This is topic Absolute screen size and chord depth in forum Film Handlers' Forum at Film-Tech Forum ARCHIVE.
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Posted by Michael Schaffer (Member # 1204) on 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.
Posted by Steve Guttag (Member # 268) on 07-01-2006, 07:37 PM:
Michael,
The length of an arc is calculated as S = R*Theta
Where S = Arc length, R = Radius and Theta = the angle of the arc in RADIANS.
If you know your geometry you can work back to get R and Theta (note Radians = Pi/180 * Degrees).
If you don't know how to work geometry and algebra it will be get a little tricky to set it up.
The Radius will be equal (C^2/8CD)+ CD/2 where C = the Chord, CD = Chord Depth.
So take a hypothetical set up where the measured chord is 60-feet and the chord depth is 8-feet. By plugging in all the numbers we get to radius of the screen to be 60.25-feet.
The Radius and Chord/2 set up a right trangle so that 2*ArcSin (C/2)/R gives us the angle theta in degrees (in this example 59.73 degrees. Multiply that by Pi/180 and we get 1.042 radians. So the arc length in this example is 62'-9.5" or there abouts...not taking into account stretching and such.
It is a lot easier to show this on paper and drawing it out.
Steve
Posted by Michael Schaffer (Member # 1204) on 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?
Posted by Richard Hamilton (Member # 321) on 07-01-2006, 11:45 PM:
Michael, SHIT!!! i just email the drawings to my screen guy!
Rick
Posted by Charles Greenlee (Member # 3856) on 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.
Posted by Steve Guttag (Member # 268) on 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.
Posted by Michael Schaffer (Member # 1204) on 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...
Posted by Larry Myers (Member # 738) on 07-02-2006, 03:54 PM:
The U of R or University of Rochester has a computer program called Genesee that will tell you everything you want to know about a lens. The object of a lens designer is to try to design a lens that will operate at several distances. Enample in resolution values, one lens design might give a 400 resolution value at 50 ft but only 100 value at 10 ft and 300 feet. Amother design might give 250 resolution value from 10 ft to 300 ft. So a custom lens is the only way to go if you know the projector will only be used at 50 ft. Although customs lenses can run in the $10,000 range. Better to buy a stock $2000 lens that operates nicely from 10 ft to 300 ft.
Oh yes, the easy way to do a curved screen is to attach a string to the projector. Let out the string to the middle of the would be screen. Then trace the curve going back and forth holding the string tight.
Posted by Thomas Hauerslev (Member # 566) on 07-03-2006, 03:49 AM:
"....attach a string to the projector. Let out the string to the middle of the would be screen. Then trace the curve going back and forth holding the string tight."
This way the light will be reflected into the projector - which is undesireable - and a waste of light. The center of the screen curvature (circle) should be 2/3 of the distance between the screen and projector, thereby reflecting most of the light back towards where the majority of the audience usually sits.
If the projection distance is 24 meters, put the string 8 meters from the projector, and then do what Larry suggest - and you will have an impressive curve.
Posted by Charles Greenlee (Member # 3856) on 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.
Posted by Larry Myers (Member # 738) on 07-03-2006, 01:28 PM:
Again it's a mix and match thing. Sure if you make the curve exactly the way I said, you MAY more or less have a light reflection problem. On the other hand, you will have the curve that an uncorrected lens might have. Since lens corrections are all over the place, you really got to know what the specs are for that lens to get it exactly in. I would say about .000000001% of the population would know how to read a lens designer lens spec. So the bottom line is, just buy a newer name brand stock lens. If you would like a cerve in your screen, just push in the middle of the screen 2% of the width. That is, a 100 inch wide screen would be pushed in about 2 inches. A 50 foot wide screen would be pushed in about 12 inches. That should correct any errors in a flat field lens since by design, it's almost impossible to get a fully corrected flat field lens without screwing something else up in the lens design.
