The Motion-Sensing Hairs of Arthropods
107
tuned to best frequency ranges between 40 Hz and 600 Hz. The variation of hair
length in a cluster fractionates both the intensity and frequency range of a stimulus
(Barth et al. 1993) and, as a result, trichobothria can function as displacement,
velocity, and acceleration sensors over different frequency ranges. Primarily
because of the effects of dynamic viscosity on their effective inertia, the resonance
frequencies of filiform hairs in water tend to be much lower than for hairs in air
(for hairs of similar geometrical and mechanical characteristics). Hairs in water
appear to work as low-frequency (l-150 Hz) sensors and, whereas in some
receptors physiological threshold values follow water velocity, they follow
acceleration in others (Bleckmann 1994). Also, the most typical motion-sensing
hairs in water tend to be very short, correlating with the smaller values of the
boundary layer thickness in water compared to air at the same frequency
(Devarakonda et al. 1996).
Building mainly on the work of Fletcher (1978) and Shimozawa and Kanou
(1984), Humphrey et al. (1993, 1997) derived a physical model that describes the
motion of a hair protruding from a solid substrate where it is driven by the
oscillating movement of a viscous fluid (air or water). Using Stokes' (1851)
theory, their model accounts for the important effect of the "added" or "virtual"
mass force acting on the hair, and the dependence of this force and that of the
viscous drag on frequency. In their study, straight hairs are modeled as constant
diameter cylinders of length Land effective diameter d. Subsequently, Shirnozawa
et al. (1998) considered the variation of hair diameter with length for calculating
the moment of inertia and the added mass and drag forces. The bulk of these
effects can be captured using a length-averaged effective diameter for the hair.
Humphrey et al. (1993, 1997) show that for a fluid oscillating atf(Hz) parallel
to the longitudinal axis of a cylindrical substrate of diameter D (m), Stokes'
( 1851) velocity distribution for a fluid oscillating parallel to a flat surface is
accurate providedjD 2 /v > 20/rc, where v (m 2 s. 1 ) is the fluid kinematic viscosity. In
such cases, the thickness of the viscous-dominated boundary layer near the
substrate is given by o = 4.5 (vl7if/ 12 and it is possible to obtain a closed form
analytical solution for hair motion (Humphrey et al. 1993 ). In agreement with
experiments (Barth et al. 1993 ), this solution shows that hairs oscillate at the
frequency of the oscillating fluid medium but possess resonance frequencies,
Wres((f)' that decrease with increasing hair length. The solution also shows that the
hair maximum deflection angle increases linearly with increasing far field fluid
velocity amplitude, U0 , and approximately linearly with increasing hair length;
although the lengths of the trichobothria of the spider Cupiennius salei
infrequently exceed the substrate boundary layer thickness (Barth et al. 1993).
While a corresponding analytical solution is not obvious for the case of a fluid
oscillating perpendicular to the cylindrical substrate, results based on rigorous
numerical calculation (Humphrey et al. I 993) reveal significantly higher values of
hair deflection angle, velocity, and acceleration compared to a parallel flow for the
same values of Uo and f This is because in the perpendicular orientation substrate
surface curvature has the effect of accelerating the flow near the substrate. In
contrast, maximum deflection angle and velocity resonance frequencies do not
depend on flow magnitude or direction.
107
tuned to best frequency ranges between 40 Hz and 600 Hz. The variation of hair
length in a cluster fractionates both the intensity and frequency range of a stimulus
(Barth et al. 1993) and, as a result, trichobothria can function as displacement,
velocity, and acceleration sensors over different frequency ranges. Primarily
because of the effects of dynamic viscosity on their effective inertia, the resonance
frequencies of filiform hairs in water tend to be much lower than for hairs in air
(for hairs of similar geometrical and mechanical characteristics). Hairs in water
appear to work as low-frequency (l-150 Hz) sensors and, whereas in some
receptors physiological threshold values follow water velocity, they follow
acceleration in others (Bleckmann 1994). Also, the most typical motion-sensing
hairs in water tend to be very short, correlating with the smaller values of the
boundary layer thickness in water compared to air at the same frequency
(Devarakonda et al. 1996).
Building mainly on the work of Fletcher (1978) and Shimozawa and Kanou
(1984), Humphrey et al. (1993, 1997) derived a physical model that describes the
motion of a hair protruding from a solid substrate where it is driven by the
oscillating movement of a viscous fluid (air or water). Using Stokes' (1851)
theory, their model accounts for the important effect of the "added" or "virtual"
mass force acting on the hair, and the dependence of this force and that of the
viscous drag on frequency. In their study, straight hairs are modeled as constant
diameter cylinders of length Land effective diameter d. Subsequently, Shirnozawa
et al. (1998) considered the variation of hair diameter with length for calculating
the moment of inertia and the added mass and drag forces. The bulk of these
effects can be captured using a length-averaged effective diameter for the hair.
Humphrey et al. (1993, 1997) show that for a fluid oscillating atf(Hz) parallel
to the longitudinal axis of a cylindrical substrate of diameter D (m), Stokes'
( 1851) velocity distribution for a fluid oscillating parallel to a flat surface is
accurate providedjD 2 /v > 20/rc, where v (m 2 s. 1 ) is the fluid kinematic viscosity. In
such cases, the thickness of the viscous-dominated boundary layer near the
substrate is given by o = 4.5 (vl7if/ 12 and it is possible to obtain a closed form
analytical solution for hair motion (Humphrey et al. 1993 ). In agreement with
experiments (Barth et al. 1993 ), this solution shows that hairs oscillate at the
frequency of the oscillating fluid medium but possess resonance frequencies,
Wres((f)' that decrease with increasing hair length. The solution also shows that the
hair maximum deflection angle increases linearly with increasing far field fluid
velocity amplitude, U0 , and approximately linearly with increasing hair length;
although the lengths of the trichobothria of the spider Cupiennius salei
infrequently exceed the substrate boundary layer thickness (Barth et al. 1993).
While a corresponding analytical solution is not obvious for the case of a fluid
oscillating perpendicular to the cylindrical substrate, results based on rigorous
numerical calculation (Humphrey et al. I 993) reveal significantly higher values of
hair deflection angle, velocity, and acceleration compared to a parallel flow for the
same values of Uo and f This is because in the perpendicular orientation substrate
surface curvature has the effect of accelerating the flow near the substrate. In
contrast, maximum deflection angle and velocity resonance frequencies do not
depend on flow magnitude or direction.