scholarly journals Biomechanics of Flight in Neotropical Butterflies: Aerodynamics and Mechanical Power Requirements

1991 ◽  
Vol 159 (1) ◽  
pp. 335-357 ◽  
Author(s):  
ROBERT DUDLEY
Keyword(s):  
Energy Storage ◽  
Elastic Energy ◽  
Center Of Mass ◽  
The Body ◽  
Mechanical Power ◽  
Morphological Data ◽  
Vertical Force ◽  
Forward Flight ◽  
Insect Wings ◽  
Inertial Energy

A quasi-steady aerodynamic analysis of forward flight was performed on 15 species of neotropical butterflies for which kinematic and morphological data were available. Mean lift coefficients required for flight typically exceeded maximum values obtained on insect wings under conditions of steady flow, thereby implicating unsteady aerodynamic mechanisms even during fast forward flight of some butterflies. The downstroke produced vertical forces on average 18% in excess of those necessary to support the body weight through the wingbeat, while the upstroke contributed minimal or negative vertical force. Estimated effective angles of incidence (αT of the wings averaged 39° during the downstroke and −22° during the upstroke; spanwise variation in αT was greater than the average difference between half-strokes. Total mechanical power requirements of forward flight averaged 12.5 W kg−1, for the case of perfect elastic storage of whig inertial energy, and 20.2 W kg−1, assuming zero elastic energy storage. Energetic costs of the erratic trajectories during forward flight increased mechanical power requirements by an average of 43%, assuming perfect elastic storage. Fluctuations in horizontal kinetic energy of the center of mass were principally responsible for this dramatic increase. When comparing different species, total mechanical power increased linearly with forward airspeed (assuming perfect elastic energy storage of inertial energy) and scaled with mass0.26 If no elastic energy storage was assumed, mechanical power was independent of airspeed and was proportional to mass0.36. Estimated metabolic rates during flight averaged 22 and 36 ml O2 g−1 h−1, for the cases of perfect and zero elastic storage, respectively. Note: Mailing address: Smithsonian Tropical Research Institute, APO Miami, FL 34002, USA.

Maximum speed and mechanical power output in lizards.

1997 ◽  
Vol 200 (16) ◽  
pp. 2189-2195 ◽  
Author(s):  
C T Farley
Keyword(s):  
Body Mass ◽  
Power Output ◽  
Center Of Mass ◽  
The Body ◽  
Mechanical Power ◽  
Stride Frequency ◽  
Maximum Speed ◽  
Muscular System ◽  
Running Speed ◽  
Mechanical Power Output

The goal of the present study was to test the hypothesis that maximum running speed is limited by how much mechanical power the muscular system can produce. To test this hypothesis, two species of lizards, Coleonyx variegatus and Eumeces skiltonianus, sprinted on hills of different slopes. According to the hypothesis, maximum speed should decrease on steeper uphill slopes but mechanical power output at maximum speed should be independent of slope. For level sprinting, the external mechanical power output was determined from force platform data. For uphill sprinting, the mechanical power output was approximated as the power required to lift the center of mass vertically. When the slope increased from level to 40 degrees uphill, maximum speed decreased by 28% in C. variegatus and by 16% in E. skiltonianus. At maximum speed on a 40 degrees uphill slope in both species, the mechanical power required to lift the body vertically was approximately 3.9 times greater than the external mechanical power output at maximum speed on the level. Because total limb mass is small in both species (6-16% of body mass) and stride frequency is similar at maximum speed on all slopes, the internal mechanical power output is likely to be small and similar in magnitude on all slopes. I conclude that the muscular system is capable of producing substantially more power during locomotion than it actually produces during level sprinting. Thus, the capacity of the muscular system to produce power does not limit maximum running speed.

A treadmill-mounted force platform

1989 ◽  
Vol 67 (4) ◽  
pp. 1692-1698 ◽  
Author(s):  
R. Kram ◽  
A. J. Powell
Keyword(s):  
Full Range ◽  
Center Of Mass ◽  
Reaction Force ◽  
Vertical Displacement ◽  
The Body ◽  
Force Platform ◽  
Vertical Force ◽  
Vertical Ground Reaction Force ◽  
Contact Phase ◽  
Frictional Forces

Muscle, bone, and tendon forces; the movement of the center of mass, and the spring properties of the body during terrestrial locomotion can be measured using ground-mounted force platforms. These measurements have been extremely time consuming because of the difficulty in obtaining repeatable constant speed trials (particularly with animals). We have overcome this difficulty by mounting a force platform directly under the belt of a motorized treadmill. With this arrangement, vertical force can be recorded from an unlimited number of successive ground contacts in a much shorter time. With this treadmill-mounted force platform it is possible to accurately make the following measurements over the full range of steady speeds and under various perturbations of normal gait: 1) vertical ground reaction force over the course of the contact phase; 2) peak forces in bone, muscle, and tendon; 3) the vertical displacement of the center of mass; and 4) contact time for the limbs. In our treadmill-force platform design, belt forces and frictional forces cause no measurable cross-talk problem. Natural frequency (160 Hz), nonlinearity (less than 5%), and position independence (less than 2%) are all quite acceptable. Motor-caused vibrations are greater than 150 Hz and thus can be easily filtered.

