Gear Ratio & Telescope Tracking Discussion - SteveJustin1963/Telescope-Tec1 GitHub Wiki

Gear Ratio & Telescope Tracking Discussion – Clean Markdown Summary

Original Question

"If I gear a 300 mm diameter gear to a 10 mm shaft, what is the ratio?"

Key Clarification (Very Important!)

  • The shaft diameter (10 mm) is NOT the gear diameter.
  • Gear ratio is determined by the pitch diameters (or number of teeth) of the two meshing gears β€” not by shaft size.
  • A 10 mm shaft can carry a gear of almost any diameter (e.g., 10 mm, 50 mm, 300 mm, etc.).

So the question as originally asked cannot be answered without knowing the actual gear diameters.

Hypothetical Scenario Discussed (What You Probably Meant)

Single Stage

Small gear (assume 10 mm pitch diameter) drives large gear (300 mm pitch diameter)

Gear Ratio = 300 / 10 = 30 : 1
(Speed reduction: input turns 30Γ— for output to turn once)

Two-Stage Compound Reduction ("30:1 twice")

Input β†’ 10 mm gear β†’ 300 mm gear (stage 1)
              ↑           ↓ (same shaft)
          300 mm gear β†’ another 300 mm gear (stage 2)
                           ↓
                      Final output

Each stage = 30:1
Total ratio = 30 Γ— 30 = 900 : 1

This is the configuration that was used for the telescope tracking calculations below.

Stepper Motor Steps for 30Β° Movement (900:1 gearbox)

Assuming standard hobby stepper: 200 steps/rev (1.8Β° per step)

Item Value
Steps per motor revolution 200
Total steps per output rev 200 Γ— 900 = 180,000
Output degrees per motor step 360Β° / 180,000 = 0.002Β°
Steps needed for 30Β° output 30 / 0.002 = 15,000 steps

Answer: 15,000 full steps (or pulses) β†’ moves final shaft exactly 30Β°.

Sidereal Tracking Speed (Polar Axis Tracking)

Goal: Turn the telescope at sidereal rate (~15 arcsec/second = 15.04Β° per hour)

Item Calculation Result
Sidereal day length 23 h 56 min 4 sec = 86,164 seconds
Steps for one full output revolution 200 Γ— 900 = 180,000 steps
Required average pulse rate (full steps) 180,000 / 86,164 β‰ˆ 2.09 Hz (2.09 steps/sec)

Problem with 2.09 full steps/sec

β†’ Noticeable jerking every ~0.48 seconds β†’ bad for astrophotography.

Solution: Use Microstepping

Microstepping Pulse rate needed Smoothness
1/8 ~16.7 Hz Acceptable
1/16 ~33.4 Hz Very good (most common choice)
1/32 ~66.9 Hz Excellent
1/64 ~133.8 Hz Extremely smooth

With 1/16 or higher microstepping β†’ completely smooth motion.

Is a 12V 2A Hobby Stepper Motor Powerful Enough?

Yes β€” easily.

  • 12V 2A steppers are common NEMA 17 size (very popular in 3D printers and telescopes).
  • With 900:1 reduction, torque at the output is multiplied 900Γ— β†’ enormous torque.
  • Perfect for driving a Dobsonian or equatorial mount for visual use and even long-exposure astrophotography (if backlash is controlled).

What If You Use a DC Motor Instead?

Feature Stepper + Microstepping DC Motor + Encoder (closed loop)
Motion smoothness Extremely smooth with microstepping Naturally smooth
Speed accuracy Perfect (digital pulse counting) Needs PID + encoder
Complexity Simple (just send pulses) More complex feedback system
Cost Lower Higher (encoder + good driver)
Drift over hours Zero Possible without good control

Recommendation:
Stick with the stepper motor + high microstepping.
It is simpler, cheaper, more accurate, and already solves the jerking problem perfectly.

Final Summary – Your Best Setup for Smooth Sidereal Tracking

  • Gearbox: 900 : 1 (two stages of 10 mm β†’ 300 mm)
  • Motor: Standard NEMA 17 12V stepper (200 steps/rev, ~2A)
  • Driver: Any driver that supports 1/16 or 1/32 microstepping (A4988, DRV8825, TMC2209, etc.)
  • Controller: Arduino / Raspberry Pi / OnStep / Teensy, etc.
  • Required pulse rate: ~33–67 Hz (totally trivial for any microcontroller)

β†’ Result: Perfectly smooth, accurate sidereal tracking with zero jerking and huge torque reserve.

You’re good to go! Clear skies! 🌟