Flying High
And the Forces Involved
CE 361
Submitted on February 16, 1996
Submitted by Jeff Edwards and Aaron VanderVeen
As long as mankind has been able to imagine, they have wanted to
fly like the birds. It hardly seemed fair that the smartest
animals in all of creation should be confined to walk around on
the earth while other lesser animals were able to soar through
the sky. However unfair this was, the fact remained that mankind
had only a brain and no wings, so man made the best of what he
had and used his mind to allow heavier than air flight to become
a reality. Man made plenty of futile (and fatal) attempts to fly
before the Wright brothers helped to vault flying to the common
occurrence it is today.
Considerable credit must be given to Leonardo do Vinci for the
first scientific efforts to fly. He studied the flight of birds
and constructed an aircraft with wings designed to flap.
Laughable as it may seem on the surface, this was undoubtedly the
work of a brilliant scientist, and had there been an available
power unit and the wings of the craft rigid, there is virtually
no doubt that da Vinci would have been the first man to fly.
Jumping ahead now a couple of hundred years, F.H. Wenham first
patented the "two-surface" type of airplane like the one the
Wright brothers eventually flew. He also on June 27, 1866 read
the most knowledgeable paper ever presented to the Aeronautical
Society of Great Britain. In this paper he described his own
experiments with models and aeroplanes of sufficient size to
carry the weight of a man.
Several other attempts followed these, but none were really
successful until Orville and Wilbur Wright became the first men
to complete a successful heavier than air flight in 1903. In the
years prior to their flight, man had worked out the fundamental
theories of flight. The last hurdle remaining to be topped was
the proper means of propulsion, which the Wright's successfully
attacked.
Following their success, those who scoffed at the idea of heavier
than air flight quickly became inspired to try and build their
own "flying machine." With continued successes, and the military
recognition of airplanes in 1914, the industry expanded greatly.
Before and during the first World War, however, airplanes were,
as a whole, unsteady and low-powered. There was little
scientific analysis and laboratory development during this
period. Trial and error was the main form of development, and as
a result there were many casualties. To the average man, an
aviator was something of a daredevil, but much credit must be
given to them for keeping the industry alive after the war.
Eventually, however, this experimental period gave way to
theoretical analysis in laboratories and wind tunnels. Finally,
the airplane industry took its place in the scientific world. It
was there that the important theories of aerodynamics began to
influence the design, safety, and efficiency of airplanes. The
most efficient shape for airfoils was determined by analysis and
elimination. Higher powered engines and new metals contributed
greatly in this period of refinement.
Whether you are talking about the old biplanes, or today's jet
airplanes, the basic forces remain the same today as they were in
the early 1900's. As shown below, there are four main forces
that act upon an airplane while it is in flight. These forces
are lift, weight, thrust, and drag.
Lift is the main force of interest in this report, but each of
the forces will now be briefly discussed.
Thrust
Thrust is the force that is provided by the engines of the
airplane and moves the airplane forward through the air. The
engine provides power to the propeller (or the axial-flow fan in
a turbofan or jet engine) which then displaces a large mass of
air backward. This displacement of air develops the forward
thrust that carries the aircraft through the air. Horsepower is
the measure of force most commonly associated with engines, and
requirements increase as a function of velocity cubed. In other
words, to go twice as fast, you need eight times as much
horsepower. Thrust is balanced by frictional forces (drag) when
an airplane is in straight and level flight. When the force of
thrust is greater than that of drag, the aircraft accelerates
until drag force again equals the thrust force at which time the
aircraft ceases to accelerate and continues at a constant
speed.
Drag
Drag is the term given to the force which is caused by the air
particles striking and flowing around the airplane as it moves
through the air. Aside from lift, drag is the most important
force which acts upon the wing of airplanes. As the speed of the
airplane increases, drag increases proportionally to the square
of the velocity. In other words, if you go twice as fast, the
drag is four times greater. Drag is balanced by thrust when an
airplane is in straight and level flight. When the force of drag
is greater than the thrust force, the airplane will decelerate
until the thrust force equals the drag force again at which point
the aircraft ceases to decelerate and continues at a constant
speed.
