# Calculating focal length of a PrimeFocus dish that has a hole in the middle

#### a33

##### SatelliteGuys Pro
Hi guys!

For calculating the focal length and f/D of a prime focus dish, you have to measure width and depth of the dish. That is commonly known.
Focal length = W^2 / (16 * d)

Has anyone ever had the problem of wanting to measure the exact depth of a dish, that has a hole in the middle? Or that has a plate in the middle (holding the arm for the LNB), that doesn't continue the parabolic shape of the reflector?

I don't know if this really could be a problem, but if it is, there is a simple solution to still get exact measurements of the dish, to calculate the focal length from.
For this solution you don't need measurements at the dish center anymore.

You just need the length of a chord, somewhere on the dishface ("A chord of a circle is a straight line segment whose endpoints both lie on the circle").
And at the exact midpoint of that chord, you need to measure the depth (perpendicular to the dish face, of course).
From those inputs you can again calculate the focal length: Focal length = (chordlength)^2 / (16 * depth) .

So, it is basically the same equation as above, but it can be used for any chord on the PF dish; not just the chord at the middle.

The principle behind this method is a special property of paraboloid dishes, that is described in the attachment of this post: Calculation of the focal length of an offset satellite dish antenna, Revisited - SatsUK
Any slice taken out of a parabola, parallel to the symmetry axis of the paraboloid, will give the necessary inputs to calculate the one and only focal length of that paraboloid (see e.g. figure 1 on page 2).

For prime focus dishes this property is even simpler than for offset dishes, as the dish face of a PF dish is always (by definition) perpendicular to the symmetry axis of the paraboloid. So you can use any chord.
(For offset dishes, the choice of chords is limited to chords perpendicular to the long (height) axis of the dish; so: parallel to the dish width axis.)

I hope this method can be of use to someone!
So I thought I'd share it with you.

Greetz,
A33