radius of curvature

Hello Detective (Chapter 17)

Part 1   Part 2   Part 3   Part 4   Part 5   Part 6   Part 7   Part 8   Part 9   Part 10   Part 11   Part 12   Part 13   Part 14   Part 15   Part 16   Part 17   Part 18   Part 19   Part 20   Part 21   Part 22   Part 23   Part 24   Part 25   Part 26  Part 27  Part 28  Part 29  Part 30  Part 31  Part 32  Part 33  Part 34   Part 35   Part 36   Part 37   Part 38  Part 39   Part 40     Part 41   Part 42   Part 43   Part 44   Part 45   Part 46   Part 47   Part 48   Part 49   Part 50  Part 51  Part 52  Part 53  Part 54  Part 55   Part 56  Part 57 Part 58 Part 59 Part 60

You all made it back to Sherlock’s flat where all the books were still stacked.

“They’ll be back in China by tomorrow.” John said as Sherlock took of his coat and scarf.

“No they won’t leave without what they came for. We need to find their hideout. A rendezvous. Somewhere in this message it must tell us.” Sherlock said, running his hand over the pictures on the wall.

“Well, I think perhaps I should leave you to it.” Sarah said awkwardly

“No, you don’t have to go. You can stay.” John said at the same time as Sherlock said, “Yes, it’d be better if you left now.”

“He’s kidding please stay if you’d like.” John said, covering up for Sherlock’s behavior.

“Is it just me or is anyone else starving?” Sarah asked nicely.

“Oh, God.” Sherlock groaned. You stepped on his foot forcefully to shut him up. “Ow.” He whispered while giving you a dirty look. You glared back.

John went to the kitchen to look for some food. You knew there was never anything in that fridge but body parts. Sherlock sat down at his desk and began looking through all the evidence again. You stood next to him and did the same. Sarah was roaming around the sitting room, inspecting everything.

“So this is what you do. You solve puzzles for a living.” Sarah asked.

“Consulting detective.” Sherlock corrected her rudely.

“Oh. And you too.” She asked me.

“No, I actually work for Scotland Yard.” You said smiling.

“What are these squiggles?” Sarah asked, now standing on the other side of Sherlock, pointing down to the pictures.

“They’re numbers. An ancient Chinese dialect.” Sherlock said, his patience wearing thin.

“Oh, right. Well, of course I should have known that.” Sarah said. Sarah picked up one of the papers and Sherlock looked as if he was going to blow a gasket. You squeezed his arm highly and shook your head. Silently telling him to behave.

“So these numbers, it’s a cipher?” Sarah asked.

“Exactly.” Sherlock said through gritted teeth.

“And each pair of numbers is a word?” She said again. The two of you looked at her, extremely surprised.

“How did you know that?” You asked.

“Well. two words have already been translated, here.” She said pointing to the picture that we had brought to Soo Lin and Dimmock must have brought back from the museum.

“Soo Lin must have started to translate the code for us. We didn’t see it. ‘Nine’ ‘mill’.” He read.

“Nine million quid. For what?” You asked.

“We need to know the end of this sentence. Ugh the museum, the restoration room. We must have been staring right at it.” He groaned as he slipped on his coat.

“At what?” John asked, emerging from the kitchen.

“The book John, the book. The key to cracking the cipher. Soo Lin used it to do this. Whilst we were running around the gallery, getting shot at. She started to translate the code. It must be on her desk.” Sherlock yelled as he ran out of the flat.

“He’s certainly something else, isn’t he.” Sarah stated. You smiled and nodded.

Suddenly a phone buzzed and interrupted your thoughts. It was Sarah’s, she read it quickly.

“Oh hell. It’s the hospital. I’m so sorry, one of my patients has gone into labor.” She said, scurrying to get her things. After some goodbyes she left the flat.

“Are you hungry?” John asked.

“Actually yeah.” You answered.

“I’ll order takeaway.” He stated and walking into the kitchen to get the phone.

You tried to clear the table a little while John ordered some food. After a couple minutes you heard a knock at the door. You were taking off your jacket as John went downstairs to get it.You heard a bang downstairs.

“John, is everything okay?” You asked, standing up. The moment you turned around you saw him. Zhi Zhu. You made a move for your gun but he was too quick. He pulled his arm back and his gun made contact with your head, knocking you out cold.

You woke up to the sound of a woman’s voice, it was one you recognized. Your head was pounding and your wrists were burning.

“A book is like a magic garden, carried in your pocket.” She said, as your eyes focused in the dark room you recognized her to be the woman from the circus. To your right was John, tied to a chair just like you. But you had a gag in your mouth, he didn’t. The ropes were digging into your wrists and you groaned from the pain in your head. You could feel the blood dried to the side of your face from being pistol whipped.

