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Beginner's
Guide to Aerodynamics
Dimensional Analysis Activity
Subject
Area: Physics
Grade Level: 11
- 12
National Science
Standard:
- Explore change,
constancy, and measurement with respect to derived and fundamental units.
National Technology
Standards:
- Research
Tools - Use content-specific tools, software and simulations (e.g.,
environmental probes, graphing calculators, exploratory environments,
Web tools) to support learning and research.
- Problem-Solving
and Decision-Making Tools - Routinely and efficiently use on-line
information resources to meet needs for collaboration, research, publications,
communications, and productivity.
Objective:
After
studying various pages of a NASA Web-based textbook, you will use dimensional
analysis to verify actual aeronautic equations.
Beginner's Guide
to Aerodynamics is a "textbook" of information prepared at NASA Glenn
Research Center to help you better understand how airplanes work. Click
Beginner's Guide Index to access
the list of slides available at Beginner's Guide to Aerodynamics. Open
the slides called Bernoulli's Equation,
Newton's Second Law, Simple
Aircraft Motion, The Lift Equation,
The Lift Coefficient, and Pitot
Tube to retrieve and verify actual aeronautic equations with dimensional
analysis.
Equations used:
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Name
or description of equation
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Equation
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Dynamics
Pressure (middle term of the total pressure equation)
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P = r *
V2 / 2
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Force (Algebraic
Form)
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F = m *
a
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Force (with
mass constant)
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F = m *
(V1 - V0) / (t1 - t0)
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Velocity
(if force and mass remain constant)
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V = a *
t + V0
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Displacement
(if force and mass remain constant)
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X = (a *
t2) / 2 + V0 * t + X0
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Lift equation
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L = Cl *
r * V2 / 2 * A
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Lift Coefficient
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Cl = L /
(r * V2/ 2 * A)
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| Velocity
squared equation |
V2
= 2 * (Pt - Ps) / r |
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Then using the
information shown at Dimensional
Analysis Activity, complete the problems designed
to demonstrate your ability to perform binary mathematical operations.
Assessment:
You will
be evaluated on the accuracy or feasibility of your answers.
Evaluation:
You will
demonstrate the ability to change derived units into fundamental units
and perform binary mathematical operations on the units.
Submitted by:
Michael
Burich, Shaw High School, East Cleveland, Ohio
E-mail: burich@juno.com
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