The amount of lift generated by an object depends on a number of factors,
of the air, the
velocity between the object and the
viscosity and compressibility of the air,
surface area over which the air flows, the
of the body, and the body's inclination to the flow, also called the
angle of attack.
In general, the dependence on body shape, inclination,
air viscosity, and compressibility is very complex.
One way to deal with complex dependencies is to characterize the
dependence by a single variable. For lift, this variable is called the
lift coefficient, designated "Cl".
For given air conditions, shape, and
inclination of the object, we have to determine a value for Cl to
determine the lift.
For some simple flow conditions
and geometries, and low inclinations, aerodynamicists
can now determine the value of Cl mathematically. But, in general, this
parameter is determined experimentally using
For thin airfoils, at small angles of attack, the lift coefficient is approximately
two times pi (3.14159) times the angle of attack expressed in radians.
Cl = 2 * pi * angle (in radians)
The modern lift equation states that lift is equal to the
lift coefficient (Cl) times the density of the air (r) times half of the
square of the velocity(V) times the wing area (A).
L = .5 * Cl * r * V^2 * A
By the time the Wrights began their studies, it had been determined that
lift depends on the square of the velocity and varies linearly
with the surface area of the object.
Early aerodynamicists characterized the dependence on the properties of the air
by a pressure coefficient called
Smeaton's coefficient which represented the
pressure force (drag) on a one foot square flat plate moving at one mile per hour through
the air. They believed that any object moving through the air converted some
portion of the pressure force into lift, and they derived a different version of the
which expressed this relationship.
Today we know that the lift varies linearly with the density of the air.
Near sea level
the value is .00237 slugs/cu ft, or 1.229 kg/cu m,
but the value changes with air temperature and pressure.
The pressure and temperature vary in a rather complex way with
The linear variation with density and the variation with the square of the
velocity suggests a variation with the dynamic pressure which we
So modern aerodynamicists include a factor of 1/2 into the definition of the modern
lift equation to reference the aerodynamic forces to the dynamic pressure
(1/2 density times velocity squared).
NOTICE: The modern lift equation and the lift equation used by the Wright brothers
in 1900 are slightly different. The lift coefficient of the modern equation is referenced
to the dynamic pressure of the flow, while the lift coefficient of the earlier times
was referenced to the drag of an equivalent flat plate. So the value of these two
coefficients would be different even for the same wing and the same set of flow conditions.
Using the modern lift equation,
and the lift coefficient given above, one can calculate the amount of lift
produced at a given velocity for a given wing area. Or, for a given velocity,
you can determine how big to make the wings to lift a certain weight.
Here's a Java program that you can use to investigate the designs of the
Wright aircraft from 1900 to 1905 which uses the modern lift equation.
Due to IT
security concerns, many users are currently experiencing problems running NASA Glenn
educational applets. The applets are slowly being updated, but it is a lengthy process.
If you are familiar with Java Runtime Environments (JRE), you may want to try downloading
the applet and running it on an Integrated Development Environment (IDE) such as Netbeans or Eclipse.
The following are tutorials for running Java applets on either IDE:
You can download your own copy of this applet by pushing the following button:
The program is downloaded in .zip format. You must save the file to disk and
then "Extract" the files. Click on
"Lift.html" to run the program off-line.
You can change the values of the velocity, angle of attack, temperature,
pressure, and wing area by using the
sliders below the airfoil graphic, or by backspacing, typing in your value,
and hitting "Return" inside the input box next to the slider.
By using the drop menu labeled "Aircraft" you can choose to investigate any of
the Wright aircraft from 1900 to 1905. At the right bottom you will see
the calculated lift and to the right of the lift is the weight of the
The aircraft designated "-K" are kites and the weight does not include
a pilot. The aircraft designated "-G" are gliders and the weight does include
For design purposes, you can hold the wing area constant and vary the speed and
angle of attack, or hold the speed constant and vary the wing area and angle of
attack by using the drop menu next to the aircraft selection.
In this simulation, the change in weight due to change in wing area has been
you can choose to have a plot of the lift or the lift coefficient by using
the drop menu. You can plot lift versus angle of attack, velocity or wing area by
pushing the appropriate button below the graph.
You can perform the calculations in
either English or metric units by using the drop menu labeled "Units".
Finally you can turn on a "Probe" which you can move around
the airfoil to display the local value of velocity of pressure. You must
select which value to display by pushing a button and you move the probe
by using the sliders located around the gage.
Select an aircraft and then find the flight conditions that produce a lift greater
than the weight. You can check with the individual aircraft pages to see how
big the Wrights designed their wings. Remember that determining the lift is
only a part of the design problem. You will find that a higher angle of attack
produces more lift. But it also produces more
lift to drag ratio
is an efficiency factor for the aircraft and directly related to the
The Wrights were aware that they needed both high lift and low drag (which they called
"drift"). You will also find that increasing the wing area increases the lift.
But in the total design, increasing wing area also increases the weight.
NOTICE: In this simple program we have approximated the
entire aircraft (both wings and the canard) by a single flat plate. So
you can expect that our answer is only going to be a very rough estimate.
Engineers used to call this a "back of the envelope" answer, since it is
based on simple equations which you can solve quickly. Engineers still
use these kinds of approximations to get an initial idea of the solution
to a problem. But they then perform a more exact (usually longer, harder,
and more expensive)
to get a more precise answer.
You can view a short
of "Orville and Wilbur Wright" discussing the lift force
and how it affected the flight of their aircraft. The movie file can
be saved to your computer and viewed as a Podcast on your podcast player.