As discussed on the airplane cruise
slide, an airplane can maintain a constant speed and level flight in
which the weight is balanced by the
lift, and the drag
is balanced by the thrust. However, if the
forces become unbalanced, the aircraft
moves in the direction of the greater force. We can compute the
acceleration of the aircraft from Newton's Second
Law of Motion. If the mass m of the aircraft remains a constant
we can use the familiar form of the equation to solve for the acceleration a
F = m * a
a = F / m
where the net force F is the
difference between the opposing forces; lift minus weight or thrust
The mass m of the aircraft is determined by the
of the aircraft.
If the force and the mass remain constant, the basic
equations of motion can
be solved. For a constant force and constant mass, the
acceleration remains constant. The velocity V at any time t
is the acceleration times the time, plus the initial velocity Vo:
V = a * t + Vo
Similarly, the location X at any time t is given by 1/2 the
acceleration times the time squared, plus the initial location Xo,
plus the initial velocity times the time.
X = .5 * a * t^2 + Vo * t + Xo
Note that these equations can be used only if the mass and the
force are constant.
The mass of an aircraft remains fairly
constant during cruise since the only loss is for the fuel which is consumed.
Fuel mass is normally a small percentage of the mass of an aircraft.
However for aircraft, the lift and drag forces
are themselves functions of the square of the
velocity. So we can assume a constant force for only a very small
amount of time. To solve the actual equations of motion for an
aircraft, we must use calculus and integrate the equations of motion.
The integration can be performed analytically or numerically.
Also note that on this slide we solve the equations of motion in
only the x-direction. The forces, accelerations, velocities and
displacements are all
vector quantities which
are defined in three spatial directions and time. The x-direction is
of the more complex three-dimensional motion.
that demonstrates the information found on
this slide is also available at this web site.
The applet presents problems that you
must solve by using the equations of motion.
Basic Aircraft Motion:
- Beginner's Guide Home Page