|
|
This topic comprises 2 pages: 1 2
|
|
Author
|
Topic: Absolute screen size and chord depth
|
Michael Schaffer
"Where is the
Boardwalk Hotel?"
Posts: 4143
From: Boston, MA
Registered: Apr 2002
|
posted 07-01-2006 07:07 PM
For curved screen installations, is there a formula for calculating the actual size of the screen based on the width measured in a straight line across from the left to the right edge and the chord depth, the distance between the phyiscal middle of the screen and the middle point of that straight line? In order to arrive at the actual size of the screen.
I can work it out by drawing the diagram on paper, but I can't derive a simple formula.
If the screen was curved around 180°, then the relationship between the straight line (in that case, the diameter) and the chord depth (the radius) would be simply 2/1 and the actual screen size simply diameter x π /2. OK, but how do you calculate the relationship between the straight line (an intersection of the circle, or whatever that is called in English) and the chord depth, in this case a segment of the radius. Or do they change proportionally, in other words the intersecting straight line from left to right edge will always yield the actual screen size
if taken x π/2? I am a little confused. Probably a very simple case of not seeing the forest because of the trees.
| IP: Logged
|
|
|
|
Michael Schaffer
"Where is the
Boardwalk Hotel?"
Posts: 4143
From: Boston, MA
Registered: Apr 2002
|
posted 07-01-2006 09:44 PM
Thanks for the explanation. Although I went through this hell at one point in my life long ago, geometry has never been my strength, it really makes my head smoke. I have a hard time working it out on paper, too. I can mostly follow your explanation though, so
2*ArcSin (C/2)/R
in the given example
2*ArcSin (60/2)/60.25
2*ArcSin 0.4979
2* 29.8611
=59.7222 degrees
then
*π/180
=1.0423
*60.25
=62.7985
or in more realistic figures, 62.8' or 62'9.6'' or let's say 62.10''
Yes, that makes sense. I can not say that I understand every single step fully, I would have to do a little more reading up, but I understand it far enough to "accept" it and work with it.
So, a screen with, let's say, a chord length of 35' and a chord depth of 1.5' would have a radius of (35^2/8*1.5)+1.5/2=102.85
Applying the next steps of the formula,
2*ArcSin (C/2)/R
2*ArcSin (35/2)/102.85
2*ArcSin 0.1701
2*9.7936
=19.5872 degrees
*π/180
=0.3418 radians
Then,
102.85*0.3418
=35.1541 or roughly 35'2" - the curvature would be extremely shallow, but it is a practice example only anyway.
But it starts to make sense to me. I need a little bit more reading up to understand every step, but the formula as such seems easily enough appliable (with a little cheating - I use a ArcSin calculator, if I tried to work that out on paper, my head would fail from overheating).
So the complete formula would look like this:
((C^2/8CD)+ CD/2)*((2*ArcSin(C/2)/R)*0.0174)
Do you usually curve the screen around the portholes in your designs, and do you get the actual screen (arc) size from CAD, or do you calculate it according to this method for each project?
| IP: Logged
|
|
|
|
Charles Greenlee
Jedi Master Film Handler
Posts: 801
From: Savannah, Ga, U.S.
Registered: Jun 2006
|
posted 07-02-2006 02:47 AM
Curved screen? The Tara had one, it was only curved along one axis. It was smaller than the one at the Wynnsong now, which is flat.
Catch me up. I know optically, light radiates out. So the larger a screen, the more it will see distortion of the images outward. Thus, you will need a screen curved to a point where the light hits it squarely and evenly. In other words, your radius should be your distance to the projector, on both the vertical and horizontal axis. That's just on an ideal standpoint. We now have lenses that correct for the distortion, designed specially for flat screens. We have lenses designed for horizontally curved screens, like the Tara. And then there's the lenses for the concave screens, like I described above. Which setup would you think is better? To use a correting lens on a flat screen, or just bite the bullet and set up a curved or concave screen? Which one is more comfortable for the audience, I suspect that a concave screen might be a bit odd to look at.
| IP: Logged
|
|
Steve Guttag
We forgot the crackers Gromit!!!
Posts: 12814
From: Annapolis, MD
Registered: Dec 1999
|
posted 07-02-2006 07:55 AM
Moving from most recent to older...
Lenses are not as flat field corrected as you would like to think...they have much better depth of focus than they used to and this gives them that appearance. If you think about it...a 50mm lens does not know how far the screen is away so how does a designer design it for a flat screen. If the screen happens to be closer then the lens will move towards the screen to maintain focus but in doing so, moves away from the film plane so if it was designed to be x distance from the film plane it is no longer there. I have noted that lens designers do expect a curved film plane...a modern lens on a straight gate does not do as well as an older design. I have also noted that some lenses do better on curved screens than others. All lens manufacturers and every engineered projection process has come to the same conclusion that the screen has to be curved for optimum presentation...how much to curve it though varies greatly.
Since I calculate my own curved screens (for best light, or whatever the reason it is being curved), I end up having to specify the actual size the screen must be ordered. I then also have to check with whomever is making the frame to ensure that we are on the same page as far as arc length vs chord.
quote: Michael Schaffer
Do you usually curve the screen around the portholes in your designs, and do you get the actual screen (arc) size from CAD, or do you calculate it according to this method for each project?
