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Talk:Blender 3D: Noob to Pro/Import and Render a SolidWorks Model

Tutorial Authors Wanted on Official Blender MediaWiki!
The main Blender documentation and tutorial authors are now working on the Official Blender MediaWiki. If you're considering helping write Blender tutorials or documentation, please consider helping us at the official wiki instead.--Popski 17:49, 18 July 2006 (UTC)

This should be merged into the Blender 3D book. --Mijokijo 23:29, 9 August 2005 (UTC)
 * Agree. Quality tutorial BTW. Congratulations! :)--Popski 09:20, 10 August 2005 (UTC)
 * Thanks for the compliment! I'm not sure where it would fit in the Blender 3D book, because it's rather a quick case-study tutorial. It doesn't belong in the Noob to Pro section anyway, because regular Blenderheads have no use for this (apart from the hdri section, a subject on which I haven't found decent tutorials - the biorust.com tutorial isn't worth much IMO)... --1983 22:00, 14 August 2005 (UTC)
 * Done :o) --1983 11:16, 17 August 2005 (UTC)

*Crash*
Hello i am probably jumping the gun, but am trying to setup up a simple yayfray render, with the hdr image as instructed in this tut, i get to applying the hdr image, setting all the yayfray stuff cache ect, and i hit the old f12 and bam "windows is sorry" shut blender down ect wtf help stephen@eggandmilk.co.za
 * I had the same problem, but you just have to install Yafray. I was assuming that Blender installed it, but seemingly that's not true.

Thanks!
Thanks so much for this tutorial. I had never used Blender before and was able to pick it right up. The instructions were very clear and worked perfectly for the medical device rendering that I urgently needed for work

blue pic
Hey,

I have followed yourre instructions, but my pic came out blue, with almost no shade or textures, i can't figure out what Ive done wrong? does anyone know what to change??

rudivanerp@gmail.com

Russian?
What is this?

Рендер с добовленными матерьялами Для визуализации, вы можете непосредственно нажать F12, или сначала зайти в установки визуализации(F10). Because of the render settings we use (GI and an HDRI environment), my render took about 3 minutes on a AMD64 3200 [...]

Black render
I followed everything to the letter yet got a black render. No model, no ground plane, nothing :-( Have I missed something here? I'm using Blender 2.48a and Yafaray r299.

 * UPDATE* I double checked Yafaray was installed, the script is there but Blender's console reports this:

''Couldn't FIND registry key for yafray, is it installed? Error loading yafray plugin: The specified module could not be found.''

It also can't find Python but it is also installed!! I have tried uninstalling and reinstalling them all to no avail.

I finally downloaded Yafray (NOT Yafaray) and it all worked with Python 2.5.4 I think I might give up though since the render output is just fog. Thanks for the tutorial anyway, I guess it helped some people.
 * Update 2*


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Talk:General Anatomy/Nervous System

Hi, I just found the abandoned site about the Nervous system and tried to set up a logical and helpful way to explain the anatomical systematics of this challenging topic. I'd appreciate if anyone feels up to comment on that.

I think the distinction between the functional and localizational aspect has to be made in order to get things right, especially the nomenclature that is always mixed up by people since they don't understand the difference between terms that describe function and terms that name positions.

I have started to insert both the English terms for anatomical structures but also added the Latin anatomical description in Italic according to the recent (Parisian) Nomina anatomica and Terminologia anatomica from 1998. I would like to please every author who wants to contribute to attach to this system for two reasons. First, the english manner of anglifying medical terms generates a certain degree of misunderstanding as the plethora of medical phrases and descriptions contain some ambiguity. The nomina anatomica is the conventional language that anatomists use and that all medical personnel around the world should attach to. I know this is far from reality as english-speakers dominate the medical literature and they do not study, publicize and converse in proper Latin terms. Nevertheless, if WikiBooks aims to generate reliable textbooks at least the minimal standard for such project would be the use of the correct language. The second reason for using both forms lies in the fact that a minority - but a large one - from some European countries will be able to fluently read into the matter as they are trained to use the Latinized nomenclature.

I have started to set up a preliminary division of chapters. I would suggest to everyone who would like to contribute to concentrate on four main sections for each structure as can be already seen in the spinal cord chapter:

(1) Gross anatomy

(2) Microscopic anatomy

(3) Internal organization

(4) Function

Any suggestions?

Okay, that's it for the beginning. See you later.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Talk:General Anatomy/Nervous System


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Jet Propulsion/Thermodynamic Cycles/Turbojet cycle

Adding a compressor to a ramjet powered by a turbine in the exhaust allows increased combustor inlet temperature, and a consequent increase in possible thermal efficiency. The turbine however is limited in the temperature it can handle, so maximum power is also limited.

In the T-S diagram below the presence of the compressor allows us to raise the combustor inlet temperature (3). The raising of the combustor segment increases the cycle area and the thermal efficiency.

Addition of an afterburner (5-6) allows thrust augmentation as can be seen from the increased area of the diagram shown below. The afterburner operates in the higher entropy range and has lower efficiency than the base turbojet.


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Diagnostic Radiology/Musculoskeletal Imaging/Joint Disorders/Reiter syndrome

Reiter's Syndrome is an inflammatory spondyloarthropathy, characterized by the classic triad of nongonococcal urethritis, conjunctivitis, and arthritis. The eponym "Reiter's arthritis" has been replaced by the more descriptive terminology reactive arthritis because of Dr Reiter's experiments in Nazi concentration camps.

Etiology
Reactive arthritis generally occurs about 1 to 3 weeks after a systemic infection. Chlamydia trachomatis is the bacteria most often associated with reactive arthritis, but several different bacteria acquired through the digestive tract, including Salmonella, Shigella, Yersinia, and Campylobacter, are associated with reactive arthritis as well.

Reactive arthritis is usually self-limited, and generally lasts less than 6 months. The disease tends to remit, but recurs intermittently in 35% of cases, and 25% of patients will have chronic low grade symptoms. These recurrences may manifest as only one of the constellation of symptoms seen in the acute attack.

Although the reason why only some people are affected after infection is unclear, the HLA-B27 haplotype has been found to increase a person's chance of developing reactive arthritis. Approximately 80% of people with RS are HLA-B27 positive.

Clinical Findings
Mild constitutional symptoms generally appear within 1–3 weeks. Urethritis may be postdysenteric or postvenereal. Musculoskeletal symptoms are mainly muscle pains (myalgias), asymmetric joint stiffness in the lower extremities, or low back pain.

A scoring system for diagnosis of reactive arthritis-like spondyloarthropathy exists. Two or more of the following establishes the diagnosis ( one from musculoskeletal system).

 * 1) Asymmetric oligoarthritis predominantly of the lower extremity
 * 2) Sausage shaped finger (dactylitis), toe, heel pain, or other enthesitis
 * 3) Cervicitis or acute diarrhea within one month of arthritis
 * 4) Conjunctivitis or iritis
 * 5) Genital ulceration or urethritis

Radiologic Findings
Skeletal abnormalities develop in up to 80% of patients. Initial attacks of pain subside, only to recur later, leaving progressive changes at joints and entheses (sites of musculotendinous insertions). The classic radiographic findings are:

 * 1) Normal mineralization (osteoporosis in acute phase)
 * 2) Periostitis
 * 3) Ill define erosions
 * 4) Bilateral asymmetric distribution
 * 5) Joint space narrowing
 * 6) Fusiform soft tissue swelling

The imaging appearance is similar to psoriatic arthritis. However the distinction is made based on the distribution. Reactive arthritis predominantly involves the lower extremities, primarily the feet, ankles, knees, and sacroiliac joints.

Feet
Reactive arthritis has a predilection for metatarsophalangeal joints and first IP joint over the distal and proximal interphalangeal joints. The arthritis is initially seen involving one joint only. There may be swelling of the entire digit giving the appearance of a sausage. Early on a periostitis of the phalanges may be noted. Later on uniform joint space narrowing, and marginal erosions with adjacent bone proliferation occur.

Calcaneus is involved in more than 50% of patients, hence the name "lover's heel". Painful erosions and reactive spurs are very common at the attachment sites of Achilles tendon and plantar aponeurosis in calcaneus.

Ankle
Usually there is fluffy periostitis of tibia and fibula with soft tissue swelling. Uniform joint space loss may occur and erosions are less frequent.

SI Joint
Bilateral asymmetric involvement is characteristic. Erosive changes are first seen on the iliac side of the true synovial joint. Because of the asymmetry, radiographically it may appear as unilateral involvement and indistinguishable from septic arthritis. However bone scan may show uptake in both SI joints. Ankylosis is less frequent.

Spine
Involvement is typically around thoracolumbar junction (lower three thoracic or upper three lumbar). Early involvement occurs as paravertebral ossification. As the disease progresses large bulky bony bridges form between adjacent vertebral bodies.

Differential Diagnosis
Involvement is typically around thoracolumbar junction (lower three thoracic or upper three lumbar). Early involvement occurs as paravertebral ossification. As the disease progresses large bulky bony bridges form between adjacent vertebral bodies.

Fig. 1 Sclerosis and ill-definition of both SI joints is noted in this patient with reactive arthritis.

Fig. 2 Bony proliferation (arrows) is noted along the anterior margin of the lumbar spine in this patient with reactive arthritis.

Fig. 3 Erosion of the 3rd and 5th metatarsal heads is noted.

Fig. 4 Prominent erosion of the posterior calcaneus is noted adjacent to the retrocalcaneal bursa.

Treatment
Three therapies are used in reactive arthritis: NSAIDS for acute inflammation, antibiotics for infection, and sulfasalazine or methotrexate for chronic disease.

Prognosis
The prognosis for patients with reactive arthritis is generally good. Most people will have complete recovery of the initial illness 2 – 6 months after symptom onset. Approximately 20% of people with reactive arthritis will have mild, chronic symptoms that usually present as back pain and arthritis. There are a small percentage of people who will develop persistent, severe deforming arthritis. For these unfortunate few, treatments are generally not effective.


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Jet Propulsion/Thermodynamic Cycles/Turbofan cycle

The fan allows a reduction in the average exhaust velocity compensated by a larger mass flow for a given thrust.

Modern military aircraft use afterburning of combined bypass and core flows for high augmentation ratios.


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Chess Opening Theory/1. e4/1...e5/2. Nf3/2...Nc6

2...Nc6 - King's Knight Opening
2...Nc6 is the natural move, combining defence of the pawn with control of the d4 square and avoiding committing another pawn for now.

White's responses
White has multiple choices here which can lead to very different games.

 * /3. Bb5/ is the most played. White puts pressure on the knight defending the pawn.
 * /3. Bc4/ is quieter. Instead of attacking the knight, White chooses to target the weak f7 pawn.
 * /3. d4/ is aggressive. Subsequent play may result in a very open game.
 * /3. Nc3/ is the quietest common continuation.
 * /3. c3/, the Ponziani opening, opens the white diagonal for the queen, allows for an eventual d4 pawn push, and controls d4 and b4 (possible plants by the black knight) at the expense of hemming in the knight.

