## Calculating Projector Throw Distance For SOS

These are some distilled notes on projector throw distances and lens calculations. In general, if you can, use the lens calculator for the projector (like at projectorcentral.com)

What follows is a description of how to calculate minimum distance a projector/lens can be from the sphere and consequently helps define the room configuration for a particular SOS. The critical specifications are needed from the projector lens specification:

- The throw ratio
- The aspect ratio

In projector lens calculations, everything is proportional. The throw ratio is the the distance (or throw distance) from the center of the lens to the screen, divided by the width of the screen. For SOS, the screen is located at a distance as measured from the front of the lens to the center of the sphere. On zoom lens, the throw ratio is usually represented by two numbers which correspond to either end of the zoom stops. For example, the Sony VPL-FE40 standard zoom lens has a throw ratio (TR) of:

- 1.91 - 2.41 : 1

Obtain the TR from the projector and/or /lens manufacture specification. Sometimes its hard to find these numbers!

Using the throw ratio, you can calculate the size of the projected image at various distances. For our 68" diameter sphere, we use 72" as the minimum height that the projected image needs to be. The other number needed for this calculation is the aspect ratio of the projector image. These are usually fixed based on the type of projector. For example, common aspect ratios are 4:3 (SXGA) or 16:9 (1080P) or 16:10 (WUXGA). As an aside, given the throw ratio and the height of an image, you can calculate the width of the projected image using: (Height * 4/3 for SXGA aspect ratio) or (Height * 16/9 for 1080P aspect ratio) or Height * 16/10 for WUXGA aspect ratio).

For SOS, we need an image height of 72", which makes the width of the projected image for a 4:3 aspect ratio lens, 72" * 4/3 = 96"

Using the throw ratio's and the aspect ratio, you can now calculate the minimum and maximum throw distances for any given projector lens. The following parameters are needed in the formula but most of them are fixed, with usually the throw ratio the only thing that needs to be researched

- Sphere Diameter (plus some margin)
- Throw Ratio
- Throw Distance
- Image Width and Height for the projector (Used to calculate the aspect ratio)

**ThrowDistance = SphereDiameter * (ImageWidth/ ImageHeight) * ThrowRatio**

**Throw ratio: 1.91:2.41****Aspect ratio: 4/3 (calculated from 1400/1050)****Sphere Diameter (plus some margin): 72"**

**72" * 4/3 * 1.91 = 183.36" (or 15.28 feet minimum projector placement)****72" * 4/3 * 2.41 = 231.36" ( or 19.28 feet optimal maximum projector placement)**

The smaller number represents the closest the projector can be to the sphere and still illuminate the entire sphere. The larger number represents the optimal, farthest distance from the sphere that should be used to maximize the number of pixels used to display data. Any distance past that maximum, the projected image starts to become larger than the sphere and the actual data must scaled smaller to fit onto the 6' sphere.

### Summary

Getting this throw distance number accurate is important! If you miscalculate, then the room geometry may not work for your SOS configuration. Sometimes a very expensive thing to fix. The formula is simple since almost all of the numbers are fixed based on the aspect ratio. The two varients of the formula:

**min_projector_distance_in_inches = 96 * min_throw_ratio**(for 4:3 aspect ratio projectors: 1024x768, 1400x1050, 1600x1200)**min_projector_distance_in_inches = 128 * min_throw_ratio**(for 16:9 aspect ratio projectors: 1920x1080, 1080P, etc)