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Attitude Control

Attitude control

In the context of spacecraft, attitude control is control of the angular position and rotation of the spacecraft, either relative to the object that it is orbiting, or relative to the celestial sphere. In flight dynamics, the orientation is often described using three angles called yaw, pitch, and roll.

Sensors

The conventional sensor is an inertial guidance system. It tracks the current position and angle based on earlier position, and acceleration. Measurement of angular velcity is also critical, for attitude control systems that simulate frictional dampening to prevent oscillating corrections. Another common sensor is a sun sensor. This can be as simple as some solar cells and shades, or as complex as a steerable telescope. Another common sensor is a star tracker. This is usually a small (1 inch) telescope mounted at a fixed angle to a rotating bearing. A photocell or solid-state camera arrangement sees the star. There are 57 bright navigatonal stars in common use. One of the most commonly used is Sirius (the brightest). However, for more complex missions entire starfield databases are used to identify position. Another sensor is an Earth horizon indicator. This instrument can detect certain wavelengths of emitted light from the 'limb' of the Earth's atmosphere just at the horizon. It can be a scanning or a staring instrument.

Algorithms

Algorithms calculate how to thrust (or whatever) from the sensors. The most efficient algorithm calculates a direct, single movement from the current position to the desired position. One way of calculating this is to take a standard efficient movement, and rotate and parameterize it, adjusting the actuator numbers to match.

Actuators

Attitude control can be maintained by ; Thrusters : The conventional, low-risk solution is to use thrusters (usually monopropellant rockets), organized in a Reaction control system. However, they use fuel. In normal station-keeping, the fuel-efficiency of an attitude control system is determined by the smallest time it can thrust. In practice, controllers successfully adjust down to this amount, and then the spacecraft oscillates slightly, with a tiny blip of thrust in one direction, and a few tens of seconds later, an opposing blip of thrust. To conquer this fuel limitation on mission lengths and masses, sometimes auxiliary attitude control systems are used that can resolve lower angular velocities, notably momentum wheels and solar sails. The Soviet Luna 3 spacecraft was the first 3-axis stabilized spacecraft to employ an attitude control system with inertial guidance and compressed nitrogen microthrusters. ; Momentum wheels : These are electric motors that spin in the direction opposite to the direction the spacecraft needs to turn. Since they're computer controlled, and usually a small fraction of the spacecraft's mass, they give precise control. The biggest problem is that they move, and therefore their bearings can fail. To increase lifetimes, they can have magnetic bearings. ; Precession : Two counter-rotating gyroscopes have net zero momentum. If their axes point in the same direction, then pulling two nearby bearings together will cause both gyroscopes to precess in the same direction, rotating the spacecraft. Pushing the bearings apart causes rotation in the opposite direction. Both gyroscopes can also be used as momentum wheels to roll the spacecraft, permitting full-authority attitude control with only two wheels and minimal (or no) use of attitude jets. ; Solar sails : Small solar sails and thermal radiation adjustment devices (adjustable reflectors) have been successfully used (e.g. on Pioneer 10) to make small attitude control and velocity adjustments. This can save large amounts of fuel on a long-duration mission by damping the oscillation rates more precisely than thrusters can achieve. ; Mass distribution or Gravity Gradient : A great virtue of this system is that it requires no control system. This is how the earliest satellites were stabilized. In orbit, a long spacecraft will spontaneously orient so that its long axis points at the planet's center of mass. This is caused by a tidal force. The upper part is moving faster than orbital speed, and pulls away. The lower part is moving slower than orbital speed and pulls down. Sometimes tethers are used to connect two parts of a satellite, spread by a tide. A problem with simple tethers is that meteroroids as small as a grain of sand can cut them. ; Spin Stabilization : For a mid-range of attitude control accuracy, the entire satellite itself can spin on a particular axis to maintain its orientation. This creates an axis of momentum which will maintain its orientation despite small perturbations. Precision control can then be enhanced with other actuators. This is only applicable to certain missions with a primary axis of orientation that does not need to change dramatically over lifetime of the satellite and no need for extremely high precision pointing. It is also useful for missions with instruments that must scan the starfield or the Earth's surface or atmosphere. ; Magnetic field coils or (on very small satellites) permanent magnets : These exert a moment against the local magnetic field. This only works where a magnetic field exists. One classic field coil is actually a conductive tether in a planetary magnetic field. ; Pure passive attitude control : For low resolution attitude control in an Earth orbit, tidal and magnetic pointing can be combined with viscous damping to get a completely passive system. Simple uncontrolled magnets and tidal pointing have a limited pointing accuracy, because the spacecraft can oscillate around energy minima. A simple solution to this oscillation is a viscous damper, a small can or tank of fluid mounted in the spacecraft, possibly with internal baffles to increase internal friction. Fast oscillation of the satellite will be turned into heat within the viscous damper. Slow oscillations have less effect.Where the satellite needs to have a preferred end (like a camera) point at the planet, usually several small electrically-fired solid fuel rockets are mounted on one end, each with thrust enough to flip the satellite end-for-end.

Spacecraft

, 2004.]] A spacecraft is a vehicle that travels through space. Spacecraft include robotic or unmanned space probes as well as manned vehicles. The term is sometimes also used to describe artificial satellites, which have similar design criteria.

Overview

The term spaceship is generally applied only to spacecraft capable of transporting people. A space suit has at times been called a miniature spacecraft or spaceship, emphasizing its purpose of keeping its wearer alive while traveling in the vacuum of outer space. The spacecraft is one of the primal elements in science fiction. Numerous short stories and novels are built up around various ideas for spacecraft. Some hard science fiction books focus on the technical details of the craft, while others treat the spacecraft as a given and delve little into its actual implementation.

Examples of past or existing spacecraft

Manned
- Apollo Spacecraft
- Gemini Spacecraft
- International Space Station
- Mir
- Mercury Spacecraft
- Shuttle Buran
- Shenzhou Spacecraft
- Space Shuttle
- Soyuz Spacecraft
- SpaceShipOne
- Voskhod Spacecraft
- Vostok Spacecraft Unmanned
- Cassini-Huygens
- Cluster
- Deep Space 1
- Genesis
- Mars Exploration Rover
- Mars Global Surveyor
- Mars Pathfinder
- Pioneer 10
- Pioneer 11
- Progress
- SOHO
- Stardust
- Viking 1
- Viking 2
- Voyager 1
- Voyager 2
- WMAP

Spacecraft under development

- Crew Exploration Vehicle
- Kliper
- Automated Transfer Vehicle
- H-II Transfer Vehicle
- Ansari X Prize (incl. a list of spacecraft in various stages of completion as of 2005) The US Space Command, according to its "Long Range Plan", is currently planning to develop a weaponized spaceship, which has yet to be announced.[http://www.fas.org/spp/military/docops/usspac/]

External links

- [http://science.hq.nasa.gov/missions/phase.html NASA: Space Science Spacecraft Missions]
- [http://www.skyrocket.de/space/ Gunter's Space Page - Complete information on spacecraft]
- [http://www.cinespaceships.net/ Cinespaceships - Database on spaceships in movie]
- ja:宇宙船

Celestial sphere

In astronomy and navigation, the celestial sphere is an imaginary rotating sphere of "gigantic radius", concentric with the Earth. All objects in the sky can be thought of as lying upon the sphere. Projected, from their corresponding terrain equivalents, are the celestial equator and the celestial poles. Many ancient societies believed that the stars were equidistant from the Earth and that this sphere was a real model of the universe. This model is a useful abstraction, but not correct. Everything we see in the sky is so very far away that their distances are impossible to gauge just by looking at them. Since their distances are indeterminate, you need only know the direction toward the object to locate it in the sky. In this sense, the celestial sphere model is a very practical tool for positional astronomy. As the Earth rotates on its axis, the objects on the celestial sphere will appear to rotate around the celestial poles every 24 hours; this is diurnal motion. For example the Sun will typically appear to rise in the east and set in the west, as will the stars, planets and moon. On each subsequent night, a given star will rise ~4 minutes earlier than it rose the previous night. Superimposed on diurnal motion is; intrinsic motion as the objects change their relative positions, with respect to Earth. For example, over the course of a year the Sun, relative to the background stars, will follow a bisecting great circle (known as the ecliptic). The celestial sphere is divided by projecting the equator into space. This divides the sphere into the north celestial hemisphere and the south celestial hemisphere. Likewise, one can locate the Celestial Tropic of Cancer, Celestial Tropic of Capricorn, North Celestial Pole, and South Celestial Pole. As the earth rotates from west to east, the celestial sphere appears to rotate from east to west. If a star is sufficiently near the celestial pole that is above the horizon, the star is also always above the horizon, encircling the pole; such stars are circumpolar. The directions toward various objects in the sky can be quantified by constructing a celestial coordinate system.

