For scientists, work is the product of a
acting on an object times the distance that the objet moves.
As an example shown on the slide, the Wright
is acted upon by the
force (F) from time (t) equals zero to some later time (t > 0)
and travels some distance (s). The work (W) done on the aircraft during this
time is F times s.
W = F * s
The units of work in the metric system is the Joule, which is equal to
one Newton times one meter.
In the English system the unit of work is the British thermal unit (Btu)
which is equal to 777.9 pounds times one foot.
Notice that the units of work are the same as the units of energy.
Work and energy are related to one another as we shall see in our studies of
In our simple example, the force is a constant value
aligned with the
of the aircraft. In most real
applications, the force varies along the flight path in both
magnitude and direction. The work is then equal to the integrated
value of the component of the force in the direction of the
displacement with the angle between the force and displacement
given by the Greek symbol "phi".
It is important to note that work is only done on (or by) the
component of the force aligned with the path.
Using a cruising
aircraft as another example, the lift is
defined to be the force perpendicular to the flight path. Lift does
no work on a cruising aircraft because the displacement is
perpendicular to the force. Similarly, if an aircraft was stopped at
the end of the runway with the brakes on and the engines at full
throttle, the engines do no work on the aircraft because the
displacement distance is zero.
The Wright brothers used their knowledge of work and
the time rate of change of work, to determine
the minimum power requirements for their
1903 engine design.
Power is equal to the force acting on an object times the velocity
of the object.
The brothers were able to make rather accurate estimates of the drag force on their
based on the flight tests of the
1901 wind tunnel results.
Knowing the drag and the desired flight velocity they computed the
power requirements for the engine in order to develop
to overcome the drag of the aircraft.
In the previous examples, we have been concerned with the work
done by a force applied to a solid object. For a gas,
work is done when the volume
of a gas is changed at some pressure.
Pressure represents a force per unit area and the volume
can be related to the surface area and a distance travelled by that
surface when the volume changes. (force / area * area * distance =
force * distance = work). Notice that to
produce work, the volume of a gas must change.
- Re-Living the Wright Way
- Beginner's Guide to Aeronautics
- NASA Home Page