# What Makes Airplanes Fly? History, Science and Applications ofAerodynamics

## CONTENTS OF CURRICULUM UNIT 90.07.10

- Narrative
- I. Introduction
- II. Rationale and General Objectives of the Unit
- III. Historical Overview of the Development of Aircraft4
- IV. The Mathematical Application
- II. An Introduction to Graph Theory
- Sample Lesson Plan 1
- Sample Lesson plan 2
- Sample Lesson Plan 3
- Sample Lesson Plan 4
- Sample Problems For Class Discussion
- Bibliography

### Unit Guide

## Historical Developments of the Aircraft Industry with Mathematical Applications

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## Sample Problems For Class Discussion

- 1. Write down the vectors that represent the following journeys.
- ____ a) from A to B b) from C to D c) from E to F d) from G to H.

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- 2. The following shows a Map of an island.

*(figure available in print form)*

- ____ a) Write the stages of the journey using vectors.
- ____ b) How many stages are there?
- ____ c) Add up the vectors of the journey.
- ____ d) Show the journey from Port Charles to Jacob’s point via the lighthouse.
- e) Give your partner some vectors and have him (her) give your destination.

### Extension Activities : Using bearings and Scale Drawing

- 1. A pilot wants to fly from city C to a city B, a distance of 1200 miles. The city B is on a bearing of 082° from C. Due to a pending storm, the pilot makes a detour and refuels at city A. The distance of A from C is 700 miles and the bearing is 175°. Find the distance of A to B, and the bearing the pilot has to take.
- 2. (500 miles, 090o) is a journey taken by an aircraft. Find the single journey represented by (500, 090°) followed by (375, 250°).
- 3. A pilot is to make a “round trip “ from New York calling at three airports (Dulles, Washington International;Atlanta, Georgia; and Cleveland, Ohio.)
- ____ a) plot the path of the aircraft. (use an atlas to get the bearing).
- ____ b) what bearing must the pilot take to return straight to New York from Cleveland?
- 4. Use any three cities of your choice (select some foreign cities).
- ____ a) Draw a graph of the path between them.
- ____ b) Give the bearing the pilot will take for the return trip.

### Latitude and Longitude

- 1. Draw a large sketch of the earth, marking in the center, the North and South poles, the equator, and Greenwich meridian.
- 2. On a sketch of the earth draw in the following.
- ____ a) the 50° N circle of latitude.
- ____ b) the 30° W longitude line.
- ____ c) the 60° E longitude line.
- ____ d) the point A with latitude 40° N and Longitude 30° W.
- ____ e) the point with latitude 20° S longitude 10° E.
- 3. Use a Map to locate various cities and write their latitude and longitude as a vector (latitude, longitude.)