Mechanics of running under simulated low gravity

1991 ◽  
Vol 71 (3) ◽  
pp. 863-870 ◽  
Author(s):  
J. P. He ◽  
R. Kram ◽  
T. A. McMahon
Keyword(s):  
Normal Gravity ◽  
Human Subjects ◽  
Center Of Mass ◽  
The Body ◽  
Vertical Force ◽  
Low Gravity ◽  
Vertical Stiffness ◽  
Mass Spring Model ◽  
Linear Spring ◽  
Mass Spring

Using a linear mass-spring model of the body and leg (T. A. McMahon and G. C. Cheng. J. Biomech. 23: 65–78, 1990), we present experimental observations of human running under simulated low gravity and an analysis of these experiments. The purpose of the study was to investigate how the spring properties of the leg are adjusted to different levels of gravity. We hypothesized that leg spring stiffness would not change under simulated low-gravity conditions. To simulate low gravity, a nearly constant vertical force was applied to human subjects via a bicycle seat. The force was obtained by stretching long steel springs via a hand-operated winch. Subjects ran on a motorized treadmill that had been modified to include a force platform under the tread. Four subjects ran at one speed (3.0 m/s) under conditions of normal gravity and six simulated fractions of normal gravity from 0.2 to 0.7 G. For comparison, subjects also ran under normal gravity at five speeds from 2.0 to 6.0 m/s. Two basic principles emerged from all comparisons: both the stiffness of the leg, considered as a linear spring, and the vertical excursion of the center of mass during the flight phase did not change with forward speed or gravity. With these results as inputs, the mathematical model is able to account correctly for many of the changes in dynamic parameters that do take place, including the increasing vertical stiffness with speed at normal gravity and the decreasing peak force observed under conditions simulating low gravity.

scholarly journals Estimates of Running Ground Reaction Force Parameters from Motion Analysis

2017 ◽  
Vol 33 (1) ◽  
pp. 69-75 ◽  
Author(s):  
Gaspare Pavei ◽  
Elena Seminati ◽  
Jorge L.L. Storniolo ◽  
Leonardo A. Peyré-Tartaruga
Keyword(s):  
Motion Analysis ◽  
Ground Reaction Force ◽  
Center Of Mass ◽  
Reaction Force ◽  
The Body ◽  
Vertical Force ◽  
Vertical Stiffness ◽  
Leg Stiffness ◽  
Force Peak ◽  
Body Center

We compared running mechanics parameters determined from ground reaction force (GRF) measurements with estimated forces obtained from double differentiation of kinematic (K) data from motion analysis in a broad spectrum of running speeds (1.94–5.56 m⋅s–1). Data were collected through a force-instrumented treadmill and compared at different sampling frequencies (900 and 300 Hz for GRF, 300 and 100 Hz for K). Vertical force peak, shape, and impulse were similar between K methods and GRF. Contact time, flight time, and vertical stiffness (kvert) obtained from K showed the same trend as GRF with differences < 5%, whereas leg stiffness (kleg) was not correctly computed by kinematics. The results revealed that the main vertical GRF parameters can be computed by the double differentiation of the body center of mass properly calculated by motion analysis. The present model provides an alternative accessible method for determining temporal and kinetic parameters of running without an instrumented treadmill.

scholarly journals A novel flight style allowing the smallest featherwing beetles to excel

2021 ◽  
Author(s):  
Sergey E. Farisenkov ◽  
Dmitry Kolomenskiy ◽  
Pyotr N. Petrov ◽  
Nadejda A. Lapina ◽  
Thomas Engels ◽  
...  
Keyword(s):  
Body Size ◽  
Energy Storage ◽  
Elastic Energy ◽  
Three Dimensional ◽  
The Body ◽  
Wing Beat ◽  
Wing Motion ◽  
Aerial Vehicles ◽  
Performance Results ◽  
Computational Analyses