“Chinese proverb Mr. Holmes.” She said to John. You were sure you heard her right, she called John by Sherlock’s name.  He looked about as confused as you were.

“I’m not… I’m not Sherlock Holmes.” He argued.

“Forgive me if I do not take your word for it.” She said, reaching into the breast pocket of his jacket to get his wallet. He groaned in pain.

“Debit card, name of S Holmes.” You remembered Sherlock telling you a few days ago how John had gotten in a row with a machine at the store so he gave him his card.

“Yes, that’s not actually mine. He lent that to me.” John tried.

“And a check for 5,000 pounds made out in the name of Mr. Sherlock Holmes.” She said. You were the one who gave that to John to look after.

“Yeah, he gave me that to look after.” John said.

“Tickets from the theatre collected by you, name of Holmes.” She said. Sherlock was the one who booked the tickets. This was all just a huge misunderstanding. But yet here we are, kidnapped in the Black Lotus hideout.

“ I realise what this looks like. But I’m not him.” John said.

“We heard it from your own mouth. I am Sherlock Holmes and I always work alone.” She said. They must have been following us. John said that, mocking Sherlock, when he left the two of us outside at Soo Lin’s flat.

“Did I really say that? I suppose there’s no use me trying to persuade you I was doing an impression.” John began until the woman pulled out a small gun and pointed it at his head.You tried to yell ‘Stop’ but it just came out as muffled noise.

“I am Shan.” She said, John shifted uncomfortably in his seat, the gun was still pointed at his head. “Three times we tried to kill you and your companion, Mr. Holmes. What does it tell you when an assassin misses?” She said. ‘Misses!’ You tried to yell again. Hot metal slicing open your skin isn’t quite the same as missing. She smiled a creepy smile at you when she understood what you were trying to yell. She cocked her gun and slowly pulled the trigger. You squeezed your eyes together tightly, waiting for the sound, but it never came. The gun let out a quiet click, telling us it wasn’t loaded.

“It tells you that they’re not really trying.” She cooed. John and I let out a sigh of relief. She then proceeded to load the magazine into the gun. “Not blank bullets now. If we wanted to kill you, Mr. Holmes, we would have done it by now. We just wanted to make you inquisitive.Do you have it?

“Do I have what?” John asked, confused.

“The treasure.” She stated calmly.

“I don’t know what you’re talking about.”

“I would prefer to make certain..” This whole time you had been so worried about John that you neglected to look right in front of you. Then you did, that was your mistake. In front of you was the same large, wooden, crossbow seen in tonight’s show. When Shan unveiled it tears escaped your eyes. You tried to wiggle free but the robes wouldn’t budge.

“Everything in the West has its price. And the price for her life, information.” Shan said to John. Two men came and picked up your chair from the sides. They placed you right in front of the crossbow, so you were looking down the barrel, so to speak.

“I’m sorry, I’m sorry.” John kept repeating as you cried and tried to yell.

“Where’s the hairpin? The Empress pin valued at nine million sterling?” Shan said. All you could think about was that arrow piercing through you.”We already had a buyer in the West, and then one of our people was greedy, he took it, brought it back to London, and you Mr. Holmes have been searching.”

“Please, please. Listen to me. I’m not Sherlock Holmes. You have to believe me I haven’t found whatever it is you’re looking for .” John pleaded.

“I need a volunteer from the audience.” Shan yelled.

“No, please, please!” John yelled.

“Ah, thank you, lady. Yes, you’ll do very nicely.” Shan said approaching you. You continued to wiggle, scream, and try to break free. All the while tears were streaming down your face. Shan pulled out her dagger and pierced the sandbag just as she had done in the show.

“Ladies and gentlemen, from the distant moonlit shores of NW1, we present for your pleasure, Sherlock Holmes’ pretty companion in a death-defying act.”

“Please!” John yelled once more.

Shan pulled an origami Lotus out of her pocket and placed it onto your lap. It was the same one found at Soo Lin’s death, the same we pulled out of Van Coon’s throat. They all meant the same thing. Death.

“You’ve seen the act before. How dull for you. You know how it ends.” Shan said, but all you wanted to do was ram your fist into her smug little face.

“I’m not Sherlock Holmes!” John yelled.

“I don’t believe you.” Shan yelled back.

“You should, you know.” A voice came from behind you as more tears spilled down your face.The weight was lowering closer and closer to the bowl, but you didn’t want him to see this.”Sherlock Holmes is nothing at all like him. How would you describe me, John? Resourceful? Dynamic? Enigmatic?”

