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LEARNING ACTIVITY WORKSHEET - Week Two

Please review the full assignment prompt and the Week 5 Final Paper instructions located within the classroom and in the POL 201 Course Guide before beginning this assignment.

Utilizing the worksheet below, develop detailed paragraphs that focus on the first main point for your final paper. For each section, a minimum of one fully-developed paragraph is required. A fully developed paragraph should be a minimum of 5-7 sentences in length. Each paragraph should include at least one in-text APA citation that provides support for the topic.

At least two scholarly sources from the Ashford University library (not including your textbook) with in-text citations utilized within your paragraphs are required. Two new sources should be utilized each week to meet the minimum of eight required sources for the final paper. By finding and supporting your material with these sources each week, you will have the research necessary to construct a strong final paper. For help with writing and citations, please review the handouts and tutorials provided by the Ashford Writing Center.

1. Federalism:

A. One advantage to a national policy that must be implemented by one agency of the federal bureaucracy.

(Use the space below to complete this section.)

B. One disadvantage to a national policy that must be implemented by one agency of the federal bureaucracy.

(Use the space below to complete this section.)

C. One option to maintain the advantage of the national policy discussed above.

(Use the space below to complete this section.)

D. One option to improve the disadvantage of the national policy discussed above.

(Use the space below to complete this section.)

2. Reference List (utilizing full APA citations)

(Use the space below to complete this section.)

NEF1201 Engineering Mathematics 2, Semester 2, 2016

PBL Exercise 2: Aerofoils

An aerofoil or airfoil is the shape of the cross-section of an aeroplane wing, or any other structure used to increase lift, like helicopter rotors, or propellers, or turbine blades. Spoilers on cars, designed to decrease lift, are also in the shape of aerofoils.

Figure 1 shows a design for an aeroplane wing, and the cross-section of a spoiler from a high-performance sports car. Notice that the spoiler is the shape of an upside down wing.

Figure 1: Two aerofoils

In order to model air-flow over and around wings and spoilers, we need a mathe- matical way of describing the aerofoil shape. One way is to start with a circle C in the complex plane which passes through the point z = 1 and for which the point z = −1 is in its interior.

For each point z ∈ C apply the mapping

w = z + 1

z .

As you move around the circle, the collection of all the points w will form the shape of an aerofoil. This is illustrated in figure 2 overleaf. The black dots show some points on the circle, and the open dots show their positions as mapped onto the aerofoil.

1. The picture shown was generated using a circle with centre at (−0.11, 0.43). Using your calculator, or any other computational device, verify the computation: map enough points on the circle in order to be able to sketch an aerofoil shape.

2. Experiment with circles with other centres. Which centre, in your (group’s) opin- ion, gives the most realistic “wing-like” shape?

As a reference for aerofoils, check out the database at http://m-selig.ae.illinois.edu/ads/coord\_database.html

which lists many hundreds of them. Have a look especially at the ones labelled “high lift”.

1

x

yj

1−1

Figure 2: Mapping a circle to an aerofoil

2

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