External link

- [http://skyandtelescope.com/observing/skychart/# SkyandTelescope.com SkyChart] Category:Spherical astronomy Category:Celestial coordinate system ja:天球 th:ทรงกลมฟ้า

Flight dynamics

Flight dynamics is the study of orientation of air and space vehicles and how to control the critical flight parameters, typically named pitch, roll and yaw. Pitch is rotation around the lateral or transverse axis. This axis is parallel to the wings, thus the nose and tail both pitch up or down. An aircraft pitches up to climb and pitches down to dive. Roll is rotation around the longitudinal axis—an axis drawn through the body of the vehicle from tail to nose. This is also known as bank. Yaw is rotation about the normal axis—an axis perpendicular to the pitch and roll axes. If an airplane model placed on a flat surface is spun or pivoted around the center of mass (coordinate origin) it would be described as yawing. Aerospace engineers develop control laws and control systems to allow pilots to control their aircraft in the three dimensions described above.

Inertial guidance system

An inertial navigation system provides the position, velocities and attitude of a vehicle by measuring the accelerations and rotations applied to the system's inertial frame. It is widely used because it refers to no real-world item beyond itself. It is therefore immune to jamming and deception. (See relativity and Mach's principle for some background in the physics involved). An inertial guidance system consists of an Inertial Measurement Unit (IMU) combined with control mechanisms, allowing the path of a vehicle to be controlled according to the position determined by the inertial navigation system. These systems are also referred to as an inertial platform.

Overview

Inertial guidance systems were originally developed for navigating rockets. American rocket pioneer Robert Goddard experimented with rudimentary gyroscopic systems. Dr. Goddard's systems were of great interest to contemporary German pioneers including Wernher von Braun. A typical inertial navigation system uses a combination of accelerometers, and solves a large set of differential equations to convert these readings into estimates of position and altitude, starting off from a known initial position. All inertial navigation systems suffer from integration drift, as small errors in measurement are integrated into progressively larger errors in velocity and especially position. This is a problem that is inherent in every open loop control system. Inertial navigation may also be used to supplement other navigation systems, providing a higher degree of accuracy than is possible with the use of any single navigation system. For example, if, in terrestrial use, the inertially tracked velocity is intermittently updated to zero by stopping, the position will remain precise for a much longer time, a so-called zero velocity update. Control theory in general and Kalman filtering in particular, provide a theoretical framework for combining of the information from various sensors. One of the most common alternative sensors is a satellite navigation radio such as GPS.

Inertial navigation systems in detail

INSs have angular and linear accelerometers (for changes in position); some include a gyroscopic element (for maintaining an absolute positional reference). Angular accelerometers measure how the vehicle is rotating in space. Generally, there's at least one sensor for each of the three axes: pitch (nose up and down), yaw (nose left and right) and roll (clockwise or counterclockwise from the cockpit). Linear accelerometers measure how the vehicle is moving in space. Since it can move in three axes (up & down, left & right, forward & back), there is a linear accelerometer for each axis. A computer continually calculates the vehicle's current position. First, for each of six axes, it integrates the sensed amount of acceleration over time to figure the current velocity. Then it integrates the velocity to figure the current position. Inertial guidance is impossible without computers. The desire to use inertial guidance in the Minuteman missile and Project Apollo drove early attempts to miniaturize computers. Inertial guidance systems are now usually combined with satellite navigation systems through a digital filtering system. The inertial system provides short term data, while the satellite system corrects accumulated errors of the inertial system. An inertial guidance system that will operate near the surface of the earth must incorporate Schuler tuning so that its platform will continue pointing towards the center of the earth as a vehicle moves from place to place.

Basic schemes

Gimbaled Gyrostabilized platforms

Some systems place the linear accelerometers on a gimballed gyrostabilized platform. The gimbals are a set of three rings, each with a pair of bearings initially at right angles. They let the platform twist in any rotational axis. There are two gyroscopes (usually) on the platform. Two gyroscopes are used to cancel gyroscopic precession, the tendency of a gyroscope to twist at right angles to an input force. By mounting a pair of gyroscopes (of the same rotational inertia and spinning at the same speed) at right angles the precessions are cancelled, and the platform will resist twisting. This system allows a vehicle's roll, pitch and yaw angles to be measured directly at the bearings of the gimbals. Relatively simple electronic circuits can be used to add up the linear accelerations, because the directions of the linear accelerometers do not change. The big disadvantage of this scheme is that it uses many expensive precision mechanical parts. It also has moving parts that can wear out or jam, and is vulnerable to gimbal lock. The primary guidance system of the Apollo spacecraft used a 3-axis gyrostabilized platform, feeding data to the Apollo Guidance Computer. Maneuvers had to be carefully planned to avoid gimbal lock.

Fluidically Suspended Gyrostabilized Platforms

Gimbal lock constrains maneuvering, and it would be nice to eliminate the slip rings and bearings of the gimbals. Therefore, some systems use fluid bearings or a flotation chamber to mount a gyrostabilized platform. These systems can have very high precisions. Like all gyrostabilized platforms, this system runs well with relatively slow, low-power computers. The fluid bearings are pads with holes through which pressurized inert gas (such as Helium) or oil press against the spherical shell of the platform. The fluid bearings are very slippery, and the spherical platform can turn freely. There are usually four bearing pads, mounted in a tetrahedral arrangement to support the platform. In premium systems, the angular sensors are usually specialized transformer coils made in a strip on a flexible printed circuit board. Several coil strips are mounted on great circles around the spherical shell of the gyrostabilized platform. Electronics outside the platform uses similar strip-shaped transformers to read the varying magnetic fields produced by the transformers wrapped around the spherical platform. Whenever a magnetic field changes shape, or moves, it will cut the wires of the coils on the external transformer strips. The cutting generates an electric current in the external strip-shaped coils, and electronics can measure that current to derive angles. Cheap systems sometimes use bar codes to sense orientations, and use solar cells or a single transformer to power the platform. Some small missiles have powered the platform with light from a window or optic fibers to the motor. A research topic is to suspend the platform with pressure from exhaust gases. Data is returned to the outside world via the transformers, or sometimes LEDs communicating with external photodiodes.

Strapdown systems

Lightweight digital computers permit the system to eliminate the gimbals, creating "strapdown" systems, so called because their sensors are simply strapped to the vehicle. This reduces the cost and increases the reliability by eliminating some of the moving parts. Angular accelerometers called "rate gyros" measure how the angular velocity of the vehicle changes. The trigonometry involved is too complex to be accurately performed except by digital electronics. However, digital computers are now so cheap that rate gyro systems are now practical. The Apollo lunar module used a strapdown system in its backup Abort Guidance System (AGS).

Types of sensors

Laser gyros

Laser gyroscopes were supposed to eliminate the bearings in the gyroscopes, and thus the last bastion of precision machining and moving parts. A laser gyro moves laser light in the two opposite directions around a circular path. As the vehicle rotates through some angle, the distance traveled around the loop by the two beams becomes different in the two directions. The interferometric phase-shift between the two beams is proportional to the angle of rotation (Sagnac effect). In more sensitive gyros (see ring laser) the interferometer oscillation rate is proportional to the rotation rate. In practice, at low rotation rates the electromagnetic peaks and valleys of the light lock together. The result is that there is no change in the interference pattern, and therefore no measurement change. To unlock the counter-rotating light beams, laser gyros either have independent light paths for the two directions (usually in fiber optic gyros), or the laser gyro is mounted on a piezo-electric crystal that rapidly rotates the gyro back and forth through a small angle to decouple the light waves. Alas, the shaker is the most accurate, because both light beams use exactly the same path. Thus laser gyros retain moving parts, but they do not move as far.

Vibrating gyros

Less expensive navigation systems intended for use in automobiles, may use a Vibrating structure gyroscope to detect changes in heading, and the odometer pickup to measure distance covered along the vehicle's track. This type of system is much less accurate than a higher-end INS, but is adequate for the typical automobile application where GPS is the primary navigation system, and dead reckoning is only needed to fill gaps in GPS coverage when buildings or terrain block the satellite signals.

Brandy snifter gyros

If a standing wave is induced in a globular brandy snifter, and then the snifter is tilted, the waves continue in the same plane of movement. They don't tilt with the snifter. This trick is used to measure angles. Instead of brandy snifters, the system uses hollow globes machined from piezoelectric materials such as quartz. The electrodes to start and sense the waves are evaporated directly onto the quartz. This system has almost no moving parts, and is very accurate. However it is still relatively expensive due to the cost of the precision ground and polished hollow quartz spheres.

