Force for Takeoff
Problem or "Will the airplane get off the ground?"
If
so instructed by your teacher, print out a worksheet page for these problems.
Materials needed:
 Computer with access
to the World Wide Web and FoilSim.
 Graphing calculator
such as TI83 or TI92.
The situation:
Given a Boeing 737 carrying
150 passengers:
Use a weight of 140000
pounds for the Boeing 737. This weight allows for the inclusion of the internal
components of the airplane (engine, fuel tanks, landing gear, etc.), the
total weight of the passengers, and the total weight of their luggage and
cargo.
Access FoilSim and set
the following conditions:
Airspeed: 50 mph
Altitude:
0
Angle: 5
Thickness:
12.5%
Camber: 5.0%
Area: 1000 sq ft.

Creating the data
set:
Input various values
for the airspeed of the airplane. Each time an airspeed is entered, FoilSim
will calculate the lift. Generate a set of airspeed and lift values. Record
these values on the table on the Forces
for Takeoff Worksheet or make a printout of them.
When the set of values
is complete, enter these values into the calculator using the stats or data
mode.
Using the data set:
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 appropriateness
of the fit;
 the variation relationship
between airspeed and one of the components that determines lift;
 the appropriateness
and the ease of predicting when the airplane will be able to take off
based on the plot and graph.
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 this. State (in writing) the method used to create this set
of values.
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.
 The comparison or
contrast between the plot and the "airspeed vs. lift" plot.
 The appropriateness
and the ease of predicting when the airplane will be able to take off
based on the plot.
 The appropriateness
or need for creating a "best fit" equation and graph for the "airspeed
vs. net force" plot.
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?
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.
Step 6.
Summarize the information
provided by the "airspeed vs. lift" and the "airspeed vs. net force" plots
or graphs. Include the following:
 Which plot is more
easily used to picture when the airplane will leave the ground?
 Which plot provides
a better understanding of the other plot?
 Give the information
provided by the equation that may not be provided by the scatter plot.
 Which type of variation
does each situation model?
 What can you observe
about the coefficients of the equations?
 Print out copies
of tables, plots, and graphs to support your summary.
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.
