Archive for the ‘Coriolis’ Category

Southern Storm

Sorry for yesterday’s error. Of course a storm in the southern hemisphere is like a letter “p”; both 6 and 9 are left-turning spirals. But a storm in the southern hemisphere is a right spiral, a backwards 6, with the tail upwards towards the equator.

Here is a hurricane off the coast of Brazil. The image comes from an astronaut in 2004. A hurricane in this location is unprecedented, so it has no name. It’s just The Hurricane off the coast of Brazil. You can see the letter “p” on its side, or perhaps a lower case “e”. In any case, a left spiral.

Hurricane off Brazil

Hurricane off Brazil


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Corey’s Bow #10: Hurricane

Corey’s family had planned to go home through the Bahamas because Dad wanted to be in a warm place after Wellington in winter, and Mother wanted go right round the world, not back across the Pacific. Alas! As the day of departure drew near, it gradually became clear that there would be no trip through the Bahamas this year. A late-season storm was developing into a hurricane, and the Bahamas were off-route indefinitely; they would have to make new plans.

Corey looked at the pictures of the hurricane. They were beautiful in their way, heavy lines of cloud gracefully spiraling inwards, counter-clockwise.

Hurricane spiraling left

Hurricane spiraling left

Counterclockwise… To the left? “Hey, wait a minute,” Corey exclaimed. “Aren’t the Bahamas in the northern hemisphere? How come the winds are going left?” He brought the picture to his dad.

“Dad, why do the winds turn left when my arrows always turn right?” he asked.

Pete was building a model train with the Barkers’ wonderful set of cars and tracks, but he stood up for a minute and looked over Corey’s shoulder.

“They’re trying to,” he observed and then sat down again. Corey watched him for a second, frowning.

“Trying to what?” he asked.

“Go right,” answered Pete and then flipped the switch so the train gave a long, loud whistle. Corey covered his ears.

“How can winds try anything?” he shouted. Pete didn’t seem to be listening; he stood up to survey his train.

“How do you know what the winds are “trying” to do?” demanded Corey when it was quiet again.

“Look,” said Pete. He leaned over Corey’s picture an­d quickly drew two arrows on top of the storm image.

Pete's hurricane lines showing that the winds are trying to go right.

Pete's hurricane lines showing that the winds are trying to go right.

“Hey, don’t draw on it!” cried Corey, but Pete just shrugged; he was already back to his train.

Dad was quiet for a minute. “It is a left-turning spiral,” he began, “A counter-clockwise storm like all northern storms.” His finger traced the winds coming into the storm from each direction.

“But the wind is not an arrow,” he continued. “It’s just a word for moving air. Air is the arrow, and Pete is right. Each parcel of air seeks to go straight to the center of the storm, but it goes off to the right and then it keeps being corrected by the tug of the storm center.”

“Being corrected!” said Corey thoughtfully. “Being corrected is why it curves then. Gaspard says that a curve is a continuously corrected motion. So the air is like an arrow that always wants to go straight to the right, but a continuous correction pulls it to the left.”

“Yes,” agreed Dad. “As the wind comes closer to the center of the storm, always staying to the right, it goes faster and faster always to the right but it also receives a stronger and stronger correction to go left instead of straight. You notice the hole in the middle of the storm? It never does get there.” He winked at Pete, who had sneaked a look at him but now quickly turned away.

Corey was not quite satisfied.

“But why does the air go towards the storm anyway,” he had to know. “Why doesn’t it just stay where it is and leave the storm alone? I don’t get it. Nobody is shooting the air; the wind isn’t some kind of bowman, or blow-man or something…”

“Whoa! Whoa!” Dad shook his head and waited for Corey to settle down a little.

“In the center of the storm” he began, “there is a space of soft, thin air, called low-pressure air. If it were in a balloon, the balloon would deflate. Low pressure is like a valley in the field of the air, and, just as rivers run into a valley, air wants to run into the low pressure space. But it can’t get there because it keeps racing off to the right, past the storm. Then the valley pulls the air in again so the air changes direction; but it still heads straight off to the right and the valley has to pull it again. So to you, it seems to be spiraling left, but to itself, it’s just going straight and being pulled sideways all the time.” He drew more arrows.

Dad draws continually corrected right turns.

Dad draws continually corrected right turns.

Corey studied the pictures and the arrows for a while in silence.

“Then what if the storm begins at the equator,” he finally asked. There was a momentary silence.

“They don’t,” said Pete. (How did he know?)

“They don’t,” agreed Dad. “Very rarely, partly because the hottest latitude moves around a little between June and December, a strong storm can form in the South China Sea, but hurricanes and typhoons usually weaken anywhere near the equator. Our hurricanes never start there; and they don’t cross and go south.” He waited for Corey to catch up with this thought.