Some more uncommon moves:

 * /3. Nxe5/, the Irish Gambit, sacrificing a knight for a pawn.
 * /3. g3/, the rarely seen Konstantinopolsky Opening
 * /3. Be2/, a passive reply called the Inverted Hungarian Opening or Tayler Opening.
 * /3. b4/, a very rarely seen gambit called the Pachman Wing.
 * /3. c4/!?, Dresden Opening, not allowing d5 and after Nf6 transpose to Nimzowitch variation Nc3!, is not bad

Statistics

 * Estimated next move popularity
 * Bb5 48%, Bc4 26%, d4 14%, Nc3 9%, c3 1%. All other moves less than 1%.

Theory table
.

'''1. e4 e5 2. Nf3 Nc6'''


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Muggles' Guide to Harry Potter/Characters/Lord Voldemort

Overview
Lord Voldemort (pseudonym) is perhaps the most notorious Dark wizard ever known and the most powerful and dangerous of all time. It is said that the only wizard he ever feared is Albus Dumbledore. Voldemort apparently believes nothing is worse than death; perhaps his greatest weakness is his inability to love. This is because his mother, Merope Gaunt, gave Tom Riddle Senior (Voldemort's father) a love potion. Because Voldemort was conceived under a love potion, he isn't able to feel or express love in his life.

Voldemort's wand is made from yew wood and contains a phoenix feather core. It is considered a "brother" to Harry Potter's holly wand because the feather in each was donated by the same phoenix, Fawkes, who is Albus Dumbledore's beloved pet.

Voldemort's chosen name originates from the French "vol de mort", or "flight from death" in English. This is an excellent example of the series' possibly excessive matching of name to character; Voldemort's main desire in the series is to escape and/or conquer death (since he seems to fear it more than anyone else in the series).

Philosopher's Stone
Voldemort killed James and Lily Potter as he attempted to murder their one-year-old son, Harry. Harry survived, but Voldemort's body was destroyed when his curse rebounded upon him, though some doubted he was truly gone. The attack left Harry with a lightning-bolt shaped scar on his forehead.

Rubeus Hagrid, introducing Harry, now eleven, to the Wizarding world, mentions Voldemort, and explains how Harry made him vanish. Hagrid personally believes there was too little that was still human in Voldemort to die.

While at Mr. Ollivander's wand shop, Harry tries one particular wand which Ollivander had evidently been holding in reserve. It suits Harry perfectly. Mr. Ollivander tells him, "It is very curious indeed that you should be destined for this wand when ... its brother gave you that scar... I think we must expect great things from you, Mr. Potter ... After all, He-Who-Must-Not-Be-Named did great things – terrible, yes, but great."

Voldemort is first seen during the climactic battle in Hogwarts' dungeon. Voldemort's surviving spirit possesses Professor Quirrell's body, controlling Quirrell as he attempts to steal the Philosopher's Stone and kill Harry. It is revealed that it was Voldemort who was driving many events in the story:

 * Voldemort, aided by Quirrell, had attempted to steal the Stone from Gringotts Bank, not knowing that Hagrid had removed it earlier that same day.

 * Harry's scar first pains him at the Welcome Feast, when Professor Snape is looking at him. Voldemort by now is riding the back of Quirrell's head, concealed by a turban, and may be the reason Harry's scar pains him. Harry notes that Quirrell was not wearing a turban at the Leaky Cauldron.

 * At Voldemort's apparent bidding, Quirrell hexed Harry's broom during the Quidditch match against Slytherin. Harry was saved by Professor Snape. (Harry thought Snape was the one that jinxed his broom but in the final chapter, Quirrel reveals that it was himself who jinxed Harry's broom.

 * It was Quirrell, again at Voldemort's instructions, who was killing the unicorns in the Forbidden Forest so Voldemort could drink their blood to sustain his tenuous life. Harry's scar seared when he encountered the robed figure that killed all the unicorns.

 * In the end, Voldemort propels Quirrell through an elaborate security maze protecting the Philosopher's Stone at Hogwarts. He wants Harry, who also bypassed the security, to fetch the Stone, then orders Quirrell to kill him. During the battle with Quirrell and Voldemort, Harry is nearly incapacitated by pain searing inside his scar. With Quirrell's defeat and brutal death, Voldemort is forced to flee his body and find a new host.

Harry realizes, and Professor Dumbledore confirms, that his scar causes him pain whenever Voldemort is nearby. Dumbledore theorizes that when Voldemort's killing curse rebounded off Harry, it left a lasting connection between Harry and Voldemort. He withholds any additional details, however.

Chamber of Secrets
Voldemort never acts directly in this book; instead, the story is driven by a remnant of his younger self, Tom Marvolo Riddle, contained in a magical diary, when he still used his birth name, Tom Riddle. Details are under that character entry.

Prisoner of Azkaban
Lord Voldemort is not seen directly, as he hides and regains strength. At the end, Peter Pettigrew (Wormtail) returns to serve him after escaping Harry Potter, Sirius Black, and Remus Lupin.

Goblet of Fire
Voldemort is heard, though remains unseen, when he occupies the old Riddle manor in Little Hangleton. Frank Bryce, the elderly Muggle caretaker, investigates when he sees lights in the supposedly deserted house. Inside, he eavesdrops on Voldemort and Pettigrew. Voldemort mentions his one faithful servant, apparently not Pettigrew, and the two plot to murder someone named Harry Potter. When Frank is discovered, Voldemort kills him.

His scar searing, Harry awakens from a nightmare—Voldemort has just murdered someone. Pain in his scar can indicate that Voldemort is nearby, and Harry worries about being attacked on Privet Drive. Much later, Harry has another dream that Pettigrew is being punished.

During the Triwizard Tournament, Harry and Cedric Diggory simultaneously grab the trophy, only to discover it is a Portkey that transports them to a cemetery. There, Voldemort orders Pettigrew to kill Cedric and bind Harry.

Voldemort's body is like a hideous baby, with snake-like, scaled skin, slitted eyes, and a grown man's malevolence. To restore Voldemort's body, Harry's blood, Voldemort's father's bone, and Pettigrew's own flesh (his right hand) are added to a potion, making him human. Exulting in his newly restored self, Voldemort briefly taunts Harry, then, ignoring the whimpering Pettigrew, summons his Death Eaters.

Voldemort greets his servants, including Lucius Malfoy. One is promptly tortured for doubting the Dark Lord would return. Voldemort says he never forgives, nor forgets, and he requires repayment for his Death Eaters having denied him. He rewards Pettigrew's service, conjuring him a magical silver hand to replace the severed one.

After his failed attack on baby Harry, Voldemort's disembodied soul had wandered for years, occupying small animals, then attached itself to a weak wizard. After failing to capture the Philosopher's Stone and losing his host, he was a detached spirit again until Pettigrew found him. One true ally was left who could capture Harry Potter, but until then, Pettigrew crafted him a rudimentary body and sustained him with Nagini's venom. With Harry's blood inside him, he can now overcome the protection Lily's death had given Harry.

Harry's wand is returned, and he is forced to duel Voldemort. Harry casts the Disarmament spell as Voldemort hurls the Killing Curse. A golden stream unites their wands, and a gold light dome forms around them. Harry's wand heats up, and he forces the light beads that have formed on the stream into Voldemort's wand. Cedric's shade ejects from Voldemort's wand, then Frank Bryce, Bertha Jorkins, and James and Lily Potter emerge. His parents explain they can briefly protect Harry when he breaks the stream. When the connection is broken, the shades rush at Voldemort as Harry Summons the Triwizard Cup, transporting himself and Cedric's body to Hogwarts.

Professor Moody, who is actually Voldemort's servant, guides Harry to his office, then admits he rigged the Tournament. As he is about to fatally curse Harry, Dumbledore bursts in and stuns Moody, who is revealed to be Barty Crouch Jr., disguised by Polyjuice Potion. Under Veritaserum, Barty confesses that he and Pettigrew kidnapped Moody so Barty, Jr. could assume his identity, specifically to lure Harry into Voldemort's trap.

After Dementors have sucked out Barty's soul before he could confess, Cornelius Fudge discounts Harry's story, claiming Dumbledore fabricated it. After Fudge's angry departure, Dumbledore assigns missions for Hagrid and Madam Maxime; for Professor Snape; and also Sirius Black.

At the Leaving Feast, Dumbledore informs the entire school that Voldemort has returned and murdered Cedric Diggory. Dumbledore believes students should know the truth despite the Wizarding world's denial.

Order of the Phoenix
The Wizarding world doubts claims that Voldemort has returned, leaving Harry edgy all summer. He listens to the Muggle news for any unexplained deaths or possible magical disturbances, and scans the Daily Prophet for any signs. Ron's and Hermione's deliberately vague letters only increase the tension, fuelling Harry's anger.

After a Dementor attack near his home, Harry is taken to Number 12, Grimmauld Place, Sirius Black's home and now headquarters for the Order of the Phoenix. The Order believes Voldemort remains hidden while rebuilding his organization, though Harry's announcing his return has impeded Voldemort's efforts. Harry learns Voldemort may be seeking a powerful weapon. When Hermione notices Harry's scar hurting him, Harry discounts it, claiming it happens frequently now.

At Hogwarts, some Gryffindors doubt Harry and Dumbledore's claims regarding Voldemort. Neville supports Harry, echoing his grandmother's belief that Dumbledore is far more trustworthy than the Daily Prophet.

Soon, Harry runs afoul of the new Defence Against the Dark Arts teacher, and Ministry spy, Dolores Umbridge, for claiming Voldemort has returned. She assigns him two weeks detention that is tantamount to torture. When Umbridge happens to touch Harry's hand, his scar sears, causing Harry to suspect she could be linked to Voldemort. He stubbornly refuses to tell Dumbledore, feeling stung by the headmaster's continually avoiding him. Sirius assures Harry that the Order believes there is no connection between Umbridge and Voldemort.

Fed up with Umbridge's completely useless lessons, Hermione and Ron urge Harry to teach students real defensive magic. He reluctantly agrees, and Dumbledore's Army is formed. Zacharias Smith complains that the Disarming Charm (incantation: Expelliarmus) Harry demonstrates is too easy until Harry explains how he effectively used it against Voldemort.

Harry repeatedly dreams about a long corridor with a doorway at the end that he longs to enter. His scar hurting seems related to Voldemort, and Harry can feel the Dark Lord's emotions.

Meanwhile, Hagrid returns from his secret mission to recruit the Giants against Voldemort. Hagrid failed because Death Eaters had already offered bigger rewards.

Shortly before Christmas, a terrible pain awakens Harry after he saw Mr. Weasley being attacked at the Ministry. Dumbledore alerts the Order, then sends the Weasley children and Harry to Grimmauld Place. When Dumbledore briefly glances into Harry's eyes, Harry feels the snake he saw in his dream wanting to attack Dumbledore.

Harry and the Weasley children happen to overhear Mad Eye Moody say that Harry and Voldemort may share a mental connection. Harry, fearing Voldemort can see into Headquarters through him, wants to leave until Dumbledore delivers a stern message: "Stay where you are." Harry relents, but fears Voldemort could be possessing him until Ginny, having been possessed by him, assures Harry he is not.