“Late…” John sighed.

“That’s a semi-automatic. If you fire it, the bullet will travel at over 1,000 metres per second. The radius curvature of these walls is nearly four metres. If you miss, the bullet will ricochet. Could hit anyone. Might even bounce off the tunnel and hit you.” Sherlock spoke.

You felt the robes at your back being tugged. Then you realized Sherlock was behind you trying to untie them. As you turned around to look at him you saw Zhi Zhu strangling Sherlock with the red silks from the show. You turned back to the crossbow to see John scooting his chair closer and closer to it. He was so close before he fell to his side. The weight was an inch from the bowl. You closed your eyes, knowing what was to come.

You heard the sound of the crossbow release.

You opened your eyes slowly to the scene around you. John was lying on his side, still tied to the chair. The crossbow was turned to the side. Zhi Zhu laid on the floor with the arrow deeply imbedded in him. Sherlock was behind you, trying to untangle himself from the silk. Shan was running down the corridor, never to be seen again.

As Sherlock threw the silks off of him he bent down to untie you. Your heart was pumping so hard.

“It’s all right. You’re going to be all right. It’s over now.” Sherlock said softly. He removed the gag from your mouth and moved in front of you to help you stand up. He grabbed both of your hands and gently lead you to your feet. You wrapped your arms around him and held on tight. When you released he brought his hands to your cheek to wipe your tears. While his hand still rested on your cheek, you boldly placed yours on the back of his head. You ran your fingers through his curls and pressed your lips to his. He seemed surprised at first, but after a second he kissed you back. You slowly pulled away.

“Thank you for saving my life.” You whispered. He smiled, his eyes full of compassion.

Sherlock called Dimmock and his team to tell him we had found the Black Lotus’ hideout. They were there within a few minutes. Sherlock took of his coat and placed it around your bare arms.

“We’ll just slip off. No need to mention us in your report.” Sherlock said to Dimmock.

“Mr. Holmes…” Dimmock began, but Sherlock cut him off.

“I have high hopes for you, Inspector. A glittering career.” Sherlock said, beginning to walk off.

“I go where you point me.” Dimmock said.

“Exactly.” Sherlock said, joining you.

When we made it to a cab Sherlock read us the cipher. Nine mill for jade pin, dragon den black tramway. He said it was instructions for all their London operatives. A message. What they were trying to reclaim. When the cabbie stopped in front of your flat, Sherlock insisted that he go in with you, just to make sure you’re okay.

You unlocked the door to your flat and had a strong urge to just fall into bed. You hadn’t slept in it for days. Some kind of vacation this was. You took off Sherlock’s large coat and hung it up on the rack next to the door.

“Would you like some tea?” You asked him.

“Sure.” He smiled.

“Great. There’s the kitchen.” You pointed and smirked. He laughed and got up and made two cups of tea.

“I’m going to take a quick shower. Make yourself at home, turn on the TV.” You suggested as you stepped into your room. After a quick shower you examined the wound on your head. You have never been pistol whipped before. Definitely wasn’t fun. You decided that it wasn’t deep enough to require stitches, just a butterfly bandage would do. You could tell a bruise was starting to form under it, fun.

After slipping on some grey sweatpants like shorts and a pink tanktop you re joined Sherlock in the living room.  He was shouting things abusively at the TV.

You smiled and sat next to him on the couch. He handed you your cup of tea, along with two pills.

“Take these. It will help with the pain,” He said, you thanked him and took the pills. You sat next to him for a few hours and watched TV. You laughed at how petty and uneducated they were. Keeping Up with the Kardashians seemed to be the only thing on, but it was fun to make fun of them. Soon you fell asleep on Sherlock’s shoulder. He lifted you off the couch and placed you in your bed. Your eyes fluttered open as he pulled the blankets over you.

“Sherlock…” You whispered as he was leaving the room, he turned around at the sound of your voice.

“Please stay,” you said, placing your hand on the open place on your king sized bed, “I just, don’t want to be alone tonight.”

He nodded, clearly he was tired too. He slipped off his shoes and crawled under the covers. You fell asleep only minutes later, but you felt safer with him by your side.

Hours had passed just fine, until you started to have a nightmare. You could see the weight lowering into the bowl, but this time, it wasn’t you in front of the crossbow, it was Sherlock. You were tied up across from him, Shan holding a gun to your head. As the weight hit the bowl and the arrow made contact with Sherlock’s body you jolted away, a scream escaped your lips. Your breathing was heavy and you noticed you had woken Sherlock up too.