Quartz rate sensors

This system is usually integrated on a silicon chip. It has two mass-balanced quartz tuning forks, arranged "handle-to-handle" so forces cancel. Electrodes of aluminum evaporated on the forks and the underlying chip both drive and sense the motion. The system is both manufacturable and inexpensive. Since quartz is dimensionally stable, the system has a good possibility of accuracy. As the forks are twisted about the axis of the handle, the vibration of the tines tends to continue in the same plane of motion. This motion has to be resisted by electrostatic forces from the electrodes under the tines. By measuring the difference in capacitance between the two tines of a fork, the system can determine the rate of angular motion. Current state of the art non-military technology (2005) allows to build small solid state sensors that can be used in cinematic measures of body movements. This kind of devices have no moving parts, and weight about 50 grams. Other solid state devices basing on the same physical principles are currently used to stabilize images taken with small cameras or camcorders. These can be extremely small (≈5mm) and are built with MEMS (Microelectromechanical Systems) technologies. ----

Pendular accelerometers

The basic accelerometer is just a mass on a spring with a ruler attached. The ruler may be an exotic electromagnetic sensor, but it still senses distance. When the vehicle accelerates, the mass moves, and ruler measures the movement. The bad thing about this scheme is that it needs calibrated springs, and springs are nearly impossible to make consistent. A trickier system is to measure the force needed to keep the mass from moving. In this scheme, there's still a ruler, but whenever the mass moves, an electric coil pulls on the mass, cancelling the motion. The stronger the pull, the more acceleration there is. The bad thing about this is that very high accelerations, say from explosions, impacts or gunfire, can exceed the capacity of the electronics to cancel. The sensor then loses track of where the vehicle is. Both sorts of accelerometers have been manufactured as integrated micromachinery on silicon chips.

Accelerometer-only systems

Some systems use four pendular accelerometers to measure all the possible movements and rotations. Usually, these are mounted with the weights in the corners of a tetrahedron. Thus, these are called "tetrahedral inertial platforms", or TIPs. When the vehicle rolls, the masses on opposite sides will be accelerated in opposite directions. When the vehicle has linear acceleration, the masses are accelerated in the same direction. The computer keeps track. TIPs are cheap, lightweight and small, especially when they use micromachined integrated accelerometers. However, as of 2002 they are not very accurate. When they are used, they are often used in small missiles.

External links

- [http://www.imar-navigation.de/download/inertial_navigation_introduction.pdf A history of inertial navigation systems] (.pdf format)

External links

Examples of manufacturers: [http://www.imar-navigation.de iMAR GmbH, Germany] [http://www.northropgrumman.com Northrop Grumman, USA] [http://www.honeywell.com Honeywell Inc., USA] [http://www.sagem-ds.com/fra/index.html Sagem, France] [http://www.seg-nav.de SEG, Germany] [http://www.lital.it Lital, Italy (a division of Northrop Grumman, USA)] [http://www.dewamerica.com/products/sensors/inertial/ Dewetron, Austria] [http://www.xsens.com/ Xsens, Nederlands] miniature solid state sensors Category:Aviation Category:Aerospace engineering Category:Spacecraft components Category:Missile guidance ja:%E6%85%A3%E6%80%A7%E8%AA%98%E5%B0%8E%E8%A3%85%E7%BD%AE

Thruster

A thruster is a small propulsive device used by spacecraft and watercraft for station keeping, attitude control, or long duration low thrust acceleration. See also:
- spacecraft propulsion
- monopropellant rockets
- hall effect thruster
- ion thruster
- magnetoplasmadynamic thruster
- pulsed inductive thruster
- pulsed plasma thruster Category:Spacecraft components Category:Marine propulsion

Monopropellant rocket

A monopropellant rocket (or "monoprop rocket") is a rocket that uses a single chemical as its power source and propellant. Usually the propellant is admitted to a reaction chamber that contains a silver or platinum sponge catalyst. The most commonly used monopropellant is hydrazine (N₂H₄), a chemical which is characterized as "strongly reducing". The most common catalyst is granular alumina coated with iridium (aka. Shell-405). There is no igniter with hydrazine. Shell 405 is a spontaneous catalyst, that is, hydrazine decomposes (combusts) on contact with the catalyst. The reaction is highly exothermic and produces an 1800 °F (1000 °C) gas that is a mixture of nitrogen, hydrogen and ammonia. There are some unique chemical compounds that burn by themselves—no oxygen required! This is because the chemical when energized, spontaneously decomposes and then the decomposition products are exhausted to produce thrust. Another monopropellant is hydrogen peroxide, which when purified to 90% or higher is self-decomposing at high temperatures, or with a catalyst. Engineers long ago realized the usefulness of monopropellant chemicals for satellite propulsion and attitude controls. Because only one chemical is used, the system is very simple, and thus very reliable. Most monopropellant rocket systems consist of a fuel tank, usually a titanium or aluminum sphere, with a ethylene-propylene rubber bladder filled with the fuel. The sphere is then pressurized with helium, which pushes the fuel out to the motors. A pipe leads from the bladder to a poppet valve, and then to the reaction chamber of the rocket motor. Usually, there's not just one motor, but two to twelve, each with its own little valve. The attitude control rocket motors for satellites and space probes are often very small, an inch or so in diameter, and mounted in clusters that point in four directions. They look almost like toys. The rocket is fired when the computer sends direct current through a small electromagnet that opens the poppet valve. The firing is often very brief, a few thousandths of a second, and usually sounds like a pebble thrown against a metal trash can. If the motor stays on for long, it makes a piercing hiss. Monopropellants are not as efficient as some other propulsion technologies. Engineers choose monopropellant systems when the need for simplicity and reliability outweigh the need for high delivered impulse. If the propulsion system must produce large amounts of thrust, or have a high specific impulse, as on the main motor of an interplanetary spacecraft, other technologies are used.

Reaction control system

A reaction control system (abbreviated RCS) is a subsystem of a spacecraft. Its purpose is attitude control and steering. An RCS system is capable of providing small amounts of thrust in any desired direction or combination of directions. An RCS is also capable of providing torque to allow control of rotation (pitch, yaw, and roll). This is contrast to a spacecraft's main engine, which is only capable of providing thrust in one direction, but is much more powerful. Reaction control systems are used:
- for attitude control during re-entry;
- for stationkeeping in orbit;
- for close maneuvering during docking procedures;
- for control of orientation, or 'pointing the nose' of the craft;
- as a backup means of de-orbiting. Because spacecraft only contain a finite amount of fuel and there is little chance to refill them (aside from visits by a Space Shuttle, which are very rare), some alternative reaction control systems have been developed so that fuel can be conserved. For stationkeeping, some spacecraft (particularly those in geosynchronous orbit) use high-specific impulse engines such as arcjets, ion thrusters, or Hall Current thrusters. To control orientation, a few spacecraft use momentum wheels which spin to control rotational rates on the vehicle.

Location of Thrusters on Space Capsules

The placing of the approach or translation engines (which cause the spacecraft to move) on the surface of a spacecraft has one important requirement that the placing of the orientation thrusters (which cause the spacecraft to turn) does not. If the direction of thrust of the former does not pass through the center of mass of the spacecraft, when tracked backward from the nozzle, the spacecraft will turn as an unwanted side effect. Sometimes this is unavoidable, but spacecraft are not operated by automatically firing the orientation thrusters to counteract this because such a system might fail. So a separate step of re-orientation is required afterward. Translation thrusters thus have less of a variety of permissible locations than do orientation thrusters. In the Apollo spacecraft, both the Service Module and the Lunar Module, as well as the Chinese Shenzhou spacecraft, they are grouped in blocks of four, which are themselves attached to the outside of the spacecraft at each end of the two axes of a cross-section of the spacecraft through the long axis. Used in a variety of combinations, these thrusters are sufficient for both approach and orientation. Other designs use separate sets of thrusters. A similar pattern is seen in the forward compartments of the Mercury and Gemini spacecraft. This is the equivalent of removing the two nozzles from each of the blocks of four which point in the longitudinal directions, then pushing the blocks inward, and cutting slots for the exhaust to escape. (This grouping is then rotated by 45 degrees.) These thrusters, however, are only used after the re-entry rockets or other modules have been jettisoned; any translation of the spacecraft that they would provide is a mere by-product. Indeed, the Mercury spacecraft has no separate capacity for translation at all. The re-entry modules of both Apollo and Soyuz have their thrusters ungrouped. A pair of translation thrusters to go forward are located at the rear of both the Gemini and Soyuz spacecraft; the counter-acting thrusters are similarly paired in the middle of each spacecraft, pointing a bit outward besides forward. These act in pairs to prevent the spacecraft turning. The thrusters for the lateral directions are mounted as close to the center of mass of each of these spacecraft as well, but Gemini has only one engine for each of the directions while Soyuz continues with pairs. None of these engines is intended for orientation. For that purpose, both Gemini and Soyuz have engines at the extreme rear of the spacecraft. Here Soyuz uses engines only one-tenth the power of the others, arranged in a unique pattern, while Gemini has engines arranged in the same pattern of eight as it uses for re-entry. Gemini has no main orbit maneuvering engine as do the Apollo Service Module or Soyuz. It was light enough to change orbit without a separate engine. Finally, Soyuz has a thruster at the rear of the spacecraft that points parallel to each solar panel, but which is not used for rendezvous at all. Instead, when the solar panels are pointing to the sun, the option exists to use this motor to spin the spacecraft to keep it pointing to the sun by gyroscopic action. Otherwise, a computer system would be kept running to automatically keep the panels so pointed, wasting electricity and propellant. The spin is stopped by the counterpart engine on the other side.

