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+ Contact Glenn         ## 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:

Name or description of equation
Equation

Dynamics Pressure (middle term of the total pressure equation)

P = r * V2 / 2

Force (Algebraic Form)

F = m * a

Force (with mass constant)

F = m * (V1 - V0) / (t1 - t0)

Velocity (if force and mass remain constant)

V = a * t + V0

Displacement (if force and mass remain constant)

X = (a * t2) / 2 + V0 * t + X0

Lift equation

L = Cl * r * V2 / 2 * A

Lift Coefficient

Cl = L / (r * V2/ 2 * A)
Velocity squared equation V2 = 2 * (Pt - Ps) / r

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

Related Pages:
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