“Hey, shh. It was just a dream. Everything’s fine. I’m right here.” Sherlock whispered, wrapping his arms around you as tears escaped your lips.

“Promise you’ll never leave me.” You cried.

“I promise. I could never leave you.” He said, rubbing soothing circles into your back. He pulled you down, your head resting on his chest. You fell asleep with his arms wrapped around you.

The next morning you woke up, alone in your bed. Your heart sunk until you heard clanging in the kitchen. You crawled out of bed and wrapped your robe around you. You saw Sherlock in the kitchen with his hair a mess and his sleeves rolled up. You smiled at the sight.

“Goodmorning.” You smiled as you saw him cooking.

“Ah, she lives.” He joked. He turned around the handed you a cup of tea.

“Thank you. I didn’t know you cooked.” You said.

“I don’t usually. My kitchen is a little messy.” He smiled.

“Of course. Now don’t get any ideas about sticking eyeballs in my microwave. I’d like to get my security deposit back someday. I don’t need you blowing things up in here.” You smirked and sipped your tea.

“We’ll have to go back to the bank today.” Sherlock stated. You nodded and ate your breakfast.

You slipped into a simple black sleeveless dress with white trim around the bottom. Accompanied with some small white heel you were ready to go. Luckily your wound was easily covered by your hair.

As you were walking out the door, you thanked Sherlock again for everything. For saving your life, for breakfast, for staying.

“Two operatives based in London.” Sherlock began as he helped you out of the cab. “They travel over to Dalian to smuggle those vases. One of them helps himself to something, a little hairpin.”

“Worth nine million pounds.” You added.

“Eddie Van Coon was the thief he stole the treasure when he was in China.” Sherlock said.

“How do you know it wasn’t Lukis? Even the killer didn’t know that.” You asked.

“Because of the soap.” Sherlock stated with a smile on his face.

We made it back up to the trading floor to see Van Coon’s secretary. Sherlock had come to see her before while you had gone to get Lukis’ journal from Dimmock.

“He brought you a present.” Sherlock said as we walked through the door.

“Oh, hello.” She said, remembering him.

“A little gift when he came back from China.”

“How do you know that?” She asked.

“You weren’t just his PA were you?” Sherlock asked.

“Someone’s been gossiping.” She said, annoyed.

“No.” sherlock stated.

“Then I don’t understand why…” Amanda, the PA, began.

“Scented hand soap in his apartment, 300 millilitres of it. Bottle almost finished.” Sherlock stated

“Sorry?” Amanda asked, confused.

“I don’t think Eddie Van Coon was the kind of chap to buy himself handsoap, not unless he had a lady coming over. And it’s the same brand as that hand cream there on your desk.” Sherlock said.

“Look, it wasn’t serious between us. It was over in a flash, it couldn’t last. He was my boss.” Amanda explained.

“What happened? Why did you end it?” You asked.

“I thought he didn’t appreciate me. Took me for granted. Stood me up once too often. We’d plan to go away for the weekend, and then he’d just leave. Fly off to China at a moment’s notice.”

“And he brought you a present from abroad to say sorry.” Sherlock said. You noticed the jade pin sticking out of her bun.

“Can I just have a look at it.” Sherlock asked, extending his hand.

“He said he bought it in a street market.” Amanda explained as she took it out of her hair.

“Oh, I don’t think that’s true. I think he pinched it.” Sherlock said.

“Yeah, that’s Eddie.” Amanda laughed.

“Didn’t know its value, just thought it would suit you.” Sherlock turned it around in his hand.

“What’s it worth?” Amanda asked curiously. Sherlock smiled, knowing his reply would shock her.

“Nine million pounds.” He said, and as expected Amanda freaked out.

“Oh my god, oh my god.” She said, standing up. “Nine million.” She nearly fainted.

You snuck out of the office to go talk to Sebastian, as instructed by Sherlock. He stood when you walked in the room and shook your hand.

“So did you two manage to figure out how he got in?” Sebastian asked.

“Of course. The balcony. “ You smiled.

He wrote out the check, annoyingly. The answer was so simple he was almost angry about all the money its cost him.

“He really climbed up onto the balcony?” He asked, placing the 20,000 pound check into an envelope.

“Nail a plank across the window and all your problems are over.” You answered with a smile.

He rolled his eyes and smiled slightly as he handed it to you. You thanked him and left to go join Sherlock in the lobby.

Sherlock hailed a taxi for the two of you to return to Baker Street. You told John about what had transpired at the bank.

“Over a thousand years old, and it’s sitting on her bedside table every night.” John said.

