How do I calculate the range of focal lengths required to shoot sports in an arena? Say for example I'm in an arena 20x48 and can stand anywhere at the short side up to a few feet away from it if necessary. And assuming a 2.5 x 2.5m capture area.
Calculating required focal length?
- Thread starter Energize
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Trigonometry using the effective angle of view of the lens.
The angle of view:
a = 2arctan(d/2f) ,
where d is the sensor size in mm for either the horizontal, vertical or diagonal that you are interested in, and f is the lens focal length (in mm).
E.g., For a 50mm lens on full frame sensor you get a horizontal angle of view of 39.6
To calculate the horizontal length that would be captured at a distance s from the camera with the above lens with angle of view a you use the following formula:
L = 2*s*sin(a/2)
E.g., at 20m you get 13.5m horizontal coverage.
If you want to do what you then you need to invert the above equations.
The angle of view:
a = 2arctan(d/2f) ,
where d is the sensor size in mm for either the horizontal, vertical or diagonal that you are interested in, and f is the lens focal length (in mm).
E.g., For a 50mm lens on full frame sensor you get a horizontal angle of view of 39.6
To calculate the horizontal length that would be captured at a distance s from the camera with the above lens with angle of view a you use the following formula:
L = 2*s*sin(a/2)
E.g., at 20m you get 13.5m horizontal coverage.
If you want to do what you then you need to invert the above equations.
Soldato
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They really need an app for that...
I can't be bothered to do trig to work out focal length
kd
I can't be bothered to do trig to work out focal length
kd
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lol yea
Soldato
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There are a few online tools you can use, eg http://www.canon.com/bctv/calculator/calculator3.html or http://www.giangrandi.ch/optics/lenses/focalcalc.html
Agree need an app but it's something you get used to quickly.
Why don't you go to the place early and suss out good locations?
Agree need an app but it's something you get used to quickly.
Why don't you go to the place early and suss out good locations?
Soldato
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Just take a 18-200mm lens with 1.4x, 1.7x & 2x TCs. All bases covered! 
A few caveats:
the horizontal, vertical and diagonal angles of views are all different, just use that dimensions from the sensor. The lenses normally advertise the diagonal angle of view only.
Different sensor have different sizes, e.g. the 1.6x and 1.5x crop sensors.
Focal length of lenses are rounded up (or down), and can very depending on focal distance. E.g. the new Nikon and d Canon 70-200 are more like a 80-180mm at close focal distances. Lots of lenses claim to be 18-xxmm but they vary between say 17.4 and 19mm. plus or minus 1mm at the wide end changes the angle of view quite a lot, especially at the 10-12mmm on crop cameras.
That stuff is actually easy, the difficulty is knowing how far away the subject actually is, most people are not very good at estimating and you cannot (easily) automate that. However, you can offer a large number of fixed sizes like length or breadth fo football pitch, basket ball court. You could automate this to a certain extent, take a photo with he smartphone and have the user manually highlight a human and enter an approximate height of that person, you can then find the distance to that person with known camera parameters form the phone. I wrote a computer vision algorithm that did something similar, but it is very sensitive an accurate height measurement at close distance and at long distances very sensitive to how accurately the subject was selected.
the horizontal, vertical and diagonal angles of views are all different, just use that dimensions from the sensor. The lenses normally advertise the diagonal angle of view only.
Different sensor have different sizes, e.g. the 1.6x and 1.5x crop sensors.
Focal length of lenses are rounded up (or down), and can very depending on focal distance. E.g. the new Nikon and d Canon 70-200 are more like a 80-180mm at close focal distances. Lots of lenses claim to be 18-xxmm but they vary between say 17.4 and 19mm. plus or minus 1mm at the wide end changes the angle of view quite a lot, especially at the 10-12mmm on crop cameras.
That stuff is actually easy, the difficulty is knowing how far away the subject actually is, most people are not very good at estimating and you cannot (easily) automate that. However, you can offer a large number of fixed sizes like length or breadth fo football pitch, basket ball court. You could automate this to a certain extent, take a photo with he smartphone and have the user manually highlight a human and enter an approximate height of that person, you can then find the distance to that person with known camera parameters form the phone. I wrote a computer vision algorithm that did something similar, but it is very sensitive an accurate height measurement at close distance and at long distances very sensitive to how accurately the subject was selected.
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