Projector Throw Distance

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:

• Throw ratio
• 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 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).

Using the throw ratio 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. Usually the throw ratio is the only thing that needs to be researched.

• Sphere Diameter plus some margin ($d_{\mathrm{sphere}}$)
• Throw Ratio ($r_{\mathrm{throw}}$)
• Image Width ($w_{\mathrm{image}}$) and Height ($h_{\mathrm{image}}$) for the projector (used to calculate the aspect ratio)

$$d_{\mathrm{throw}}=d_{\mathrm{sphere}}\times \frac{w_{\mathrm{image}}}{h_{\mathrm{image}}}\times r_{\mathrm{throw}}$$

For a Sony VPL-FE40 with a standard zoom lens:

• Throw ratio: 1.91:2.41
• Aspect ratio: $\frac{4}{3}$ (calculated from $\frac{1400}{1050}$)
• Sphere Diameter (plus some margin): 72"

$$\begin{array}{ccc}{d}_{\mathrm{min\; throw}}& =& 72\times \frac{4}{3}\times 1.91=\mathrm{183.36"}\\ d_{\mathrm{max\; throw}}& =& 72\times \frac{4}{3}\times 2.41=\mathrm{231.36"}\end{array}$$

The smaller number, $d_{\mathrm{min\; throw}}=\mathrm{183.36"}$, is the minimum distance in inches the projector needs to be from the sphere. The larger number, $d_{\mathrm{max\; throw}}=\mathrm{231.36"}$, is the maximum distance in inches that the projector can be placed away from the sphere.

Projectors should be places as far from the sphere as possible without being further than the maxmimum throw distance. Placing the projectors farther away maximizes the number of pixels used to display data. Placing the images farther than the maximum throw distance causes the image to be larger than the Sphere and requires that the image be scaled down to fit the sphere.