During his Occlumency lessons with Snape, Harry recognizes the long hallway as one at the Ministry of Magic. Harry, Ron, and Hermione later conclude that the weapon Voldemort seeks is in the Ministry. Harry can feel Voldemort's joy when ten Death Eaters escape Azkaban prison, leading Hermione to suspect the Dementors have defected to Voldemort. Meanwhile, Harry wonders if Snape's lesson are actually opening his mind to Voldemort rather than blocking it.

Harry dreams that Voldemort is torturing someone after being told his plan will fail. When a patient at St. Mungo's Hospital dies, Harry and Hermione conclude he had been under the Imperius curse to steal the weapon. Voldemort likely had him killed because he was recovering from the protective spells that temporarily drove him insane.

In his next Occlumency lesson, Snape suddenly breaks Harry's vision just as he reaches the doorway and finds it open. Shortly after Dumbledore's ouster from Hogwarts, Harry dreams about the corridor and the door again, this time entering a room with rows of shelves containing dusty phials. What he wants is almost within his grasp, but he is awakened.

Harry "sees" Voldemort torturing Sirius and rushes to the Ministry of Magic, unaware it is a trap. He and fellow Dumbledore's Army members are ambushed by Death Eaters seeking a prophecy concerning Harry and Voldemort. Sirius and Order of the Phoenix members arrive in time and neutralize the Death Eaters, though Bellatrix Lestrange kills Sirius. Voldemort appears, but Dumbledore's sudden arrival erupts into a fierce duel. Finally, Voldemort possesses Harry, but Harry's overwhelming emotions of love and friendship drive him out. Voldemort escapes with Bellatrix.

Back in his office, Dumbledore tries to calm a distraught Harry by claiming responsibility for Sirius' death; had he been more open with Harry, he would have recognized Voldemort's trap. The curse leaving Harry's scar had forged a link between Harry and Voldemort, enabling Harry to sense Voldemort's emotions and, occasionally, see his thoughts. Voldemort only recently discovered the link. Dumbledore had been avoiding Harry to prevent Voldemort from gaining information, and it is why Snape was teaching Harry Occlumency, though their mutual animosity made that impossible. Voldemort implanted false images into Harry's mind to lure him into an ambush.

Dumbledore also explains why Harry was placed with the Dursleys: Lily's sacrificing herself to save Harry cast a powerful magical charm that has protected him from Voldemort ever since. Only his remaining in a home with his mother's blood kin – his Aunt Petunia - sustains the charm's effect. Despite the Dursleys' cruelty, Harry's physical safety was more important than his emotional well-being.

A prophecy made shortly before Harry's birth is why Voldemort wanted to kill him. Voldemort only heard its first half, and he needed Harry to recover the copy stored at the Ministry. The prophecy, about someone with "the power to vanquish the Dark Lord," could have referred to either Harry or Neville Longbottom. Because Voldemort chose to kill Harry, a "half-blood" like himself, he marked Harry as his equal. The power that Harry has and Voldemort lacks is love. Its power protected Harry from Voldemort, and that strength will enable him to defeat the Dark Lord. Dumbledore also confirms that, according to the prophecy, one must kill the other.

With the Ministry finally admitting that Voldemort has returned, Dumbledore is re-instated as Headmaster of Hogwarts, and in his other offices.

Half-Blood Prince
Cornelius Fudge introduces new Minister for Magic Rufus Scrimgeour to the British Prime Minister. Fudge reports that the recent crises plaguing the Muggle world is due to Lord Voldemort having returned. As a result, Fudge has resigned permanently.

Meanwhile, Narcissa Malfoy pleads for Severus Snape's help. Voldemort has assigned her son, Draco, a nearly impossible and probably fatal task. She believes Voldemort is risking Draco's life to punish her husband, Lucius, for his failure at the Ministry. Bellatrix Lestrange, however, questions Snape's loyalty, though Snape refutes this, saying he has earned Voldemort's trust. Snape refuses to attempt to change the Dark Lord's intent, but agrees to swear an 'Unbreakable Vow' to protect Draco and complete this mission should Draco fail.

After publicly acknowledging Voldemort's return, the Ministry has flooded the Wizarding realm with propaganda planted in the Daily Prophet, and published pamphlets containing supposedly useful information.

Dumbledore speculates that Voldemort found Harry's mind too painful to inhabit and will not attempt to possess him again. Voldemort is likely also worried that Harry will peer into his own mind, and is probably blocking contact using Occlumency.

Harry and Dumbledore study Lord Voldemort's early years by viewing donated memories in Dumbledore's Pensieve. Voldemort's mother, Merope Gaunt, is Salazar Slytherin's direct descendant, and his father is Tom Riddle, a Muggle. During this time period, Voldemort is known by his birth name, Tom Marvolo Riddle. In a later session with the Pensieve, Dumbledore notes Tom's changed appearance and comments about his using the name Voldemort. As this study was done using Riddle's birth name, additional details are under that character topic.

Voldemort has informed Draco about the Room of Requirement, and has ordered him to murder Dumbledore. This is likely the same mission Narcissa Malfoy was distressed about, suspecting Draco would fail and then be killed by Voldemort. Snape fulfils the Unbreakable Vow by killing Dumbledore in Draco's place. As Snape and Draco flee Hogwarts, Snape prevents the other Death Eaters from killing Harry, saying Voldemort wants Harry for himself.

Deathly Hallows
At Malfoy Manor, the Dark Lord's new headquarters, Voldemort holds court with his Death Eaters. Believing Harry's wand is more powerful against his own, its twin, Voldemort demands Lucius Malfoy's wand. Malfoy's position at the table's far end reflects how much he has fallen from Voldemort's favour, while Snape now sits beside the Dark Lord. Voldemort also taunts Bellatrix Lestrange, even though she serves him faithfully. Charity Burbage, the Hogwarts' Muggle Studies professor, is suspended and tightly bound above the table. For having advocated inter-marriage with Muggles, Voldemort casts a Killing Curse at her, ending her life. He then feeds her body to Nagini for "dinner."

The Order of the Phoenix, meanwhile, is transferring Harry to a safe house shortly before his late mother's magical protection ends. Six protectors paired with a Harry Potter decoy will fly to separate safe houses, while the real Harry goes with Hagrid. As the group takes off, Death Eaters, tipped off by Snape, immediately attack. When Harry is identified by his signature Disarming spell, Voldemort suddenly appears. In the screaming confusion, Harry's wand independently casts a golden spell, shattering Voldemort's borrowed wand. Harry and Hagrid barely reach the safe house alive. Everyone arrives safely except "Mad-Eye" Moody, who apparently has been killed.

Harry, fearing he is endangering everyone, wants to leave The Burrow, but is overruled. Shortly after, he "sees" Voldemort torturing Ollivander, demanding to know how Harry destroyed his borrowed wand, though Ollivander does not fully understand the reason. Harry, eager to start his quest, sarcastically remarks to Ginny that Voldemort will not just kill himself. She correctly guesses that Harry's mission is to kill Voldemort, though Harry pretends he was only joking to allay her fears. Harry "dreams" that Voldemort is searching for someone named Gregorovitch, and recalls Mr. Ollivander once mentioning that Gregorovitch crafted Viktor Krum's wand.

Kingsley Shacklebolt sends a warning that the Ministry of Magic has fallen to Voldemort, and Minister Rufus Scrimgeour is dead. As Death Eaters attack The Burrow, Harry, Ron, and Hermione escape to Grimmauld Place. Harry again watches through Voldemort's eyes as a terrified Draco Malfoy is forced to torture a Death Eater for letting Harry escape.

Sirius' brother, Regulus Arcturus Black is identified as the mysterious R.A.B. who left the note inside the fake Locket Horcrux. Kreacher tells Harry that Mundungus Fletcher stole the real Locket Horcrux from Grimmauld Place, and explains its connection to Regulus: when Voldemort needed a house-elf's assistance to hide a locket in a sea cave, Regulus sent Kreacher. Voldemort abandoned Kreacher to die there, but he returned to his master. Regulus retrieved the real Locket Horcrux, replacing it with a fake, though he died in the attempt. Harry, still upset by Kreacher having betrayed Sirius, is bothered more by Voldemort abusing the house-elf.

Voldemort now controls the Ministry: Muggle-born wizards and witches are being rounded up and their wands confiscated. All magical children in England must only attend Hogwarts, now headed by Severus Snape.

After the Trio recover the real Locket Horcrux, Ron requests they avoid speaking Voldemort's name aloud—it feels jinxed. (Note: for the remaining story, Harry, Hermione, and Ron generally only use Voldemort's common euphemisms such as, "You-Know-Who", and "He-Who-Must-Not-Be-Named", though, for brevity, this summary will continue to call him Voldemort.)

Shortly after, Harry "sees" Voldemort demanding something that Gregorovitch claims was stolen long ago. In Gregorovitch's memory, a young, blond thief Stunned Gregorovitch and escaped with a wand. Voldemort then kills Gregorovitch.

Ron leaves the mission, and Harry and Hermione go to Godric's Hollow to see Bathilda Bagshot. After Harry is led upstairs, Nagini, Voldemort's snake, pours from Bathilda's dead body as it crumples to the floor. As Harry is attacked, Hermione rescues him just as Voldemort appears. While recovering, Harry sees into the Dark Lord's memories, watching as, sixteen years before, Voldemort kills his parents and attempts to murder Harry.

Hermione shows Harry Rita Skeeter's book, The Life and Lies of Albus Dumbledore and a photo of Gellert Grindelwald, the blond thief who stole the Elder Wand from Gregorovitch. Voldemort also has Grindelwald's photo, taken from Bathilda's house.

Ron returns bearing a spare wand to replace Harry's destroyed one, and he updates them about the Wizarding world—speaking Voldemort's name summons Death Eaters or Snatchers (Voldemort's bounty hunters). The Trio seeks out Xeno Lovegood for information about a mysterious symbol. He tells them about the Peverells and the Tale of the Three Brothers and the Deathly Hallows. Harry believes the Hallows could make him invincible against Voldemort. A ring handed down from the Peverells could contain the Resurrection Stone, and it may be hidden inside the Snitch that Dumbledore bequeathed to Harry. Harry's own Invisibility Cloak may also be a Hallow, while Voldemort seeks only the Elder Wand, the third Hallow.

Harry inadvertently speaks Voldemort's name, and Snatchers immediately appear. As the Trio and other captives are taken to Malfoy Manor, Harry sees Voldemort inside a tall tower where an old man (Gellert Grindelwald) says he knows what Voldemort wants, but claims he never had it. With Dobby's help, the Trio, along with the other prisoners, escape Malfoy Manor to Shell Cottage. While there, the goblin Griphook agrees to help Harry break into Bellatrix Lestrange's Gringotts vault, that Harry now suspects contains another Horcrux. Mr. Ollivander confirms that Voldemort seeks the Elder Wand, believing it is more powerful against Harry's. Despite its bloody history, only capture, not murder, is necessary to win the wand's allegiance. Harry watches as Voldemort removes the Elder Wand from Dumbledore's tomb.

