Tuesday, February 10, 2009

CIH Explained - Easy Math

The purpose of this page is to simplify issues such as calculating the Throw Ratio [TR] needed for using an anamorphic lens with a projector. Rather than redoing the CIH Explained page, I have added this page and will focus on the math needed for working out what I would like to call a "best practices method" of calculation for the screen size and seating distances in your room. This method work in every room.


The size of the screen is best found by dividing the room's length by 4.5. I've used 4.5 as it a 'round' number. The actual number you use can be anything between 3.68 and 5.18 and where '4.43' is the middle and 4.5 is simply rounded up. Dividing the room's length by the chosen number gives you a screen height within an idea range for that room. Once you know your image height, you can easily work out both Seating Distances and Throw Ratio. The reason I choose to use the room length is that is generally a fixed value and it makes sense to work within the limits of the parts of the system [the room itself] that you generally can not change. For this example I am using 6m which is the length of a typical car port or garage [a room that is often retrofitted to be a home cinema].

1a: Room length of 6000mm / 4.5 = screen height of 1333mm

If you are planning on an AT screen, be sure you take into account the distance needed behind the baffle wall as this effectively reduces your room length.

1b: Room length 6000mm - [AT cavity] 600mm = new room length of 5400mm.

1c: New room length of 5400mm / 4.5 = new screen height of 1200mm.


The aspect ratio is simply the width in relation to the height to denote the shape of the screen. 35mm film CinemaScope has an Aspect Ratio of 2.39:1 meaning the projected image is 2.39 times wide as it is high. As it turns out, our Home Theatre equivalent is 2.37:1. This is partially because TV's evolution to wide screen has been based on 1.33x steps [where SD is 1.33, HD is 1.78:1 [1.33 x 1.33] and Scope is 1.78 x 1.33], but also because of the optical expansion of 1.33x anamorphic lenses on a 16:9 projector. The actual math requires the decimal point to be taken to at least 7 places.

2a: 1.3333333 x 1.3333333 = 1.7777777

2b: 1.7777777 x 1.3333333 = 2.3703702.

2c: Screen Height of 1333mm x Aspect Ratio of 2.37 = Scope Screen Width of 3159mm


With 1080 projectors, you can sit as close as 2x the image height but should not sit further back than 4x. These are based on SMPTE recommendations. SMPTE's preferred distance is 3x the image height and the THX 36 degree rule is 3.68x the image height and both fit within the 2x to 4x range.

3a: Screen Height of 1333mm x 2.00 = 2666mm [closest seating distance]

3b: Screen Height of 1333mm x 3.00 = 3999mm [SMPTE Preferred]

Screen Height of 1333mm x 3.68 = 4905mm [THX
furthest seating distance]

Note that in the 6000mm deep room, you are off the back wall, so allowing for Back Surround speakers to be placed behind the seating location[s].


The diagram above shows that the beam angles become wider when using a Horizontal Expansion Anamorphic Lens. To ensure the best results, the TR really needs to be as long as possible. I have recommended a TR of not less than 2.0 [or greater] be used with the Aussiemorphic Lens MK3 for most HT projectors. There will be some cases that require the projector to be mounted way further back than the calculated TR of 2.0:1 gives.

The 2 easiest ways to find the Throw Ratio and or Projector Mounting distance is to use the following math.

4a: Scope Screen Height x 1.78 x TR [in this case 2.2 = distance of projectors lens from screen.

Scope Screen Height of 1333mmm x 1.78 x 2.2 + 5220mm.

4b: Scope Screen Width x 0.75 x TR [in this case 2.2 = distance of projectors lens from screen.

Scope Screen
Width of 3159mm x 0.75 x 2.2 = 5212mm.

The 8mm difference will not make any noticeable difference. Again, this page is an example and your individual projector may need to be mounted further back or closer. If the projector can not be mounted back far enough, the screen height may need to be reduced.


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