## Math Problem Statement

6.22 The coefficient of performance of wind turbines is often expressed by the empirical formula

Cp = 20((1/TSR+B)-(0.02/1+B^3) - 0.1B + 0.002B^3 - 0.003)*e^(15(1/TSR+B)-(0.02/1+B^3)) a. Plot the coefficient of performance with respect to the TSR for angle of attack equal to 0°, 10°, 20°, and 30°.

b. Find the maximum Cp and the TSRideal for a pitch angle equal to 30°.

## Solution

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## Math Problem Analysis

### Mathematical Concepts

Calculus

Algebra

Exponentials

Optimization

### Formulas

Cp = 20((1/TSR+B)-(0.02/1+B^3) - 0.1B + 0.002B^3 - 0.003) * e^(15(1/TSR+B)-(0.02/1+B^3))

### Theorems

Maximum/minimum theorem

Exponentiation rules

### Suitable Grade Level

Undergraduate Engineering/Physics

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