How to optimise stiffness for a projector screen?

[guyburns]

I am thinking about building a projector screen out of MDF. Here Down Under the available sizes are: http://www.misterplywood.com.au/products/mdf. Building such a screen will be easier than the normal frame with stretched fabric type, but I am concerned about its long-term flatness. So I thought I could stiffen the board with aluminium screwed or glued onto the back of the board.

I want to try to minimise weight and cost of the screen by optimising the thickness of the board and the size of the stiffening aluminium. A board 12 mm thick, for example, won't need as much stiffening as a 6 mm board, but it would be twice the weight.

Regarding the aluminium, I can obtain three types: L-shape, U-shape, and box-shape in various thicknesses. There are two variables: T (thickness) and L (length of cross-section). For a given weight of aluminium, how do I optimise the stiffness? Do I use a section which is thin (T = 1.6 mm) but with a large cross-section (L = 40 mm), or a thicker piece (T = 3 mm) with a smaller cross-section (L = 20 mm)?

I have the problem, then, of optimising the board thickness combined with the shape/thickness of the aluminium.

I am hoping there are simple equations that relate stiffness to T and L, given that the aluminium will be fixed to the back of the MDF board. Does anyone know those equations?

Without resorting to equations, what is the likely optimum stiffness combination: 6 mm, 9 mm, or 12 mm board; combined with what cross-section and thickness of aluminium: L, U or box-section?

I don't know if this is of any use, but MDF has a specific gravity of about 0.75; aluminium 0.25.

 

[enosis_]

What type of forces will be acting upon this screen - indoor or outdoor use?

 

[Vadar2012]

It'd be much easier if you work out the forces that will be acting on it and we can design something that will limit the deflection to a desired degree. This will optimise the design much better than guessing a stiffness value. Draw us a free-body-diagram and then we can help you out.

 

[guyburns]

Thanks for the replies. An initial design consists of a sheet of 9 mm MDF, 3000 x 1775, weighing ~37 kgs with aluminium stiffening on the back. The screen will be indoors, supported from three chains attached to the aluminium stiffeners at the screen end, and to three exposed timber beams at the ceiling end. I imagine the screen to be hanging at a slight angle, with the back of the screen pushing against curtains that are already in place. See attached drawing which is drawn looking horizontally.

So basically the screen is hanging under its own weight. I assume it won't move around too much. If it does (somebody bumps it, for example, or drafts of air) I might tie it down to the floor with a bungee cord or somesuch.

What I am mostly concerned about is the board warping in the long term because of humidity/temperature changes throughout the year if it is left unbraced.

 

[M Quack]

I guess you would get the best flatness with L-shaped stiffeners.

Also, just a 4 stiffeners around the outside will to little to keep the center from bulging, e.g. when the MDF expands due to humidity. I would probably go for some kind of grid structure on the back, with 30-50cm between struts and 25mm x 10mm Al profiles (the 10mm edge screwed to the MDF).

 

[256bits]

How does the surface of the MDF perform for best viewing pleasure?
Before you build will you have good solid colors and contrast from the surface?

http://www.practical-home-theater-guide.com/Projector-screen.html

 

[Vadar2012]

I just assumed that he knew what he was doing when it camed to the visibilty and quality of the picture on the MDF surface.

Thanks for the diagram that helped to see what you were talking about. You don't think a 9mm thick MDP board is a little over the top? If you really want to use it I'd just outline the back edges with some angled sections like M Quack suggested. Much cheaper than a huge plate of Aluminium. Not a good application for Al anyway.

Why don't you just buy one of those roller screens and attach that to the roof? Those are designed for good picuture visibility and will roll up when not in use. Will save you a lot of work.

 

[guyburns]

A few comments on the suggestions offered:

1. You don't think a 9mm thick MDP board is a little over the top?
I don't know. Probably. When I looked at 12 mm sheets in the hardware store, in stacks of about a dozen, supported 1 m apart, the stack had waves in it. The 18 mm stack didn't, indicating to me that there may be some minimum thickness required so the sheet is not too wavey to start with. But I really don't know. Maybe 6 mm would be okay and the supporting ribs would keep it stiff.

2. Why don't you just buy one of those roller screens and attach that to the roof?
I had thought of that, and have spent many hours researching over the last year. But there just seems to be too many problems (for example, ) unless you pay $thousands.

3. How does the surface of the MDF perform for best viewing pleasure?
I don't know yet, but before I go ahead I'll be comparing a mini version painted flat white, with my old slide projector screen, versus a screen in a friend's home theatre. My gut feel is that there won't be much difference. One of my hobbies is 3-screen audio-visuals, and I've shown them at various local venues projecting onto temporary screens (up to 6m x 2m) made of:

• paper (I used to work at a paper mill and had access to huge sheets);
• black-plastic weed mat painted white (the paint mostly fell off and ended up all over the stage when we pulled it down);
• white plasterboard walls;
• three 12 mm chipboard screens.

Here's not the place to discuss projection screens, but I suspect the difference between a painted flat surface and the best professional screens, in my situation, would be like the difference between 44.1 kHz/16-bit audio and 192 kHz/24-bit audio: not discernible.

Anyway, what I also came here for are equations. I had a pretty good search for Moment of Inertia formulas (I think that's what I'm looking for), and found some referenced to the centre of gravity of each shape (L, U, box) but couldn't find any referenced to one of the flat sides:

Q: Does the location of the reference axis make any difference to relative stiffness (see next para)?

I like playing around with formulae (retired electrical engineer here), so if anyone can point me to a site that has stiffness formulae I'd be most appreciative. I'm not interested in absolute numbers (this isn't a strict design process), just relative stiffness numbers so that I can say: "I should buy 25 x 10 mm L-shape, because that is 30% of the price, but has 75% of the stiffness of ***".

 

[Vadar2012]

I'm happy to help you with the equations, I'm a mechanical design engineer, but I think you're over thinking it. There's nothing to really to calculate. You'll find that the angled sections don't really differ much in price. I get stuff manufactured all the time. The smallest size will be way more than you need. Since it's just an inside application, I personally wouldn't even bother with the steel backing, with a 9mm thick board. I'd just buy one of the nice rollup ones so you don't have a gigantic hunk of plywood hanging around.

 

[M Quack]

http://www.projectorcentral.com/paint_perfect_screen_$100.htm

This gives some hints about what paint to use.

I would not try *exactly* the paint they recommend without some testing, but the hints to use a satin finish and use a paint that produces a smooth surface sound very reasonable.

 

[greentlc]

I was a cabinetmaker for several years. I can say that it will be a good idea to paint both sides with the same number of coats of paint. Otherwise one side will be more exposed to seasonal changes in humidity and the board will warp, even if screwed to aluminum brackets. Maybe not right away, but over a number of years the screws will work themselves loose.