Gyroscope Degrees Of Freedom
Understanding gyroscopes and their degrees of freedom (DOF) — and how each aviation instrument (like the ADI, HSI, or turn coordinator) uses them.
🧭 1️⃣ What “Degrees of Freedom” Means
A degree of freedom (DOF) in a gyroscope = a direction in which the spin axis can move or pivot.
🌀 A gyroscope can have up to 3 degrees of freedom:
- Spin axis — the rotor spinning itself.
- Inner gimbal — allows tilting about one axis.
- Outer gimbal — allows movement about another axis (perpendicular to the inner).
⚙️ 2️⃣ Degrees of Freedom in Aviation Gyros
| Instrument Type | Gyro Type | Degrees of Freedom | Main Axis of Sensing | What it Measures / Indicates |
|---|---|---|---|---|
| Turn Indicator (old) | Rate Gyro | 1 DOF | Yaw rate | Rate of turn (standard rate turn) |
| Turn Coordinator | Rate Gyro (canted) | 1 DOF (canted 30°) | Yaw + roll rate | Coordinated turn (yaw + roll) |
| Directional Gyro (DG) | Space Gyro | 2 DOF | Vertical | Heading (yaw reference) |
| Attitude Indicator (AI / Horizon) | Space Gyro | 2 DOF | Horizontal | Pitch and roll attitude |
| Gyro Compass / INS Platform | Free Gyro or Tied Gyro | 3 DOF | All | True heading, attitude, position reference |
⚙️ 3️⃣ How to Identify the Degrees of Freedom
You can identify the DOF by looking at how many gimbals the gyro has and what motions it can make:
| Degrees of Freedom | Physical Structure | Behavior | Example Instrument |
|---|---|---|---|
| 1 DOF | Fixed gyro rotor on a single pivot | Measures rate about one axis only | Turn indicator, turn coordinator |
| 2 DOF | Rotor mounted in inner + outer gimbal rings | Maintains fixed orientation in space (until torqued) | Attitude Indicator, Directional Gyro |
| 3 DOF | Free to move in all three axes (x, y, z) | Can maintain a stable platform (INS, gyro compass) | INS platform, IRS unit |
⚙️ 4️⃣ Visual Summary (mental picture)
[3 DOF] Free Gyro (INS)
┌─────────────┐
│ Outer Gimbal│ → moves about one axis
│ ┌────────┐ │
│ │ Inner │ │ → moves about second axis
│ │ Gimbal │ │
│ │ ● │ │ → spinning rotor (third axis)
│ └────────┘ │
└─────────────┘
[2 DOF] Directional / Attitude Gyro
┌────────┐
│ Gimbal │ → 1 axis
│ ● │ → rotor spins on 2nd axis
└────────┘
[1 DOF] Turn Coordinator
● (rotor)
│ fixed to measure rate about 1 axis (yaw/roll)
⚙️ 5️⃣ Quick Recognition Tips (for exams)
| Instrument | Gyro Type | Degrees of Freedom | Tied or Free? |
|---|---|---|---|
| Turn Indicator | Rate Gyro | 1 DOF | Tied |
| Turn Coordinator | Rate Gyro (canted) | 1 DOF | Tied |
| Directional Gyro | Space Gyro | 2 DOF | Tied |
| Attitude Indicator | Space Gyro | 2 DOF | Tied |
| INS Platform | Free Gyro | 3 DOF | Free |
💬 6️⃣ “Tied” vs “Free” Gyros
- Free gyro: Can move freely in all axes — used in stable platforms (e.g., INS).
- Tied gyro: Movement is restricted or referenced to the aircraft’s axes or gravity — used in attitude or heading indicators.