An interactive
Java applet
that demonstrates the information found on
this slide is also available. The applet presents problems that you
must solve by using the range equation.
Aircraft Range
An airplane can cruise at a
constant speed and level flight in which the lift is equal to the
weight, and the thrust is equal to the drag. Since there is no net
external force on the aircraft, the
aircraft maintains a constant airspeed, as described by Newton's
first law of motion. The distance that the
aircraft flies is then given by a simple rate equation:
d = V * t
where d is the distance, V is the velocity
and t is the time aloft. The maximum distance that the airplane
can fly is
called the range R:
R = V * t max
Maximum Time Aloft
Airplanes, unfortunately, cannot stay in the air forever. There is a
time limit, or maximum time t max, that an airplane can stay aloft.
The time limit is usually determined by the amount of fuel that
the aircraft can carry. When the
airplane runs out of fuel, the engine stops. Drag then slows the
airplane, decreasing the lift. Eventually the airplane comes back to
earth. We can determine maximum time available using the rate
equation. The general rate equation is "rate
times time equals amount". If we do a little algebra, we can rearrange the
equation to solve for the time:
time = amount / rate
The max time for an aircraft equals the amount of fuel that we
have divided by the rate that the fuel is being burned. The amount of fuel
is called the fuel load and is denoted by M (given in
units of kilograms or pounds mass). The rate at which the fuel is
being burned is the
fuel mass flow rate
(given in kilograms
per hour or pounds mass per hour and denoted by mf).
The maximum flight time (t max) is then equal to the fuel load divided
by the fuel mass flow rate
t max = M / mf
The fuel mass flow rate depends on the
type of engine
used and the throttle setting chosen by the pilot.
The fuel mass flow rate is related to the thrust F by a factor called
the specific fuel consumption (TSFC). The
specific fuel consumption equals the fuel mass flow rate divided by the thrust.
TSFC = mf / F
Using algebra, we can determine the fuel mass flow rate:
mf = TSFC * F
Collecting all
this information, we arrive at a final equation for the maximum
flight time:
The maximum time aloft is equal to the fuel
load divided by the specific fuel consumption times the
thrust
t max = M / (TSFC * F)
A summary of information needed to determine the
range is given on a separate page.
Aircraft Design
What does this tell us? Obviously, if we carry more
fuel we can fly longer in time and farther in distance than if we
carried less fuel. If our engine has a low specific fuel consumption
we can also fly longer. Turboprop and
turbofan engines have low specific fuel
consumption and are used on long range airliners. If we can run the
engine at a low throttle setting, producing a minimum amount of
thrust we can also fly longer. But we must produce enough thrust to
equal drag in a cruise condition. Aircraft with a low drag, or a high
L/D ratio, require less thrust and can fly
longer and farther than aircraft with a low L/D ratio.
Aerodynamicists try to design aircraft with high L/D ratios and
engines with low specific fuel consumption.
NOTE: On this page, we have taken a very simple view of
aircraft range  for academic purposes. In reality, calculating the
range is a complex problem because of the number of variables. An
aircraft's flight is not conducted at a single ground speed but
varies from zero at takeoff, to cruise conditions, and back to zero
at landing. Extra fuel is expended in climbing to altitude and in
maneuvering the aircraft. The weight constantly changes as fuel is
burned; so the lift, drag, and thrust (fuel consumption
rate) also continually change. On real aircraft, just
like with your automobile, there is usually a fuel reserve. The pilot
makes sure to land the plane with fuel still on board.
Activities:
Guided Tours

Cruising Aircraft:

RangeGames:
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