Location of Thrusters on Spaceplanes

The suborbital X-15 and a companion training aerospacecraft, the NF-104 AST, which would zoom to an altitude that rendered their aircraft controls unusable, established the basic locations for thrusters on winged vehicles not intended to rendezvous in space; that is, those that only have orientation thrusters. Those for pitch and yaw are located in the nose, forward of the cockpit, and replace a standard radar system. Those for roll are located at the wingtips. The X-20, which would have gone into orbit, continued this pattern. Unlike these, the Space Shuttle has many more thrusters, for it does rendezvous in orbit. No nozzles are on the underside of the craft, which would have pierced the heat shield. And the rearward-facing thrusters are located in the tail.

Momentum wheel

] A momentum wheel is a type of flywheel used primarily by spacecraft to change their angular momentum without using fuel for rockets or other reaction devices. They increase the pointing precision and reliability of a spacecraft, and may also reduce the mass fraction needed for fuel. Momentum wheels are usually implemented as special electric motors. Both spin-up and braking are controlled electronically by computer controls. The strength of the materials of a momentum wheel establishes a speed at which the wheel would come apart, and therefore how much angular momentum it can store. Since the momentum wheel is a small fraction of the spacecraft's total mass, easily-measurable changes in its speed provide very precise changes in angle. It therefore permits very precise changes in a spacecraft's attitude. For this reason, momentum wheels are often used to aim spacecraft with cameras or telescopes. Over time momentum wheels may build up stored momentum that needs to be cancelled. Designers therefore supplement momentum wheel systems with other attitude control mechanisms. The most efficient practice is probably to use high-efficiency attitude jets such as ion thrusters, or small, lightweight solar sails on the ends of projecting masts or solar cell arrays. Most spacecraft, however, also need fast pointing, and cannot afford the extra mass-fraction of three attitude control systems. Designers therefore usually use conventional monopropellant attitude jets to cancel momentum wheels, as well as for fast pointing.

Electric motor

An electric motor converts electrical energy into mechanical motion. The reverse task, that of converting mechanical motion into electrical energy, is accomplished by a generator or dynamo. In many cases the two devices differ only in their application and minor construction details, and some applications use a single device to fill both roles. For example, traction motors used on locomotives often perform both tasks if the locomotive is equipped with dynamic brakes.

Operation

Most electric motors work by electromagnetism, but motors based on other electromechanical phenomena, such as electrostatic forces and the piezoelectric effect, also exist. The fundamental principle upon which electromagnetic motors are based is that there is a mechanical force on any wire when it is conducting electricity while contained within a magnetic field. The force is described by the Lorentz force law and is perpendicular to both the wire and the magnetic field. In a rotary motor, there is a rotating element, the rotor. The rotor rotates because the wires and magnetic field are arranged so that a torque is developed about the rotor's axis. Most magnetic motors are rotary, but linear types also exist. In a rotary motor, the rotating part (usually on the inside) is called the rotor, and the stationary part is called the stator. The motor contains electromagnets that are wound on a frame. Though this frame is often called the armature, that term is often erroneously applied. Correctly, the armature is that part of the motor across which the input voltage is supplied or that part of the generator across which the output voltage is generated. Depending upon the design of the machine, either the rotor or the stator can serve as the armature.

DC motors

One of the first electromagnetic rotary motors was invented by Michael Faraday in 1821 and consisted of a free-hanging wire dipping into a pool of mercury. A permanent magnet was placed in the middle of the pool. When a current was passed through the wire, the wire rotated around the magnet, showing that the current gave rise to a circular magnetic field around the wire. This motor is often demonstrated in school physics classes, but brine is sometimes used in place of the toxic mercury. This is the simplest form of a class of electric motors called homopolar motors. The modern DC motor was invented by accident in 1873, when Zénobe Gramme connected a spinning dynamo to a second similar unit, driving it as a motor. The classic DC motor has a rotating armature in the form of an electromagnet with two poles. A rotary switch called a commutator reverses the direction of the electric current twice every cycle, to flow through the armature so that the poles of the electromagnet push and pull against the permanent magnets on the outside of the motor. As the poles of the armature electromagnet pass the poles of the permanent magnets, the commutator reverses the polarity of the armature electromagnet. During that instant of switching polarity, inertia keeps the classical motor going in the proper direction. (See the diagrams below.) inertia inertia inertia
DC motor speed generally depends on a combination of the voltage and current flowing in the motor coils and the motor load or braking torque. The speed of the motor is proportional to the voltage, and the torque is proportional to the current. The speed is typically controlled by altering the voltage or current flow by using taps in the motor windings or by having a variable voltage supply. As this type of motor can develop quite high torque at low speed it is often used in traction applications such as locomotives. However, there are a number of limitations in the classic design, many due to the need for brushes to rub against the commutator. The rubbing creates friction, and the higher the speed, the harder the brushes have to press to maintain good contact. Not only does this friction make the motor noisy, but it also creates an upper limit on the speed and causes the brushes eventually to wear out and to require replacement. The imperfect electric contact also causes electrical noise in the attached circuit. These problems vanish when you turn the motor inside out, putting the permanent magnets on the inside and the coils on the outside thus designing out the need for brushes in a brushless design. However such designs need electronic circuits to control the switching of the electromagnets (the function that is performed in conventional motors by the commutator).

Wound field DC motor

The permanent magnets on the outside (stator) of a DC motor may be replaced by electromagnets. By varying the field current it is possible to alter the speed/torque ratio of the motor. Typically the field winding will be placed in series (series wound) with the armature winding to get a high torque low speed motor, in parallel (shunt wound) with the armature to get a high speed low torque motor, or to have a winding partly in parallel, and partly in series (compound wound) for a balance. Further reductions in field current are possible to gain even higher speed but correspondingly lower torque. This technique is ideal for electric traction (see Traction motor) and many similar applications where its use can eliminate the requirement for a mechanically variable transmission.

Universal motors

A variant of the wound field DC motor is the universal motor. The name derives from the fact that it may use AC or DC supply current, although in practice they are nearly always used with AC supplies. The principle is that in a wound field DC motor the current in both the field and the armature (and hence the resultant magnetic fields) will alternate (reverse polarity) at the same time, and hence the mechanical force generated is always the same. In practice the motor must be specially designed to cope with the AC current (impedance/reluctance must be taken into account), and the resultant motor is generally less efficient than an equivalent pure DC motor. The advantage of the universal motor is that AC supplies may be used on motors which have the typical characteristics of DC motors, specifically high starting torque and very compact design if high running speeds are used. The negative aspect is the maintenance and reliability problems caused by the commutator, and as a result such motors will rarely be found in industry but are the most common type of AC supplied motor in devices such as food mixers and power tools which are only used intermittently. Continuous speed control of a universal motor running on AC is very easily accomplished using a thyristor circuit while stepped speed control can be accomplished using multiple taps on the field coil. Household blenders that advertise many speeds frequently combine a field coil with several taps and a diode that can be inserted in series with the motor (causing the motor to run on half-wave DC with half the RMS voltage of the AC power line). Unlike the other common forms of AC motors (induction motors and synchronous motors), universal motors can easily exceed one revolution per cycle of the mains current (that is, exceed 3000 rpm on a 50 Hz system or 3600 rpm on a 60 Hz system). This makes them especially useful for certain appliances such as blenders, vacuum cleaners, and hair dryers where high-speed operation is desired. With the very low cost of semiconductor rectifiers, some applications that would have previously used a universal motor now use a pure DC motor, usually with a permanent magnet field. This is especially true if the semiconductor circuit is also used for variable-speed control.

