Table 1: Direct Access
to the Sub-Disciplines of Aerospace Engineering
DESIGN-CENTERED INTRODUCTION
TO AEROSPACE ENGINEERING
5.
FORCE BALANCE IN FLIGHT
When an aircraft flies, the wings (and the horizontal
tails to some extent) support the weight of the whole aircraft. The rest
of the aircraft just hangs on these "lifting surfaces". Of course the wings
and tails themselves have weight. On most aircraft, the wings contain most
of the fuel. A large aircraft like a Boeing 747 might have 250,000 lbs
of fuel when it takes off on an intercontinental journey.
We can use Newton's Laws of Motion to calculate the acceleration
of an aircraft, and thus to decide how the forces on the aircraft must
be balanced to make it go in a desired direction.
Newton's First Law of
Motion
This defines the concept of equilibrium. It says:
An object continues to be in a state of rest or
uniform motion unless there is a net force acting on it.
Note that something can be moving at a steady rate, if all the forces
actin on it are balanced out. Thus, for example, even if the lift on an
airplane is enough to equal the weight, it may not stay up, if it
started with a downward velocity. it will just keep coming down at a steady
pace. When all the forces are balanced out, the object is said to be in
a state of equilibrium.
What happens if there is a net force in some direction?
Newton's Second Law of Motion gives us the answer, below. This forms the
basis of most of the calculations that you will do in this course. Before
we go on to that, let's state Newton's Third Law of Motion:
Newton's Third Law of Motion:
Every action has an equal and opposite reaction.
Here the words "action" and "reaction" denote forces. This is useful
when we consider how to describe all the forces wich need to be balanced
out. For example, if the engine of an airplane produces thrust which pulls
forward on the aircraft, then the aircraft pulls on the engine in the opposite
direction, saying, "wait for me!".
Newton's Second Law of Motion:
Force = Rate of Change of Momentum.
The momentum of an object is its mass times its velocity.
If the mass is constant, the momentum can change because velocity changes.
Rate of change of velocity is acceleration. Thus,
Force = (mass)*(acceleration)
Force and acceleration are vectors: they have magnitude
and direction. If two vectors
and
are
equal, i.e.,
then,
and
. In
other words, two vectors can be equal only if their corresponding components
are equal. Using this, we can rewrite the vector equation relating force
and acceleration as a set of "scalar" component equations, one along each
direction. This is very simple:
Along x, the forces according to the airplane diagram
above, are Thrust and Drag. Thus,
Thrust - Drag = (mass)*(acceleration along x)
Along z, the forces are Lift and Weight. Thus,
Lift - Weight = (mass)*(acceleration along z).
It may not always be possible to have the thrust acting
exactly along x, or the lift exactly along z. So we should develop a more
general relation, which accounts for the components of each force along
each of our selected directions. First, lets look at this refined diagram
and define a few terms:
The
"Freestream
Vector 
". This is equal and opposite to the flight velocity.
Lift is perpendicular to the
freestream vector
(but it may be up, down or sideways).
Drag is parallel to
.
Thrust is along the thrust direction
(modern fighter aircraft have "thrust vectoring nozzles" which can point
the thrust in arbitrary directions. Usually, commercial aircraft have the
thrust vector pointing forward, almost along the aircraft fuselage, but
they also have "thrust reversers" which can point the thrust backwards.
Weight acts towards the center of the earth (or whatever
the closest massive heavenly body is). The two component equations are:
Lets consider some special cases:
Case 1:
When the aircraft is flying almost level
;
. So, if L>W, the vehicle accelerates upwards. Also, if T>D, the vehicle
accelerates forward. If L=W, the aircraft flies level, or rises and falls
at constant speed. If T=D, the aircraft flies at constant speed.
Case 2:
Acceleration is zero, but
.
If W>0, then the aircraft is sinking. From these we note:
1) If the lift is greater than the weight, then the aircraft
will accelerate upwards.
2) If the thrust is greater than the drag, the aircraft
can climb if the thrust acts at an angle to the flight direction. So there
are different ways of achieving the same result. Let's consider sideward
forces.
Sideward Forces: Turn
, the centrifugal force. Note that
is the
centripetal force: the force directed towards
the center.
is the radial acceleration. By Newton's 3rd Law of Motion, the centrifugal
force is the reaction, which is equal and opposite to the centripetal force.
Note: To pull tighter turns, (i.e., smaller R), at a
given value of U,
must be made larger. If we are not to lose height during this turn,
must be as large as W.
AERODYNAMIC CONTROL SURFACES:
If the lift on one wing
is changed relative to the other, the aircraft tends to roll, and this
causes a turn, as seen above.
If the lift
(side force) on the vertical tail is changed, the aircraft tends to yaw.
Then the aircaft must roll to avoid sideslipping.
