A <centripetal speed-gain error> is an error in a calculated centripetal correction caused by a multiplicative scale error in the measured <angular velocity>. For true centripetal magnitude $C=r\omega^2$ and indicated speed $\widehat\omega=g\omega$, the computed magnitude with correct radius is
$$
\widehat C=g^2C,\qquad
\frac{\widehat C-C}{C}=g^2-1.
$$
Writing $g=1+\epsilon$ gives exact relative error $2\epsilon+\epsilon^2$. The leading relative error is therefore twice the speed-scale error, rather than equal to it.

For an original example, let $r=0.020\,\mathrm m$ and $\omega=100\,\mathrm{rad/s}$, giving $C=200\,\mathrm{m/s^2}$. A1% high speed indication gives $\widehat C=204.02\,\mathrm{m/s^2}$, an overestimate4.02m/s². Subtracting that value from a radial reading would leave an error of the opposite sign if the true motion were otherwise modeled correctly. The example illustrates sensitivity; it is not a measured calibration error of a particular sensor.

Radius error combines with speed gain. If the indicated radius is $r+\delta r$, then
$$
\frac{\widehat C}{C}=\left(1+\frac{\delta r}r\right)g^2.
$$
To first order, relative error is $\delta r/r+2\epsilon$. Apparent cancellation between these terms at one condition does not separately identify either calibration parameter. An independent radius measurement or speed reference helps distinguish their contributions.

An additive speed offset $b$ behaves differently:
$$
\widehat\omega=g\omega+b,\qquad
\widehat C-C=r[(g^2-1)\omega^2+2gb\omega+b^2].
$$
Measurements at several speeds can distinguish the quadratic scale contribution from the linear and constant offset contributions, subject to the remaining model and measurement errors. Near zero true speed, a relative-error description becomes unsuitable even though the absolute expression remains meaningful.

The same gain factor applies to the first-order ripple correction $2r\omega_0\varepsilon$ when both mean speed and ripple amplitude share that speed scale. The resulting mismatch enters the <centripetal amplitude-error budget>, while relative channel timing enters the <centripetal phase-error tolerance>. A primary rotating MEMS-sensor experiment identifies rotating-frame components and reconstructs a rotation reference, making the physical need for consistent speed and timing information concrete.<Evaluation of MEMS-Based Wireless Accelerometer Sensors in Detecting Gear Tooth Faults in Helicopter Transmissions by David G. Lewicki and others>[Printed pp.19–21, rotating-frame components; pp.24–25, timing reconstruction]{ref}

At a specified operating point, the <sensitivity coefficient> to speed is $\partial C/\partial\omega=2r\omega$. A speed <standard uncertainty> therefore contributes approximately $2r|\omega|u(\omega)$ to the correction's <standard uncertainty>, with radius uncertainty and any <covariance> included separately.<Guide to the expression of uncertainty in measurement by JCGM>[§5.1.3 and §5.2, sensitivity coefficients and correlated inputs]{ref}


 Centripetal speed-gain error (source code)