Weight
Weight is the force due to gravity. It acts around and upon us
every day. It is the force which results from the attraction of
two bodies containing mass to one another. The earth's gravity
causes objects to be accelerated towards the earth at a constant
acceleration of 9.81 m/s^2(32 ft/s^2). This force is balanced by
lift when an airplane is in straight and level flight. If the
force of the weight is greater than the force of the lift on the
airplane, the airplane will begin to loose altitude until the
lift force is increased to balance the force of the weight (or
until it meets the ground).
Lift
Lift is to be the main focus of this report. It is the upward
directed force produced by two natural forces, pressure
and deflection. Lift depends upon a number of factors
which will be discussed in detail later, but among them are
factors such as airfoil shape, velocity of the airfoil, and also
weather factors such as temperature.
The force listed above as pressure refers to the pressure
difference between the top of the airfoil and the bottom of the
airfoil. This pressure difference is determined by Bernoulli's
equation:
(p/rho)+(v^2/2g)+z=constant, or
(p1/rho)+v1^2/2g)+z1=(p2/rho)+(v2^2/2g)+z2
Stated in words, Bernoulli's equation means that the total energy
at one point in a steady flow stream of a fluid is equal to the
total energy at any other point in the stream along its path of
flow, provided no energy is added to the fluid or taken from it
or otherwise lost between the two points. The following
illustration should help to clarify Bernoulli's equation:
The energy contained in the air must remain constant from point 1
to point 2 in the diagram above. Thus in order to maintain the
energy as a constant, the particles must arrive at point 2 at the
same time independent upon which path (over or under the foil) is
taken. Since the path over the foil is longer (due to the shape
of the foil) the air particles must travel faster over the top of
the foil than they need to travel under the bottom of the foil.
Bernoulli's equation then necessitates that there be a pressure
drop accompanying this increase in velocity. The air above the
foil then has a lower pressure than the air below the foil, and
results in the lifting action on the wing.
The other natural force which affects the lift a wing supplies an
airplane is the deflection. This force is the result of
Newton's Third Law of motion which, stated in words, is "For
every action, there must be an equal and opposite reaction." The
diagram below should help to explain this:
As the air particles strike the underside of the wing, they are
deflected downward and to the rear. According to Newton's Third
Law, this deflection force must also have an equal and opposite
force upward and forward resulting in a lift force. Adding the
vertical portion of this force to the force resulting from the
pressure difference will give the total amount of lift an airfoil
will generate.
The amount of lift force generated can be determined from the
following equation:
F=C*rho*(v^2/2)*A
where F is the lift force, C is the lift coefficient, rho is the
density of the air, v is the velocity of the foil with respect to
the air, and A is the projected chord area. The amount of lift
generated by this equation depends upon several variables such as
the velocity of the foil, the length of the wing, and weather
effects such as temperature.
The deflection force is taken into account in the above equation
as the lift coefficient (C). The lift coefficient is a function
of the angle of attack (the angle that the airfoil makes with the
air stream). The theoretical lift coefficient can be calculated
from this equation:
C=2*pi*sin (alpha)
where alpha is the angle of attack. Actual values are around 90%
of this theoretical value. The following diagram should help to
clarify the concept of angle of attack:
The above diagram also shows the chord length of the airfoil
which is used in calculating the chord area (A) in the lift force
equation. The chord area is calculated by multiplying the chord
length by the length of the airfoil. Thus it would seem that the
greatest lift would be gained by making a wing either very long
lengthwise, by increasing the chord length, or by a combination
of both. This would be true except for the fact that the other
main force acting upon an airplane's wing is, as mentioned
earlier, drag.
The drag force on a wing can be calculated by an equation exactly
like the lift equation with the exception that the drag
coefficient is put in place of the lift coefficient. The
equation for drag on an airfoil is:
F=Cd*rho*(v^2/2)*A
where Cd is the drag coefficient and can be read off a chart
based upon Reynold's number. Also included in the drag force
equation is the chord area term. Thus, the longer the chord
area, the more drag will be generated. Therefore one must reach
a compromise between the drag force and the lift force an airfoil
will generate.
