Sinusoidal Harmonic Acceleration

Written by Travis M. Moore
Last edited 21-Feb-2020

Rotational Chair Testing

Rotational testing (RT) is exactly what it sounds like: the patient is seated in a chair that rotates (slowly!). Think of it as an over-engineered swivel chair. The patient is seated so that the axis of rotation is between the patient's ears (the yaw plane). As you can imagine, this type of motion moves the fluid in the horizontal semicircular canals (hSCC).

"Another hSCC test? What about calorics?!" While it is true that calorics assess the hSCCs, there are several reasons why RT is still beneficial. For example:1,2

  • Patients tolerate RT better than calorics
  • The rotational stimulus is better controlled than caloric stimulation
  • The rotational stimulus is more natural than caloric stimulation
  • RT assesses the vestibular system at multiple frequencies

Let's pay special attention to that last point: RT testing at multiple frequencies. Recall that caloric stimulation is roughly equivalent to rotation at 0.003 Hz. To get an idea of how slow this is, convert the frequency to the period.

That means it would take approximately 5.5 minutes to complete one full rotation! (1/0.003 Hz = 333.3 seconds = 5.5 minutes) Even a Tai Chi master would have trouble moving that slowly! The frequencies tested using the rotary chair are: 0.01, 0.02, 0.04, 0.08, 0.16, 0.64 Hz. Complete rotations would take anywhere from 1.6 minutes (0.01 Hz) to 1.6 seconds (0.64 Hz). These frequencies cover a much more natural range of head movements.

Sinusoidal Harmonic Acceleration

Sinusoidal harmonic acceleration (SHA) simply means that the rotation of the chair at a given frequency is constant and smooth. Review the module on simple harmonic motion if you need a refresher. Because of the sinusoidal nature of the rotations, a handy way to plot the data is by using sine waves. We have actually already discussed this concept during our discussion of smooth pursuit testing in the module on ocular motility testing.

While smooth pursuit uses a back-and-forth form of simple harmonic motion as the stimulus moves from one end of the display to the other, RT uses a circular movement. While smooth pursuit compares the velocity of the roving dot to the velocity of the eyes following it, RT compares the eye movements evoked by the rotation (slow phase eye velocity of the nystagmus) to the velocity of the chair rotation. In other words, both tests are comparing eye and stimulus movements by representing each as a sine wave. Because of these similarities, we use the same parameters to talk about RT as we do for smooth pursuit: phase, gain, and symmetry.

Phase Angle

Test Your Understanding

Answer One
Answer Two
Answer Three


1Jacobson, G. P., & Shepard, N. T. (2016). Balance Function Assessment and Management (Second ed.): Plural Publishing.
2Cyr, D. G. (1991). Vestibular system assessment. In W. Rintelmann (Ed.), Hearing assessment (pp. 739-804). Austin, TX: Pro-Ed.
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