Paul V. Cochrane
This is a “make and take” exercise for the class room. The students will make a helicopter and experiment with it, and make some observations. To begin with we will have to have some good quality paper (ditto), rulers scissors and #2 pencils for good dark lines.
Here is where we will do some work. Have the students copy the pattern from the blackboard onto their papers. I know that it would be better to have me make the copy and put it into the ditto but here I am going for some eye-hand coordination skills. Make two sets of “plans”, we will need them. This helicopter is a paper plane and to function it relies on a different set of laws (from the normal paper airplane).
(figure available in print form)
Test Flights
-
1. Drop the helicopter. Which way did it spin? What do you think caused it to spin? How would you reserve it spin? Have you seen anything in nature which spins like this? (Seeds from trees)
-
2. Cut off one half of a rotor (blade). Drop the helicopter. How does it behave. Cut the entire rotor off. What happens? If dropped up side down, what will happen? Try it.
-
3. Add weights to the helicopter and observe what happens (after dropping it). Try changing the lengths of the rotor, color the rotors for a patterned effect.
Some Sample Lesson Plans
One of the nice parts to a basic geometry course is that you have time to do a lot of constructions. The students have to follow directions, written and oral, and have a change to use their eye hand coordination skills. Here is a lesson which I have taken from
Whitewings
by Yasuaki Ninomiya, in which he shows how to determine the center of gravity on a non-rectangular wing plane (paper). The diagrams are Fig 15 and 16 on page 29 from the same book. Here are his instructions and they will make a wonderful lesson in my classes.
“Make a sketch of the wing in which Tt is the chord length at the wing tip and Tr is the chord length at the wing root. Extend line Tt the distance of the line Tr and extend line Tr the distance of the line Tt. Connect the two points (T&R) at the end with a dotted line. Find 1/2Tr and 1/2Tt and divide the wing with another dotted line. These two lines form point M. Draw a line parallel to the planes body through M. This line will be the Mean Aerodynamic Chord Length of the wing. The center of gravity should be placed at a point 25% or 50% of the MAC as seen in Fig 16.”
You will supply a suitable non-rectangular wing pattern, rulers, compass (for bisecting Tr and Tt). The students should understand that serious mathematics enters into any serious endeavor.
(figure available in print form)
(figure available in print form)
Another suggestion is this. Teach a quick lesson on buoyancy. Take some plasticine and a dish pan filled with water. Make a good sized ball of plasticine and place it into the water. It will sink. Now fashion this same ball of plasticine into the shape of a box and place back into the water and it will float. Finally take and put some weights in your plasticine “boat” and see how much the water will support. Students should be made to see that while a ball of plasticine is heavier than an equal amount of water we can get the water to support it if we reshape the ball there by increasing its total volume. It’s this that makes it (plasticine) and iron and cement float on water. We can work into this lesson idea of the volume of rectangular solids and hopefully on to the calculation of the volumes of spheres and a good study of hot air and hydrogen balloons. The students can really get involved in this part.
(figure available in print form)
There are all sorts of activities you can do, paper airplane contests in which longest flights, most acrobatic awards are given. If you have a few dollars you can take care of 2 to 3 classes. For $6.29 plus tax I picked up a discounted package of paper airplanes in a kit called
Paper Airplane Power
which contains 72 paper airplanes (6 different designs) on a pad. All are brightly colored and look like they would be fun to make and fly (outside). Along with this kit is an instruction booklet (32 pages). All of this is done by Louis Weber, C.E.O. Publications International, Ltd. Lincolnwood, Illinois (1989). I found it at the Price Club in North Haven. Its a nice gift for the students.
