Short, honest answer first: you can’t get absolute F or D from the dish shape alone without at least one real measurement. A parabola has no inherent scale.
But — and this is the useful bit — you can work them out with one simple physical measurement. Here are the practical ways people actually do it.
What you must know (minimum)
You need one length scale, otherwise F and D are indeterminate.
That can be:
- Dish diameter
- Dish depth
- Focal point location
- Two points on the surface with spacing
- Rim angle plus one physical length
Without any length, there is no solution.
Practical ways to find F and D
Method 1: Measure the diameter (easiest)
Just measure across the rim.
D = measured rim-to-rim distance
Once D is known, everything else follows.
Method 2: Find the focal length directly (very common)
This works even if the dish is mounted.
- Point the dish at the Sun (or a distant lamp at night)
- Move a card or your feed back and forth until the spot is smallest
- Measure from dish vertex to that point
That distance is f
Then: F/D = f / D
or rearrange to get D if you later measure F/D
Method 3: Measure depth with a straightedge
If you can reach the dish face:
- Lay a straightedge across the rim
- Measure depth d to the centre
Now you have: f = D^2 / (16 d)
So if you know d and measure D later, you get f.
Method 4: Use two surface points (no rim access)
If the rim is obscured:
- Pick two points on the dish surface
- Measure:
- Horizontal separation x
- Height difference y
- Use the parabola equation: y = x^2 / (4 f)
Solve for f: f = x^2 / (4 y)
Once f is known, D comes from the rim geometry.
Method 5: Rim angle + one length
If you can measure the rim angle theta:
F/D = 1 / (4 * tan(theta / 2))
Then: f = (F/D) * D
But you still need either f or D numerically.
Bottom line
- Shape alone is not enough
- One real measurement is mandatory
- After that, everything falls out cleanly