixed up with ma ciphering.....

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Post Options Post Options   Thanks (0) Thanks(0)   Quote Trailblazer Quote  Post ReplyReply Direct Link To This Post Posted: December/28/2014 at 08:45
Originally posted by Voodoo6 Voodoo6 wrote:

I plumb guess I gots ma gizzintus mixed up with ma ciphering.....




That's exactly what happened! Big Grin
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Post Options Post Options   Thanks (0) Thanks(0)   Quote Rancid Coolaid Quote  Post ReplyReply Direct Link To This Post Posted: December/30/2014 at 10:01
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Post Options Post Options   Thanks (0) Thanks(0)   Quote RifleDude Quote  Post ReplyReply Direct Link To This Post Posted: December/30/2014 at 11:35
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Post Options Post Options   Thanks (0) Thanks(0)   Quote Peddler Quote  Post ReplyReply Direct Link To This Post Posted: December/30/2014 at 11:38
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Post Options Post Options   Thanks (0) Thanks(0)   Quote Nixterdemus Quote  Post ReplyReply Direct Link To This Post Posted: October/12/2018 at 10:22
Yes, rise Lazarus rise or was that Vlad the impaler? Perhaps the Mummy would be more PC as I risk peril in awaking the dead thread.

In a variable riflescope specs is ER 3.3-3 imply that at the lowest end of magnification the ER is 3.3mm whilst the highest end ER is 3mm?

Thus in the case of a listed 3.3-3.6 ER the shorter ER would correspond w/the lowest power as the longer ER relates to the highest power?


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Post Options Post Options   Thanks (0) Thanks(0)   Quote koshkin Quote  Post ReplyReply Direct Link To This Post Posted: October/12/2018 at 12:55
Originally posted by Nixterdemus Nixterdemus wrote:

Yes, rise Lazarus rise or was that Vlad the impaler? Perhaps the Mummy would be more PC as I risk peril in awaking the dead thread.

In a variable riflescope specs is ER 3.3-3 imply that at the lowest end of magnification the ER is 3.3mm whilst the highest end ER is 3mm?

Thus in the case of a listed 3.3-3.6 ER the shorter ER would correspond w/the lowest power as the longer ER relates to the highest power?



Not necessarily.  Typically, eye relief of most scopes is shorter at high power, but there are a few out there with longer eye relief at high power.  Scope manufacturers do not list it in any sort of a consistent manner, so by looking at the specsheet there is not easy way to tell.  Typically, the smaller number is for the highest magnification, but not necessarily.

ILya
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Post Options Post Options   Thanks (0) Thanks(0)   Quote Nixterdemus Quote  Post ReplyReply Direct Link To This Post Posted: October/12/2018 at 21:05
Thanks for the reply.  So, my point is moot eh? C'est la vie, mon frere.

Maybe I've distorted yet another personal conclusion as well in which your expertise could be of service. If nothing else freeing me from even more ignorance. No claims to whether or not it'll take.

When looking at specs of variable power riflescopes I multiply each low/high power by its corresponding FOV. I determine bias betwixt the twain by which has the higher value. As a rule the higher power finds favour in a slightly better FOV percentage wise when compared to the lower power/FOV. Or so it seems to me.

I always presumed that was due to the lower magnification having somewhat ample FOV, comparitively speaking, and especially in a SFP a bit extra FOV is handy at maximum power which usually subtends w/reticle at that power.

Any nuggets to be gleaned here or is me wee formula total crappola? I take my results w/a grain of salt. Mainly use it for comparision amongst similar priced optics. 
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Post Options Post Options   Thanks (0) Thanks(0)   Quote koshkin Quote  Post ReplyReply Direct Link To This Post Posted: October/13/2018 at 18:06
With most scopes, FOV does not scale linearly at low magnifications.  There are some where it does, not with most.  If you start at maximum magnification and measure FOV at intermediary steps as you lower magnification, you will see it change linearly for a while until you get close to the minimum magnification where it starts to deviate from linearity.

That is a form of tunneling where internally, the limiting aperture transitions from one stop to another.  For similar reasons, you will also notice that at low magnification, most scope do not use the entire objective lens.  At high magnifications, the limiting aperture is the objective lens diameter, but at low magnifications, it is some internal aperture that acts as a stop.

Also, many scopes do not have the actual claimed magnification range, so if it is marked 5x to 25x, it is not necessarily a 5x erector ration.  They sometimes round up a little.

ILya


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