Wind Energy Education
2-Year Transfer Curriculum
Sample Course
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WE 1310
Analytical Methods in Wind Energy
3 Credit Hours
www.texaswindenergyinstitute.ttu.edu
© Texas Tech University 2011
WE 1310
Required Textbook:
No textbook is required other than the lecture notes.
Reference Books:
• Title: The Nature of Mathematical Modeling
Author: Neil Gershenfeld
Publisher: Cambridge University Press, 344 pp. 1998
• Title: Calculus
Authors: Strauss, Bradley and Smith
Publisher: Prentice Hall
© Texas Tech University 2011
WE 1310
Expected Learning Outcomes:
Upon completion of this course, the student will:
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Have a complete understanding of one-dimensional mathematical wind modeling
Know the properties of uni-dimensional mathematical wind models (especially for
the catalog of the main functions used in wind energy)
Be proficient in the calculation methodologies associated with the aforementioned
topics
Be able to solve contextual wind problems related to wind tendencies, wind cycles,
and wind forecasting
Be capable to solve simple wind model problems that include ordinary differential
equations with constant coefficients
Be familiar with the extensions of wind mathematical wind models to two and three
dimensions
Be familiar with the resolution of wind problems using transformations of
coordinates (Cartesian, polar, cylindrical, spherical)
© Texas Tech University 2011
WE 1310
Course Units:
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Unit I: Wind as a vector. The continuum hypothesis and its atmospheric case;
dimensional analysis
Unit II: One-dimensional continuum wind model
Unit III: Local properties of the one-dimensional continuum wind model
Unit IV: Practical Applications of Unit III
Unit V: Global properties of the one-dimensional continuum wind model
Unit VI: Practical Applications of Unit V
Unit VII: The two-dimensional continuum wind model
Unit VIII: The tri-dimensional continuum wind model
Unit IX: Practical Applications of Unit VII and VIII
© Texas Tech University 2011
WE 1310
Sample Topic: Mathematical Modeling for Wind Energy
• Mathematical models are abstract models that use Mathematics in order to describe the
behavior of distinct systems or phenomena. Those mathematical models are representations
of the essential attributes of existing systems (natural or constructed). Such representations
contain knowledge of the represented systems in utilizable forms.
• There exist different types of mathematical models, including but not limited to Analytical
Models, Numerical Models, Observational Models, and Statistical Models.
• Analytical Models are usually made with analytical functions (although not always).
They are of great value no only because of their inherent power, but also as the bases for the
introduction of numerical and statistical models. Analytical solutions allow the performing
of manipulations implied by the models at minimal cost. The prize one pays for such
power, however, is restricted applicability; and the real world is often too complex to get
described in simple ways.
© Texas Tech University 2011
The process itself simulates an infinite growing Helicoid: the applications generate new data
WE 1310
Sample Illustrative Slide:
Slide 1: Wind as a mathematical entity
Wind is air in motion
To characterize any mechanical motion one has to specify the following aspects:
-Initial and final points, and the actual trajectory;
-Motion direction;
-Motion rate
Important features of a vector:
Magnitude, Direction and Sense
(Most authors in English consider only two
features magnitude and direction – because
sense is included in direction)
© Texas Tech University 2011
WE 1310
Sample Assessment Questions:
1)
What is the distinction between mathematical and
physical modeling?
2)
Why are analytical models important?
3)
Enumerate and explain the main features of the wind
vector.
© Texas Tech University 2011