“And New Zealand’s rare hurricanes spin to the right,” he added. “Clockwise.”

Corey took a deep breath as he pondered this.

“Dad,” he said at last, with a sigh, “I didn’t know you knew so much.”

“I didn’t know Pete knew so much,” answered Dad. “Anyway, let’s go to France instead of the Bahamas. How about it, Marie?”

“I’d rather go to France than the Bahamas any day,” answered Mother. “Allons!”

(Which means, in French, “let’s go,” and that meant that she really wanted to be in France, not some steamy, stormy little island.)

(To be continued…)

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Coriolis animation

In case you don’t read comments faithfully, I want you to be sure to look at this animation found by my friend Sam, the Polish chef. Notice that it has movement from north to south in the northerh hemisphere, and from south to north in the southern hemisphere. Notice also that lovely ring of clouds over the equator. As I mentioned, they are always there, not terribly conspicuous if you don’t look for them, but perfectly definite when you do.

As always, animations only do the easy part of the Coriolis effect. What happens from south to north in the northern hemisphere is where people get confused; and what happens from north to south in the southern hemisphere is hopeless. But not for you because we talked about it in class, using a globe, and  explaining, to the surprise of many, that a man standing still on the equator is going 1000 miles an hour towards the east, and the arrow he shoots keeps that eastwards motion. So, unless he shoots along the line of the equator itself, his arrow lands many miles east of any target. At our latitude, I think we’re going eastwards at about 750 miles an hour; the arrow would land 250 miles east, assuming no friction…

All very unexpected. Named after a French engineer of the 19th century. You can research his life for your science project. I’ve never been able to find much; he was a good Catholic when that was not the way to get advancement.

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#9  Latitude Gardens

That night, Corey fell asleep wishing he could tell Gaspard what he had learned in New Zealand. He wondered if GGC-1835 had a southern hemisphere…

“Of course I have a southern hemisphere!” said Gaspard.

They were walking along with a bright patch of buttercups to their left, a most unusual planting in what Corey concluded must be the most unusual garden ever planted. It was only a few rows wide, but it stretched away to the horizon both north and south as far as he could see. It wasn’t all buttercups, of course. And it wasn’t all level, either, for soon they were walking up a steep hill towards a patch of merry forsythia in golden bloom. The forsythia was a massive bush, and more of the golden shrubbery was spaced 25 yards to the left and right, crosswise to the garden. Gaspard called it the Summer Circle, “Yes, yes of course! It goes all round the asteroid.”

Corey thought he must have seen one of these bushes from the top of the pine tree. Gaspard agreed: “it’s about 30 degrees north of the equator.”

Past the forsythia, they found anise, carrots, daisies, bush beans, and then they were looking down along some ferns and asters into a little valley with cattails and a willow at the bottom and several more herbs and flowers and some kind of fruit tree up on the farther hillside.

“Peaches,” said Gaspard, “and ripe enough, but too high to reach. I suppose you might drop me one – just knock the branch of course, so we don’t have peach soup.”

It was not hard to drop several. Corey missed the first shot, being uncertain of how much turning to expect, but in the slow motion of the flight, and in the disturbance of the leaves, he knew exactly where his arrow went – six inches to the right — and he was on target after that.

They crossed the valley and ate their peaches which had hardly bruised in the thick grass below the tree. Then Gaspard said he wanted to walk south and let Corey see how the arrows changed their flight curve with latitude.

It turned out that the plantings were Gaspard’s latitude garden, and each bed marked a change of 1º of latitude, “so I know where I am,” he said, “but the arrow’s flight doesn’t change the same amount with each latitude,” he added.

“I know,” answered Corey. “I figured it out once and then Pete had an equation. But I don’t know how much it changes.”

Gaspard smiled. “Pete,” was all he said, shaking his head.

They faced south and Corey shot his arrows one by one at the start of each planting: towards the beans, towards the daisies, towards the carrots and then the anise, even towards a spray of forsythia hanging outside the line of the garden.

By the time he ran out of arrows, they were retrieving them as they walked, and he could see how they were closer and closer to his visual mark. When a bright patch of sunflowers came in sight, Gaspard proposed one more shot and then a picnic at the equator, for indeed the sunflowers marked the center latitude on GGC-1835.

