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Work and Energy for Variable Forces01:10

Work and Energy for Variable Forces

When an object is acted upon by a variable force, the amount of work done and the change in energy of the object can be more complex to calculate compared to when a constant force is applied. Work is the product of force and displacement, while energy is the capacity of a system to do work. When a constant force is applied to an object, the work done can be calculated as the product of the force and the distance moved in the direction of the force. However, when a variable force is applied, the...
Energy Conservation and Bernoulli's Equation01:16

Energy Conservation and Bernoulli's Equation

Applying the conservation of energy principle or the work-energy theorem to an incompressible, inviscid fluid in laminar, steady, irrotational flow leads to Bernoulli's equation. It states that the sum of the fluid pressure, potential, and kinetic energy per unit volume is constant along a streamline.
All the terms in the equation have the dimension of energy per unit volume. The kinetic energy per unit volume is called the kinetic energy density, and the potential energy per unit volume is...
Energy Diagrams - I01:14

Energy Diagrams - I

The dynamics of a mechanical system can be easily understood by interpreting a potential energy diagram. Since energy is a scalar quantity, the interpretation of the dynamics of the system becomes even simpler.
Take the example of a skater on a parabolic ramp. The potential energy at different points along the ramp will be proportional to the height of the ramp, which varies quadratically with the horizontal position on the ramp. As the skater moves down the ramp from the highest position,...
Kinetic Energy for a Rigid Body01:13

Kinetic Energy for a Rigid Body

Imagine a solid object involved in a general planar movement, with its center of mass pinpointed at a spot labeled G. The object's kinetic energy relative to an arbitrary point A can be quantified for each of its particles - the ith particle in this case. This measurement is achieved through the employment of the relative velocity definition. The position vector, known as rA, extends from point A to the mass element i.
Static and Kinetic Frictional Force01:05

Static and Kinetic Frictional Force

One of the simpler characteristics of sliding friction is that it is parallel to the contact surfaces between systems, and is always in a direction that opposes the motion or attempted motion of the systems relative to each other. If two systems are in contact and moving relative to one another, then the friction between them is called kinetic friction. For example, kinetic friction slows a hockey puck sliding on ice.
However, if two systems are in contact and are stationary relative to one...
Conservation of Mechanical Energy01:05

Conservation of Mechanical Energy

The mechanical energy E of a system is the sum of its potential energy U and the kinetic energy K of the objects within it. What happens to this mechanical energy when only conservative forces cause energy transfers within the system—that is, when frictional and drag forces do not act on the objects in the system? Also assume that the system is isolated from its environment; in other words no external force from an object outside the system causes energy changes inside the system.
When a...

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Related Experiment Video

Updated: May 17, 2026

Building an Enhanced Flight Mill for the Study of Tethered Insect Flight
12:09

Building an Enhanced Flight Mill for the Study of Tethered Insect Flight

Published on: March 10, 2021

A coupled kinematics-energetics model for predicting energy efficient flapping flight.

Hesam Salehipour1, David J Willis

  • 1Physics Department, University of Toronto, 60 St. George St., Toronto, Ontario, Canada M5S 1A7.

Journal of Theoretical Biology
|October 23, 2012
PubMed
Summary

A new computational model predicts bird and bat flight energetics and kinematics by analyzing optimal power and aerodynamics. This method, applied to bats and birds, shows reasonable predictions compared to experimental data.

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Last Updated: May 17, 2026

Building an Enhanced Flight Mill for the Study of Tethered Insect Flight
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Published on: March 10, 2021

Flapping Soft Fin Deformation Modeling using Planar Laser-Induced Fluorescence Imaging
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A Simple Flight Mill for the Study of Tethered Flight in Insects
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A Simple Flight Mill for the Study of Tethered Flight in Insects

Published on: December 10, 2015

Area of Science:

  • Biomechanics
  • Aerodynamics
  • Computational Biology

Background:

  • Understanding the complex interplay between energy expenditure and movement in flying animals is crucial for biomechanical research.
  • Existing models often simplify the intricate aerodynamic forces and kinematic parameters governing avian and chiropteran flight.

Purpose of the Study:

  • To develop and validate a novel computational model for predicting the energetic and kinematic interdependencies in bird and bat flight.
  • To assess the model's accuracy by comparing its predictions with experimental data from various species.

Main Methods:

  • A wake-only aerodynamics method was employed within a modular computational framework (offline, intermediate, online).
  • The model incorporates a design space sweep of aerodynamic parameters and animal-specific physical characteristics.
  • Amplitude-frequency response surfaces were generated and analyzed for specific flapping motions.

Main Results:

  • The computational model successfully predicted flight energetics and kinematics for a fruit bat (Cynopterus brachyotis), a thrush nightingale (Luscinia luscinia), and a budgerigar (Melopsittacus undulatus).
  • Predictions derived from the model demonstrated reasonable agreement with available experimental data for the studied species.

Conclusions:

  • The presented computational model offers a robust tool for analyzing the energetics and kinematics of bird and bat flight.
  • This approach advances our ability to simulate and understand the biomechanics of animal flight through integrated aerodynamic and kinematic analysis.