Posted by Charles Greenlee (Member # 3856) on 07-04-2006, 03:10 AM:
Yeah, I think if I ever get my own screen, one big enough to worry about it, I'd get one that is curved. Ideally the concave would be best, but the minor abberation you'd get from not curing it top-to-bottom would be barely noticable, if at all. Whereas, lateral curving will make a difference. My personal pref. though.
Posted by Ari Saarinen (Member # 3188) on 07-04-2006, 04:43 AM:
Few years ago in ITEA seminar at CinemaExpo... Schneider, THX and some others... did made a presentation where they did describe they experiments with screen which was made variable curvatures... some how they did came up that best curvature for screens should be approx. 4,5 to 5 % from the width of the screen... so 10 meter wide screen should be 45 to 50 cm deeper in the middle.
Posted by Michael Schaffer (Member # 1204) on 07-04-2006, 07:22 AM:
Hey Ari, how is Finnkino doing? Do you remember what the reasoning behind this very simple basic rule was?
Posted by Ari Saarinen (Member # 3188) on 07-04-2006, 07:41 AM:
We doing just fine... hot summer (+30 C)... cold beer... and watching soccer games... wonder what happens today for Germany... Italy is hard to beat.
If I remember correctly it was about how optics design are try to be fixed for flat screens but those still works better with slight curvature... and of course you need to use gain screen when you go for curve, but you surely knew that. I think there was also Harkness involved with that experiment.
Posted by Steve Guttag (Member # 268) on 07-04-2006, 09:27 AM:
It was Schneider, Harkness, USL (they at least supplied the light meters) and Famous Players....the experiment was more than flawed and the "conclusions" were almost embarassing. Their "optimum" curve was what formed the 1/20 rule. If you use the Schneider lens program and have it calculate the curve, it will give you the 1/20.
The flaw in the plan was that they kept their projection point fixed so as to not take into account that where the light starts doesn't have an affect on where it ends up.
To calculate a curved screen for optimum light, one needs to take into acount where the projector is, what the dispersion of the screen is and where the seating audience is. At that point, you can think of the screen as a big light reflector (which it is). Thus, a long skinny theatre can typically have a more radically curved screen than a short fat one (presumming the projector is always at the rear most part of the theatre).
Some lenses do better with curved screens than others...Schneider does not do as well as ISCO as the radius becomes notably shorter than the throw. I've also noted that Schneider is hypersensitive to being absolutley square to the projection plane. ISCO clearly has designed their current lenses for curved film planes.
If your screen gain is 30% or less, then you really can't curve it very much (and why would you want to since curving the screen will introduce geometric artifacts).
Personally, I love curved screens...deep curve ones too. But you can't approach this stuff with mere rules of thumb...you have to really know what you are doing to make them work properly.
Posted by Richard Fowler (Member # 893) on 07-04-2006, 12:41 PM:
Mr. "G" last post is right on the money
Posted by Charles Greenlee (Member # 3856) on 07-04-2006, 09:10 PM:
Sounds good to me. I don't know the rules in detail there, much more than I already stated, so having some elaboration does help me learn for later on.
Posted by Ari Saarinen (Member # 3188) on 07-05-2006, 02:17 AM:
I partly agree with Steve, but there is so much other bad and more critical things what cinema designers do too often with screens... like making full screen for 1,85:1 format and moving only top masking, ending up horrible keystone with 18" raisers(distorsion goes way bigger than 3%), too high gain screens "hot spot", etc...
Posted by Steve Guttag (Member # 268) on 07-05-2006, 06:20 AM:
Using the correct curve on a higher gain screen will mitigate the hot spot...using PC-Cine adapters or shifting the lens turret will mitigate the keystone artifact of a top-only masking system...I'm not advocating the top-only or having Scope being anything but the biggest picture...just saying that the problems you mention can be negated.
Steve
Posted by John Pytlak (Member # 331) on 07-05-2006, 09:20 AM:
For gain screens that reflect light much like a mirror (i.e., angle of incidence equals angle of reflection), simple ray tracing is the most accurate way to determine the screen curve. The light from the projector lens should be reflected back to the prime seating area.