Corey agreed; he was hungry again, and he remembered Gaspard’s French bread and butter. They passed some white peonies, broad leaved comfrey, golden daylilies, deeply fringed parsley, and several other plantings before they reached the equator and sat in the shade of the sunflowers. The north equatorial section was taller with pale yellow flowers while the south equatorial planting was a crowd of shorter sunflowers with flaming red centers. A narrow path of white stones passed between them and beyond, apparently wrapping itself around the whole asteroid. Corey’s arrow to the equator was off his sights by less than half an inch.

He ate contentedly for a few minutes and then gave a quick little sigh of frustration. “Isn’t there anywhere that you just shoot where it looks right and the arrow goes there?”

“Hmmm,” said Gaspard. “Good question!” He was buttering his last crust very carefully and looking sideways at Corey, a twinkle in his eye.

“I mean, a kind of Isabela Island,” continued Corey. “It made me like to use my eyes! But here we are at the equator and I’m still off a little. Not very much, but…”

“Hmmm,” said Gaspard again, nodding his head with a slight frown betrayed by his twinking eyes.

Corey sat very still. Into his mind flew the image of Dad with the verse about turning left in the south…

Suddenly, he jumped up, grabbed his bow, and ran south along the latitude garden. As he ran, he noticed that the plantings were the almost the same as those in the northern gardens, only warmer and richer colors. He passed golden clover, fragrant cilantro, red Hibiscus, a borage bed full of bees, and more until he came to the red peonies.

When he reached these, he turned around to aim away to the north at a drooping white peony that hung to the side of its plot. Gaspard had moved well away from the garden and was smiling broadly.

“I wonder will my arrow turn left, then right?” wondered Corey. “No, that’s silly. The arrow goes straight but it might seem to be going left into the garden at first, and then right back out to my target. I wonder…” He aimed precisely where his eye told him, pulled his bow and let the arrow fly. It made a beautiful arc just slightly towards tallest sunflower, and then straightened itself back out to cut the white peony cleanly from its stem.

Gaspard went to pick up the arrow — and the peony — and turned to meet the young bowman as he came running up. Corey was so happy he was almost crying.

“I did it; I did it!” he called.

When he had caught his breath, he had to settle one question.

“So then the arrows went straight by the Wolf Volcano because I was shooting across the equator?” he asked eagerly.

“You may have been shooting across the equator,” said Gaspard. “Certainly Isabela Island sits at your equator, and Wolf Volcan is precisely upon it. But more importantly, your world is bigger than mine and your arrows move faster there. The sine anywhere near the equator is very small, and you could not have measured the curve whether you were precisely on the equator or just nearby.”

Corey gave a sigh of contentment.

“Hey,” he said shyly, rubbing his toe in the grass. “Do you have an apple tree?”

But Gaspard did not answer. When Corey looked up, he was in Wellington, and his arrows were beside him, smelling slightly of peaches. The sun was rising, and a large vase of red and white peonies stood on the windowsill. He did not remember seeing them before.

(To be continued…)

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Corey’s Bow #4 GGC-1835

(If you’re new to the blog, you’ll want to go to Corey’s Page and get up to speed with this story.)

Corey’s Bow #4: Meeting on GGC 1835

Corey slept fitfully. The next day, he went out and sat on the back of his wagon, deep in thought. He was not moving; his target was not moving – “unless you count the rotation of the earth as a movement,” he thought. But anyway, he and his bow and arrow were also moving right along with the earth, so that didn’t count.

He sighed, let his bow slip to the ground, and dropped his head into his hands.

“So there, laddie, what’s ailing you,” asked a kind voice. Corey looked up to see a large, rather angular but kindly face leaning over him, with a broad forehead surrounded by hair so thick it made him think of a bear, only it was very neatly combed. “I see you have a good bow here,” the visitor continued, “and I wonder if you’ve come to shoot in my park?”

Suddenly, Corey realized that he was not sitting in the wagon at all, but on a kind of wooden chair or ledge with an amazing, tall, wooden observation tower directly behind him. Meanwhile his feet were dangling comfortably over a low, mossy depression in the soil right before the tower. Startled, he glanced around and saw that he was indeed in some kind of park. The grass was emerald green and neatly mowed all around him, and the sun was climbing into the sky in a rather odd way off to his left. Where was he?

As if in answer to his thought, the park man said, “This is my asteroid, GGC 1835. I thought you would like it because it is so small, but still big enough for your bow. Would you like to shoot something?”

Corey stood up, looked off in the distance, and saw no targets but a low-growing shrub, some sort of pine with a cone at the top, dancing slightly in the wind. He shrugged and then looked at his bare feet. “I do like your asteroid, sir, but I don’t know if I can hit anything. Something is wrong, at least on Earth where I live, and when I shoot, it doesn’t go straight as it should. Except on Isabela Island.”


