Field of View

[turumti]

How does one calculate the actual field of view, i.e the width of the image that you will see at 1000 yards from the Field of View angle stated by the manufacturer?

And how does one reconvert it. For example, what would be Field of View (in degrees) of a of a pair of binoculars, if the manufacturer's date states ,"Field of View at 1000 yards is 300 feet".


I will apprciate any help. Thanks.

[Surveyor]

How does one calculate the actual field of view, i.e the width of the image that you will see at 1000 yards from the Field of View angle stated by the manufacturer?

And how does one reconvert it. For example, what would be Field of View (in degrees) of a of a pair of binoculars, if the manufacturer's date states ,"Field of View at 1000 yards is 300 feet".


I will apprciate any help. Thanks.

The equation Angle=2(atan(.5FOV/Dist)) will get your there. Because of edge distortions, etc. usually atan(FOV/dist) would be a close enough approximation. For example atan(150/3000)=2.8624d degs. times 2=5.7248 degs.

atan(300/3000)=5.7106 degs,

Going the other way FOV=2(tan(1/2 angle)*dist)) or approx. FOV=tan(ang)dist.

Ron

[Tero]

You can find tables like this on the net
http://www.quarry.nildram.co.uk/Binocs.htm

most of us get at least 6 degrees, but want 8 degrees of course!

[Pileatus]

How does one calculate the actual field of view, i.e the width of the image that you will see at 1000 yards from the Field of View angle stated by the manufacturer?

And how does one reconvert it. For example, what would be Field of View (in degrees) of a of a pair of binoculars, if the manufacturer's date states ,"Field of View at 1000 yards is 300 feet".


I will apprciate any help. Thanks.
Divide by 52.5.

Your 300' at 1000 yards would be 300/52.5 = 5.7 degrees

Examples
Ultravid 420' = 420/52.5 = 8 degrees
Nikon SE 8X32 393' = 393/52.5 = 7.5 degrees

John

[Petesot]

turumti

Here are all the useful FoV related formulae in MS Excel format. Just copy and paste into a spreadsheet and set up the cell references as indicated.

In the following two cases, replace ‘A1’ in the formula, with the cell reference containing the angle of view.

The FoV in m at 1000m

=(((TAN((A1/2)*PI()/180))*1000)*2)

The FoV in ft at 1000yds

=(((TAN((A1/2)*PI()/180))*3000)*2)


In the following two cases, replace ‘B1’ in the formula with the cell reference containing the FoV in m at 1000m.

The FoV in ft at 1000yds

=(B1-0.0000144151)/0.333333291

The angle of view

=((ATAN((B1/2)/1000))*180/PI())*2


In the following two cases, just replace ‘C1’ in the formula with the cell reference containing the FoV in ft at 1000yds.

The FoV in m at 1000m

=(0.333333291*C1)+0.0000144151

The angle of view

=((ATAN((C1/2)/3000))*180/PI())*2

[ceasar]

Ron and Pete,
Your formula's are great and I'm sure my son, who is a Physics and Math Major at a local University would approve of them, but for myself, I like John Traynor's math the best!

Cordially,

Bob :scribe:

[Petesot]

Yes Bob, I like the simple calculations too ;)

For convenience, I provided a useful means to convert FoV in ft at 1000yds to m at 1000m and vice versa - I’ve found comparing specifications listed in US/UK websites a bit frustrating at times.

I also forgot to mention that Apparent FoV is simply the angle of view multiplied by the magnification. An AFoV of 60 degrees or more is desirable, but only one 7x42 that I know of delivers this and very few 8x42’s manage it, whereas roughly 70% of 10x42’s (costing more than ~£200) provide or exceed 60 degrees Apparent FoV.

[elkcub]

Field of view is a measure of the perimeter section of a circle with a reference radius. If the radius is 1000 yards=3000 ft, then the circle has a perimiter of 2*Pi*R = 18849.56 ft. and each degree of the circle has a section length of 18849.56/360 = 52.36 ft, — since there are 360 degrees in the circle. This is usually rounded to 52.4 ft., or 52.5 as in John Traynor's statement.

So if you are given the section length as X ft., then the angular measure in degrees is simply X/52.4

There nothing to be gained by using trig functions, which really estimate the wrong thing anyway; namely, the distance betwween to points on a line tangent to the reference circle. For small angles this is perfectly acceptable, but for large angles the error increases. Besides, dividing by 52.4 is just a lot easier.

Blue skies,
Ed

[John Russell]

Even the manufacturers get their knickers in a twist on this one.
Swift in their literature convert metres to feet (eg: 372ft/113m) and mix up their units.
A FOV of 113m @ 1000yds excludes comparisons and is guaranteed to confuse everyone!

[Surveyor]

I believe Ed has a valid point but I have just always assumed that the image plane was flat (hence plane) and my old optics books gave the formula with tangent functions. Like Ed said at 8 or 10 degrees, who is going to "see" the diffenence.

[hinnark]

turumti

Here are all the useful FoV related formulae in MS Excel format. Just copy and paste into a spreadsheet and set up the cell references as indicated.

In the following two cases, replace ‘A1’ in the formula, with the cell reference containing the angle of view.

The FoV in m at 1000m

=(((TAN((A1/2)*PI()/180))*1000)*2)

The FoV in ft at 1000yds

=(((TAN((A1/2)*PI()/180))*3000)*2)


In the following two cases, replace ‘B1’ in the formula with the cell reference containing the FoV in m at 1000m.

The FoV in ft at 1000yds

=(B1-0.0000144151)/0.333333291

The angle of view

=((ATAN((B1/2)/1000))*180/PI())*2


In the following two cases, just replace ‘C1’ in the formula with the cell reference containing the FoV in ft at 1000yds.

The FoV in m at 1000m

=(0.333333291*C1)+0.0000144151

The angle of view

=((ATAN((C1/2)/3000))*180/PI())*2


Thank you, Pete for this useful Excel ready formulas. I have to use arctan instead of ATAN, though.

Steve

[ghostrider]

Just look through them, the more you can see the wider the field of view. Simple.

[hinnark]

Just look through them, the more you can see the wider the field of view. Simple.

Right. But for the widest field of view, don´t use any binocular at all.

[Sancho]

Just look through them, the more you can see the wider the field of view. Simple.
Now that´s my kind of maths ;) .

[elkcub]

Surveyor,

You might wish to consider the so-called "focal plane" concept for telescopes/binoculars:
http://www.aoe.com.au/astronomical_glossary.html

Focal plane. The plane (usually this is actually the surface of a sphere of large radius) where the image is formed by the main optics of the telescope. The eyepiece examines this image.

Ed

[turumti]

Surveyor,

You might wish to consider the so-called "focal plane" concept for telescopes/binoculars:
http://www.aoe.com.au/astronomical_glossary.html



Ed

Gentlemen,

Thank you so much for all your help. I really appreciate it.

Regards,

Salman