I don't get the "porthole" part. I don't do "scope radius" screens as a general rule. Most of my curved screens have a radius notably shorter than the throw in order to get better light.
In order to do that, I use one of two programs (one I wrote in Mathematica some years ago) that uses some calculus to find the maxima of light reflected back to the audience based on projector(s) location, screen size/location and audience seating area.
Since I already have the radius and chord when I design the screens, I'm already at S=R*Theta part.
I did the rest for your benefit. I'm reasonably comfortable with geometry and rather than memorize a formula, I just generate them as needed. My memory isn't so good about some things (and extremely good in others...normally trivial crap that doesn't seem to help)...as such I found it much easier to memorize the basics or the root of things...and then just generate the rest on an as-needed basis. Most things on an arc have the radius multiplied by something. So in this case, it is the radius multipled by the angle equals the arc length...if it were velocity of a shutter blade of say 12" it would be the radius times the angular speed . Most 2-wing shutters run at 1440RPM so multiply that by 2Pi to get 9047.79 Rad/Min. Multiply by 12-inches to get 108,573.4 inches/min at the outer part of the 12-inch blade. As you can see it is the exact same concept so it is easy to remember since one can use it any time one needs to work with angular travel. At least that is how I keep it all straight.
For me, the CAD part comes at the end when the design needs to go into a blueprint and also for the screen/frame fabrication.
If all you need is the arc length all of the time, why not set up a spread sheet with the formulas you need and then make a template of it...most every computer nowadays has some spreadsheet program on it (Excel if you have Microsoft office). Then you can bang em out as needed without having to remember anything (but where you put the template). I do this for amplifier power now...I got tired of loading the information into my calculators since that requires logrithmic summations and such...very doable on an HP calculator but once you do it more than a few times, it is more efficient to just set up a spread sheet that is ready willing and able.
| IP: Logged
|
|
Michael Schaffer
"Where is the
Boardwalk Hotel?"
Posts: 4143
From: Boston, MA
Registered: Apr 2002
|
posted 07-02-2006 02:24 PM
quote: Steve Guttag
if it were velocity of a shutter blade of say 12" it would be the radius times the angular speed . Most 2-wing shutters run at 1440RPM so multiply that by 2Pi to get 9047.79 Rad/Min. Multiply by 12-inches to get 108,573.4 inches/min at the outer part of the 12-inch blade. As you can see it is the exact same concept so it is easy to remember since one can use it any time one needs to work with angular travel.
I don't quite understand where this comes in handy?
quote: Steve Guttag
I don't get the "porthole" part. I don't do "scope radius" screens as a general rule. Most of my curved screens have a radius notably shorter than the throw in order to get better light.
I meant around the approximate lens location, of course, not the porthole. That isn't a point location anyway. In the finished setup, the ideal lens location is then found by moving the projector closer and further away.
So I understand that most of the screen setups you design are actually curved deeper?
quote: Steve Guttag
I did the rest for your benefit. I'm reasonably comfortable with geometry and rather than memorize a formula, I just generate them as needed. My memory isn't so good about some things (and extremely good in others...normally trivial crap that doesn't seem to help)...as such I found it much easier to memorize the basics or the root of things...and then just generate the rest on an as-needed basis.
Thanks for taking the time to explain that. Generally, it is indeed better to be able to break something down to the basics and fully grasp these elements, then there is less to memorize and more flexibility in daily application. But like you said, we all have different areas which we can grasp easier and "see through" while others may be less accessible to us, so it is necessary sometimes to sit down and make the head smoke, even if a subject does not come to us easily...
| IP: Logged
|
|
|
|
|
|
Charles Greenlee
Jedi Master Film Handler
Posts: 801
From: Savannah, Ga, U.S.
Registered: Jun 2006
|
posted 07-03-2006 04:22 AM
But, like a flat screen will feather at the corners and edges, a screen that is too curved will also distort at the edges. On a white screen, the light is reflected in almost a uniform spread, so the curvature would have minimal effect on how well the light was reflected back. However, if the screen is curved to the radius from the projector, all of the light/image, will fall on it evenly, producing an even, undistorted image. Now on a silver screen, or a glass bead screen, that's another question. I think those do have a directional bias.
| IP: Logged
|
|
|
|
|
|
|
|
|
|
|
|
|
|
All times are Central (GMT -6:00)
|
This topic comprises 2 pages: 1 2
|
Powered by Infopop Corporation
UBB.classicTM
6.3.1.2
The Film-Tech Forums are designed for various members related to the cinema industry to express their opinions, viewpoints and testimonials on various products, services and events based upon speculation, personal knowledge and factual information through use, therefore all views represented here allow no liability upon the publishers of this web site and the owners of said views assume no liability for any ill will resulting from these postings. The posts made here are for educational as well as entertainment purposes and as such anyone viewing this portion of the website must accept these views as statements of the author of that opinion
and agrees to release the authors from any and all liability.
|
Home
Printer-friendly view of this topic