AC motors

A typical AC motor consists of two parts: # An outside stationary stator having coils supplied with AC current to produce a rotating magnetic field, and; # An inside rotor attached to the output shaft that is given a torque by the rotating field. There are two fundamental types of AC motor depending on the type of rotor used:
- The synchronous motor, which rotates exactly at the supply frequency or a submultiple of the supply frequency, and;
- The induction motor, which turns slightly slower, and typically (though not necessarily always) takes the form of the squirrel cage motor. The rotating magnetic field principle, though commonly credited to Nikola Tesla in 1882 or thereabouts, was productively employed by mainstream scientists such as Michael Faraday and James Clerk Maxwell in the 1820s. Tesla, however, exploited the principle to design a unique two-phase induction motor in 1883. Michael von Dolivo-Dobrowlsky invented the first modern three-phase "cage-rotor" in 1890. Introduction of the motor from 1888 onwards initiated what is known as the Second Industrial Revolution, making possible the efficient generation and long distance distribution of electrical energy using the alternating current transmission system, also of Tesla's invention (1888)[http://www.tfcbooks.com/tesla/system.htm]. The first successful commercial three phase generation and long distance transmission system was designed by Almerian Decker at Mill Creek No. 1 [http://www.electrichistory.com] in Redlands California.[http://www.redlandsweb.com] Although the statement that "AC motors generally come in two types: single phase and three phase" is often made, this distinction is of insufficient importance to assign the term "types." What is actually meant is that, for more important purposes of commercial power distribution, AC motors are commonly employed in a "three-phase" system whereby three discrete waveforms--each logically displaced 120 degrees from its neighbor--are transmitted in unison. It is common for an individual subscriber to have only one of these phases actually present on the premises, allowing only single phase motors to be used.

Three-phase AC induction motors

For higher-power applications where a polyphase electrical supply is available, the three-phase (or polyphase) AC induction motor is used. The phase differences between the three phases of the polyphase electrical supply create a rotating electromagnetic field in the motor. Through electromagnetic induction, the rotating magnetic field induces a current in the conductors in the rotor, which in turn sets up a counterbalancing magnetic field that causes the rotor to turn in the direction the field is rotating. The rotor must always rotate slower than the rotating magnetic field produced by the polyphase electrical supply; otherwise, no counterbalancing field will be produced in the rotor. Induction motors are the workhorses of industry and motors up to about 500 kW in output are produced in highly standardized frame sizes, making them nearly completely interchangeable between manufacturers (although European and North American standard dimensions are of course different). There are two types of rotors used in induction motors. Most use the squirrel cage rotor. An alternate design, called the wound rotor, is used when variable speed is required. In this case, the rotor has the same number of poles as the stator and the windings are made of wire, connected to slip rings on the shaft. Carbon brushes connect the slip rings to an external controller such as a variable resistor that allows changing the motor's slip rate. In certain high-power variable speed wound-rotor drives, the slip-frequency energy is captured, rectified and returned to the power supply through an inverter. Compared to squirrel cage rotors, wound rotor motors are expensive and require maintenance of the slip rings and brushes, but they were the standard form for variable speed control before the advent of compact power electronic devices. Transistorized inverters with variable frequency drive can now be used for speed control and wound rotor motors are becoming less common. (Transistorized inverter drives also allow the more-efficient three-phase motors to be used when only single-phase mains current is available.) Several methods of starting a polyphase motor are used. Where the large inrush current and high starting torque can be permitted, the motor can be started across the line, by applying full line voltage to the terminals. Where it is necessary to limit the starting inrush current (where the motor is large compared with the short-circuit capacity of the supply), reduced voltage starting using either series inductors, an autotransformer, thyristors, or other devices are used. A technique sometimes used is star-delta starting, where the motor coils are initially connected in wye for acceleration of the load, then switched to delta when the load is up to speed. Transistorized drives can directly vary the applied voltage as required by the starting characteristics of the motor and load. This type of motor is becoming more common in traction applications such as locomotives, where it is known as the asynchronous traction motor. The speed of the AC motor is determined primarily by the frequency of the AC supply and the number of poles in the stator winding, according to the relation: :

N_ = 120F/p

where :N_s = Synchronous speed, in revolutions per minute :F = AC power frequency :p = Number of poles, usually an even number but always a multiple of the number of phases Actual RPM for an induction motor will be less than this calculated synchronous speed by an amount known as slip that increases with the torque produced. With no load the speed will be very close to synchronous. When loaded, standard motors have between 2-3% slip, special motors may have up to 7% slip, and a class of motors known as torque motors are rated to operate at 100% slip (0 RPM/full stall). The slip of the AC motor is calculated by: :

S = (N_ - N)/N_

where :N_r = Rotational speed, in revolutions per minute. :S = Slip, in percent. As an example, a typical four-pole motor running on 60 Hz might have a nameplate rating of 1725 RPM at full load, while its calculated speed is 1800. The speed in this type of motor has traditionally been altered by having additional sets of coils or poles in the motor that can be switched on and off to change the speed of magnetic field rotation. However, developments in power electronics mean that the frequency of the power supply can also now be varied to provide a smoother control of the motor speed.

Three-phase AC synchronous motors

If connections to the rotor coils of a three-phase motor are taken out on slip-rings and fed a separate field current to create a continuous magnetic field (or if the rotor consists of a permanent magnet), the result is called a synchronous motor because the rotor will rotate in synchronism with the rotating magnetic field produced by the polyphase electrical supply. A synchronous motor can also be used as an alternator. Nowadays, synchronous motors are frequently driven by transistorized variable frequency drives. This greatly eases the problem of starting the massive rotor of a large synchronous motor. They may also be started as induction motors using a squirrel-cage winding that shares the common rotor: once the motor reaches synchronous speed, no current is induced in the squirrel-cage winding so it has little effect on the synchronous operation of the motor. Synchronous motors are occasionally used as traction motors; the TGV may be the best-known example of such use.

Single-phase AC induction motors

A polyphase induction motor will continue to rotate even if one phase is disconnected, at reduced torque. However, a polyphase motor at standstill will not generate any net starting torque if connected only to a single-phase supply. The key to the design of single-phase motors, then, is to provide a rotating magnetic field to produce starting torque. A common single-phase motor is the shaded pole motor, which is used in devices requiring lower torque, such as electric fans or other small household appliances. In this motor, small single-turn copper "shading coils" create the moving magnetic field. Part of each pole is encircled by a copper coil or strap; the induced current in the strap opposes the change of flux through the coil (Lenz's Law), so that the maximum field intensity moves across the pole face on each cycle. Another common single-phase AC motor is the split-phase induction motor, commonly used in major appliances such as washing machines and clothes dryers. Compared to the shaded pole motor, these motors can generally provide much greater starting torque by using a special startup winding in conjunction with a centrifugal switch. In the split phase motor, the startup winding is designed with a higher resistance than the running winding. This creates an LR circuit which slightly shifts the phase of the current in the startup winding. When the motor is starting, the startup winding is connected to the power source via a set of spring-loaded contacts pressed upon by the not-yet-rotating centrifugal switch. The starting winding is wound with fewer turns of smaller wire than the main winding, so it has a higher resistance. The extra resistance creates a small phase shift, not more than about 30 degrees, between the flux due to the main winding and the flux of the starting winding. The starting direction of rotation may be reversed simply by exchanging the connections of the startup winding relative to the running winding. The phase of the magnetic field in this startup winding is shifted from the phase of the mains power, allowing the creation of a moving magnetic field which starts the motor. Once the motor reaches near design operating speed, the centrifugal switch activates, opening the contacts and disconnecting the startup winding from the power source. The motor then operates solely on the running winding. The starting winding must be disconnected since it would increase the losses in the motor. In a capacitor start motor, a starting capacitor is inserted in series with the startup winding, creating an LC circuit which is capable of a much greater phase shift (and so, a much greater starting torque). The capacitor naturally adds expense to such motors. Another variation is the Permanent Split-Capacitor (PSC) motor. This motor operates similarly to the capacitor-start motor described above, but there is no centrifugal starting switch and the second winding is permanently connected to the power source. PSC motors are frequently used in air handlers, fans, and blowers and other cases where a variable speed is desired. By changing taps on the running winding but keeping the load constant, the motor can be made to run at different speeds.

Single-phase AC synchronous motors

Small single-phase AC motors can also be designed with magnetized rotors (or several variations on that idea). The rotors in these motors do not require any induced current so they do not slip backward against the mains frequency. Instead, they rotate synchronously with the mains frequency. Because of their highly accurate speed, such motors are usually used to power mechanical clocks, audio turntables, and tape drives; formerly they were also much used in accurate timing instruments such as strip-chart recorders or telescope drive mechanisms. The shaded-pole synchronous motor is one version. Because inertia makes it difficult to instantly accelerate the rotor from stopped to synchronous speed, these motors normally require some sort of special feature to get started. Various designs use a small induction motor (which may share the same field coils and rotor as the synchronous motor) or a very light rotor with a one-way mechanism (to ensure that the rotor starts in the "forward" direction).

