Appendix B

Charts and Coordinates

Coordinates are used extensively in the Air and Space field to define performance, establish shapes or to specify the "state of a substance." The following examples of applications are given to help the reader understand what they are and how they are used.

A two-dimensional XY plot of flight duration
Lay out a horizontal line divided into increments of 50 units (0, 50, 100 ---) to 500. This is the number of propeller turns wound into a rubber motor.

From the left end of the horizontal line (the origin) draw a vertical line divided into equal increments of 5 units (0, 5, 10, 15 ---) to 120. This is the number of seconds of flight duration.

The horizontal line is called the X-axis. The vertical line is called the Y- axis.

A distance measured parallel to the X-axis to a point is called an X- coordinate or abscissa. A distance measured parallel to the Y-axis to the same point is called a Y-coordinate, or simply an ordinate.

Time a series of flights starting with 50 turns on the rubber motor and increasing the number by 50 for each subsequent flight. From each 50-turn increment on the X-axis, plot the flight time on the Y-axis. Enter each resulting point on the chart and connect the dots to establish a performance curve.

This first curve could represent two strands of rubber, and a second or more curves could be added to the chart for three, four or more strands. At some point the added turns on the rubber will cause it to break. Also, added strands will increase rubber weight, offsetting the gains made in flight time by the additional energy obtained from the added strands. The shape of the curves will show the relationship between the energy stored (number of turns) and flight duration. Is it a straight line indicating a same constant flight increase per turn, or will it gradually reach a peak and drop off when the rubber unwinds faster due to the quicker energy release experienced with the higher number of turns? How will changing the length of the rubber motor affect the curve? Plots such as these help to visualize the best settings or adjustments for your model.

There are practical limitations to the accuracy of results of such an experiment. When done out of doors, wind conditions may have an adverse affect. Updraft (thermal) conditions would produce faulty positive results. Best information would be obtained during morning calm, or flying indoors.

Coordinates are used extensively to define airfoils. Some Web site references were given to airfoil software in Chapter13. For an overview of the subject see the UIUC Airfoil Coordinates Database. Here you will find airfoil data and links to useful related sources.

A three-dimensional plot defining a solid object.
When using a drafting program on a computer, an operator can enter a series of X-and Y-coordinates to define the object in one view. Then in an adjacent view enter Y-and Z-coordinates which define the side view of the object. The Z-axis is a horizontal line at right angles to both the X- and Y-axis. The origin of the X-and Y-axes is also the origin of the Z-axis. The result of "connecting the dots" on a computer-aided drafting program is a complete definition of the solid object. Working with a computer this way has a tendency to make one feel as if you are seeing the development of the object from within the computer.

It's interesting to note that a whole airliner has been, and is done in this way and individual parts that happen to interfere with one another (occupy the same space) are highlighted and corrections are made.

Two three-dimensional plots of moving objects
The March, 2002 issue of Air and Space magazine describes the timing of a launch of the Space Shuttle in order to rendezvous with the International Space Station. The Space Station is orbiting at 17,000 miles per hour. The earth at the launch site rotates at 1,035 miles per hour. Rocket fuel constraints limit the launch window to between 2.5 minutes and 10 minutes for a rendezvous. Any longer and the shuttle will not have enough fuel to catch the station. It takes three teams of specialists to pull it off. Try that on your desk-top computer.

Return to Appendix A

Proceed to Appendix C

Copyright 2002, Robert S. Munson. All Rights Reserved