Flight speed generally correlates positively with animal body size [1]. Surprisingly, miniature featherwing beetles can fly at speeds and accelerations of insects three times as large [2]. We show here that this performance results from a previously unknown type of wing motion. Our experiment combines three-dimensional reconstructions of morphology and kinematics in one of the smallest insects, Paratuposa placentis (body length 395 μm). The flapping bristled wing follows a pronounced figure-eight loop that consists of subperpendicular up and down strokes followed by claps at stroke reversals, above and below the body. Computational analyses suggest a functional decomposition of the flapping cycle in two power half strokes producing a large upward force and two down-dragging recovery half strokes. In contrast to heavier membranous wings, the motion of bristled wings of the same size requires little inertial power. Muscle mechanical power requirements thus remain positive throughout the wing beat cycle, making elastic energy storage obsolete. This novel flight style evolved during miniaturization may compensate for costs associated with air viscosity and helps explain how extremely small insects preserved superb aerial performance during miniaturization. Incorporating this flight style in artificial flappers is a challenge for designers of micro aerial vehicles.

Three-dimensional kinematics and limb kinetic energy of running cockroaches.

1997 ◽  
Vol 200 (13) ◽  
pp. 1919-1929 ◽  
Author(s):  
R Kram ◽  
B Wong ◽  
R J Full
Keyword(s):  
Kinetic Energy ◽  
High Speed ◽  
Mechanical Energy ◽  
Center Of Mass ◽  
Three Dimensional ◽  
The Body ◽  
Morphological Data ◽  
Fast Running ◽  
Total Mechanical Energy ◽  
Reaction Forces

We tested the hypothesis that fast-running hexapeds must generate high levels of kinetic energy to cycle their limbs rapidly compared with bipeds and quadrupeds. We used high-speed video analysis to determine the three-dimensional movements of the limbs and bodies of cockroaches (Blaberus discoidalis) running on a motorized treadmill at 21 cm s-1 using an alternating tripod gait. We combined these kinematic data with morphological data to calculate the mechanical energy produced to move the limbs relative to the overall center of mass and the mechanical energy generated to rotate the body (head + thorax + abdomen) about the overall center of mass. The kinetic energy involved in moving the limbs was 8 microJ stride-1 (a power output of 21 mW kg-1, which was only approximately 13% of the external mechanical energy generated to lift and accelerate the overall center of mass at this speed. Pitch, yaw and roll rotational movements of the body were modest (less than +/- 7 degrees), and the mechanical energy required for these rotations was surprisingly small (1.7 microJ stride-1 for pitch, 0.5 microJ stride-1 for yaw and 0.4 microJ stride-1 for roll) as was the power (4.2, 1.2 and 1.1 mW kg-1, respectively). Compared at the same absolute forward speed, the mass-specific kinetic energy generated by the trotting hexaped to swing its limbs was approximately half of that predicted from data on much larger two- and four-legged animals. Compared at an equivalent speed (mid-trotting speed), limb kinetic energy was a smaller fraction of total mechanical energy for cockroaches than for large bipedal runners and hoppers and for quadrupedal trotters. Cockroaches operate at relatively high stride frequencies, but distribute ground reaction forces over a greater number of relatively small legs. The relatively small leg mass and inertia of hexapeds may allow relatively high leg cycling frequencies without exceptionally high internal mechanical energy generation.

CENTER OF MASS-BASED ADMITTANCE CONTROL FOR MULTI-LEGGED ROBOT WALKING ON THE BOTTOM OF OCEAN

2015 ◽  
Vol 74 (9) ◽  
Author(s):  
Addie Irawan ◽  
Md. Moktadir Alam ◽  
Yee Yin Tan ◽  
Mohd Rizal Arshad
Keyword(s):  
Buoyancy Force ◽  
Center Of Mass ◽  
The Body ◽  
Total Force ◽  
Vertical Force ◽  
Hexapod Robot ◽  
Admittance Control ◽  
Foot Placement ◽  
Robot Locomotion ◽  
Foot Motion

This paper presents a proposed adaptive admittance control that is derived based on Center of Mass (CoM) of the hexapod robot designed for walking on the bottom of water or seabed. The study has been carried out by modeling the buoyancy force following the restoration force to achieve the drowning level according to the Archimedes’ principle. The restoration force needs to be positive in order to ensure robot locomotion is not affected by buoyancy factor. As a solution to regulate this force, admittance control has been derived based on the total force of foot placement to determine CoM of the robot while walking. This admittance control is designed according to a model of a real-time based 4-degree of freedom (DoF) leg configuration of a hexapod robot that able to perform hexapod-to-quadruped transformation. The analysis focuses on the robot walking in both configuration modes; hexapod and quadruped; with both tripod and traverse-trot walking pattern respectively. The verification is done on the vertical foot motion of the leg and the body mass coordination movement for each walking simulation. The results show that the proposed admittance control is able to regulate the force restoration factor by making vertical force on each foot sufficiently large (sufficient foot placement) compared to the buoyancy force of the ocean, thus performing stable locomotion for both hexapod and quadruped mode.

