Force for Takeoff or "Will the airplane get off the ground?" Answers

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 Note: Observations are made using a first quadrant window with the following settings:

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:

1. 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.
   
2. the appropriateness of the fit; If the correct regression is chosen, the fit of the graph is appropriate with an R² correlation of 1.
   
3. 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.
   
4. 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 this---state (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:

1. The "meaning" of the plot. This plot compares the netforce required to lift the plane off the ground with the airspeed of the plane.
   
2. The comparison or contrast between the plot and the "airspeed vs. lift" plot. This plot is different in looks because the x-intercept occurs much farther to the right of the first plot.
   
3. 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.)
   
4. 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 x-value of the intersection should approximate the x-intercept 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:

1. Which type of variation does each situation model? Reiterate the main points of the problem.
2. What can you observe about the coefficients of the equations? Provide a written guideline for a lab report.
3. 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.