A specimen of *D. nana* collected by C. G. Messing near the Christensen Research Institute, Madang, Papua New Guinea was used to obtain morphological data. The specimen weighed 0.2 × 10^{−3} N in air and 5 × 10^{−4} N in water, has 10 arms of 3.3 cm length and 40 cirri (Fig. 2). The length of the cirri averages 0.63 cm, and their diameter at mid-cirrus is 0.2 cm (Fig. 3).

If *D. nana* were to swim using its cirri rather than its arms, the thrust generated by cirri would have to be at least equivalent to weight in water (WIW) of *D. nana*, i.e., sufficient to overcome the gravitational force. To generate such upward thrust, we assume that each cirrus completes a power stroke (Fig. 4). The power stroke begins with the cirrus oriented with its distal tip pointing upwards, 45° above the horizontal. It then pivots aborally around its base subtending a 90° angle, such that at the end of the stroke the distal tip points downward, 45° below horizontal. The cirrus remains straight throughout the power stroke, pivoting only around its base. The 90° power stroke and the orientation of the cirrus are conservative assumptions that would result in the production of maximal thrust.

To calculate the thrust generated by a cirrus during the power stroke, we developed an analytical model based on biomechanical principles. The model is described in detail in Janevski and Baumiller (2010), and here we provide a brief summary. During the power stroke, the cirrus moves through the water at some average velocity, *U*. It thus experiences a force of drag that can be estimated using the following formula

$$ D = {\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 2}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{$2$}}C_{\text{d}} \rho SU^{2} $$

(1)

where *C*
_{d} is the drag coefficient, *p* is the fluid density, *U* is as above, and *S* is the surface area of the object perpendicular to the direction of motion (Vogel 1994).

To estimate the drag coefficient (*C*
_{d}) of cirrus, we assumed that because it resembles a circular rod it has an equivalent coefficient of drag, which for a circular rod is 0.5 (Hoerner 1965). The value of *ρ* employed was that of seawater, 1.024 g cm^{−3}. The value of *S* was calculated as the product of the average length of each cirrus and its average diameter.

Estimating the velocity of the cirrus is more complicated. In addition to the detailed knowledge of its skeletal morphology, one needs to know the length of ligament between cirrals and its placement relative to the central ridge. Moreover, the ligament’s mechanical properties, such as its speed of contraction, must be known. Morphological data were obtained directly for the specimen of *D. nana*, while the length and position of the ligament were estimated using published scanning electromicrographs of the cirri of the isocrinid *Metacrinus rotundus* (Fig. 2 in Birenheide et al. 2000). There are few data on mechanical properties of crinoid ligament; however, the speed of contraction has been reported by Motokawa et al. (2004). In experiments with a six-element (6 mm) arm piece of the isocrinid, *Metacrinus rotundus*, they found a maximum bending speed of 43.5 μm s^{−1}. According to their calculations, this corresponds to ligament shortening speed of 0.05*L*
_{0} s^{−1}, where *L*
_{0} is the initial length of the ligament. Assuming these values, the tip of a 12-element long cirrus of *D. nana* would have a maximum bending velocity of 100 μm s^{−1}.

The above data can now be used to calculate the drag experienced by a cirrus in a power stroke using Eq. 1. It must be noted, however, that the calculation is made more complicated by the fact that the cirrus pivots around its base such that the linear velocity is not constant at all points—it is 0 at the cirrus base and maximum at the tip. Also, in calculating drag we are interested only in its vertical component as that is what works against the downward force of gravity. Given the above, we use a slightly modified expression for drag perpendicular (*D*
_{t}) to the cirrus developed by Janevski and Baumiller (2010):

$$ D_{\text{t}} = C_{\text{d}} \rho U^{2} S/6 $$

(2)

To calculate the vertical component of drag (*D*
_{V}), the following expression was used (see Janevski and Baumiller 2010 for details):

$$ D_{\text{V}} = D_{\text{t}} \left( {1/\omega } \right)\left( {\cos \left( \alpha \right) - \cos \left( {\alpha + \theta } \right)} \right) $$

(3)

where *D*
_{t} is the total drag calculated from Eq. 2, *ω* is the angular velocity, *α* is the starting position of the cirrus with respect to vertical, and *θ* is the angle through which the cirrus rotates.

To calculate the total thrust that could be produced by cirri, we assumed that at any given moment half of the 40 cirri are in the power stroke while half are in a recovery stroke, thus the vertical component of drag calculated in Eq. 3 for each cirrus must be multiplied by 20. We also assume conservatively that cirri do not produce thrust in the opposite direction during the recovery stroke, and thus ignored this negative contribution in our calculations.