“Yes, really. I don’t know what to do.”

“Well, let’s see,” answered his new friend. “Why don’t you go ahead and shoot that pine cone; it’s large enough, and I should like to eat the seeds if they are ripe.”

Standing in the center of the depression, Corey shot. He missed, but the flight of the arrow was the loveliest sight he had ever seen. It seemed to be going in slow motion, as if the air were thick (but his breathing was easy) so he could watch the arc of its flight and even though it curved to the right, it flew so gracefully that his heart leapt, and he almost applauded. He looked up with awe.

“Of course you are Gaspard,” he said, smiling. “My name is Corey. I see that my arrow has gone to the right, and I think I see why: I am at the North Pole…”

“The North Hole,” Gaspard interjected.

“At the North Hole, then,” Corey continued, glancing down at the moss, “and since I am standing still and your asteroid is turning, my arrow missed completely.”

Gaspard smiled. “Very well then. You seem to understand your problem perfectly.”

“No I don’t,” said Corey. “Because in my world, I live at 42º latitude and that’s not at all the same as the North Pole. And anyway, my arrow always goes to the right — north, south, east, or west. If it were just about the turning of the earth, it would go right when I shoot south, but then left when I shoot north, while east and west should work perfectly.”

Gaspard looked thoughtful. Then, “let’s try it,” he suggested.

They walked south (there was no other direction to go) and passed an inconspicuous white path on the way. Gaspard called it the Park Circle and said it went all the way around the North Hole. As they walked, the sun quickly climbed the sky, and the tree seemed to climb the sky as well. It was a towering specimen, a little sequoia whose its height had been hidden over the curve of the asteroid. Corey picked up his arrow, many feet from the base of the tree, and then looked up where the rapidly climbing sun shone through its majestic branches.

“How long is your day?” he asked.

“Just two hours,” answered Gaspard. “Two of day, two of night, and 8 miles around the globe. If I walk fast enough, I can stay at noon even on the equator. I could never do that on Earth!”

Corey chuckled and fitted his bow. Carefully, he aimed towards the North Hole, or rather towards the observation tower just peeping over the horizon. The arrow arced gracefully north – no, northeast. It spiraled gently around and though he couldn’t see its actual fall, it seemed to draw in from the east before it disappeared near the tower. Corey’s mouth fell open as he lowered his bow and looked at Gaspard.

“You are moving,” Gaspard reminded him. “You are moving east and your bow and your arrow were moving east with you. Did you think that the arrow would forget the motions of its bow and just go north?”

Corey was speechless. So northbound flights turned right after all, just like southbound flights… He scratched his head.

(To be continued…)

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Corey returned from Isabela Island much encouraged. His eyes were indeed amazing; his bow was perfect; his arrows were straight; his aim was faultless. It took a few days to regain the habit of shooting to the left, but he was more cheerful about it, knowing there was nothing wrong. Of course he still wondered, got discouraged, and sometimes he didn’t even want to shoot his bow. One such morning, however, Pete called to him excitedly, “The Jumblies are here!”

The Jumblies. Wow! What a perfect day! The Jumblies, grandchildren of the couple across the street, always had good games, and there were five of them, Jack, Sarah, Scott, Kip, and Jenna, so they could really play great games. Corey and Pete raced through breakfast and ran outside. The Jumblies were pulling a wagon, throwing balls, calling and shrieking with delight. Their new game was called “Vector in the Ball.” Jenna was in the wagon with a ball, Kip was pulling, and Jack was standing by the sidewalk with another ball. There was a tree in the yard across from Jack. The game was that just as Kip pulled Jenna between Jack and the tree, she and Jack were both supposed to throw their balls at the tree. The hilarity was that Jenna simply could not hit the tree, and Scott and Sarah had to scramble for the balls to start over. Corey and Pete watched for a few minutes before Jenna saw them.

At once, she scrambled out of the wagon, calling them to take a turn. Pete got in first and Kip and Jenna pulled him. As they crossed in front of the tree, Jack and Pete threw their balls as hard as they could. Jack’s bounced off the tree; Pete’s went off to the side and never came close. Jenna squealed and clapped.

“Try again,” she called, jumping up and down. “Corey, you take Jack’s place.” So Pete rode the wagon back and threw his ball again. It went wide on the other side of the tree, while Corey’s ball bounced his a knobby section of bark and bounced sideways. After a few passes, Pete climbed out and Jenny made Corey take a turn in the wagon.

“You try it,” she giggled. Scott and Pete pulled. Jack returned to his post, and as he came by, Corey threw hard and fast. He almost got it, but not quite. They turned the wagon, and he tried again. This time, he thought he would throw the ball backwards a little, since it was falling somewhat past the tree, but he still missed, and now it was Jack’s turn in the wagon. Sarah and Scott both had to pull him because he was so big, but everyone was eager to watch.

