
Wing Shapes and
Areas


Subject Area(s):

Algebra I/Geometry

Grade
Level:

810



National Mathematics
Standards:
National Technology Standards:

Mathematics as Problem Solving:
 Students will be able to apply integrated
mathematical problemsolving strategies to solve problems
from within and outside mathematics.
 Students will be able to use, with increasing
confidence, problemsolving approaches to investigate and
understand mathematical content.
Mathematics as Communication:
Students will be able to express mathematical
ideas orally and in writing.
Mathematical Connections:
Students will be able to recognize equivalent
representations of the same concept.
Algebra:
Students will be able to use tables and graphs
as tools to interpret expressions, equations, and
inequalities.
Geometry from a Synthetic Perspective:
Students will be able to represent problem
situations with geometric models and apply properties of
figures.
Technology research tools:
Use contentspecific tools, software and
simulations (e.g., environmental probes, graphing
calculators, exploratory environments, Web tools) to
support learning and research; select and use appropriate
tools and technology resources to accomplish a variety of
tasks and solve problems.
ProblemSolving and DecisionMaking Tools:
Routinely and efficiently use online information
resources to meet needs for collaboration, research,
publications, communications, and productivity.

Objectives:

 After reading the explanation given below, use
FoilSim to determine the weight of the aircraft that can
be lifted by a pair of wings of each type.
 Design a unique planform of a wing to lift a plane
weighing 11500 pounds.

About FoilSim:
FoilSim is an interactive
simulation software package that examines the airflow around various shapes
of airfoils. As you change parameters such as airspeed, altitude, angle
of attack, thickness and curvature of the airfoil, and size of the wing
area, the software calculates the lift. The package was created at the NASA
Glenn Research Center.
FoilSim II is a Java applet program that executes inside the browser of your computer.
It is available on the World Wide Web at
http://www.grc.nasa.gov/WWW/K12/airplane/foil2.html.
You can also
download the program to run offline.
Shown below is a screen
shot from the program's controls and displays. You may change the values
of the variables by using the slider or the input box on the left of the
slider.
To use the slider:
 Click the mouse
pointer on the arrows at the ends of the slider.
 Click the mouse
pointer anywhere between the slider and the arrow.
 Drag the slider
with the mouse.
To use the input
box:
Simply select the
value in the input box, key in the new value, and press Enter or Tab when
finished. The button on the slider will move corresponding to the value
typed in the box.
To begin working on the problems, click on Wing
Area Investigations.
Assessment:

You, or you and your partner(s), will be evaluated on the
accuracy or feasibility of your answers and creativity in
design.

Evaluation:

You will demonstrate the ability to use information found
on the World Wide Web and in FoilSim to complete
calculations involving area and lift and to design a unique
wing planform.

Submitted by:

Paula L. Phillips, North Olmsted High School, North
Olmsted, Ohio