One may also think that an idea for increasing the amount of lift
an airfoil will generate would be to increase the angle of attack
that the airfoil has with the airstream, thus increasing the lift
coefficient term. This only works to a point, however, and once
this point is passed, a phenomenon called a stall occurs. A
stall is when the airflow about the airfoil is broken up and the
airflow breaks away from the upper surface at a point called the
separation point, as shown in the following diagram:
At this critical angle the lift resulting from Bernoulli's
Theorem is reduced, rendering the airfoil ineffective. The lift
immediately breaks down and the drag becomes excessive. This
phenomenon can result in a crash if the plane is at too low of an
altitude to recover from it. The only way to recover from a
stall is to decrease the angle of attack and increase the thrust
to increase velocity and regenerate enough lift to pull the
aircraft out of the descent into which it has gone.
A stall can also be caused by decreasing the power too far. The
minimum speed at which an aircraft can maintain flight is called
the stalling speed. One must be extremely careful, especially
when landing because the plane is traveling at an airspeed very
close to the stalling speed. Taking off can also be a problem if
there is not enough room or thrust to overcome this stall speed.
One must be extremely careful, especially when landing or taking
off, not to go slower than this speed since doing so can result
in a fatal crash. This phenomenon is based on the fact that for
any fixed wing arrangement, there is a dynamic pressure below
which an airplane of a given wing loading cannot fly.
A proven way to increase the lift an airfoil is capable of
generating is the flap. Flaps are movable panels on the inboard
trailing edges of the wings. They are hinged so they can be
extended downward into the flow of air beneath the wings to
increase lift and drag. The primary purpose of the flaps is to
permit a slower airspeed during a landing approach. Flaps can
also be used to shorten takeoff distances.
Flaps have several advantages. First, as mentioned previously,
flaps result in higher lift coefficients, permitting a lower
speed in landing. Also, flaps can be used as "air brakes", which
results in a shorter run on the ground when stopping the plane.
A steeper gliding angle is possible without an increase in
velocity. Flaps have several disadvantages also. Among them are
that their use results in a high drag when the angle of attack is
increased making it more difficult to control the flight path,
the possibility of mechanical failure, and extending along the
trailing edge between the ailerons can result in interference
with the functioning of the ailerons.
As mentioned earlier, weather can also affect the amount of lift
generated. If you look at the equation for lift again, you will
notice the term rho in the equation. This is the density of the
air in the air stream through which the airfoil is passing.
Density of air varies with changes in temperature. Different
values of density can be looked up in a chart and the density can
vary greatly from place to place. For example if one were to fly
from Houghton (temp. of -10 degrees C) to Florida (temp. of 30
degrees C) the density would change from 1.342 kg/m^3 to 1.164
kg/m^3. This lower density results in a lower lift force on the
airplane in Florida.
The field of aircraft design is not new, but it is not resting on
its laurels either. Research continues on aircraft design trying
to make airplanes more efficient and also to make them safer.
New aircraft are being designed daily, and there is no telling
where this research may lead. For example, when planes were
first invented, the majority of people thought that planes could
never be used for mass transportation or for hauling cargo, both
of which are major uses for planes today. Back then, who could
have even imagined something the size of a Boeing 747 flying
across the ocean, or of a craft which looks like an airplane
being
lifted by rockets into space and landing on a runway to be used
again. In the same way, who can say where today's research and
technology development may someday lead. Maybe someday, flights
to the moon will be as common as it is to fly from Chicago to
Detroit today.
References
Potter, Mearle and Wiggert, David. Mechanics of Fluids.
Prentice Hall. 1991
Gillmet, T. and Nietsch, Erich. Simplified Theory of
Flight. D. Van Nostrand Co. 1941
Microsoft. Pilot's Handbook. 1986
Taylor, Chatfield and Ober. The Airplane and It's Engine.
McGraw-Hill Book Co. 1940
Jackman, Russel, and Chanute. Flying Machines Construction
and Operation. Charles Thompson Co. 1912
Warner. Airplane Design Aerodynamics. McGraw-Hill Book
Co. 1926