The threshold of perception of angular acceleration as a function of duration

The threshold for rotation about the yaw axis was determined for constant acceleration stimuli as a function of their duration in the range from 3 to 25 s. From the torsion-swing model the following theoretical equation can be derived: 1 $$a_{{text{thr}}} = {C mathord{left/ {vphantom {C {left[ {1 - exp left( { - {{t_s } mathord{left/ {vphantom {{t_s } {tau _1 }}} right. kern-nulldelimiterspace} {tau _1 }}} right)} right]}}} right. kern-nulldelimiterspace} {left[ {1 - exp left( { - {{t_s } mathord{left/ {vphantom {{t_s } {tau _1 }}} right. kern-nulldelimiterspace} {tau _1 }}} right)} right]}}$$ , where a _thr=acceleration amplitude at threshold, t _s =duration of the acceleration, τ₁=time constant, C=threshold for very long stimuli. According to this formula the Mulder product (i.e. the product of the threshold acceleration amplitude and the duration of the stimulus) is constant for durations up to 0.3 τ₁. The best fit of this theoretical function to the somatosensory data is found for τ₁=14.5 s, and C=0.22⁰/s ². The time within the Mulder product is constant (about 5s) is doubtless due to the mechanics of the semicircular canals. For the oculogyral data a lower value of τ₁ is found. We do not have any explanation for this lower value.