The Elephant And The Flea: Looking Backwards to the Future

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This reflects the difficulty in eliciting these sorts of activities in an experimental environment. The P. Additionally, it can be seen from Fig.

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As expected, there is considerable variation in the landing position compared to the reference landing coordinates for different jumping tasks. For short jumping tasks, the actual landing point was close to the landing reference coordinates, but for long jumping tasks there were larger variations. To better demonstrate the take-off and landing behaviours, take-off and landing snapshots are shown in Fig. Example jump trajectories. Green circles indicate the location of the centre of mass at take-off. Red circles represent the location of the centre of mass at landing.

No marker at the end of the trajectory indicates that the spider left the measurement field of view before landing. Leader lines from the ends of each trajectory indicate the landing platform location for that particular task. Blue lines are examples of the experimentally measured trajectories. Visual comparison of body attitude and leg arrangement at the start and end of the jumping tasks.

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The starting frame is the instant of take-off. First, for take-off: a the body attitude is dependent on the jumping task and b both third and fourth legs are used during jumping; however, their relative contribution to the force production could only be confirmed through experimental force plate measurement which is beyond the scope of the current work.

Note that Parry and Brown 19 suggest for S. Our videos show that the third leg is the last to leave the take-off platform. This may be due to reduced precision of control for these more challenging jumps, or due to limited visual capabilities affecting the ability to correctly estimate the required trajectory. In either case, it appears that in the presence of uncertainty, the jumps tend to overshoot, which from a behavioural point of view is probably a better strategy than undershooting.

However, importantly, the spider does attempt this task. Clearly the spider can jump this distance, but chooses not to, possibly for the simple reason that it cannot properly see the landing platform. In addition to these initial observations, our experiment allows us to conduct a quantitative analysis.

The definition of the leg plane is necessarily approximate because the tips of the legs do not ordinarily lie in the same plane; however, even an approximate estimation of this plane is of interest and since the angle of plane may vary by significant amounts during a jump, the effect of uncertainty in measurement is mitigated to some extent.

Variations of the body angle and leg plane angle from take-off to landing.

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Take-off and landing are as defined in Fig. From the results presented in Fig.

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It is generally more positive head up for ascending jumps; this may be related to the limited field of view of the eyes and the need to face the jump target. The body attitude at landing is generally increased over the attitude at take-off, i.

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The leg plane angle is generally more positive than the body angle throughout the jump and generally increases at a greater rate, i. The rate of change of the body and leg plane angles are approximately constant during the jump trajectory, hence the net torque acting on the overall spider is approximately zero. It should be noted that several insects are capable of aerial righting in mid-air, e.

However, the time scale of the reported behaviours is significantly longer than that of the jumps reported herein and hence it is probable that aerial righting does not contribute significantly in the present case. We use the jumping trajectories for the 15 jumping tasks to analyse the jumping performance. Dot-line plots of Fig. The principal measurements are of the take-off velocity, time to take-off, and the take-off angle. We then derive the kinetic energy, acceleration and specific power from the take-off velocity and the time to take-off. The velocity at take-off varies between 0.

The time to take-off varies between Note that the jumping tasks with the maximum and minimum values of take-off velocity coincide with the minimum and maximum time to take-off, respectively. If the stroke length remains constant, then v and t are inversely related consistent with the experimental observation made above. Generally, as shown in Fig. The kinetic energy is derived from the velocity at take-off hence correlation is implicit.

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The minimum and maximum values of acceleration are 1. In general, the variations of kinetic energy, acceleration, and specific power all will increase as the horizontal gap increases and the vertical gap becomes more positive. Contour plots of jumping characteristics of the Phidippus regius spider.

Measured jumping trajectories matched closely with ballistic trajectories predicted from initial conditions at take-off; see examples provided in Fig. The forces acting on the spider during flight are due to gravity, air resistance and silk line tension The silk line force is considered negligible As a conservative estimation of the drag force, we assume that the spider is sphere of diameter equal to the body reference length.

