Table 7.

Estimated maximum power requirements to overcome inertia during stridulation in S. borellii and S. vicinus

SpeciesMass1 (mg)fws (s-1)Opening time2 (ms)Closing time3 (ms)Distance the COM moves4 (mm)Mean opening velocity of tegmen COM5O (m s-1)Est. power to overcome inertia during opening6 (μW)Mean closing velocity of tegmen COM7, C (m s-1)Est. power to overcome inertia during closing8 (μW)Est. max. power to overcome inertia9 (μW)Est. KE power + Strid. power10 (μW)Percent. P lost to inertia÷(KE + Strid. P11)
S. borellii 5.3556.411.42.700.4241050.116811316270%
S. vicinus 6.41502.73.70.640.2371080.0801212014782%
S. borellii÷S. vicinus 0.830.42.43.14.21.81.01.450.670.91.30.7
  • 1 The mass of both tegmina (from Table 1).

  • 2 The time between the end of the sound pulse and the start of the next pulse.

  • 3 The difference between the average period and the opening time (see 2).

  • 4 Twice the estimated length of the file that was stridulated. The length of the file that was stridulated was determined from the number of teeth struck during the closing stroke (Table 1) and from inter-tooth distance starting at the portion of the file just prior to where the maximum tooth depth is reached (Fig. 5). This distance was multiplied by 2 to give the displacement of the tegmen's center of mass (COM). The distance from the attachment of the tegmen to the thorax to the center of mass is about twice the distance from the attachment to the center of the file.

  • 5 The average velocity of the COM during either the acceleration or the deceleration of opening (O). Assuming tegminal opening operates as in Gryllus campestris, the tegmina use about half of the opening stroke to accelerate to peak velocity and the second half to decelerate to rest (Elliott and Koch, 1985). Thus, we conservatively (under)estimated the peak opening velocity as the movement of the center of mass (previous column) divided by the closing time.

  • 6 Calculated as 4fws(0.5mv̄O2). The constant 4 is used because there are two wings and each closing stroke has an acceleration and deceleration.

  • 7 The average velocity of the center of mass during closing (C). The closing stroke contains brief periods of acceleration and deceleration at its beginning and finish. Most of stroke is occupied with stridulation where velocity is roughly constant. The energy required to overcome inertia at the start and end of the closure can be calculated using the mean velocity since it essentially equals the velocity changes at the start and finish of the closing cycle.

  • 8 Calculated as 4fws(0.5mv̄C2). See 6 and 7.

  • 9 The sum of the estimated maximum opening and closing power requirements for overcoming tegminal inertia.

  • 10 The sum of estimated power requirements for overcoming inertia (see 9) and the KE transfer model power estimates (Table 6).

  • 11 The ratio of the two previous columns; it is an estimate of the percentage of the energy requirement for stridulation that is used to overcome inertia.