After Harry, Ron, and Hermione escape Gringotts with the Cup Horcrux, Harry sees Voldemort's fury after finding out what was stolen. Though he believes his other Horcruxes are safe, he will check on them, including one hidden at Hogwarts. Harry, Ron, and Hermione then race to Hogwarts. Harry knows Nagini may also be a Horcrux and that Voldemort is aware his Horcruxes are under attack.

In Hogsmeade, Aberforth Dumbledore helps the Trio sneak into Hogwarts through the Room of Requirement where Dumbledore's Army members are hiding. Harry feels Voldemort's rage as he discovers the Locket Horcrux is missing. Meanwhile, the Order and other allies begin secretly pouring into Hogwarts to prepare for battle. Harry frantically searches for Ravenclaw's lost diadem, another Horcrux, as Voldemort and his army march to Hogwarts. Snape, ousted from the school, re-joins Voldemort, while Professor McGonagall and the other faculty secure the castle. Outside Hogwarts, Voldemort's voice offers a reward for Harry Potter.

As the battle begins, Harry, Ron, and Hermione find the Diadem Horcrux inside the transformed Room of Requirement. Draco Malfoy, Crabbe, and Goyle attempt to stop them but fail, and the Diadem is destroyed. Draco may have been trying to regain Voldemort's favour.

Harry locates Voldemort in the Shrieking Shack. Hiding inside, Harry, Ron, and Hermione overhear Voldemort tell Snape that he suspects Snape actually commands the Elder Wand by having murdered Dumbledore. To gain its allegiance, Voldemort orders Nagini to kill Snape, then leaves. Dying, Snape hands Harry his memories.

Voldemort's voice announces that Harry Potter has one hour to surrender, otherwise, everyone at Hogwarts will die. Harry, meanwhile, watches Snape's memories in a penseive. Snape had deeply loved Harry's mother, Lily, but Snape's affiliation with future Death Eaters at Hogwarts acrimoniously ended their friendship. Snape carried the prophecy to Voldemort, but when Voldemort said Lily must die, Snape defected to Dumbledore, who swore Snape to spy on Voldemort in exchange for Lily's protection. But Peter Pettigrew's betrayal allowed Voldemort to kill James and Lily. Dumbledore held Snape to his promise, saying that all he could do now was to protect Harry, Lily's child.

In a different memory, Snape has temporarily contained a deadly curse in Dumbledore's hand that was infected when he put on the Ring Horcrux. Dumbledore has about one year to live. They discuss Voldemort's plot to use Draco to murder Dumbledore. Voldemort expects Draco to fail so he can then kill Draco to punish Lucius Malfoy. Voldemort likely anticipates Snape will finish Draco's task, but once Dumbledore is dead, the Dark Lord will no longer need a spy at Hogwarts. Dumbledore charges Snape with protecting the school once he is gone.

In yet another memory, Dumbledore tells Snape that Voldemort's soul shard had fastened itself to Harry, creating the link between Voldemort and Harry. However, to defeat Voldemort, Harry, and the soul fragment, must be killed by Voldemort. Snape is dismayed that Dumbledore protected Harry only to sacrifice him to Voldemort.

Sometime later, Dumbledore's portrait tells Snape that to retain Voldemort's trust, he must reveal Harry's true departure date from Privet Drive to the Dark Lord. If Snape can plant the idea to have multiple Potter decoys into Mundungus Fletcher's mind, Harry may escape unscathed.

Harry goes to the Forbidden Forest and surrenders himself to Voldemort, who casts a Killing Curse. Harry, believing himself dead, appears to be in a deserted King's Cross Station. On the floor, a small, flayed creature wails in pain. Albus Dumbledore appears and explains that when Voldemort used Harry's blood to re-animate himself, he unintentionally extended Lily Potter's protection; Harry's life was then tethered to Voldemort's.

Dumbledore speculates the two wands, already connected by their identical magical cores, had merged closer during Harry and Voldemort's duel. The wands' masters were also tied by their souls and blood, though Harry was the stronger wizard; Voldemort feared death, while Harry embraced the possibility, enabling his wand to imbibe some powers from Voldemort's, making it more powerful than any wand Voldemort wielded, even the Elder Wand. Now Harry can choose to "continue on" or return to the living world. Harry chooses to return.

Returning to himself, Harry pretends to be dead while Voldemort displays his body to the allies. Several things then happen simultaneously: the students' families begin arriving as reinforcements; many magical denizens, including the Centaurs, join the allies; and Neville beheads Nagini with the Sword of Gryffindor, destroying the final Horcrux.

Death Eaters storm the castle. Inside, Molly Weasley kills Bellatrix after a fierce duel. Enraged, Voldemort attempts to fatally curse Molly, but Harry's shield charm blocks him. Harry tells Voldemort that Dumbledore outsmarted him, planning his own death so that Snape was never the rightful owner of the Elder Wand. But Draco Malfoy unknowingly won the wand's allegiance when he disarmed Dumbledore atop the Astronomy Tower, only to lose its allegiance when Harry captured Malfoy's wand. Because Harry willingly sacrificed himself to Voldemort, the same magic that once protected Harry (the magical protection that his mother gave him), now protects his allies. Voldemort casts Avada Kedavra as Harry simultaneously conjures Expelliarmus. But Voldemort's Killing Curse rebounds, reflected by Harry's blood protection and the Elder Wand's allegiance to him. With all his Horcruxes destroyed, Voldemort dies instantly. After he dies, his dead corpse is taken to a different chamber in the Great Hall in Hogwarts (away from the bodies of 50 others who died fighting him). He died on May 2, 1998 at the age of 71 after trying to be immortal through Horcrux creation. Then his soul suffered a horrible fate: eternal torment in Limbo. Because his soul was completely damaged through all his Horcrux creations, he could not choose to return to the living world as a ghost or move on. His soul was trapped in Limbo forever.

Strengths
Lord Voldemort is an exceptionally brilliant and potent wizard. He was one of the most powerful wizards to ever exist. When Dumbledore first met him at the orphanage he was already aware of his magical abilities and used it to control and punish. This control of his powers mark him as a prodigy even as a young child. He becomes so proficient in Dark magic that Albus Dumbledore recognizes that he has entered into magical realms unknown to the average wizard. He apparently can fly without a broom, and his spells and curses are powerful and often deadly.

As a youth, Tom Riddle used his charm and guile to conceal his Dark and deceptive nature from all his Hogwarts teachers except Albus Dumbledore. Despite his cruelty and violence, Voldemort's charisma allowed him to recruit a devoted following while offering little in return. He becomes so powerful, that his Death Eaters remain loyal mainly out of fear, knowing they will be tortured or killed for any slight misstep. Once entering the Dark Lord's service, there is no leaving it.

Voldemort is also an accomplished Legilimens, able see into almost anyone's mind. There is some question as to whether he can penetrate Severus Snape's mind, or whether Snape's skill at Occlumency has protected him from that. Dumbledore is also likely able to block Voldemort.

We note that Voldemort is also originator of several spells that many in the Wizarding world thought impossible, including the ability to enter nearly closed windows by changing into "smoke", and possibly the ability to fly (Wizarding flight routinely involves charming an object such as a broom, carpet, car, or motorcycle to fly, and then riding that object). It could be argued, in fact, that Voldemort is a more powerful wizard than Albus Dumbledore; for more on that, see the Greater Picture section of this article.

Weaknesses
An insatiable lust for power compels Voldemort to utilize any means to achieve total domination over the wizarding world. He is loyal to no one, and he never hesitates to kill anyone, including his own followers, either when he is enraged, or when it serves his purpose. This was significantly undermining his power base, as his servants' loyalty to him was weakening.

There is only one wizard Voldemort fears: Albus Dumbledore, recognized as among the greatest and most powerful wizards ever. Once Dumbledore is dead, Voldemort seeks the Elder Wand, believing it will make him invincible, though he never bothers to understand why it is powerful.

Voldemort considers death the worst possible fate and has gone to extreme lengths seeking immortality. Dumbledore comments that when Harry and Voldemort duelled in the graveyard, Harry was the stronger wizard because he was prepared to die, if necessary, while Voldemort feared death despite his recent resurrection.

Voldemort is overconfident and continually ignores minor details, which often lead to his failures. In particular, he discounts any magic he is unable to understand, particularly that of non-human races like house-elves. While he recognizes that love can have a magical effect, he never understands it and underestimates its power, considering most emotions a weakness, and it remains a purely academic concept. He himself is unable to love anyone or anything, though he is somewhat sentimentally attached to Hogwarts castle, considering it the only home he has ever known. While possessing Harry's body in Harry Potter and the Order of the Phoenix, Harry's deep yearning to be rejoined with his beloved slain godfather drives Voldemort out. Harry's emotions are so overpowering and disturbing to Voldemort that he never attempts to possess Harry again, and he will consistently discount love's power.

Although Dumbledore mostly discounted it, because Voldemort so strongly believed in the prophecy stating that a "chosen one" would vanquish him, his actions became largely responsible for it eventually coming true. In effect, he created what he feared. By "marking" Harry as his enemy and killing his parents, he set the boy on a predetermined path leading to their eventual confrontation. Voldemort also failed to understand that love significantly empowered Harry, and always attributes Harry's repeated successes to luck and help from others, such as from Dumbledore. He also fixates on Harry's wand, believing it is the only thing standing between himself and Harry's ultimate defeat. Although the twin cores in Harry's wand and Voldemort's are unable to attack each other, Voldemort attributes some super-magical power to this. This mistaken belief is fueled by Snape, as Voldemort's closest confidant, who has claimed that Harry is only a moderately competent wizard, not a particularly strong one. Whether or not Snape actually believes this or was deliberately misleading the Dark Lord, Voldemort accepts Snape's words as fact.

Relationships with Other Characters
Voldemort calls Death Eaters his true family, though he has compassion for none, using them only as servants rather than comrades, eliminating them almost capriciously if they fail him in some way, are unfortunate enough to be in close proximity when he is enraged, or if it serves his evil plan. Indeed, Voldemort murders Severus Snape, who he probably considered among his most trusted and valuable Death Eaters after Snape killed Dumbledore, solely in an attempt to gain more magical power although he did express regret at doing so. Voldemort also shows no respect or allegiance to Bellatrix Lestrange, his most fanatical follower; he does rescue her during the Battle at the Ministry, though likely because she was still useful to him, rather than feeling any loyalty to her.

Voldemort became obsessed with Harry Potter after he failed to kill the one-year-old boy – livid that a helpless infant caused his downfall. He later seeks revenge on Harry to prove that he, Voldemort, is the most feared and powerful wizard of all time. Voldemort considers Harry weak in comparison to himself and he always discounted how love's power has aided Harry. But after possessing Harry's mind, Harry's overwhelming emotions for his friends and family are so overpowering and disturbing to Voldemort that they drive him out. He never attempts to possess Harry again.

Even from an early age, Voldemort considered himself superior to all other wizards except one – Albus Dumbledore, said to be the only one he ever feared. When he first met the eleven-year-old Tom Riddle, Dumbledore sensed this wizard was different, though he never suspected the young boy would become the most malevolent Dark wizard ever known. At Hogwarts, Dumbledore resolved to keep an eye on Riddle while concealing his suspicions, hoping Tom had abandoned his thieving and cruelty. Tom, meanwhile, cultivated a false facade, charming many, while quietly sowing his evil empire, recruiting fellow Slytherins to become his first Death Eaters. Dumbledore suspected Tom was engaging in some Dark activities at Hogwarts, particularly after a Muggle-born girl was killed. From then on, he watched Riddle even more closely, but could never prove he was involved in anything while he was still a student at Hogwarts.