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  8. The drag coefficient calculated based on the relation recommended in 22 , 30 is approximately 0. Based on these values, the maximum aerodynamic drag for the highest speed take-offs is less than 4. To better understand the jumping behaviour of P. Here, maximum travel distance related to minimum energetic cost of transport and minimum travel time for a given power budget are considered. Expressions to evaluate the trajectory take-off angle corresponding to both optimum conditions are derived based on 5 and final forms of the governing equations are as follows:.

    Note that equations 1 and 2 describe the optimum take-off angles for the assumption of a ballistic trajectory.

    For the maximum distance, the optimum angle identified is by definition the least energy consuming jump among the many ways to reach that goal. This comparison supports our hypothesis, demonstrating that as the jumping challenge becomes harder typically ascending and further jumps , jumps approach energy optimum conditions; i. Contour plots for comparison of measured take-off angles for different jumping tasks with the theoretical take-off angles required for a minimum cost of transport and b , c minimum time of flight.

    Plots show the magnitude of the difference in angle for clarity of interpretation. In each case darker colours correspond to jumping at closer to the respective optimum conditions. In plot c , minimum flight time angles are computed based on a reference take-off velocity equal to the take-off velocity of each task.

    The expression for minimum time represented by equation 2 requires a reference velocity, v max. Two approaches can be used to select this reference velocity. Our first approach is to use a single absolute maximum velocity corresponding to the maximum energetic capability of the spider. This provides an objective comparison of all tasks against what would be possible if the spider always jumped at its maximum speed. However, this comparison becomes less meaningful when jumps are not made at the maximum speed.

    This provides a more representative test of time optimality for jumps where the take-off velocity is much less than the absolute maximum velocity, but is arguably weaker overall in that it does not provide a comparison with the global minimum time possible. The second approach is shown in Fig. Comparison of Fig. This again supports our hypothesis that for short distances, time of flight is prioritised. Note that dot-line plots of Fig.

    There might be a concern on the value used within Fig. More importantly, the conclusion from Fig. This fact is illustrated through comparing Fig. We believe it is instructive to compare the jumping performance of P. In contrast, S. Despite these differences in mass and scale, all three species are very close in terms of g -force at take-off and specific power which are the performance metrics most relevant to jumping.

    It is also worth noting that P. However, there is some uncertainty of the exact travel distance reported for S. The jumping performance of spiders is comparable to that of jumping insects. Following the classification proposed by Burrows and Dorosenko 31 , we classify jumping insects into two main categories: 1 those expected to employ muscle contraction for jumping, and 2 those thought to employ a catapult mechanism.

    Clearly, this classification does not stop the possibility of an insect employing either mechanism, or a combination of both. Nonetheless, this exercise remains instructive because it provides a logical criterion to classify jumping. The data upon which Fig. Values shown in the figure correspond to the jump with highest take-off velocity recorded in the literature sometimes this is an individual jump, but on other occasions it is a mean value if that is all that is available.

    Eight insect groups 36 different species fall within the muscle contraction limits, and nine insect groups 42 different species fall within the catapult category. Second, the mean value of the time to take-off for the catapult group is around an order of magnitude less than the muscle contraction group. Third, there is a similar wide variation of take-off angle for both groups, with average of around 45 degrees.

    Finally, g -force is strongly correlated with specific power, and hence g -force may be used to differentiate between the two groups. As shown in Fig. Comparison of the jumping characteristics of the different insects. Spiders are highlighted with red circles.

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    Insects are classified into two main groups: a muscle contraction group and a catapult mechanism group. The sub-figures are: a The velocity magnitude at take-off, b time to take-off, c trajectory angle at take-off, d kinetic energy of the jump, e the ratio of the jumping acceleration at take-off to gravitational acceleration g-force , and f the specific power of the jump relative to the muscle mass. Spiders clearly fall within the muscle contraction group: values for take-off velocity and time to take-off are very close to the group mean.