Longer legs may convey two mechanical benefits to Crematogaster (Decacrema) ants climbing on waxy Macaranga stems, which are illustrated by a simple two-leg model in Figure 8.7:
1. Longer-legged ants could achieve a greater normal force F± by grasping around the stem (Figure 8.7A).
2. The perpendicular detachment force acting on the front legs is smaller in longer-legged ants because of the longer lever arm (Figure 8.7B).
Insects climbing up a cylindrical stem can hold on more firmly by drawing each foot toward the other, which increases the tarsal ground reaction force F± (Figure 8.7A). However, leg contraction is limited by the concomitantly growing shear forces F| |, which will cause the legs to slide on larger diameter stems. The proportion of tangential to normal force gained by leg adduction depends on the distance d between the tarsi and the stem diameter D:
To prevent slipping, this proportion should not exceed the static friction coefficient ^ (i.e., the proportion of friction force to normal load) of the tarsus on the waxy stem surface:
Assuming that ants rely wholly on friction in clinging to a stem with typical friction coefficient, p < 1, Equation 8.2 suggests that in the absence of adhesive forces, climbing ants can only enhance attachment by grasping around the stem if d > 0.71 x D, i.e., if the legs subtend at least one quarter of the stem circumference. This situation, however, would be different if the ants were able to dig the tips of their claws into the stem surface. When claws interlock with the substrate, they generate a new contact surface that is more nearly perpendicular to the adduction force. This would have the effect that the ants can cling to the stems even if d < 0.71 x D .
The second possible advantage of longer legs is related to the increased distance between front and hind leg footfall positions. The perpendicular force acting on the front legs tending to topple the ant from the stem during upward climbing depends on the height h of the center of gravity above the stem surface and the distance s between front and hind footfall positions (Figure 8.7B):
Assuming a constant height of the center of gravity above the stem, longer legs would reduce the detachment force acting on the upper legs of climbing ants. Unlike the increase of normal force achieved by grasping around the stem, this effect would not only be beneficial on a cylindrical twig but also on a plane vertical substrate.
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