scholarly journals The cost of hovering and forward flight in a nectar-feeding bat, Glossophaga soricina, estimated from aerodynamic theory

1993 ◽  
Vol 182 (1) ◽  
pp. 207-227 ◽  
Author(s):  
U. M. Norberg ◽  
T. H. Kunz ◽  
J. F. Steffensen ◽  
Y. Winter ◽  
O. von Helversen
Keyword(s):  
Mechanical Efficiency ◽  
Mechanical Power ◽  
Morphological Data ◽  
Power Comparison ◽  
Forward Flight ◽  
Minimum Power ◽  
Nectar Feeding ◽  
Glossophaga Soricina ◽  
Induced Velocity ◽  
The Cost

Energy expenditure during flight in animals can best be understood and quantified when both theoretical and empirical approaches are used concurrently. This paper examines one of four methods that we have used to estimate the cost of flight in a neotropical nectar-feeding bat Glossophaga soricina (Phyllostomidae), namely the use of kinematic and morphological data and aerodynamic theory to estimate the mechanical power requirements (power output) for hovering and horizontal forward flight. A hot-wire anemometer was used to measure induced velocity (the velocity of air accelerated by the wings) during hovering in order to estimate induced power. Our estimate of aerodynamic power (the sum of induced, profile and parasite powers) required for a 0.0105 kg G. soricina to hover is 0.15 W and our estimate of the inertial power (the power required to oscillate the wings) is 0.19 W. Thus, the total mechanical power for hovering is 0.34 W or 32.4 W kg-1. The mechanical power required for horizontal forward flight, near the minimum power flight speed (4.2 ms-1) for a 0.0117 kg bat is 0.14 W (12.3 W kg-1), of which 0.10 W is aerodynamic power and 0.042 W is inertial power. Comparison with our results on metabolic power requirements estimated from nectar intake gives a mechanical efficiency of 0.15 for hovering flight and 0.11 for forward flight near the minimum power speed.

Elastic energy storage in primary feather shafts

1976 ◽  
Vol 64 (3) ◽  
pp. 677-689
Author(s):  
C. J. Pennycuick ◽  
A. Lock
Keyword(s):  
Energy Storage ◽  
Kinetic Energy ◽  
Elastic Energy ◽  
High Velocity ◽  
Forward Flight ◽  
Additional Energy ◽  
Primary Feather ◽  
Present Evidence ◽  
Temporary Storage

It is proposed that the kinetic energy of a pigeon's wing, in hovering or slow forward flight, is transferred to the air at the end of the downstroke by a mechanism involving temporary storage of additional energy in bent primary feather shafts. Estimates of the amounts of energy which can be stored and recovered in this way are compared with the requirements of the theory. The hypothesis is not rejected, as far as present evidence goes. If is is correct, high-velocity pulses of calculable magnitude should be detectable in the wake.

Force platforms as ergometers

1975 ◽  
Vol 39 (1) ◽  
pp. 174-179 ◽  
Author(s):  
G. A. Cavagna
Keyword(s):  
Body Weight ◽  
Mechanical Energy ◽  
Center Of Mass ◽  
Force Plate ◽  
Vertical Displacement ◽  
The Body ◽  
Mechanical Work ◽  
Vertical Force ◽  
External Work ◽  
Total Mechanical Energy

Walking and running on the level involves external mechanical work, even when speed averaged over a complete stride remains constant. This work must be performed by the muscles to accelerate and/or raise the center of mass of the body during parts of the stride, replacing energy which is lost as the body slows and/or falls during other parts of the stride. External work can be measured with fair approximation by means of a force plate, which records the horizontal and vertical components of the resultant force applied by the body to the ground over a complete stride. The horizontal force and the vertical force minus the body weight are integrated electronically to determine the instantaneous velocity in each plane. These velocities are squared and multiplied by one-half the mass to yield the instantaneous kinetic energy. The change in potential energy is calculated by integrating vertical velocity as a function of time to yield vertical displacement and multiplying this by body weight. The total mechanical energy as a function of time is obtained by adding the instantaneous kinetic and potential energies. The positive external mechanical work is obtained by adding the increments in total mechanical energy over an integral number of strides.

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