“He’ll hit the tree anyway,” they said, “so we don’t need two runners to get the ball.” Sure enough, Jack knelt up straight as he neared the tree, and suddenly threw the ball distinctly backward; didn’t aim towards the tree at all. Sure enough, however, it hit square on. Corey watched him thoughtfully, but Pete disappeared. The game stopped for a minute when Mrs Jumbly came out to say hello.

When they were ready to start again, Pete turned up with his own wagon. He proposed that they use the street (it was a secluded dead-end) and pull two wagons and see if the riders could throw balls to each other. There was a lot of laughter and scrambling while they decided who would ride first. Then they were at it, fast and furious. The first round, both Sarah and Scott threw and their balls met in mid-air. The second round, Jack was pulling Jenna, and since he knew he would pull fast, he let Kip and Pete start first. Sarah called “throw” when the Jack was even with Pete, but neither ball reached the other wagon and then there was a scramble to return the balls to the wagoneers.

By the end of the morning, everyone but Jenna was aiming pretty well, and she made up for it by clapping the most. The rest knew, if the wagons were moving at the same speed, to throw as if they were not moving; they knew to throw the fast one back and the slow one forward if they were at different speeds. It felt all peculiar and exciting, and somehow Corey felt that it was about his bow, but he couldn’t figure it out.

“I’m not moving when I shoot,” he mused, “and neither are my targets. Just the same, it does feel like my bow problem, throwing where my eyes don’t agree. I wonder what it means…” He turned to Jack. “Where did you learn the game?” he asked, but Jack didn’t seem to hear.

It was Jenny who whispered, “Gaspard taught us; I like Gaspard,” and she gave a little skip.

“Shhh!” everyone said. “You’re not supposed to tell.”

“Can if I want,” she answered. “Anyway, Corey is my friend.” She looked up at him. “We have red hair,” she grinned. But she didn’t dare say any more that day, nor next day at the zoo, nor the next, and then the Jumblies were gone.

“Drat!” said Corey. “Something’s up, but I just don’t get it. “Vector in the Ball!” What sort of a name is that? The wagon motion was in them… that was clear enough. They went right on moving forward like the wagon the whole time they were being thrown. But I still don’t get how it’s got to do with my bow… And how come everyone knows Gaspard but me?”

Pete never said a word.

(To be continued…)

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Corey’s Bow (Part 2)

Corey got pretty good with his bow, slowly learning to adjust his aim — always to the left for distance, but perfectly true for close in. He frowned and sighed. He had really good eyesight, and he didn’t like having to correct his aim for no good reason. Then one day, he got exciting news.

“We’re going to Isabela Island,” said his mother. “Pack your bags!”

“Isabela Island!” exclaimed Corey. “Where in the world is that?”

“In South America,” said his brother Pete. (I forgot to tell you he had an amazing little brother; his brother didn’t have a bow, so I thought it wouldn’t matter at first.) “Isabela with one “l”, off the coast of Ecuador, which is on the equator. Equator, Ecuador. A Galapagos Island, too.”

“Wow,” said Corey. How did Pete know such things when he was only 8 years old? Then, what really mattered to him, “Can I bring my bow?”

Of course he could, and Corey and Pete and their mom and dad packed and went to Ecuador the next day and to Isabela Island the day after. They had many adventures, the most exciting being that Corey was allowed to shoot his bow right beside the Wolf Volcano. He was not allowed to shoot goats or pink land iguanas, of course. He had to set targets, which was slow because he was shooting so far. But how many kids get to take their bows to Galapagos? He had no complaints.

And there was an even bigger surprise waiting for him…

The first time he shot, Corey missed his target completely. As he lowered his bow and looked, his mouth fell open. His arrow had fallen distinctly to the left of the target where he had aimed out of his new habit. Quickly, and full of excitement, he fitted another arrow and shot straight where his eyes told him.

Bull’s eye! He could hardly believe it. He spent the whole afternoon with his bow and every shot after the first went precisely where his eye sent it. Pete watched and generously helped him get his arrows back. Corey could hardly contain his excitement. Every arrow perfectly true. “Do you suppose it’s got anything to do with being on the equator,” he wondered to his brother.

“Of course,” said Pete. “Gaspard told me.”

“Gaspard!” exclaimed Corey. “Do you know who he is?”

“Friend of mine,” said Pete, and he sat down beside a friendly pink land iguana with black stripes and wouldn’t say another word.

To be continued

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