Note: In previous lessons we’ve presented 3 of the classic
“4 forces of flight”, drag, lift and thrust. We
will now move on to weight.
Weight is the
last of the classic “four forces of flight” to
be discussed. In the last lesson we discussed the meaning
of vectors. If the vectors of the four forces balance we will
have non-accelerated flight, that is, no changes in airspeed
and no changes in climb (or descent) rate.
In the last lesson
we discussed the balance of thrust vs. drag. In this lesson
we will discuss the balance of lift vs. perceived weight.
“Perceived” weight includes the concept of weight,
which we are accustomed to, plus the affects of other accelerations.
1 - Classic Four Forces of Flight
Weight = mass x
acceleration. Our normal notion of weight is noted as we exist
on earth. You may not think of yourself as accelerating but
you would be accelerating if the solid earth didn’t
stop you. The gravitational pull of the earth produces an
acceleration of 32 feet per second, each second. If earth
had no atmosphere to produce drag and you jumped from an aircraft,
after one second you would have accelerated to 32 feet per
second. After two seconds you would have accelerated to 64
feet per second. After three seconds you would be traveling
at 96 feet per second …. And so on.
While you are floating
down to earth, you would not feel any force. You’d feel
weightless. When you are on the ground, you feel the force
pulling you toward earth’s center at 32 feet per second,
weight, caused by the gravitation of earth, acts toward the
center of earth. Lift acts perpendicular (at a 90 degree angle)
to an aircraft’s relative wind. As discussed in lesson
3, relative wind is approximately opposite to the flight path.
If we are in a climb or descent, the lift vector will not
point opposite to the weight vector. Figure 2 shows the vectors
in a descent.
2 - Four Forces of Flight in a Descent
Note the “component
of weight aiding thrust”. Since the weight vector is
tilted forward (relative to the aircraft) we can compute the
amount of thrust aid by drawing a line from the dashed lift
axis to the point representing the force of weight. Add this
“component of weight aiding thrust” to the thrust
vector and you would notice that its length equals the length
of the drag vector. This balance of forces assumes that you
are not accelerating. The thrust line was reduced (the pilot
reduced power) during the descent to prevent acceleration.
If you are in a car and travel from level ground to a downhill
portion of the road, you would accelerate forward unless you
side note to this discussion pertains to gliders. You can
see why you don’t need power to go downhill. You can
also see how a glider pilot can control his airspeed and descent
rate by controlling the up and down pitch of his aircraft.
A similar, opposite
analysis, applies to an aircraft in a climb. Figure 3 shows
an aircraft in a climb. The “component of weight opposing
thrust” plus drag must equal thrust in order to produce
3 - Classic Four Forces of Flight in a Climb
This is a good
place to discuss weight’s affect on both, an aircraft’s
ability to climb and on its top speed. Thrust in excess of
that need to oppose drag is necessary to produce a climb.
For analytical purposes lets call this thrust “excess
thrust”. In light aircraft of moderate performance,
thrust is much more limited than in an average car. Add to
this limitation, the fact that unlike a car, if your aircraft
is going too slow as well as too fast, drag increases rapidly.
Review the power curves/drag curves diagram that was introduced
in the last lesson.
4 (from last lesson)
Power curves/Drag curves
At any airspeed
you can measure the amount of “excess thrust”
available for climb by noting the vertical distance between
thrust and total drag. An increase in weight has the same
effect on climb performance as lowering the thrust curve.
At some point of weight increase, the aircraft would have
no excess thrust to produce a climb. This factor of reduced
margin of thrust is exaggerated at high altitudes where engines
produce less power. In the western United States (at high
airport elevations), many aircraft accidents are caused each
year, by an overloaded aircraft. The “excess thrust”
needed to support a climb is not available. In a car, excess
weight causes slower acceleration and a reduced climb ability,
however, since you have to oppose only parasitic drag, you
can affect a climb up a road at a slower speed.
While a heavy car
would accelerate slower, top speed would be affected very
little. Aircraft top speed is affected more that a car but
not by much. A heavier aircraft must fly at a higher angle
of attack to produce more lift. The higher angle of attack
causes more induced drag and usually more parasitic drag.
Luckily, since the lifting ability of a wing increases by
damaging affect of weight on speed is moderated by high cruise
speeds. Aircraft manuals often show airspeed reductions of
only 1 to 3 percent when comparing light loads vs. maximum
gross weight. In contrast, aircraft manuals often show a 30
to 50 percent reduction in climb rate when comparing light
loads vs. maximum gross weight.
A big factor on
aircraft performance is caused by an increase in the weight
vector in turns, as well as sudden (accelerated) entries into
climbs. Another acceleration is added to earths acceleration.
In a turn, force is required to pull an airplane to the center
of a circle. This pull [term - centripetal force] increases
with bank angle. An increase in the percieved weight vectors
require an increase in the offsetting lift vector.
A steeper bank
angle is needed to support a faster turn. A classic analogy
used to illustrate centripetal force is a person swinging
a pail. The faster you swing it, the steeper the angle to
the ground as well as the bigger the force felt by your arm.
5 - Lift Force in a Turn.
flight, a 60 degree bank produces a 2G (2 X gravity) acceleration.
The perceived weight of the aircraft is twice its normal weight.
As you can imagine, climb performance suffers in steep turns.
concludes the six part discussion of Simple Aerodynamics.
We hope that we touched on knowledge areas which will expand
you interest in the physics of flight. You will find good
discussion of flight physics in the many texts published for
private pilot training.
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