Calculator Inputs
Formula Used
The calculator uses spherical mirror geometry for primary grinding estimates.
- Focal length:
F = D × focal ratio - Radius of curvature:
R = 2F - Sagitta:
s = R - √(R² - (D / 2)²) - Remaining depth:
target sagitta - current sagitta - Approximate removal volume:
V ≈ π × (D / 2)² × remaining depth / 2 - Mass removed:
mass = volume ÷ 1000 × density - Grinding time:
hours = remaining volume ÷ adjusted removal rate
How to Use This Calculator
- Enter the mirror diameter and choose the unit.
- Select focal ratio or focal length as the target method.
- Add the current sagitta. Use zero for a flat blank.
- Enter blank thickness, tool diameter, density, and grit stage.
- Adjust efficiency if your grinding pressure is light or heavy.
- Press the calculate button and review the result above the form.
- Download the CSV or PDF report for shop notes.
Example Data Table
| Mirror Diameter | Target | Focal Length | Approximate Sagitta | Typical Use |
|---|---|---|---|---|
| 150 mm | f/8 | 1200 mm | 1.172 mm | Planetary starter mirror |
| 200 mm | f/6 | 1200 mm | 2.084 mm | Balanced general observing |
| 250 mm | f/5 | 1250 mm | 3.127 mm | Wide field reflector |
| 300 mm | f/4.5 | 1350 mm | 4.170 mm | Large fast telescope |
Primary Mirror Grinding Guide
A primary mirror starts as a flat blank. Grinding turns that flat face into a controlled concave curve. The curve sets the focal length. It also sets the focal ratio. A small error in sagitta can move focus by a noticeable amount. That is why careful measuring matters before glass removal begins.
Why Sagitta Matters
Sagitta is the center depth of the curve. It is measured from the rim plane to the deepest point. A fast mirror needs a deeper curve. A slow mirror needs a shallower curve. The calculator estimates this depth from mirror diameter and focal length. It also converts the depth into removal volume. That helps you plan rough grinding time.
Grinding Strategy
Start with coarse abrasive only when much glass remains. Use steady strokes. Rotate the mirror and tool often. Keep slurry wet and even. Do not rush the last part of rough grinding. Stop before the final target by a small allowance. This leaves room for fine grits to remove pits and smooth the surface.
Measuring During Work
Check the sagitta after short sessions. Clean the blank before each reading. Use a stable straightedge and a reliable gauge. Measure more than once. Record each result in your shop notebook. A slow approach prevents overshooting the target early.
Blank Safety
The center becomes thinner as the curve deepens. Thin blanks can flex during polishing and testing. This calculator compares final center thickness with mirror diameter. Always confirm your own blank quality, annealing, and support method.
Using the Estimates
Time values are planning estimates. Real speed changes with pressure, grit, tool size, stroke style, and glass hardness. The report is useful for comparing designs. Try several focal ratios. Check how each choice changes sagitta, mass removed, and center thickness. Choose a design that fits your telescope tube, mount, and observing goals.
Finishing Mindset
Good grinding is controlled and patient. The target is not only depth. It is a clean, regular curve. Fine grinding should remove previous pits fully. Polishing should begin only after the surface is uniform. When the numbers and the surface agree, your mirror project is ready for better optical testing.
Frequently Asked Questions
What is telescope mirror sagitta?
Sagitta is the center depth of the mirror curve. It is measured from a straight rim line down to the deepest center point.
Can this calculator replace optical testing?
No. It is a planning tool. Use it for rough geometry, time estimates, and shop notes. Final figuring needs real optical tests.
Which focal ratio should I choose?
A slower mirror is easier to grind and test. A faster mirror gives a shorter tube, but it needs more careful figuring.
Why does tool diameter matter?
Tool size affects contact area and grinding behavior. Very small tools can create zones. Full-size tools often give smoother control.
What is fine grinding allowance?
It is the small depth left before final grits. This helps remove coarse pits without overshooting the target sagitta.
Why enter glass density?
Density converts estimated removed volume into mass. It helps compare blank materials and track rough grinding progress.
What if my current sagitta is too deep?
Stop and remeasure first. A deeper curve means a shorter focal length. You may need to revise the design target.
Can this be used for parabolic mirrors?
Yes, for primary grinding depth estimates. The final parabolic correction is separate and must be handled during figuring and testing.