Analysis
Lord Voldemort, née Tom Marvolo Riddle, is the primary antagonist in the Harry Potter series, and the only living descendant of Salazar Slytherin (by way of his mother, Merope Gaunt, and her father Marvolo Gaunt). His only allegiance is to himself, and he is obsessed with achieving immortality and obtaining total power. Voldemort advocates pure-blood elitism, despite having a Muggle father and witch mother, making him a half-blood, and considers other "Mudbloods" as filth.

Much of Voldemort's character was shaped by his difficult and lonely childhood in a Muggle orphanage. While there, he remained friendless, partially because the Muggle orphans feared and shunned the strange boy, but also because he felt superior and apart from them. Knowing that he possessed unusual powers others lacked, Tom engaged in cruel acts against his fellow orphans, often stealing their possessions as trophies. Voldemort had a multifaceted personality, but upon entering Hogwarts, and knowing that Dumbledore at least partially understood his true nature, he crafted a new persona for himself. He became a seemingly quiet, model student, using charm and guile to win his instructors' favor and gather peers. This charisma helped fuel his later rise to power, gaining him many loyal followers who adopted his pure-blood ideology. Voldemort rarely appreciated or rewarded this loyalty, however, and ruled through fear, cruelty, and intimidation, even with his most devoted servants, solely to attain his goals.

It is unknown if Tom's Muggle father, Tom Riddle Sr., ever knew his son existed, apparently having been duped into a bogus marriage by Merope Gaunt, who probably used a love potion to entrap him. Riddle left her before Tom was born. Regardless, Tom grew up deeply loathing his father for abandoning him and his mother, who died heartbroken shortly after Tom's birth. Tom so despised his Muggle blood, that he murdered his Riddle relatives in an attempt to erase his "tainted" heritage.

Whether or not Tom would have developed any differently if either or both his parents had raised him can only be speculated about. The Riddle family would have been unable to understand or control Tom's unique powers, probably fearing and rejecting him, while he could have considered them weak, inferior, and possibly disposable. His Gaunt relatives, meanwhile, were firmly entrenched in their haughty, pure-blood beliefs, considering themselves superior to all wizards, even other pure-bloods, due solely to their ancestry and despite previous generations having squandered the Gaunt fortune that had long ago sunk the family into poverty and a low-class status. They epitomized the Slytherin belief that they were owed whatever they wanted. This environment likely would have warped Tom's development, though Merope apparently eschewed at least some Gaunt beliefs and had defied her family by marrying a Muggle, seeking a better life.

Like his Gaunt family, Voldemort is a parselmouth, the ability to speak with snakes. This trait is descended from his ancestor, Salazar Slytherin. As Slytherin's heir, in Harry Potter and the Chamber of Secrets, Tom Riddle's memory that is stored in a diary is the only one able to control the basilisk. Aware that Harry is also a Parselmouth, Riddle warns him that the basilisk will not answer him; Harry heeds his advice. When Voldemort attempted to murder baby Harry, he had unknowingly transferred some powers, including Parseltongue, to the boy. Just why this occurred is explained more fully in Harry Potter and the Deathly Hallows.

More than anything, Voldemort feared death. The name, Voldemort, can be interpreted as "flight from death" in French. To achieve immortality, Voldemort splintered his soul into multiple pieces, embedding them into objects known as Horcruxes. As long as any Horcrux survived, Voldemort could not be killed. By shredding his soul this way, it was irreparably damaged, and as Harry systematically destroyed the Horcruxes, what remained likely became even more diminished, further dehumanizing Voldemort. Harry is tied to Voldemort by one of these soul shards, but also by his blood, used in Voldemort's resurrection, and by their wands. Voldemort's yew wand contains a phoenix feather core; one of only two feathers donated to the wand maker Mr. Ollivander by Fawkes, Dumbledore's loyal companion and animal familiar. Fawkes' other feather lies within Harry's wand.

Voldemort's reputation became so Dark and evil, that merely speaking his name aloud instilled dread into most who hear it. But as powerful and terrifying as the Dark Lord was, it was said that Albus Dumbledore was the only wizard Voldemort truly feared. Voldemort admitted that he himself had never, "sought a duel," with Dumbledore, but later declares that Dumbledore is, "getting weak in old age," and he is, "not the wizard he once was". He considers Dumbledore's views regarding love and loyalty as a joke, believing only in power and the ability to use it. Voldemort's over-confidence and own self-indulgence eventually causes his downfall.

It is also interesting to note that Harry's scar never pains him in Harry Potter and the Chamber of Secrets, even when he is directly battling Tom Riddle's memory that was contained in the diary Horcrux. When Riddle attacks Harry in the Chamber, it is some forty years after the diary was created, and so the Voldemort that had inflicted the scar, and the Riddle that Harry was fighting, are quite different people. That is likely why Harry's scar fails to react to the young Riddle.

Questions

 * 1) Despite being married, Bellatrix may have harbored romantic feelings for Voldemort. Give evidence for or against this.
 * 2) If Bellatrix had romantic feelings for Voldemort, were they reciprocated by him? Explain why or why not. Just what might he feel for her?
 * 3) Would Voldemort have turned out differently if he had been raised by his parents rather than growing up in an orphanage? Give arguments both for and against this.
 * 4) Why was Dumbledore the only wizard Voldemort ever feared? Be specific in your answers.
 * 5) If Voldemort firmly believed that pure-blooded wizards are superior, why did he think that baby Harry, a half-blood, was "The Chosen One", rather than Neville Longbottom, who is a pure-blood?
 * 6) Compare and contrast the Dark wizards, Lord Voldemort and Gellert Grindelwald. Who was more evil and powerful? Give specific examples to support your answer.

Greater Picture
It is worth remembering that Voldemort, or Tom Marvolo Riddle, as he was then known, was born in 1926 on the 31st of December. His world views were mostly formed in a London orphanage, and later at Hogwarts, at about the time that the National Socialist (Nazi) party was coming to power in Germany. This may have influenced his pureblooded wizarding views, and fostered the need to eradicate the Muggles that so closely mirror Aryan purity beliefs and the Final Solution proposed in Germany at that time. The author has mentioned this similarity as well, though she notes that she was rather taken by surprise on discovering the similarities in detail. This is not to say, or imply, that Voldemort was a Nazi, or had any sympathy for the Nazi party's aims; he no doubt viewed them as, if anything, an amusing but totally insignificant side show in the useless Muggle world. However, the "racial purity" idea, involving (in this case) eliminating anyone unable to prove that they were descended only from wizarding families, certainly may have provided the basis for Voldemort's many actions.

As mentioned, Harry's scar hurts him because Voldemort's soul fragment within him, recognized and reacted to Voldemort's soul (or what was left of it) whenever the two were in close proximity, or when Voldemort was experiencing strong emotions. The soul fragment that Harry was battling in the Chamber of Secrets had been splintered off Voldemort some forty years earlier, and so likely there was little recognition there; certainly not enough for the soul fragment in Harry to recognize it. In support of this, we should also note that Harry never reported any pain in his scar during the final confrontation with Voldemort, late in Harry Potter and the Deathly Hallows, after the soul fragment that he carried had been killed.

There is a possibility that the widely held belief that Dumbledore is a more powerful wizard than Voldemort is not, perhaps, as well supported as it might be. We can see that Voldemort is wary of Dumbledore, but while Dumbledore may be, or may have been, "the only one he ever feared," still the duel in the Atrium of the Ministry does seem to end in something resembling an even match, with Voldemort retaining sufficient power to escape, then return briefly to retrieve Bellatrix from her imprisonment under the statue fragments.

It is possible that Dumbledore's powers have decreased as he aged, but we do not have enough information to guess whether or by how much. It is similarly possible that Voldemort's re-embodiment at the end of Harry Potter and the Goblet of Fire may have also rejuvenated him to some extent, but again we do not have any way to judge this.

Given that Dumbledore was the true master of the Elder Wand, having possessed it since his defeat of Grindelwald in 1945, it is reasonable to think that at least some of Dumbledore's ascendance over Voldemort in the Atrium was due to the power of that wand.

Whether or not Voldemort knew of the existence of that wand, which Dumbledore may have started wielding while Tom Riddle was still a Hogwarts student, or the story behind it, it is likely that Voldemort, fearing Dumbledore's spell-casting ability, avoided direct confrontation during his entire first rise to power. We do see Voldemort's almost overbearing confidence in himself and his existing wand, as late as the duel in the cemetery, though of course he believes his opponent then to be an effectively untutored youth depending purely on luck. And during Voldemort's second rise to power, we see him working against Dumbledore indirectly, trying to discredit him and Harry, and eliminate their allies. Thus the fact that Dumbledore did not directly face Voldemort during his first rise to power may simply be Voldemort's preferred modus operandi.

But given the limited number of times that we see Voldemort and Dumbledore in direct contention, it remains difficult to judge relative strengths. We note that Dumbledore willingly eschews the more powerful Unforgivable Curses, while Voldemort uses them freely; this might suggest that Dumbledore is more confident in his powers. But given that Dumbledore there is armed with the Elder Wand "which has never lost a duel" according to the myth, and Voldemort is using an ordinary, albeit well-tuned, wand, it seems likely that at least at that stage in their careers, Voldemort is, in fact, the stronger wizard.

In the Strengths section above, we noted that Voldemort may have originated the spell that allows him to fly, but there is some small question about that. It is noted that Snape also has that ability, and it is assumed that Snape learned it from Voldemort. We have seen that Snape may be a very inventive wizard in his own right, claiming to have originated the Sectumsempra curse; it is barely possible that Snape invented the personal flight charm and taught it to Voldemort. That is not to say that Voldemort was not the originator of a number of very powerful spells and potions; on this one, there is some small bit of doubt, however. The author certainly gives the impression that the spell was created by Voldemort, having Professor McGonagall state that Voldemort had taught it to Snape. Snape does, however, claim authorship of the Levicorpus charm, which is clearly related. Of course, refinement of that charm from simply hanging in air, to directed flight, could well be Voldemort's doing, if in fact Levicorpus was its basis.

A possible criticism against this would be that Levicorpus is not a spell very closely related to flight, as it was apparently designed to shock the opponent by making them "hang upside down" as though tied by invisible ropes. The Wingardium Leviosa levitation charm which is very widely known might be a more suitable charm to improve upon to achieve true flight. The fact that Snape was riding a broomstick early in Deathly Hallows while Voldemort himself was flying lends further credibility to the idea that Voldemort taught Snape how to fly after inventing it as a reward for his loyalty, perhaps for his successful assassination of Dumbledore.

