
Force
for Takeoff or "Will the airplane get off the ground?"
Answers
Note:
Observations are made using a first quadrant window with the following
settings:
xmin
= 0

ymin
= 0

xmax
= 300

ymax
= 200000

xscl
= 50

yscl
= 20000

Step 1.
Create a scatter plot
comparing airspeed and lift. Consider the look of the plot and determine
a regression equation that seems to best fit. State an opinion as to:
 the "meaning" of
the graph; The plot compares the airspeed
of the plane to the lift that is generated by this airfoil operating
under the given settings for angle, thickness, camber, and area.
 the appropriateness
of the fit; If the correct regression is
chosen, the fit of the graph is appropriate with an R^{2} correlation
of 1.
 the variation relationship
between airspeed and one of the components that determines lift; The
variation relationship is a direct variation relationship of a quadratic
nature, i.e., the lift varies directly with the airspeed of the plane.
The regression equation supports this.
 the appropriateness
and the ease of predicting when the airplane will be able to take off
based on the plot and graph. This is a question
for discussion. The plot and the graph show the relationship between
the airspeed and the lift, but may not necessarily allow the reader
to determine when the lift is great enough to allow the plane to achieve
actual liftoff from the ground. The same is true of the table. Unless
the reader realizes how much lift is required, a misinterpretation of
this table, plot, and graph may occur.
Step 2.
The amount
of force it will take to lift the Boeing 737 off the ground can be calculated
using Net Force = Lift  Weight. Create the third column of the
calculator "spreadsheet" by calculating the respective net force values.
There is an easy way to do thisstate (in writing) the method used to
create this set of values. The easiest way
to create the column of netforce values is to create the equation for
that column, i.e., c3 = c2  140000 where c3 is the force, c2 is the lift,
and 140000 is the weight of the plane. The calculator will then figure
out each respective force using each previously calculated lift.
Step 3.
Turn off the "airspeed vs. lift" plot and graph. Then create a
scatter plot comparing airspeed and net force. Consider the "airspeed
vs. net force" plot. State an opinion on:
 The "meaning" of
the plot. This plot compares the netforce
required to lift the plane off the ground with the airspeed of the plane.
 The comparison
or contrast between the plot and the "airspeed vs. lift" plot. This
plot is different in looks because the xintercept occurs much farther
to the right of the first plot.
 The appropriateness
and the ease of predicting when the airplane will be able to take off
based on the plot. This plot gives a better
visual of when the plane will be able to lift off the ground by helping
the reader to see that liftoff can occur only when the lift is greater
than the weight of the plane. Looking back at the table of values reinforces
this idea. The airspeed affects the lift, and the lift in turn affects
when there will be enough netforce to allow the plane to achieve actual
departure from the ground itself. (Note: Depending upon the calculator
mode, the reader may see initial force values written in scientific
notation or may see " . . . ." instead indicating forces with a negligible
impact on the ability of the plane to achieve liftoff.)
 The appropriateness
or need for creating a "best fit" equation and graph for the "airspeed
vs. net force" plot. Once again, the "best
fit" will be a direct variation of a quadratic form. The graph supports
the plot. The plot shows the approximate speed at which the plane will
obtain enough lift. The equation and the graph can be used to determine
a more specific speed at which liftoff will occur.
Step 4.
Turn off
the "airspeed vs. net force" plot (and graph if created). Turn on the
"airspeed vs. lift" graph. Then enter an equation for the total weight
of the airplane and its passengers. Find the intersection of these two
graphs. What is the meaning of the intersection? When
the "airspeed vs. lift" and the weight of the plane are graphed, the intersection
shows the point at which there will be enough lift for a 140000 pound
plane to lift off.
Step 5.
Keep the
graph of "airspeed vs. lift" and the graph of the total weight turned
on. Turn on the plot or graph of the "airspeed vs. net force." Compare/contrast
these graphs. Compare the intersection of
the "airspeed vs. lift" and the weight of the plane to the plot or graph
of the "airspeed vs. netforce." The xvalue of the intersection should
approximate the xintercept of the "airspeed vs. netforce" graph.
Step 6.
Summarize the information
provided by the "airspeed vs. lift" and the "airspeed vs. net force" plots
or graphs. Include the following:
Answers
will vary. The summary is an additional question given that may be used
to:
 Which type of variation
does each situation model? Reiterate the
main points of the problem.
 What can you observe
about the coefficients of the equations? Provide
a written guideline for a lab report.
 Print out copies
of tables, plots, and graphs to support your summary. Provide
a written guideline for an alternative assessment based on a holistic
scale.
Step 7.
Use the World Wide
Web to access the Forces on an Airplane
slide. Compare and contrast the lift and the net force needed to allow
an aircraft to leave the ground. Describe the factors that affect lift.
From
the home page:
 Force
may be thought of as a push or pull in a specific direction.
 Weight
is a force that is always directed towards the center of the earth.
 Thrust
is the force provided by the engines and moves an airplane through the
air.
 Drag
is the resistance force provided by the air as the airplane moves through
the air.
 Lift
is a "remaining" aerodynamic force at a right angle to drag and perpendicular
to the flight direction. Several components work together to produce
aircraft lift, most of which is generated by the wings of the plane.
 Netforce
is lift minus the weight of the plane.
