[Konvas] frame rate questions: put on your thinking caps and break out your calculators

[Adam Frey]

I have a few minutes this week to try and update some of the konvas.org 
FAQ. I have a few quick (but random) questions.

First question:
What are the three (or four) most used frame rates in cinematography for 
capture and projection/transfer (e.g., television, cinema theaters, and 
home theaters)?

Given, 24fps & 30fps are obviously the top two. But would the next one 
on the list be 18fps (mostly Super8)? Possibly 12fps for cartoons? Or 
some other frame rate that I'm not thinking about right now? I doubt 
60fps is going to be a number in the loop, since that's usually an HD 
recorded frame rate. I'm also wondering how much super8 is getting shot 
at 18fps anymore - I know 24fps has become the de facto frame rate for 
almost all things film.

The next question is definitely mathematical in nature:
When a film has been exposed and developed to a mean density of 1.0 and 
projected onto a single screen at the same frame rate that it was shot 
(for arguments sake, let's say that lens quality and registration issues 
are both equal and optimal for all tests. Also, let's say we're shooting 
Kodak's DOUBLE-X B&W Neg 5222/7222, so that different color curves do 
not come into play), is the final image, as perceived by the viewer, 
from Super16 @ 30fps comparable to 35mm @ 24fps? (How about when 
transfered to HDTV 1080i60? Or, along the same lines, how about when 
viewing 18fps vs 24fps in the same formats?)

Breaking it down, it should be that the 1.66:1 S16 frame (should be 
93mm^2) is close to 1/3 the resolution of 1.66:1 cropped 35mm (I believe 
it's 292mm^2), but the entire *set* of images at 30 vs 24 (frame size 
aside), which means 6 more images per second when viewed in motion, 
should be 25% greater (correct?).
btw: 93mm^2 means "ninety-three millimeters squared"

The film's sharpness (MTF or "Modulation Transfer Function"), grain 
(Granularity or "RMS Granularity"), and Spectral Sensitivity will also 
be an issue, but this means we need to bring the shutter angle and 
shutter speed into play as well...

Originally, I had been thinking that it would be something simple and 
that it would be measured in time or "per second", in which my math 
would have been as follows:

frame size x granularity x fps x time = perceived optical resolution

But, that would have been wrong. It doesn't account for the shutter 
angle/speed, giving a slightly different exposure for 24fps vs 30fps. 
The nature of film has shown that it acts differently as the different 
emulsions are exposed differently. Another thing to note is that the 
shutter speed's motion blur at 24fps will be greater than at 30fps.

Note that "exposure time" is measured in seconds, which is usually 
broken down into fractions of a second, especially when dealing with 
MoPic films. To find the shutter speed, it is:

shutter angle / 360 x fps = exposure time

OK, I'm also having a bit of an issue with determining how the 
Granularity, MTF, and Spectral Sensitivity would work into the equation 
(especially having an issue with the math). Granularity is apparently 
measured by how many grains per 0.048mm diameter circle there are. I 
know the numbers would be much higher, but why not measure them per 
square millimeter?

MTF is the sharpness. I'll be honest and say that I do not fully 
understand how this can be determined separately from the granularity, 
but I understand that films have a certain thickness, and, much like 
prescription glasses, this is probably what determines the sharpness - 
but I could be wrong. The Spectral Sensitivity is determined by exposure 
and density.

So maybe if we took the above and put it all into the equation, how 
would it work out then?:

exposure, frame size, granularity, MTF, Spectral Sensitivity, fps, & 
time = perceived optical resolution

I'm pretty sure I have the correct data at this point, just not the 
correct skills to master this equation...

Oh - and just a little something extra to think about:
If you flipped an image up for 1/48th of a second (24fps), someone's 
brain may be able to register at least a portion of the image. But what 
a person perceives at 1/60th of a second (30fps) will be reduced even 
more, as the brain had even less time to register the image. But, if 
it's an image that shows motion, the motion blur may reduce the visual 
response of the 24fps frame, but increase the visual response of the 
30fps frame...

I know there is a very similar argument in HDTV land with 720p60 vs 
1080i60. And I also know that the sports channels decided it was better 
to stick with 720p60, which reduced motion blur, while everyone else 
decided 1080i60 was better...

Be warned, I may ask more questions like this in the future...


Cheers,

Adam Frey
Director/Cinematographer
Crimson Chain Productions
http://crimsonchainproductions.com
Cell: 301-639-7146

Crimson Chain Productions
PO Box 35
Libertytown, MD 21762