Stepper motors

Closely related in design to three-phase AC synchronous motors are stepper motors, where an internal rotor containing permanent magnets or a large iron core with salient poles is controlled by a set of external magnets that are switched electronically. A stepper motor may also be thought of as a cross between a DC electric motor and a solenoid. As each coil is energized in turn, the rotor aligns itself with the magnetic field produced by the energized field winding. Unlike a synchronous motor, in its application, the motor may not rotate continuously; instead, it "steps" from one position to the next as field windings are energized and deenergized in sequence. Depending on the sequence, the rotor may turn forwards or backwards. Simple stepper motor drivers entirely energize or entirely deenergize the field windings, leading the rotor to "cog" to a limited number of positions; more sophisticated drivers can proportionally control the power to the field windings allowing the rotors to position "between" the "cog" points and thereby rotate extremely smoothly. Computer controlled stepper motors are one of the most versatile forms of positioning systems, particularly when part of a digital servo-controlled system.

Brushless DC motors

Midway between ordinary DC motors and stepper motors lies the realm of the brushless DC motor. Built in a fashion very similar to stepper motors, these often use a permanent magnet external rotor, three phases of driving coils, one or more Hall effect devices to sense the position of the rotor, and the associated drive electronics. The coils are activated, one phase after the other, by the drive electronics as cued by the signals from the Hall effect sensors. In effect, they act as three-phase synchronous motors containing their own variable frequency drive electronics. Brushless DC motors are commonly used to drive fans, the spindles within CD, CD-ROM (etc.) drives, and mechanisms within office products such as laser printers and photocopiers. They also find significant use in high-performance electric model aircraft. They have several advantages over conventional motors:
- Compared to AC fans using shaded-pole motors, they are very efficient, running much cooler than the equivalent AC motors. This cool operation leads to much-improved life of the fan's bearings.
- Without a commutator to wear out, the life of a DC brushless motor can be significantly longer compared to a DC motor using brushes and a commutator
- The same Hall effect devices that provide the commutation can also provide a convenient tachometer signal for closed-loop control (servo-controlled) applications. In fans, the tachometer signal can be used to derive a "fan okay" signal.
- The motor can be easily synchronized to an internal or external clock, leading to precise speed control. Modern DC brushless motors range in power from a fraction of a watt to many kilowatts.

Coreless DC motors

A coreless DC motor is a specialized form of an ordinary DC motor. Optimized for rapid acceleration, these motors have a rotor that is constructed without any iron core. The rotor can take the form of a winding-filled cylinder inside the stator magnets, a basket surrounding the stator magnets, or a flat pancake (possibly formed on a printed wiring board) running between upper and lower stator magnets. The windings are typically stabilized by being impregnated with epoxy resins. Because the rotor is much lighter in weight (mass) than a conventional rotor formed from copper windings on steel laminations, the rotor can accelerate much more rapidly, often achieving a mechanical time constant under 1 ms. This is especially true if the windings use aluminum rather than the heavier copper. But because there is no metal mass in the rotor to act as a heat sink, even small coreless motors must often be cooled by forced air. These motors were commonly used to drive the capstan(s) of magnetic tape drives and are still widely used in high-performance servo-controlled systems.

Linear motors

A linear motor is essentially an electric motor that has been "unrolled" so that instead of producing a torque (rotation), it produces a linear force along its length by setting up a traveling electromagnetic field. Linear motors are most commonly induction motors or stepper motors. You can find a linear motor in a maglev (Transrapid) train, where the train "flies" over the ground.

Textbooks

- Shanefield D. J., Industrial Electronics for Engineers, Chemists, and Technicians, William Andrew Publishing, Norwich, NY, 2001. A self-teaching textbook that briefly covers electric motors, transformers, speed controllers, wiring codes and grounding, transistors, digital, etc. Easy to read and understand, up to an elementary level on each subject, not a suitable reference book for technologists already working in any of those fields.
- Woodsom and Melcher, unnamed book, for graduates
- Fitzgerald/Kingsley/Kusko (Fitzgerald/Kingsley/Umans in later years), Electric Machinery, classic text for junior and senior electrical engineering students. Originally published in 1952, 6th edition published in 2002. Authors still listed as Fitzgerald/Kingsley/Umans although Fitzgerald and Kingsley are now deceased.
- Slemon and Straughen, unnamed book, less advanced
- Van E. Mablekos, title unknown, very easy reading
- Bedford and Hoft, unnamed book on power electronics, outdated Principles of Inverter Circuits (1964); John Wiley & Sons (Inverter circuits are used for adjustable frequency motor speed control)
- Dewan and Straughen, another unnamed book on power electronics
- B. R. Pelly, "Thyristor Phase-Controlled Converters and Cycloconverters: Operation, Control, and Performance" (New York: John Wiley, 1971).

References

Donald G. Fink and H. Wayne Beaty, Standard Handbook for Electrical Engineers, Eleventh Edition, McGraw-Hill, New York, 1978, ISBN 007020974X. Category:Energy conversion Category:Electromagnetic components
- Category:Nikola Tesla Category:BEV Components ja:電動機

Precession

There are two types of precession, torque-free and torque-induced, the latter being discussed here in more detail.

Torque-free precession

Only solid objects can be in torque-free precession. For example, when a plate is thrown, the plate may have some rotation around an axis that is not its axis of symmetry. When the object is not perfectly solid, internal vortices will tend to damp torque-free precession.

Torque-induced precession

Torque-induced precession (gyroscopic precession) is the phenomenon by which the axis of a spinning object (e.g. a part of a gyroscope) "wobbles" when a torque is applied to it. The phenomenon is commonly seen in a spinning toy top, but all rotating objects can undergo precession. As a spinning object precesses, the tilt of its axis goes around in a circle in the opposite direction that the object is spinning. If the speed of the rotation and the magnitude of the torque are constant the axis will describe a cone, its movement at any instant being at right angles to the direction of the torque. In the case of a toy top, if the axis is not perfectly vertical the torque is applied by the force of gravity trying to tip it over. A rolling wheel will tend to remain upright due to precession. When the wheel tilts to one side, the particles at the top are pushed to one side and the particles at the bottom are pushed the other way. However, since the wheel is rotating, these particles eventually switch places and cancel one another out. Precession or gyroscopic considerations may have a minor effect on bicycle performance at high speed. Precession is also the mechanism behind gyrocompasses. This concept is easier to understand by examining the effects of inertia, which is often stated by the phrase "A body in motion tends to stay in motion." In this case the "motion" of a rotating body is in its rotation. If an external force pushes upon the rotating body, the body will resist the force by pushing back against it, but the reaction is delayed such that it occurs at a point 90 degrees later in its rotation. If you push a spinning top to the right, it will move forward (assuming the top is spinning counter-clockwise). Gyroscopic precession also plays a large role in the flight controls on helicopters. Since the driving force behind helicopters is the rotor head (which rotates), gyroscopic precession comes into play. If the rotor head is tilted to the right, its counter-clockwise movement forces the aircraft to fly forward. To ensure the pilot's inputs are correct the aircraft has corrective linkages which tilt the rotor head to the right when the pilots push the "cyclic stick" forward, or to the left when the stick is pulled to the back.

The physics of precession

Precession is due to the fact that the resultant of the angular velocity of rotation and the angular velocity produced by the torque is an angular velocity about a line which makes an angle with the permanent rotation axis, and this angle lies in a plane at right angles to the plane of the couple producing the torque. The permanent axis must turn towards this line, since the body cannot continue to rotate about any line which is not a principal axis of maximum moment of inertia; that is, the permanent axis turns in a direction at right angles to that in which the torque might be expected to turn it. If the rotating body is symmetrical and its motion unconstrained, and if the torque on the spin axis is at right angles to that axis, the axis of precession will be perpendicular to both the spin axis and torque axis. Under these circumstances the period of precession is given by: :

T_p = \frac

In which I_s is the moment of inertia, T_s is the period of spin about the spin axis, and Q is the torque. In general the problem is more complicated than this, however. For a layman’s explanation of Precession: we will have to imagine the wheel of a gyroscope as a group of particles that are being forced to move in circle. Remember the particles want to move in a straight line. In order for the particles to move in a curved line there must be a force. This force is provided by the structure of the wheel holding the particles within the wheel. Now let’s see what happens to our accelerating particles when a torque is applied to the spinning wheel. Assume the axis of rotation created by the torque is through the center of the wheel at 90 degrees to the primary rotation of the wheel. Let’s look at a particle that is on this axis of rotation. Since the particle is on the axis of rotation there is no direct motion applied to the particle at the instant of the applied torque. But let’s look at what will need to happen at the next moment in time. The particle is now going to be forced to curve again. This time in the direction of the curve is to accommodate the tilt of the wheel. Now we have a particle that is already moving and it wants to keep moving in a straight line. So the particle will exert a force on the wheel. If you look at a particle on the other side of the wheel you will see that the force of the second particle is in the opposite direction of the first particle. That pair of unmatched forced is what causes the precession torque that is 90 degrees to the applied torque.

