Gliders

R. Shankar, The Institute of Mathematical Sciences, Chennai

Vikram, an elephant in Mudumalai sanctury, was giving a ride to his friend Lakshmi, a mahout's daughter. They were going along the path from the sanctuary office to the elephant camp when Lakshmi looked up and exclaimed, "There is a glider flying above us!"
"What kind of bird is that?" came the puzzled response.
"It is not a bird. It is a kind of aeroplane".
"There is no aeroplane flying above us. I cannot hear anything".
Elephants cannot turn their necks and look directly up. But they can hear very well so Vikram was quite confident.
"Oh! Actually it is not really a plane; it does not have an engine so it does not make any sound".
"Then how does it fly?".
Lakshmi thought a bit. Once when she had gone to a big city with her parents, they had passed a small aerodrome and that is where she had seen gliders. So she remembered what had happened and said, "They pull it up into the sky with a rope, like a kite and then they let it go. It then flies the way a bird flies without flapping its wings. That is what they call gliding."
"When I saw it, it came down very slowly and then started circling and rising. There were many big birds which were also circling and climbing along with it. ... Hey! See there it is circling and climbing!" 
The glider was now quite far away so that Vikram could see it without having to lift up his neck very much. "It looks just like a vulture but it is bigger", he remarked.
Both watched in silence for some time. "How do they turn it?" wondered Vikram. "For that matter how do they make it go down or up? Why does it not fall down like a stone?" Lakshmi did not have the answers, so she said, "I don't know. But my teacher once taught us how to make paper gliders. We could make one and see what happens".
They were back at the camp. Lakshmi went home and brought back a few sheets of paper from her old school note book. She folded the paper as shown in the picture.
First she folded it so that the top two corners met exactly at the center of the page. The top part was now like a triangle (2).
She then folded the paper at the base of the triangle so that it again was of a rectangular shape as in (3).
Again she folded both sides so that the top two corners met at the center of the page. But this time it was so that they met at the center a little above the tip of the old triangle as in (4).
The bottom tip was then folded as shown in (5).
Then, when it was folded as shown in (6), the little fold made a nice joint that held the two corners together and stopped it from opening out.
Finally she folded the two parts as shown in (7) to make the two wings.
When she now held it between her thumb and forefinger at the joint, the two wings unfolded and the sheet of paper had become a glider!
She then threw it in a slightly upward direction. It flew! It went up for a few meters, turned down and went gracefully through the air, turned to the left a bit and landed gently about ten meters from the point where she was.
"Wow! That was nice!", Vikram walked up to the glider, picked it up gently with his trunk and threw it the way Lakshmi did. Vikram was of course much taller than Lakshmi and he also threw it harder. It then really flew! It went up for a long distance and then curled around to the left when a gust of wind caught it and took it up again, finally it landed far away from both of them. They walked down to get it. Vikram picked up, held it high and just dropped it. It did not fly. It just dropped down going in one direction and another and finally hit the ground with its nose.
"You have to throw it! You can't just drop it and expect it to fly," scolded Lakshmi as she picked it up and smoothened out the crumples caused by the crash. "Why?" came the reply, "Why does it fly well only when we throw it?" Lakshmi did not have a ready answer. So she also tried it a few times. She dropped it. She threw it gently. She threw it hard. Each time they carefully observed how it flew.
"I think it needs the wind flowing along its wings," said Vikram. "Faster the wind is, the better it flies".
"Yes", said Lakshmi, "The wind along its wings must be somehow pushing it up so that it comes down slowly. Sometimes it must be pushing so hard that it goes up instead of falling down".
Vikram thought about it for a while. "Yes, I think you are right. So maybe the wind can also be made to push and pull it in a way that it turns. How can we do this for our glider?"
They both thought for some time. Then Lakshmi picked up the glider and folded the corners of the wings so that the paper pointed up at the tip. She threw it and it went up much more than before.
"Yesss!" said Vikram. "That is it! The wind is hitting the upturned corners and pushing it down. So the back of the glider is being pushed down and the front nose is going up: that is why it is going up more than before".
He picked it up and threw it again. It happened again."Now let me turn the tips down," said Lakshmi, and did exactly that. Vikram put up his trunk and threw it from a great height. Almost as soon as the glider left his trunk it turned down like a diver and crashed into the ground.
Now that they had discovered how to steer the glider, Vikram and Lakshmi played with it for hours every holiday. They turned the left tip up and the right tip down. It turned to the right. They turned the right tip up and the left tip down and it turned towards the left. They made another glider with the same sized paper but folded it so that it had larger wings. They found it was slower but stayed up for a long time.
They tried different foldings and made different wing shapes. Some gliders were fast and nifty. The others were slow and stable. Slowly they became better at folding and throwing so that they could make their gliders do all types of tricks. They really enjoyed themselves for weeks after they found out how to control the flight of their glider.