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Archive for August, 2009

If you have not been following the story of Corey and his bow, you’ll want to go to Corey’s page and catch up.

Part 5: Lunch with Gaspard

“Let’s have some lunch,” Gaspard proposed. “I have my lunch basket here by the tree, and we can talk. Perhaps you have some questions, and then we will retrieve your arrow.”

Lunch was wonderful – French bread with real butter and some kind of cool drink that tasted suspiciously like a light wine. Corey ate in silence, reflecting on his morning adventure.

Of course when he shot from the north, he thought, he was not moving at all – except for turning. He frowned.

“When I shot from the North Hole,” he began, “I was not moving very fast, but I was turning. If the arrow keeps my motion, why didn’t it continue to turn left when I shot it? Then it would not have gone to the right.”

Gaspard smiled. “A wise question, and the answer is not obvious.” He stopped for a moment to empty his glass, and added, shaking his head, “Pas de tout!” (Which means “Not at all.”) Then he looked up and smiled.

“The fact is that things only keep their motions in one direction. Turning is not a direction; it’s a continual correction of a motion.”

He buttered his bread as he went on.  “For example, your turning, right now with my asteroid, is a motion straight east, continually corrected by gravity pulling you inwards so you don’t fly off into space. When you let go an arrow, it can only keep your eastwards motion, not your ongoing correction. It gets its own correction, of course, from its own gravity; otherwise it would fly off into space.” He looked up from his buttering and raised his bushy eyebrows a moment before continuing:

“Therefore, flying from the North Hole, the arrow carries no motion. But from anywhere else,” he hesitated and shrugged, “from anywhere else except the South Hole — there is an eastwards motion.”

Corey thought about this, closing his eyes and watching his arrows in flight. “That was a beautiful flight,” he murmured.

But then he had another question.

“So when I shot north,” he began, “why did the arrow curve around before it fell?”

Gaspard smiled. “I rather suspect,” (and he winked) “that if you had ridden on the back of the arrow, you would only have seen yourself flying eastwards. A satellite flying around your earth seems to me, from here, to be flying first east, then west, then east again. But it only flies right around, eh?”

“Yes, of course.” Corey munched thoughtfully. He sighed and took another drink.

“I have one more question then.”

“Yes?”

“I understand north and south turning right, but what if I shoot east and west? Will those arrows also turn right, as they do at home?”

“Let’s try it,” answered Gaspard, standing up and brushing off the crumbs.

Corey stood up too and picked up his bow. He fitted an arrow and then looked around.

“Which way is west?” he asked.

Gaspard pointed to the tower. “There’s north. West is at a right angle to north,” he replied.

Corey fitted an arrow, drew back his bow and let it fly. Once again, he watched a soaring arc – turning to the right. A distant “plink” told him that it had landed on the stones of the North Park Circle, distinctly to the northwest, and indeed to the right of his aim.

He shook his head. “What happened this time?” he asked. “If I shoot west, all the motions should be the same and the arrow should fly true.”

Gaspard nodded. “The arrow flies true enough. The problem lies with you.”

“With me?”

(To be continued)

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Cool-edge Cumulus

Cumulus clouds can form in any air where they can get off the ground. When they are well-separated in the sky and have full and calm forms, they really do mean that the weather will be fair for a while, and in addition, they tell low-flying pilots where the updrafts are. So that’s nice; it’s like having an updraft map right there in the sky.

Cool-edge Cumulus

Cotton-edged cumulus, formed in the wake of a cold front, have frozen vapors.

But once the vapor is up there, it can freeze, and then the edges are soft and cottony, instead of clean and sharp. One day, the whole sky was filled with fresh cumulus, all of them soft-edged on every side. A cold front had just come in, and, though it was still August, it was cold on the ground and much colder in the sky.

I put in the trees so you would know I wasn’t just out of focus.

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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.”

“Really?”

“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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Humdity on high

Convection trail in late August 2009

Condensation trail in late August 2009

 

Everyone sees vapor trails from time to time. Some are long and knotted; some are short, disappearing in less than half a minute; some are swept across the sky by upper winds and persist for hours and hours. I’ve always wondered whether the length of the contrail could be used as an indicator of humidity — at least humidity on high, which is related to what’s below, even if it’s not the same. Anyway, the ability of a condensation trail to hold its own must be related to how much other water is out there.

The way you’d measure the trail would be to hold out your arm and hold up your hand as we do for astronomy; then see how many fingers it takes to cover the trail — this is a way of measuring how many degrees of sky it covers. One finger is about 1 degree. Three is about five degrees. The fist is ten, the fist with the thumb outstretched is 15°, and the measure from thumbtip to little fingertip with the hand outstretched is 22°. Graph this against the humidity in the weather report and send me the results.


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I just finished reading Eric Sloane’s Look at the Sky and Tell the Weather, which is, as I mentioned, his favorite of his books. No wonder. It’s a perfect mix of all his gifts — storytelling, reminiscence, meteorology, and graceful illustration. It follows the journey of a single mass of cold air as it plows down from Canada, across the plains, and then up towards New England and away across the ocean. Various people see or experience it in 14 different locations, and Sloane tells their stories and shares their weather lore. The funniest story, which I’ve shared with everyone I’ve met the last week, is from some Canadian bush pilots — from the 40’s and 50’s, because the original book is 1961. Do they have stories to tell!

You know, when you’re in the wilderness and something goes wrong, you just have to fix it with what is there to work with. No ordering parts, and no time to wait for them even if you could order. Do or die. So these guys get themselves into a situation where the landing gear is broken and they have to fix it before they fly home. Nothing new about that, hacking a new propeller out of the local trees is everyday stuff to them. Only this time, no trees.

Hmmm… But they do have some caribou bones. So they fit up a few long thigh bones for their landing gear and get into Anchorage where the mechanics see them coming in, and one calls out, “Good God! Now I’ve seen everything. Here comes a flying pork chop.” 

A good read, all the way.

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Cirro stratus

It’s hard to be enthusiastic about photographing high sheets, even high sheets of angel hair.  They’re probably 5 miles up, maybe six, and they’re made of ice. It implies that warm, humid air is moving in.  

 

Cirro stratus with sundog

Cirro stratus with sundog

 

 

On the other hand, this is a perfect sky for certain types of light display. Mike got a sundog for me at 7:30 in the morning. I was on the way to Mass without my camera, and called him from the car. You can see the sun through the trees at exactly the same altitude as its protecting sundog. Sundogs mean there are ice crystals in the air, and sometimes you can hardly even see the clouds that make them. If you look closely, you can see that there is much more than a spot of light; there is a whole circumsun, a whole arc around the sun. 

Actually, as I write, it’s nearly noon, and there is still a halo around the sun. It’s about 15° out, and it’ll be there as long as the clouds are cirrus and let the sun come through a little. Hold up two hands to cover the sun and take a look.

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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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