Precession of the equinoxes

The Earth goes through one complete precession cycle in a period of approximately 25,800 years, during which the positions of stars as measured in the equatorial coordinate system will slowly change; the change is actually due to the change of the coordinates. Over this cycle the Earth's north axial pole moves from where it is now, within 1° of Polaris, in a circle around the ecliptic pole, with an angular radius of 23 degrees 27 arcminutes , or about 23.5 degrees. The shift is 1 degree in 180 years (the angle is taken from the observer, not from the center of the circle). The explanation of this is: The axis of the Earth undergoes precession due to a combination of the Earth's nonspherical shape (it is an oblate spheroid, bulging outward at the equator) and the gravitational tidal forces of the Moon and Sun applying torque as they attempt to pull the equatorial bulge into the plane of the ecliptic. The portion of the precession due to the combined action of the Sun and the Moon is called lunisolar precession.

A changing north star

Polaris is not particularly well-suited for marking the north celestial pole, as its visual magnitude, which is variable, hovers around 2.1, fairly far down the list of brightest stars in the sky. On the other hand, in 3000 BC the faint star Thuban in the constellation Draco was the pole star; at magnitude 3.67 it is only one-fifth as bright as Polaris; today it is all but invisible in light-polluted urban skies. The brightest star known to have been North Star or to be predictable as taking that role in the future is the brilliant Vega in the constellation Lyra, which will be the pole star around the year AD 14,000. When viewed looking down onto the Earth from the north, the direction of precession is clockwise. When standing on Earth looking outward, the axis appears to move counter-clockwise across the sky. This sense of precession, against the sense of Earth's own axial rotation, is opposite to the precession of a top on a table. The reason is that the torques imposed on the Earth by the Sun and Moon act in the sense of trying to align its axis normal to the ecliptic, i.e. to stand up more vertically in regard to the ecliptic plane, while the torque on a top spinning on a hard surface acts in the sense of trying to make the top fall over, rather than to stand up straighter. Image:precession starchart.jpg Polaris is not exactly at the pole; any long-exposure unguided photo will show it having a short trail. It is close enough for most practical purposes, though. The south celestial pole precesses too, always remaining exactly opposite the north pole. The south pole is in a particularly bland portion of the sky, and the nominal south pole star is Sigma Octantis, which, while fairly close to the pole, is even weaker than Thuban -- magnitude 5.5, which is barely visible even under a properly dark sky. The precession of the Earth is not entirely regular due to the fact that the Sun and Moon are not in the same plane and move relative to each other, causing the torque they apply to Earth to vary. This varying torque produces a slight irregular motion in the poles called nutation. Precession of the Earth's axis is a very slow effect, but at the level of accuracy at which astronomers work, it does need to be taken into account. Note that precession has no effect on the inclination ("tilt") of the plane of the Earth's equator (and thus its axis of rotation) on its orbital plane. It is 23.5 degrees and precession does not change that. The inclination of the equator on the ecliptic does change due to gravitational torque, but its period is different (main period about 41000 years). The following figure illustrates the effects of axial precession on the seasons, relative to perihelion and aphelion. The precession of the equinoxes can cause periodic climate change (see Milankovitch cycles), because the hemisphere that experiences summer at perihelion and winter at aphelion (as the southern hemisphere does presently) is in principle prone to more severe seasons than the opposite hemisphere. Image:precession and seasons.jpg [http://hometown.aol.com/gregbenson/iceage.htm] Hipparchus first estimated Earth's precession around 130 BC, adding his own observations to those of Babylonian and Chaldean astronomers in the preceding centuries. In particular they measured the distance of the stars like Spica to the Moon and Sun at the time of lunar eclipses, and because he could compute the distance of the Moon and Sun from the equinox at these moments, he noticed that Spica and other stars appeared to have moved over the centuries. Precession causes the cycle of seasons (tropical year) to be about 20.4 minutes less than the period for the earth to return to the same position with respect to the stars as one year previously (sidereal year). This results in a slow change (one day per 58 calendar years) in the position of the sun with respect to the stars at an equinox. It is significant for calendars and their leap year rules.

Precession of planetary orbits

leap year The revolution of a planet in its orbit around the Sun is also a form of rotary motion. (In this case, the combined system of Earth and Sun is rotating.) So the axis of a planet's orbital plane will also precess over time. The major axis of each planet's elliptical orbit also precesses within its orbital plane, in response to perturbations in the form of the changing gravitational forces exerted by other planets. This is called perihelion precession. Discrepancies between the observed perihelion precession rate of the planet Mercury and that predicted by classical mechanics were prominent among the forms of experimental evidence leading to the acceptance of Einstein's Theory of Relativity, which predicted the anomalies accurately. It is generally understood that the gravitational pulls of the sun and the moon cause the precession of the equinoxes on Earth which operate on cycles of 23,000 and 19,000 years. The precession of the orbit of the Earth is an important part of the astronomical theory of ice ages. Precession is also an important consideration in the dynamics of atoms and molecules.

Notes

# Cook, David R. (1999), "U.S. Department of Energy, Environmental Earth Science Archive, Ask A Scientist" [http://www.newton.dep.anl.gov/askasci/env99/env154.htm]

References

# "Moon and Spica", StarDate July 14, 2005, University of Texas McDonald Observatory, [http://stardate.org/radio/program.php?f=detail&id=20050714] Category:Astrometry Category:Planetary science Category:Earth Category:Astrological factors ko:세차운동 ja:歳差

Pioneer 10

Launched on March 2, 1972 by an Atlas-Centaur rocket, Pioneer 10 (also called Pioneer F) was the first spacecraft to travel through the asteroid belt, and was the first spacecraft to make direct observations of Jupiter. On December 3, 1973, Pioneer 10 sent back the first close-up images of Jupiter. On June 13th 1983 it passed the orbit of Neptune, then the outermost planet because of Pluto's highly eccentric orbit. By some definitions, this made the spacecraft the first artificial object to leave the solar system. However, Pioneer 10 has still not passed the heliopause or Oort cloud. Famed for a time as the most remote object ever made by man, at last contact Pioneer 10 was over 7.60 billion miles away from Earth. (Until February 17, 1998, the heliocentric radial distance of Pioneer 10 had been greater than that of any other man-made object. But later on that date, Voyager 1's heliocentric radial distance, in the approximate apex direction, equaled that of Pioneer 10 at 69.419 AU. Thereafter, Voyager 1's distance will exceed that of Pioneer 10 at the approximate rate of 1.016 AU per year). Voyager 1 Built by TRW[http://quest.nasa.gov/sso/cool/pioneer10/mission/], the spacecraft made valuable scientific investigations in the outer regions of our solar system until the end of its mission on March 31, 1997. The Pioneer 10's weak signal continued to be tracked by the Deep Space Network as part of a new advanced concept study of chaos theory. Before 1997 the probe was used in the training of flight controllers on how to acquire radio signals from space. The last, very weak, signal from Pioneer 10 was received January 23, 2003. A contact attempt February 7, 2003, was not successful and further attempts are not planned. The last successful reception of telemetry was on April 27, 2002; subsequent signals were barely strong enough to detect. Loss of contact was probably due to a combination of increasing distance and the spacecraft's steadily weakening power source, rather than failure of the craft. However, the planetary society mentions in their Pioneer Anomaly pages that there will be one last attempt to get data from the spacecraft on March 4, 2006. After this date the spacecraft antenna will never be aligned correctly anymore. 1997 Pioneer 10 is heading in the direction of the star Aldebaran in the constellation Taurus. It will take Pioneer over 2 million years to reach it.

Fictional references

Pioneer 10 was used for target practice and easily destroyed by a Klingon Bird of Prey in the movie Star Trek V: The Final Frontier.