SMPTE Recommended Practice RP95 simplifies this into the formula:
(Projection Distance + Distance between screen and audience center) / 2 = Radius of Screen
Posted by Brian Guckian (Member # 1678) on 07-08-2006, 01:43 PM:
quote: Steve Guttag
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.
I'd like to pick up on that - is there a formal mathematical relationship (of which the mathematical formuale quoted earlier could be a subset) between say the throw, screen width on Scope, screen gain, and other factors which could be derived, and indeed, agreed?
If the 1/20 rule is flawed (albeit from a light distribution point of view) then is there a better mathematical model out there?
I'm thinking about a situation where you have enough light to use matt white, but you want to curve the screen "for optimum presentation" - and indeed curved screens being more aestheticaly pleasing. What also if you're happy with light uniformity but want to curve the screen for best focus?
It just seems curious that there is an accepted formula for deriving gain screen curvature, but there's no agreed standards for other forms of curvature, with different methods being presented in this thread.
Is it due to the specificity of lens types and designs?
Another thought that occurs is that nowadays, if you install D-cinema alongside 35mm on a curved screen (gain or no) are the lenses on those projectors designed for flat or curved screens?
Posted by Steve Guttag (Member # 268) on 07-09-2006, 10:41 AM:
Brian,
In my best double-speak...yes and no. There is a formula for a moderately gained screen (Pearlescent) that John P. mentioned and is documented by the SMPTE. However, it is an approximation based on actual measurments in an attempt to have a rule of thumb. However, even that document tells you to do "ray tracing" to achieve a properly curved screen (for best light).
I developed a calculus based program in college to do it but you do have to know the parameters of the room and the screen dispersion. ORC also had such a program which tended to come up with curves similar to mine (close enough that I don't think the frame manufacturers could make the difference between the two). Both programs are based on the concept of sending a ray of light towards the edge of the screen and seening where the cone of light reflects back. Then increasing the curve until the maximum amount of the seating area is covered.
The 1/20 rule is flawed in that it is based on nothing...just a number thrown out there...you can't come up with it from the data that was taken (hence my embarrasing comment above). It has not scientific anything behind it. What it DOES allow you to do is proclaim "Curved Screens" without going to gain screens and you can't get into too much trouble with it. Just about any lens will focus reasonably well on it (since the 1/20 rule often gets you something near a throw=radius curve).
As for curving for "optimum presenation"...that can't be done...I like curved screens...some HATE them...so what is optimum? If you have an extreme projection angle, curved screens (all of them) will accentuate that with the part of the image furthest from the projector being the most "bent."
As for getting curved screen advocates to agree on a common set of rules/formulas for "optimum" curve...forget that too. What is important to you? Light? Focus? Using the screen to put you IN the picture (deep curves like Cinerama)?
However, most of the curves fall into one of the ones I listed above...Focus, Light, effect.
As for DLP...their lenses are made with the thought of a flat screen, primarily. I do note a mild pincushion when the anamorphics are used but that probably has more to do with the anamorphic lens design than the prime lens. There ARE warping systems to pre-distort the image as it leaves the projector so it looks proper on the screen (not to be confused with the "masking" function found on most DCinema machines that merely blocks off the image to fit the curved screen like an aperture plate).
There are lenses for 35 and 70mm film designed specifically for deep curved screens and they do quite well. In fact, a Magna-Com 65 will do an excellent job of mating up with a Cinerama screen for 1.85 images..good focus and low distortion. Note these lenses are not like anamorphics, they distort the image in all directions so while the horizon lines will fit well, the vertical lines will be pincushioned. With wide aspect ratios, it is the horizontal that is most perceived to be distorted.
Posted by Brian Guckian (Member # 1678) on 07-09-2006, 08:52 PM:
Thanks for clarifying that Steve. Actually I guess it's pretty obvious DLP lenses would be designed for a flat screen surface since that seems to be the predominant design today, but it's good to check. Also useful to know that 1/20 rule has no scientifc basis.
[If I'm ever lucky enough to be in a position to order a curved screen for a cinema, I sure know who to call now...