There is also room for some doubt on whether Voldemort originated the curse on the Peverell ring, or whether he analyzed and replicated, or improved, the curse on the necklace mentioned as being in Borgin and Burkes, assuming that it, or some similarly cursed jewelry, had been in stock fifty years before we first see it. It is uncertain when Voldemort cursed the Peverell ring, except that it was not done at the same time as it was turned into a Horcrux; in Slughorn's memory, he was seen to be wearing it, and he would not be wearing an object that might kill him or one of his followers unexpectedly. We suggest that there is some question as to whether Tom Riddle hid the ring in the Gaunt shack before, or after, he had started work at Borgin and Burkes. In any event, whether he originated, replicated, improved upon, or was inspired by the curse on that necklace, or not, it is still a most impressive bit of magic for someone either still in school, or recently graduated.

Some would comment that Voldemort's using other people's spells seems out of character, given his pride and his habit of standing alone. However, Voldemort is not above using his lieutenants' abilities, even using them up if the situation seems to warrant it - notably the Malfoy family. We will also point out that the spell to create a Horcrux is not of Voldemort's devising, but that he claims credit for "having gone further than anybody along the path that leads to immortality," by creating multiple Horcruxes. Given what we know of his character, we believe that Voldemort would quite readily take a spell, enhance it, and then claim it for himself.

In an interview following the final book's publication, the author stated that Harry's parselmouth ability, along with his connection to Voldemort's thoughts, vanished when Voldemort's soul shard within Harry was destroyed. The author has further stated that Harry has never missed this ability.


text:
Chess Opening Theory/1. e4/1...e5/2. Nf3/2...Nc6/3. Bc4

= Italian Game =

3. Bc4
The Italian Game is very popular and one of the oldest openings in chess. White develops the bishop to a good square where it controls the centre and targets f7. This opening is very easy to study and one of the best choices for beginners. Black has a few responses here, but the most played are 3. Nf6, the Two Knights Defense, which ironically can lead to rather sharp lines, and 3. Bc5, the Giuoco Piano, which focuses on quiet play and developing pieces, though the Evans Gambit can subvert that.

Theory table
'''1. e4 e5 2. Nf3 Nc6 3. Bc4'''

Statistics
Estimated next move popularity Nf6 56%, Bc5 38%, Be7 3%, d6 2%, all else less than 1%


text:
Jet Propulsion/Gas turbine energy exchange

In a gas turbine processes energy is converted from one form to another.

Kinetic energy to fluid temperature

Changing the velocity of the fluid by pressure changes simultaneously changes the temperature. Compression work raises the apparent temperature of the fluid. We can relate Mach number to the internal energy of the fluid:

$$M^2 = \frac{2}{\gamma-1} \frac{u^2}{c_P T}$$

... more gas dynamics

Work addition to the fluid by blades

Combustion energy addition

Heat transfer to and from walls


text:
Chess Opening Theory/1. e4/1...e5/2. Nf3/2...Nc6/3. Bc4/3...Bc5

3...Bc5 – Giuoco Piano
White's main plan is to take control of the center with a d4 push. They must choose whether to do it right then (/4. d4/ to get a lead in development (despite the loss of the pawn)), or to prepare it with moves like /4. c3/ or /4. b4/.

White may also forget about the d4-push, and play a quieter line, by supporting the center with /4. d3/, for example.

Theory table
'''1. e4 e5 2. Nf3 Nc6 3. Bc4 Bc5'''


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Diagnostic Radiology/Musculoskeletal Imaging/Tumors Basic/Osteosarcoma

Osteosarcoma is the most common malignant primary bone tumor. Osteosarcoma tends to occur in children and young adults typically 10-25 or 30 years of age. Osteosarcomas also tend to occur in patients in the sixth decade, likely related to malignant degeneration of Paget's disease. It is said that they tend to occur most often towards the end of long bones in the metaphyseal region but they can also arise in the diaphysis and there is enough variation that this parameter is not terribly helpful in differentiation. A typical osteosarcoma is destructive with associated sclerosis from either malignant bone formation or reactive sclerosis. There are multiple types of osteosarcoma. The most common of which is the Conventional Osteosarcoma which accounts for 75% of cases. Conventional osteosarcoma is typically located around the knee and is a very aggressive lesion associated with a soft tissue mass, cortical destruction, a permeative pattern of bone change. Most demonstrate some degree of osteoid matrix. Conventional osteosarcomas commonly arise in the metadiaphysis but regularly (75%) cross the physis to involve the epiphysis. The distal femur and proximal tibia are the bones most commonly involved, followed by the humerus and iliac wing. They have a rapid doubling rate, are often large when discovered and are aggressive in appearance. Lesions are typically permeative with a wide zone of transition. Cortical breakthrough can be seen typically with a large soft tissue mass. Periosteal reaction typically presents with a Codman’s triangle or sunburst pattern. At least 90% of conventional osteosarcomas produce osteoid matrix in variable quantities which alters their radiographic appearance. Lesions that are dense appear low in signal on T1 and T2 sequences and if they are less dense, typically will be low signal on T1 and higher signal on T2 imaging.

Fig. 1 X-ray and CT demonstrate expansile mass centered in the femur with extensive osteoid matrix and cortical destruction.

Differential is quite short with a typical conventional osteosarcoma and includes Ewing's sarcoma. Metastases are said to occur in up to 10-20% of patient’s at clinical presentation and hematogenous spread to lungs or bones and lymphatic local spread are typical.

Fig. 2 AP and lateral view of knee showing intramedullary osteosarcoma of distal femur.

Fig. 3 AP pelvis shows marked sclerosis of the left ilium and a large, sclerotic soft tissue mass. CT demonstrates the sunburst or explosive dense osteoid matrix emanating from the ilium and MRI shows the large heterogeneous soft tissue mass.

Parosteal Sarcoma
Parosteal osteosarcoma is the 2nd most common type of osteosarcoma. 80% occur between the ages of 20 and 50. They are commonly found at the distal femoral metaphysis, posteriorly, less commonly in the proximal tibia and humerus. Parosteal osteosarcoma arises from the surface of the bone and is seen as a soft tissue mass often growing around the bone of origin. The osteoid matrix is typically more mature and densely sclerotic, especially centrally. MRI appearance is variable depending on the amount of osteoid formation, cellularity and presence of cartilage, usually appearing quite heterogeneous. If there is little cellularity and cartilage the lesion will be lower signal intensity. They are low grade tumors and grow slowly, but with recurrence can become more aggressive. Metastases are less common than with conventional osteosarcoma but can metastasize to the lung. Differential includes myositis ossificans, cortical desmoid tumor and osteochondroma. Myositis ossificans is typically more dense peripherally rather than centrally, helping in differentiation. Osteochondroma has more normal appearing marrow and cortical bone.

Fig. 4 Parosteal sarcoma arising from the posterior margin of the femur with a large soft tissue mass and dense osteoid matrix.

Telangiectatic Osteosarcoma
Telangiectatic osteosarcoma is a rare variant that present as an entirely lytic bone lesion with a much less aggressive appearance. Typical age is 10–25 years of age and lesions commonly occur in the metadiaphysis of long bones, similar to conventional osteosarcoma. Lesions are more geographic but portions of the mass can have a wide zone of transition and cortical breakthrough with a soft tissue mass. Lesions are highly vascular, partly necrotic and often have large pools of blood within them with soft tissue peripherally and along septa. Leading to an MRI appearance with internal septa, fluid fluid levels, peripheral heterogeneity. Telangiectatic osteosarcoma commonly enhances. Differential includes aneurysmal bone cyst and giant cell tumor.

Periosteal Osteosarcoma
Periosteal osteosarcoma are more rare than conventional or parosteal osteosarcoma and arises from the surface of the bone, most commonly in diaphyses of femur and tibia. Age of presentation is typically 10–20 years of age. Scalloping of the adjacent cortex is common and there are often spicules of bone emanating from the lesion in a sunburst pattern. Also seen commonly is periosteal reaction. Intramedullary invasion and extension is uncommon. MRI signal is typically not helpful (low T1 and high T2.) Spicules of bone emanating in sunburst pattern tend to be low T2 in signal. Differential includes juxtacortical chondroma and high-grade surface osteosarcoma.

High Grade Surface Osteosarcoma
Rare subset of osteosarcoma similar to periosteal subtype commonly occurs in the diaphyses and is more often associated with intramedullary invasion. Low Grade Intraosseous Osteosarcoma Rare entirely intraosseous tumor that is quite variable in appearance and can occur in the diaphyses or metadiaphyses. Age- <30 Soft Tissue Osteosarcoma Another rare form of osteosarcoma found most commonly in the thigh, upper extremity or retroperitoneum. Masses have variable amounts of mineralized osteoid.

Osteosarcoma in older patients (>60)
Osteosarcomas in older patients can be primary lesions but around 50% are thought to arise in pre-existing lesions like Ewing's sarcoma, dedifferentiated chondrosarcoma or previously irradiated tissues. Most lesions are entirely lytic and can occur in the facial bones, axial skeleton and in the soft tissues. Appearance varies greatly with origin.

Imaging Workup
Typical imaging of any suspected osteosarcoma should include a PA and lateral view of the chest to help rule out metastatic lesions. Specific imaging of the lesion should include X-ray - Plain films of the lesion in question or affected anatomy.

 * CT Scan - Better evaluates the bone lesion and soft tissue involvement. CT of the chest may be performed to improve sensitivity for detection of pulmonary metastasis.
 * MRI - MRI of primary lesion best evaluates the intramedullary extension and the extent of soft tissue involvement. Additionally, MRI is the most sensitive modality for detection of skip lesions or local metastases. MRI is much more accurate for determination of surgical margins than CT.
 * Bone Scan - Helpful to detect metastatic lesions.

Treatment
Treatment is usually performed with both chemotherapy and primary resection. Prior to chemotherapy administration, up to 80% of patients treated with surgical excision of primary tumor developed pulmonary metastases. Postoperative, adjuvant chemotherapy is now standard of care. Surgical excision of primary lesion remains the primary treatment modality.

MRI is important for defining the surgical margins especially in the bone marrow. Surgical margins of ~6 cm from the edge of abnormal MRI signal are considered adequate. The margins are much less extreme in the soft tissues. Surgical excision of pulmonary metastases is typically via wedge resection. Follow up imaging - Imaging protocols vary but are often done at 3 months for the first year then at 6 months for the next year or two. After the first two or three years it is common to continue with annual MRI. Additional imaging would of course be dictated by changing symptoms.


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Diagnostic Radiology/Musculoskeletal Imaging/Tumors Basic/Telangiectatic Osteosarcoma

Telangiectatic osteosarcoma This is a rare variant that present as an entirely lytic bone lesion with a much less aggressive appearance. Typical age is 10–25 years of age and lesions commonly occur in the metadiaphysis of long bones, similar to conventional osteosarcoma. Lesions are more geographic but portions of the mass can have a wide zone of transition and cortical breakthrough with a soft tissue mass. Lesions are highly vascular, partly necrotic and often have large pools of blood within them with soft tissue peripherally and along septa. Leading to an MRI appearance with internal septa, fluid fluid levels, peripheral heterogeneity. Telangiectatic osteosarcoma commonly enhances. Differential includes aneurysmal bone cyst and giant cell tumor.