External links

- [http://spaceprojects.arc.nasa.gov/Space_Projects/pioneer/PNhome.html Pioneer Project Home Page]
- [http://nssdc.gsfc.nasa.gov/database/MasterCatalog?sc=1972-012A NSSDC Pioneer 10 page]
- [http://history.nasa.gov/SP-349/sp349.htm Pioneer Odyssey, NASA SP-396, 1977] - This is an entire book about the Pioneer 10 and 11 project, with all pictures and diagrams, on-line! Scroll down to click on the "Table of Contents" link.
- [http://www.nap.edu/books/0309090504/html/ Mark Wolverton's The Depths of Space online]
- [http://www.cnn.com/2002/TECH/space/12/18/pioneer.contact/index.html A distant Pioneer whispers to Earth] - CNN article, Dec. 19, 2002
- [http://www.pioneer10.net/ PIONEER 10] - Canadian rock band of same name.
- [http://www.planetary.org/programs/projects/pioneer_anomaly/update_200511.html 2005 Pioneer Anomaly Conference ] - Mentions March 4, 2006 Contact Attempt Category:Jupiter spacecraft Category:Pioneer program ko:파이어니어 10호

Tidal force

The tidal force is a secondary effect of the force of gravity and is responsible for the tides. It arises because the gravitational field is not constant across a body's diameter. When a body is acted on by the gravity of another body, the field can vary significantly between the near side and the far side. This causes strains on the body, and may distort it or break it apart. These strains do not occur if the gravitational field is uniform, since a uniform field only causes the entire body to accelerate together, in the same direction and at the same rate. field The figure shows Comet Shoemaker-Levy 9 after it had broken up under the influence of Jupiter's tidal forces. The comet was falling into Jupiter, and the parts of the comet closest to Jupiter fell with a greater acceleration, due to the greater gravitational force. From the point of view of an observer riding on the comet, it would appear that the parts in front split off in the forward direction, while the parts in back split off in the backward direction. In reality, however, all parts of the comet were accelerating toward Jupiter, but at different rates. In the case of an elastic sphere, the effect of a tidal force is to distort the shape of the body without any change in volume. The sphere becomes an ellipsoid, with two bulges, pointing towards and away from the other body. This is essentially what happens to the Earth's oceans. Although the Earth is not falling along a line directly toward the moon, the Earth is continuously accelerating due to the moon's gravitational forces, causing it to wobble around their common center of mass. All parts of the Earth accelerate in response to the moon's gravitational forces, but to an observer on the Earth, it appears that the Earth's center remains at rest, while water in the oceans is redistributed to form bulges on the sides near the moon and far from the moon. When a body rotates while subject to tidal forces, internal friction results in the gradual dissipation of its rotational kinetic energy as heat. If the body is close enough to its primary, this can result in a rotation which is tidally locked to the orbital motion, as in the case of the Earth's moon. Tidal heating has produced dramatic volcanic effects on Jupiter's moon Io.

Mathematical treatment

For a given (externally generated) gravitational field, the tidal acceleration at a point with respect to a body is obtained by vectorially subtracting the gravitational acceleration at the center of the body from the actual gravitational acceleration at the point. Correspondingly, the term tidal force is used to describe the forces due to tidal acceleration. Note that for these purposes the only gravitational field considered is the external one; the gravitational field of the body (as shown in the graphic) is not relevant. vectorially subtracting Tidal acceleration does not require rotation or orbiting bodies; e.g. the body may be freefalling in a straight line under the influence of a gravitational field while still being influenced by (changing) tidal acceleration. Suppose that the gravitational field is due to one other body: linearizing Newton's law of gravitation around the centre of the reference body yields an approximate inverse cube law. Along the axis through the centers of the two bodies, this takes the form: :

F_t = \frac

where G is the gravitational constant, M is the mass of the body producing the field, m is the mass on which the tidal force acts, R is the distance between the two bodies and r ≪ R is the distance from the reference body's center along the axis. This tidal force acts outwards both at the near side and at the far side of the body, leading to a bulge on both sides. The tidal forces can also be calculated away from the axis connecting the bodies. In the plane perpendicular to the axis, the tidal force is directed inwards, and its magnitude is

F_t/2

in the linear approximation (1). Tidal effects become particularly pronounced near small bodies of high mass, such as neutron stars or black holes, where they are responsible for the "spaghettification" of infalling matter. Tidal forces, in combination with centripetal forces, create the oceanic tide of Earth's oceans, where the attracting bodies are the Moon and the Sun. Tidal forces are also responsible for tidal locking.

Additional effect of rotation

For two bodies rotating about their barycenter, the variation in centripetal force required for the rotation adds to the tidal force. As a simple example, consider circular orbits. Subtracting the value at the center of one body results in the expression: :

F_t = \omega^2mr + \frac

(where

\omega

is the angular frequency), i.e. one half of the other effect. This applies regardless of whether the barycenter is inside (as with tidal effect on Earth due to the Moon) or outside the body. Lateral rotation has no such effect on tidal force.

Magnetic field

:For other senses of this term, see magnetic field (disambiguation). In physics, a magnetic field is an entity produced by moving electric charges (electric currents) that exerts a force on other moving charges. (The quantum-mechanical spin of a particle produces magnetic fields and is acted on by them as though it were a current; this accounts for the fields produced by "permanent" ferromagnets.) A magnetic field is a vector field: it associates with every point in space a (pseudo-)vector that may vary in time. The direction of the field is the equilibrium direction of a compass needle placed in the field.

Symbols and terminology

Magnetic field is usually denoted by the symbol

\mathbf \

. Historically,

\mathbf \

was called the magnetic flux density, magnetic induction, or magnetic field strength.

\mathbf

was called the magnetic field (or magnetic field intensity), and this terminology is still often used to distinguish the two in the context of magnetic materials (non-trivial permeability μ). Otherwise, however, this distinction is often ignored, and both symbols are frequently referred to as the magnetic field. (Some authors call H the auxiliary field, instead.) In linear materials, such as air or free space, the two quantities are linearly related: :

\mathbf = \mu \mathbf \

where

\ \mu

is the magnetic permeability (in henries per meter) of the medium. In SI units,

\mathbf \

and

\mathbf \

are measured in teslas (T) and amperes per meter (A/m), respectively; or, in cgs units, in gauss (G) and oersteds (Oe), respectively. Two parallel wires carrying an electric current in the same sense will generate a magnetic field which will cause a force of attraction to each other. This fact is used to generate the value of an ampere of electric current. Note that while like charges repel and unlike ones attract, the opposite holds for currents: if the current in one of the two parallel wires is reversed, the two will repel.

Definition

Like the electric field, the magnetic field can be defined by the force it produces. In SI units, this is: :

\mathbf = q \mathbf \times \mathbf

where :F is the force produced, measured in newtons :

\times \

indicates a vector cross product :

q \

is electric charge that the magnetic field is acting on, measured in coulombs :

\mathbf \

is velocity of the electric charge

q \

, measured in metres per second :B is magnetic flux density, measured in teslas This law is called the Lorentz force law. (More precisely, it is the special case of that law when there is no electric field. It holds in any reference frame, although the force due to the magnetic field may be different in different frames because magnetic fields transform into electric fields under Lorentz transformations. The total force due to the electric and magnetic fields is the same in any frame.)

Current loop

A simpler form of the force equation in a wire current loop is: Force = BLi = (Tesla)x(meter length of wire)x(ampere current of wire). A more complex explanation is that if the moving charge is part of a current in a wire, then an equivalent form of the law is :

\frac   = \mathbf \times \mathbf

In words, this equation says that the force per unit length of wire is the cross product of the current vector and the magnetic field. In the equation above, the current vector,

\mathbf

, is a vector with magnitude equal to the usual scalar current,

i

, and direction pointing along the wire that the current is flowing.

Point charge generating magnetic field

The field can be computed as the sum of the contributions from individual charged particles. The magnetic flux density from a point charge is: :

\mathbf = \frac\mathbf \times \mathbf

which, for constant velocities, can be expanded into the Biot-Savart law: :

\mathbf = \frac\frac\mathbf \times \mathbf

q \

is electric charge generating the magnetic field, measured in coulombs :

\mathbf \

is velocity of the electric charge

q \

that is generating B, measured in metres per second :B is magnetic flux density, measured in teslas

Vector calculus

The most compact and elegant mathematical statements describing how magnetic fields are produced makes use of vector calculus. In free space: :

\nabla \times \mathbf = \mu_0 \mathbf + \mu_0 \epsilon_0 \frac

\nabla \cdot \mathbf = 0

where :

\nabla \times

is the curl operator :

\nabla \cdot

is the divergence operator :

\mu_0 \

is permeability :

\mathbf \

is current density :

\partial \

is the partial derivative :

\epsilon_0 \

is the free-space permittivity :

\mathbf \

is the electric field :

t \

is time The first equation is known as Ampère's law with James Clerk Maxwell's correction. The second term of this equation (Maxwell's correction) disappears in static or quasi-static systems. The second equation is a statement of the observed non-existence of magnetic monopoles. These are two of four Maxwell's equations; the notation is due to Oliver Heaviside.

Energy in the magnetic field

The general relation for nonlinear materials, the differential energy is: :

dU_H = \int_^ H \cdot dB \, dV

Where V is the volume and dV is the differential volume. For linear materials, H is proportional to B, so the above equation can be simplified: :

U_H = \frac\int_^ B \cdot H \, dV

For linear materials and a constant volume: :

U_H = \frac

Energy can produce a force, so :

F = \frac

F = \frac

Where dl is differential distance and A is the surface area. Force p