The Energy of Bird Flight

Have you ever noticed that when birds land on a branch, they usually fly in at a low level and swoop up to the branch?

If they didn't do that, they would have to absorb all the energy of their flight with their legs (and strong wing action). But by flying upward, their kinetic energy of motion is converted to potential energy of increased height, so they slow down before landing, just as a rolling ball slows down when it goes uphill. Let's see how that works.

Kinetic Energy

Kinetic energy is energy due to motion, and is represented by E_k. For the bird moving in a straight line, the kinetic energy is one-half the product of the mass and the square of the speed:

\[ \large E_{k} = \dfrac{1}{2}mu^{2} \label{1}\]

Where

m = mass of the object

u = speed of object

Example \(\PageIndex{1}\): Kinetic Energy of a Bald Eagle

Calculate the kinetic energy of a 6.8 kg (15 lb, about the biggest) bald eagle which is flying at 13.9 m s^–1 (about 30 miles per hour or 50 kilometer/hour; their top speed) ^[1].

Solution

\(\large E_{k} = \dfrac{1}{2} m u^{2} = \dfrac{1}{2} \times 6.8 \text{ kg} \times ( 13.9 \text{ m} \text{ s}^{-1} )^{2} = 657 \text{ kg}\text{ m}^{2} \text{ s}^{-2}\)

The collection of units kg m² s^–2 is given the name Joule in the SI system after James Joule (see below). In other words the units for energy are derived from the SI base units kilogram for mass, meter for length, and second for time. A quantity of heat or any other form of energy may be expressed in kilogram meter squared per second squared.

Potential Energy

Potential Energy is energy that is stored by rising in height (in the case of birds landing), or by other means. It frequently comes from separating things that attract, like rising birds are being separated from the Earth that attacts them, or by pulling magnets apart, or pulling an electrostatically charged balloon from an oppositely charged object to which it has clung. Potential Energy is abbreviated E_P and gravitational potential energy is calculated as follows:

\[\large E_{P} = mgh \tag{2}\]

Where

m = mass of the object in kg

g = gravitational constant, 9.8 m s²

h = height in m\

Notice that E_P has the same units, kg m² s^–2 or Joule as kinetic energy.

Example \(\PageIndex{2}\): Height of an Eagle's Flight

How high would the eagle flying at 30 mph need to rise to come to a complete stop, if none of the stopping power came from wings?

Solution: The eagle's kinetic energy is 657 J (from EXAMPLE 1), so all of this would have to be converted to E_P. Then we could calculate the height:

\(\large E_{P} = mgh = 657 \text{ kg} \text{ m}^{2} \text{ s}^{-2} = 6.8 \text{ kg} \times 9.8 \text{m} \text {s}^{-2} \times h \)

\( \large h = 9.9 \text{ m} \)

This is 32 feet, so it's likely that some wing action is used to convert some of the kinetic energy to heat energy in the air to do some of the slowing down, so the upward motion is somewhat less.

Our reasoning here depends on The law of conservation of energy, which states that energy cannot be created or destroyed under the usual conditions of everyday life. Whenever there appears to be a decrease in energy somewhere, there is a corresponding increase somewhere else. If the bird's E_K decreases as he slows down, his potential energy, or heat energy in the air, or other forms of energy must increase so that the total amount of energy does not change.

There are clearly many forms of energy, and it's tricky to define, but it's usually defined as the capability for doing work. For example, the flying bird could do work by crashing into a branch and breaking it (if it hadn't learned to slow down by rising), and could break the same branch by falling from a height, using E_P.

We've left out one form of energy is very important to biologists and chemists. If the eagle started on the ground and at rest, it had no E_P or E_K. Where did the energy to move or gain height come from?

It comes from the eagle's diet of 250-550 grams per day ^[2] of food that can release chemical potential energy. We even measure dietary intake in Calories, where 1 Cal = 4184 J = 4.184 kJ = 1 kcal. The capital "C" that dieticians use for measuring the energy values of foods are actually kilocalories. The calorie used to be defined as the energy needed to raise the temperature of one gram of water from 14.5°C to 15.5°C but now it is defined as exactly 4.184 J. We know that food calories heat our bodies and allow us to do useful work (and maybe gain weight), and we'll see how they're measured, and consumed, in the next sections.

The first careful experiments to determine how much work was equivalent to a given quantity of heat were done by the English physicist James Joule (1818 to 1889) in the 1840s. In an experiment very similar to our eagle wing flapping example, Joule connected falling weights through a pulley system to a paddle wheel immersed in an insulated container of water. The moving paddles transferred the energy of the falling weight into turbulent heat in the water, just as an eagle's wings convert kinetic energy into turbulent heat in the air. This allowed Joule to compare the heat energy change of the water to the E_P of the weights, and understand how energy of movement was related to heat energy. 

From ChemPRIME: 3.6: Energy

References

1. ↑ www.learner.org/jnorth/1997/critters/eagle/AnswerEagle.html
2. ↑ www.learner.org/jnorth/1997/critters/eagle/AnswerEagle.html

Contributors and Attributions

• Ed Vitz (Kutztown University), John W. Moore (UW-Madison), Justin Shorb (Hope College), Xavier Prat-Resina (University of Minnesota Rochester), Tim Wendorff, and Adam Hahn.