“He didn’t know its value. Didn’t know why they were chasing him.”Sherlock said.

“Should’ve just got her a lucky cat.” John said, causing you and Sherlock to smile.

“You mind don’t you.” John said, peaking both of your interests.

“What?” Sherlock asked.

“That she escaped. General Shan. It’s not enough that we got her two henchmen.”

“Must be a vast network, John. Thousands of operatives. We barely scratched the surface.” Sherlock said.

“You cracked the code though, Sherlock. And maybe Dimmock can track down all of them now that he knows it.” John suggested.

“Sherlock cracked this code, but all the smugglers have to do is pick up another book.” You told him.

Sherlock sat at his desk, reading the paper. John sat opposite him doing the same. For once it seemed like Baker Street was calm. No murders, no gunfire, no explosions going on in the kitchen. It almost seemed too good to be true.

everyonelikespotatissallad asks:

so, how is lift actually generated? i’ve been going through Anderson’s Introduction to Flight (6th Ed.) and while it offers the derivation of various equations very thoroughly, it barely touches on why lift is generated, or how camber contributes to the increase of C(L) 

This is a really good question to ask. There are a lot of different explanations for lift out there (and some of the common ones are incorrect). The main thing to know is that a difference in pressure across the wing–low pressure over the top and higher pressure below–creates the net upward force we call lift. It’s when you ask why there’s a pressure difference across the wing that explanations tend to start diverging. To be clear, aerodynamicists don’t disagree about what produces lift - we just tend to argue about which physical explanation (as opposed to just doing the math) makes the most sense. So here are a couple of options:

Newton’s 3rd Law

Newton’s third law states that for every action there is an equal and opposite reaction. If you look at flow over an airfoil, air approaching the airfoil is angled upward, and the air leaving the aifoil is angled downward. In order to change the direction of the air’s flow, the airfoil must have exerted a downward force on the air. By Newton’s third law, this means the air also exerted an upward force–lift–on the airfoil. 

The downward force a wing exerts on the air becomes especially obvious when you actually watch the air after a plane passes:

Circulation

This one can be harder to understand. Circulation is a quantity related to vorticity, and it has to do with how the direction of velocity changes around a closed curve. Circulation creates lift (which I discuss in some more detail here.) How does an airfoil create circulation, though? When an airfoil starts at rest, there is no vorticity and no circulation. As you see in the video above, as soon as the airfoil moves, it generates a starting vortex. In order for the total circulation to remain zero, this means that the airfoil must carry with it a second, oppositely rotating vortex. For an airfoil moving right to left, that carried vortex will spin clockwise, imparting a larger velocity to air flowing over the top of the wing and slowing down the air that moves under the wing. From Bernoulli’s principle, we know that faster moving air has a lower pressure, so this explains why the air pressure is lower over the top of the wing.

Asymmetric Flow and Bernoulli’s Principle

There are two basic types of airfoils - symmetric ones (like the one in the first picture above) and asymmetric, or cambered, airfoils (like the one in the image immediately above this). Symmetric airfoils only generate lift when at an angle of attack. Otherwise, the flow around them is symmetric and there’s no pressure difference and no lift. Cambered airfoils, by virtue of their asymmetry, can generate lift at zero angle of attack. Their variations in curvature cause air flowing around them to experience different forces, which in turn causes differing pressures along the top and the bottom of the airfoil surface. A fluid particle that travels over the upper surface encounters a large radius of curvature, which strongly accelerates the fluid and creates fast, low-pressure flow. Air moving across the bottom surface experiences a lesser curvature, does not accelerate as much, and, therefore, remains slower and at a higher pressure compared to the upper surface.

(Image credit: M. Belisle/Wikimedia; National Geographic/BBC2; O. Cleynen/Wikimedia; video credit: J. Capecelatro et al.)

2

Desert-dwelling plants like cactuses have to be efficient collectors of water. Many types of cactus are particularly good at gathering water from fog that condenses on their spines. Droplets that form near a spine’s tip move slowly but inexorably toward the base of the spine so that the cactus can absorb them. The secret to this clever transport lies in the microstructure of the spine’s surface. The Gymnocalycium baldianum cactus, for example, has splayed scales along its spines. Capillary interactions with the scales result in differences in curvature on either side of the droplet. Curved fluid surfaces generate what’s known as Laplace pressure, with a tighter radius of curvature causing a larger Laplace pressure. Because the curvature of the droplet varies from the base side to the tip side of the spine, the difference in Laplace pressures across the droplet creates a force that drives the droplet toward the spine’s base. (Image credit: C. Liu et al., source)