]
Posted by Brian Guckian (Member # 1678) on 04-07-2007, 08:24 AM:
I just wanted to bump this thread up from last time to ask if elliptical or even parabolic* screen curvatures have ever been tried in the field.
If you're looking at deep curve screens for effect (but not as deep as Cinerama), one of the things I've noticed is that ratios like 1.33, 1.37, 1.66 and 1.85 are subject to the same angle of curvature as wider 2.39 or 2.21 ratios, because the curves are cylindrical.
Thus the narrower ratios are subject to a greater degree of curvature proportionate to their width (I'm not expressing this well, but it is an aesthetic issue, as well as a design issue in terms of depth of focus for each ratio).
In theory an elliptical curve (for example) would present a flatter field towards the screen centre for narrower ratios, whilst still giving the immersive, or psuedo-immersive effect for the wide 2.39 or 2.21 ratios, or even if you wanted to show 2.76 Ultra Panavision.
Would a non-cylindrical curve of decreasing radius towards the edges of the screen present even more design issues than a standard cylindrical curve?
Just curious.
(* Curves derived from the parabola; the parabola itself being roughly u-shaped and probably unuseable)
Posted by Steve Guttag (Member # 268) on 04-07-2007, 11:20 AM:
Actually, Cinerama screens were not cylindrical. The one I measured at the Uptown in DC was more closely approximated with a 4th order function. However, it was deeply curved in the middle with the radius tapering off towards the sides. This makes sense when you think about that the projectors set up for Cinerama would then see reasonably shallow curves for their 1/3rd portion of the screen.
This style of screen also allows more viewable locations since the curve will not start to close in on itself.
Steve
Posted by Alan Gouger (Member # 543) on 04-07-2007, 01:33 PM:
I remember John Harvey who was associated with the Cinerama resurrection back in Dayton Ohio years ago promoted a deep curved screen for theater and Home Theater stating his testing resulted with focus using typical theater lens could support the deep curve.
Anyone have any memory of this?
Posted by Frank Angel (Member # 248) on 04-08-2007, 07:29 PM:
In two of my theatres, the screen must be flat because of the limitations of the fly system -- there is not enough room for a curved screen unless you take up three pipes, something the lighting guy and our rigger would kill if I even suggested it.
BUT, for me, the curve is so much of an aesthetic plus, that I refuse to abandon it. What I did years ago when this theatre was first outfitted for film projection, I decided to try using a perspective curve to give the illusion that the flat screen is actually curved. It's very simple, you just slightly curve the top and bottom mask so that the masks are dipping in toward the center of the screen on both top and bottom. On a 40ft width screen, about 4 inches into the center of the picture is all that is needed to create the "curve." This small cheat makes the screen look as genuinely curved as any real curved screen -- that mild curve of the old CinemaScope screens. And it gives the same dramatic and immersive feeling that a real curved screen does. Yes, it's an illusion, but it totally works. Ask anyone who has seen a movie projected on it.
Nice thing is, although you do loose 8 inches at the center of the picture (insignificant on a 17ft + high screen), you don't introduce any of the geometric distortion that some complain is created on real curved screen, even on the mild CinemaScope curve. On a perspective curved screen, lines remain as straight as they normally are.
In the beginning when in decided that I wanted a perspective curve on the first screen I put in our big theatre, I was a mere babe and was very nervous about doing something unconventional with the install. When I told the contractor crew that this is what I wanted, the whole bunch of them balked and poo-pooed it --told me it was never done. I held my own and insisted; the result proved to be a very positive and it has served us very well for decades.
Over the years many directors have screened their films in our facility and we've never yet gotten a negative comment about the loss of those 4 inches on top and bottom, even from the guys who made the films.
Coincidentally, as I write this, we are putting in another new screen in this same theatre and just a few days ago I had the shop cut the masonite for the bottom and top masks with this same curve. It will grace this screen again for the next couple of decades!
Once the screen and masking are up, I will post some pics of it -- perspective curve and all.
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