Gyroscopes — the physics sets the price

Every gyroscope answers the same question — what is my angular rate? — but there are only a handful of physical effects available to answer it, and each one imposes a different noise floor, scale-factor stability and sensitivity to acceleration. Understanding which effect a device uses tells you more about its real-world behaviour than any single datasheet line.

Symbols used on this page are defined in the Nomenclature → inertial navigation.

Four ways to sense rotation

Technology	Physical effect	Bias stability	Character
Vibratory MEMS	Coriolis force on a vibrating proof mass	1–1000 °/hr	tiny, cheap, low power; sensitive to vibration & temperature; the resonance couples to g
FOG (fibre-optic)	Sagnac phase shift around a fibre coil	0.001–1 °/hr	no moving parts, excellent short-term noise; performance scales with coil length & area
RLG (ring laser)	Sagnac beat frequency between counter-propagating lasers	0.001–1 °/hr	superb scale-factor stability; needs mechanical dither to avoid lock-in at low rate
HRG (hemispherical resonator)	Coriolis on a vibrating quartz shell	0.0001–0.01 °/hr	essentially no wear-out; outstanding long-life stability; favoured for long space missions

Both optical types exploit the Sagnac effect: in a rotating loop of enclosed area $A$ the two counter-propagating beams accumulate a path difference, giving a phase shift

$$ \Delta\phi = \frac{8\pi A}{\lambda c}\,\Omega $$

so sensitivity is bought with area — a big coil or a big cavity. That single relationship explains why optical gyros do not shrink indefinitely, and why MEMS (which uses a completely different effect) owns the small-and-cheap end of the market while optical owns the accurate end.

Vibratory devices instead measure the Coriolis coupling between a driven mode and a sense mode:

$$ \mathbf F_c = -2m\,\boldsymbol\Omega \times \mathbf v_{\text{drive}} $$

Because the sense signal is proportional to the drive amplitude, anything that perturbs the resonator — temperature, package stress, external vibration at the drive frequency — appears directly as rate error. This is the root cause of MEMS' g-sensitivity and thermal drift.

What actually limits each one

MEMS: thermal drift and g-sensitivity. The specs are often quoted at constant temperature and zero g; on a vibrating vehicle the effective bias can be an order of magnitude worse. Look for vibration-rectification error and bias-vs-g coefficients.
FOG: the Shupe effect — a thermal gradient along the coil mimics rotation, so winding pattern and thermal design dominate the low-frequency error. Also sensitive to magnetic fields via Faraday rotation.
RLG: lock-in at very low rates, where the two lasers pull into a common frequency and the output dead-bands. Solved with mechanical dither, which itself injects a small noise floor.
HRG: extremely stable but requires precise, expensive resonator manufacture and careful electronics; historically limited bandwidth compared to a FOG.

Reading the Allan-variance curve

A single "noise" number cannot describe a gyro, because different mechanisms dominate at different averaging times. The Allan deviation curve separates them by slope:

Region	Slope	Mechanism	Consequence
short $\tau$	$-1/2$	angle random walk (white rate noise)	averaging helps; dominates between fast updates
minimum	$0$	bias instability (flicker)	the floor — averaging longer stops helping
long $\tau$	$+1/2$	rate random walk	averaging hurts; sets unaided flight limits
longest	$+1$	rate ramp (thermal)	calibrate/compensate over temperature

Match the curve minimum to your update interval. If your aiding source fixes attitude every second, you care about the curve at $\tau\!\approx\!1$ s — buying a device whose advantage appears only at $\tau = 1000$ s is wasted money.

Representative devices

Device	Type	Bias stability	ARW	Typical use
InvenSense ICM-42688	MEMS	~100+ °/hr	~1–2 °/√hr	consumer, drones (always aided)
Analog Devices ADXRS / ADIS16547	MEMS	~0.8–5 °/hr	~0.05–0.3 °/√hr	industrial & near-tactical
KVH DSP-1760	FOG	~0.05–0.5 °/hr	~0.012 °/√hr	robotics, marine, stabilisation
Honeywell GG1320	RLG	~0.0035 °/hr	~0.0018 °/√hr	aircraft navigation
Safran Regys / NG SciRS	HRG	~0.0001–0.001 °/hr	very low	long-duration space, submarines

The Earth-rotation test

A useful sanity benchmark: Earth rotates at 15.04 °/hr. A gyro whose bias stability is worse than that cannot reliably observe Earth's rotation, which means it can never gyrocompass (find north by itself). That single comparison cleanly separates "attitude sensor that needs external heading" from "self-aligning navigation instrument":

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