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Diagnostic Radiology/Musculoskeletal Imaging/Tumors Basic/Parosteal Osteosarcoma

Parosteal osteosarcoma is the 2nd most common type of osteosarcoma. 80% occur between the ages of 20 and 50. They are commonly found at the distal femoral metaphysis, posteriorly, less commonly in the proximal tibia and humerus. Parosteal osteosarcoma arises from the surface of the bone and is seen as a soft tissue mass often growing around the bone of origin. The osteoid matrix is typically more mature and densely sclerotic, especially centrally. MRI appearance is variable depending on the amount of osteoid formation, cellularity and presence of cartilage, usually appearing quite heterogeneous. If there is little cellularity and cartilage the lesion will be lower signal intensity. They are low grade tumors and grow slowly, but with recurrence can become more aggressive. Metastases are less common than with conventional osteosarcoma but can metastasize to the lung. Differential includes myositis ossificans, cortical desmoid tumor and osteochondroma. Myositis ossificans is typically more dense peripherally rather than centrally, helping in differentiation. Osteochondroma has more normal appearing marrow and cortical bone.

Fig. 1 Parosteal sarcoma arising from the posterior margin of the femur with a large soft tissue mass and dense osteoid matrix.


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Jet Propulsion/Aerodynamics

Basic principles
Aerodynamic analysis attempts to progressively analyze the flows in the aerodynamic stages. Practical design includes substantial theoretical, computational and experimental analysis.

The stagnation or total temperatures and pressures are needed to measure the energy additions in high speed gas flows that occur in gas turbines. Using the Mach number allows us to factor in the compressibility of the gas.

Compressible fluid flow equations
See [NACA 1135: Equations, Tables, and Charts for Compressible Flow].

Continuity
In a steady flow, for any two sections of the flow on a stream tube

 * $$ \rho_1 c_1 A_1 = \rho_2 c_2 A_2 $$

or in differential form

 * $$ \frac{d}{dx} (\rho c A) = 0 $$

or

 * $$ \frac{d\rho}{\rho} + \frac{dc}{c} + \frac{dA}{A} = 0 $$

Where $$\rho$$ is the density of the fluid

$$c$$ is the velocity of the fluid

and

$$A$$ is the cross-sectional Area for the tube or channel

Momentum
The net force on the control volume matches the momentum change in the fluid

 * Adp=-ρA c dc
 * dp=-ρc dc

Energy
The change in enthalpy is balanced by the change in kinetic energy

 * dh + c dc=0

Where h is enthalpy per unit mass

and c is velocity of flow.

Enthalpy
The enthalpy of a gas h at temperature T is

 * $$h = c_p T$$

where $$c_p$$ is the constant pressure specific heat of the gas. For air $$c_p$$ is about 1.005 kJ/kg K.

Stagnation temperature
Stagnation temperature is the temperature of the gas if it is brought to rest adiabatically. Adding the kinetic energy to the internal energy of the gas we get the relation

 * $$h_t = c_p T_t = c_p T + \frac{c^2}{2}$$

 * $$T_t = T + \frac{c^2}{2 c_p} $$

where Tt is the total(stagnation) temperature of the flow.

The total enthalpy relation encapsulates the energy changes in isentropic compressors and turbines. To add energy to the flow the gas is put through a relative deceleration process against the compressor and diffuser surfaces and gains energy. To extract energy the gas is accelerated against nozzles and turbine buckets.

The Mach number of the flow is

 * $$ M = \frac{c}{a}=\frac {c}{\sqrt{\gamma R T}}$$

Substituting

 * $$T_t = T + \frac {\gamma R T M^2 }{ 2 c_p} $$

since  R= cp - cv  and  γ = cp / cv

 * $$T_t = T\left(1 + \frac {\gamma M^2 }{2} (c_p-c_v)/c_p\right) $$

 * $$\frac{T_t}{T}=\left(1 + \frac {\gamma-1}{2}M^2\right) $$

Where $$\gamma$$ (greek letter gamma) is the adiabatic expansion coefficient between pressure and volume $$p_1V_1^\gamma = p_2V_2^\gamma$$

This is the temperature if the gas is brought to rest adiabatically.

Isentropic stagnation pressure

 * $$\frac{p_t}{p}=\left(\frac{T_t}{T}\right)^{\gamma/(\gamma-1)} $$

 * $$\frac{p_t}{p}=\left(1 + \frac {\gamma-1}{2}M^2\right)^{\gamma/(\gamma-1)} $$

Isentropic stagnation density

 * $$\frac{\rho_t}{\rho}=\left(\frac{T_t}{T}\right)^{1/(\gamma-1)} $$

 * $$\frac{\rho_t}{\rho}=\left(1 + \frac {\gamma-1}{2}M^2\right)^{1/(\gamma-1)} $$

Duct flow
A steady inviscid adiabatic quasi-one dimensional flow obeys the following equations:

Differential continuity equation

 * d (ρ c A) =0

Differential momentum equation

 * dp=-ρ c dc

Differential energy equation

 * dh + c dc=0

Rearranging continuity

 * $$\frac{d\rho}{\rho}+\frac{d c}{c}+\frac{d A}{A}=0$$

Rewrite momentum equation

 * $$\frac{d p}{\rho}=\frac{dp}{ d \rho }\frac{d \rho}{\rho} = -c dc$$

 * $$\frac{dp}{ d \rho } \equiv \frac{\partial p}{\partial \rho}$$

The velocity of sound is:

 * a =(dp / dρ)1/2

Rearranging and substituting:

 * a2=(dp / dρ)

 * a2 dρ / ρ = -c dc

 * $$\frac{d \rho}{\rho}= -\frac{c dc}{ a^2 }= -\frac{c^2}{ a^2 } \frac{dc}{c} = -M^2 \frac{dc}{c}$$

Substituting into continuity equation

 * $$M^2 \frac{dc}{c}-\frac{d c}{c}-\frac{d A}{A}=0$$

We get the area velocity equation:

 * $$\frac{d A}{A} =(M^2-1) \frac{dc}{c}$$

Thus for acceleration (positive dc/c) the area must decrease for Mach numbers below 1 and increase for Mach numbers above 1.

The relationship between Mach number and duct area related to the throat area A* is:

 * $$\frac{A}{A^*}= \frac {1}{M} \left[ \frac{2}{\gamma+1}\left(1+\frac{\gamma-1}{2}M^2\right) \right]^{\frac{\gamma+1}{2(\gamma-1)}}$$

The temperature relation is

 * $$\frac{T}{T_t}= \left[ \frac{2}{\gamma+1}\left(1+\frac{\gamma-1}{2}M^2\right) \right]^{-1}$$

the pressure relation

 * $$\frac{p}{p_t}= \left[ \frac{2}{\gamma+1}\left(1+\frac{\gamma-1}{2}M^2\right) \right]^{-\frac{\gamma}{2(\gamma-1)}}$$

and the density relation

 * $$\frac{\rho}{\rho_0}= \left[ \frac{2}{\gamma+1}\left(1+\frac{\gamma-1}{2}M^2\right) \right]^{-\frac{1}{2(\gamma-1)}}$$

The figure below shows these relationships for air with γ of 1.4.

A fully expanded gas would approach a Mach number of infinity as it's temperature drops to absolute zero.

Mass flow
The figure above shows this exchange for a fluid with γ=1.4 undergoing an adiabatic expansion. Sonic velocity (Mach 1) is achieved when the pressure drops to 0.528 and the area for a particular mass flow is minimum at this Mach number. The flow at this condition is said to be choked and any further reductions in duct area will not produce acceleration of the stream. The mass flow per unit area is

 * $$ \dot{m} = A \rho v $$

 * $$ \dot{m} = A \rho_0 \left[ \frac{2}{\gamma+1}\left(1+\frac{\gamma-1}{2}M^2\right) \right]^{-\frac{1}{\gamma-1}} V $$

Nozzles
A nozzle converts internal energy of the gas into directed kinetic energy by expanding along a pressure gradient.

As the gas expands, initially the volume increment is smaller than the velocity increment and the stream tube converges. At M=1, the effects balance and for M>1 the differential volume increase is greater than the velocity increase and a divergent stream is needed. The narrowest section of the nozzle is called the "throat".

Decreasing the pressure at the exit of a nozzle of fixed geometry increases the exit velocity until the velocity in the smallest section of the nozzle becomes sonic. The nozzle is then said to be "choked" and further reduction of the exit pressure has no effect on the flow upstream of the throat.

The maximum exit velocity depends on the energy content of the source gas.

Choked flow
Choked flow is the maximum flow that can pass through a passage for a given initial total conditions. Boundary layer effects further limit the flow through real nozzles.

Diffusers
A diffuser converts relative kinetic energy into pressure.

An ideal diffuser would recover the stagnation pressure, but practical diffusers cannot bring the fluid velocity to zero and have losses. The pressure recovered by such a diffuser is:

 * $$ \pi_d = p_{t2} / p_{t0} $$

A subsonic diffuser is a divergent passage. Diffusers operate in an adverse pressure gradient regime and the boundary layer development must be carefully managed to avoid flow separation. Boundary layers can be energized by extraction or aspiration but this has energy and complexity costs.

Achieving stable supersonic diffusion without shockwaves is almost impossible, since instabilities become rapidly magnified as the flow can rapidly snap to become subsonic via a normal shockwave and accelerate in the convergent passage. Usually multiple inclined shockwaves are employed to minimize entropy rise.

Shocks
The shock is a thin boundary across which heat transfer and viscous heating make the flow subsonic. The isentropic relations above are not applicable across a shock wave. The total temperature across a shock (normal to the shock surface) remains constant but the total pressure is lost. The loss depends on the incident Mach number.

Normal shock
The Mach number M2 after the shock is:

 * $$M_2^2=\frac{1+[(\gamma-1)/2]M_1^2}{\gamma M_1^2-(\gamma-1)/2}$$

A higher incident Mach number will transition to a smaller downstream subsonic Mach number.

The density & velocity relation

 * $$\frac{\rho_2}{\rho_1}=\frac{u_1}{u_2}=\frac{(\gamma+1)M_1^2}{2+(\gamma-1)M_1^2}$$

the pressure relation

 * $$\frac{p_2}{p_1}=1+\frac{2 \gamma }{\gamma+1}(M_1^2-1)$$

and the temperature relation

 * $$\frac{T_2}{T_1}=\frac{h_2}{h_1}=\left[1+\frac{2 \gamma }{\gamma+1}(M_1^2-1)\right] \frac{2+(\gamma-1)M_1^2}{(\gamma+1)M_1^2}$$

Velocity triangles
Basic analysis of the effect of the blade rows on the airflow can be done through velocity triangles. The figure below shows a basic set of velocity triangles for compressor and turbine rows.

In the compressor the airflow is decelerated (diffused) in the velocity frame of the blade cascades. If the velocity of the inflow is u in the static frame then the rotor blades see the vector sum of u and ωr which is the velocity of the blades whirling at angular speed ω at that particular radius r. The rotor blades turn the flow incoming in the rotor frame of reference at velocity vri and diffuse it down to velocity vre. The stator sees the incoming flow at ure and diffuses it down to use and turns it back to the axial direction. The typical axial Mach number is around 0.6 and the rotor angular Mach number (ωr/a) is kept as high as possible to maximize the compression per stage. Since the fundamental gas dynamic process in the compressor is subsonic and supersonic diffusion, the limitations are imposed by the boundary layers and adverse pressure gradients which amplify them. The ultimate limit of compression is when the boundary layer diverges on the suction side of the blades and the blade row stalls.

The velocity triangles for compactness can be combined as shown on the right side since the angular velocity of the blade row is equal at inlet and exit.

In the turbine the airflow is accelerated (nozzled) in the velocity frame of the blade cascades. The incoming flow is accelerated and turned by the stators (nozzle vanes) to velocity uri and directed towards the turbine rotor. In the rotor frame of reference the flow comes in axially (or nearly so) at velocity vri and is accelerated and turned to velocity vre. The exit velocity ure then is nearly axial once the angular velocity ωr of the turbine blades is subtracted.

The turbine’s degree of reaction is the kinetic energy that occurs in the turbine rotor compared to the total kinetic change. The triangles above describe an approximately 50% reaction turbine. Impulse turbines have the rotor frame velocities vri and vre changing only in direction indicating that inlet and exit incidence angles of the blades are equal in magnitude if the axial velocity does not change.

Axial Compressors
Axial compressors are typically designed numerically since the flows in them are highly complex and three dimensional. The compression produced by the stage is determined by the tangential Mach number. The flow through the compressor depends on the axial Mach number and the area of the annulus. Improvements in design of the blades have allowed relative Mach numbers of 1.5 being achieved at the tip of the fan. The hub may be half the tip radius of the blades and the tangential velocity can vary by a factor of 2. Blades which operate supersonically for part of their span are called transonic.

Solidity is the ratio of the chord of the blades to the tangential distance subtended by the blade. Aspect ratio relates the blade chord to the blade length. The modern trend is towards lower aspect ratios. Higher aspect ratio blades tend to be lighter and blade loss is slightly less catastrophic an event. They often have part span shrouds to prevent flutter. Wide chord blades have recently been engineered to provide better performance, since they allow higher pressure ratios to be achieved. The width of the blade allows for a better shock structure in the supersonic regions of the blade, and a lower pressure gradient that delays separation. They can also avoid part span shrouds since their torsional rigidity is higher.

The blades act like staggered airfoils and they can tolerate a few degrees of incidence before the loss factor diverges. The loss factor is defined as the loss in total pressure divided by the dynamic pressure of the incident flow (pt-p). The minimum loss factor ranges from about 0.02 increasing with the inlet Mach number.

The compressor blade rows perform diffusion in reducing the velocity difference while increasing pressure.

Blade profiles
The earliest compressors employed circular arc blades. Double circular arcs have also been used, while modern compressors use more sophisticated 3D CFD designed blades.

Subsonic blades
For subsonic blades the passage widens as the air goes through it and simultaneously turns. The blades have higher inclination on the leading edge relative to the axial direction which reduces at the trailing edge resulting in a widening channel through which air must flow. The convex (surface) surface presents a large adverse pressure gradient which tends to enlarge the boundary layer. If the adverse gradient exceeds a critical level then flow separation and blade stalling occurs.

Aspirated compressor blades evacuate the suction side boundary layer and allow for larger diffusion.

Transonic blades
Fan blades are typically transonic. The incident flow approached the blade at supersonic velocity. The initial diffusion happens through a converging wedge shaped passage that creates multiple inclined shocks terminated by a stronger normal shock in the passage that makes the flow subsonic. The subsonic flow is then further diffused by a diverging passage as in subsonic blades.

Supersonic blading is easy to see in the outer periphery of the fans of commercial airliners. The leading edges are sharp and appear to be curved slightly in the opposite direction to create the supersonic wedge. The incident flow while highly 3 dimensional is qualitatively comparable to the flow into a 2D intake of a supersonic aircraft such as the F-15.

For compressor stages it is advantageous to bring the flow subsonic by the use of variable stators. Most large modern engines have variable stators that allow subsonic blading to be used while providing good performance throughout the operational envelope. The variable stator adds swirl to the flow so that the Mach number variation between root and tip is reduced preventing stall at the root of the blades.

Multistage compressors
For multiple compressor stages on a shaft the inlet Mach number progressively drops as the air is compressed and heats up.by

Mass flow
The mass flow in a duct is maximum if the Mach number is close to unity. The axial Mach number through the engine is kept close to one to reduce the blade heights. The blockage introduced by the hub and casing boundary layers, as well as the cross sectional area of the blades reduces the mass flow below the theoretical value. Actual axial Mach numbers range up to 0.6.

Loss mechanisms
Real compressors suffer from various loss mechanisms.

Tip leakage

Hub and casing boundary layers

Seal leakages

TBD

Stage performance
The corrected speed of the engine is defined as

Corrected speed $$= \frac{N}{(T_{t2}/T_t)}$$

Off design behavior
A multistage compressor operating at speeds lower than designed or with lower pressure ratio than designed, will load the front stages more than the rear stages. This can result in stalling of the front stages. Variable stators and multiple shafts can be used to solve this. Most modern turbofans have multiple shafts as well as variable stators in the front compressor stages. The variable stators balance the compression between the front and rear stages at off design conditions.

Matching
The compressor and turbine flows are “matched” to provide sufficient flow through the turbine, as well as sufficient power at the right rpm for the compressor. The temperature increase in the combustor allows us to calculate the relative areas required

Transients
Surge

To accelerate and engine the fuel added in the combustor is increased. This increases the temperature and the pressure in the combustor which now has to be generated by the compressor. If the compressor is too close to stall a surge may happen where the compressor stalls. In extreme cases the flow is reversed through the compressor and the hot combustor gases exit the front of the compressor. The cycle then continues at the Helmholtz frequency of the system till the disturbance is damped out. The engine controller is tasked with ensuring that the compressor doesn’t reach the surge line during acceleration.

In deceleration the fuel quantity is decreased and if the flame becomes too lean a flameout may occur.

Rotating stall

Unsteady flows in the compressor may cause some sections to stall (stall cells). These rotate with the blades and propagate from blade to blade, possibly exciting vibrations that can cause damage. The rotating stall precedes a full scale surge in which the compressor stalls in the entire circumference.

Centrifugal Compressor is a machine in which a particular gas or vapor is compressed by a radial acceleration by an impeller with the help of a surrounding case. It can then be arranged multistage for greater proportions of compression. The compression is largely influenced by a centrifugal pump.

In this article we will cover each and every point related to centrifugal compressor or sometimes called as radial compressor.

So let’s get started with it’s principle.

Centrifugal Compressor: Principle: The compression principle of centrifugal compressor is quite different from that of reciprocating or rotary type compressor.

When the air passes through the rotating impeller it experiences force or work which is performed by centrifugal forces. The work input takes place as an increase in pressure and velocity or speed of the air flow through the impeller. The air flow looses it’s velocity after entering in the diffuser section. The diffuser is actually a fixed or static component that escorts the air flow when it leaves the impeller. This loss in velocity eventually results in an additional increase of pressure. The impeller and the diffuser contributes about 65% and 35% of the total pressure developed or produced in the compressor. Construction: A centrifugal compressor generally consists of four components named inlet, impeller,diffusor and  collector. 1.Casing and inlet. The above mentioned components are usually protected or guarded by a casing or housing. A case house consists of number of bearings in order to provide radial and axial support of the rotor. The case also contain nozzles along with inlets and discharge flow connections in order to introduce and extract flow from the compressor.

Casing are of two types :-

a.) Horizontally split b.) Vertically split

A case is generally build of cast iron or steel.

2. Impellers. The impellers are assembled or mounted on a steel shaft and this assembly is known as compressor rotor (mostly in multi stage compressors). The rotor provide velocity to the gas with blades that are attached to a rotating disc. These blades can be forward-leaning, radial or backward-leaning depending upon the desired output. Most of the multistage compressors use backward-leaning blades as they provide the widest range of efficiency.

3. Diffuser. The impeller extracts the gas with great velocity into a diffuser passage. The diffuser usually compromise two walls which form a radial channel. Because of these arrangements the velocity of the gas decreases and dynamic pressure is converted into static pressure. The diffuser passages are small space between adjacent diaphragms which generally turns the gas flow 180° in order to direct it towards the next impeller.

4. Collector. Following the last stage impeller the gas must be collected and delivered to the discharge flange. The component used to collect the gas discharged through the diffuser is called as collector. It may also be termed as volute or scroll. The collector may also contain valves and other instrumentation in order to control the compressor.

Types: There are two types of it :- 1. Single stage centrifugal compressor 2. Multi stage centrifugal compressor

Both of these compressor work on the same principle but they do have some drastic difference in their construction and working.

So let’s study each of them separately.

1. Single stage compressor. Single stage compressors consist of only a single impeller and it is use for moving the air or other gases up to 3 to 1 compression ratio for either pressure or vacuum duty. These type of compressors are considered to have a beam design or an overhung impeller arrangement. In this type of arrangement the impeller is at the non-driving end of the shaft. One major advantage of it over the multistage compressor is that it provides high efficiency and the delivered gas is totally oil and surge free.

2. Multistage compressor. Multistage compressors consists of 1-10 impellers and it can be arranged in a variety of flow path configurations. Throughout each and every stage the temperature and the compression ratio are assumed to be constant. Multistage compressor can be arranged in straight-through, compound, and double flow configurations. Multistage compressor are also considered to have beam-type design but the impellers are located between the radial bearings.

Applications of centrifugal compressor:

1. Compressed gas or air: Centrifugal compressor is one of the most simple and efficient way to obtain or produce compressed air. They are best suited when the demand of air or gas is constant and excessive.

2. Food Industry: Food processing industry depends highly on this type of compressor as it can provide oil free compressed air which are necessary for some sensitive petitions.

3. Gas turbines: Gas turbines use either or both axial and centrifugal compressor to provide the necessary compression. Centrifugal compressors are mostly used in gas turbines such as :-

a.) Turboshaft b.) Turboprop c.) Micro turbines and d.) Auxiliary power units 4.) Oil refiners, petrochemical and chemical plants: The centrifugal compressors used for the above purposes generally have a horizontally split casing and most of them are multistage compressors. These type of compressors are generally operated by over-sized steam engines and gas turbines.

5. Refrigeration and air control: Centrifugal Compressors support a wide variety of refrigerants and thermodynamics and are also able to supply compression in water chiller cycles due to which it has a high demand for usage in refrigerators and air conditioners.

Advantages and Disadvantages: Advantages a.) When compared to other compressors, it is relatively agile and easy to manufacturer. b.) As this compressor does not require any special foundation it is highly energy efficient and reliable. c.) They consist of a small number of rubbing parts and are absolutely oil free in nature. d.) It generates a higher pressure ratio per stage than the axial flow compressor. Disadvantages. a.) They produce a limited amount of pressure and are not suitable for very high compression. b.) As they work at relatively high speed an enlightened or worldly mounting is required. c.) They are very sensitive towards problems such as stalling and choking.

This is all about centrifugal compressor principle, working, construction, types, advantages, disadvantages with its application. If you have any query regarding this article, ask by commenting. If you like this article, don’t forget to share it on social network.

title: Jet Propulsion/Aerodynamics