Misplaced Pages

#67932

136-605: The AGM-86 ALCM is an American subsonic air-launched cruise missile (ALCM) built by Boeing and operated by the United States Air Force . This missile was developed to increase the effectiveness and survivability of the Boeing B-52G and B-52H Stratofortress strategic bombers , allowing the aircraft to deliver its payload from a great distance. The missile dilutes an enemy's forces ability to respond and complicates air defense of its territory. The concept started as

272-426: A shock wave . The presence of shock waves, along with the compressibility effects of high-flow velocity (see Reynolds number ) fluids, is the central difference between the supersonic and subsonic aerodynamics regimes. In aerodynamics, hypersonic speeds are speeds that are highly supersonic. In the 1970s, the term generally came to refer to speeds of Mach 5 (5 times the speed of sound) and above. The hypersonic regime

408-450: 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 it 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

544-424: A B-52 on a radar display . Quail was designed in the mid-1950s when the normal attack profile for a strategic bomber was to fly as high and fast as possible to reduce the time the defenders had to respond to the aircraft before it flew out of range. This was effective against interceptor aircraft but of little use against surface-to-air missiles (SAMs), whose attack times were measured in seconds. This led to

680-463: A French aeronautical engineer, became the first person to reasonably predict the power needed for sustained flight. Otto Lilienthal , the first person to become highly successful with glider flights, was also the first to propose thin, curved airfoils that would produce high lift and low drag. Building on these developments as well as research carried out in their own wind tunnel, the Wright brothers flew

816-482: A continuum. Continuum flow fields are characterized by properties such as flow velocity , pressure , density , and temperature , which may be functions of position and time. These properties may be directly or indirectly measured in aerodynamics experiments or calculated starting with the equations for conservation of mass, momentum , and energy in air flows. Density, flow velocity, and an additional property, viscosity , are used to classify flow fields. Flow velocity

952-420: A conventional or nuclear warhead. The LRSO program is to develop a weapon that can penetrate and survive integrated air defense systems and prosecute strategic targets. Both conventional and nuclear versions of the weapon are required to reach initial operational capability (IOC) before the retirement of their respective ALCM versions, around 2030. The technology development contracts were to be submitted before

1088-510: A decoy. This would allow it to act as a decoy for much of its flight, and then deliberately approach a selected defensive site and attack it. As such, the program was renamed Subsonic Cruise Armed Decoy, retaining the SCAD acronym. For this role, the accuracy of the original INS guidance hardware was not enough. While a similar system was also used in SRAM, its shorter range and much shorter flight times meant

1224-440: A flotation chamber to mount a gyrostabilized platform. These systems can have very high precisions (e.g., Advanced Inertial Reference Sphere ). 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 presses against the spherical shell of the platform. The fluid bearings are very slippery and

1360-410: A flow field) enables the calculation of forces and moments acting on the object. In many aerodynamics problems, the forces of interest are the fundamental forces of flight: lift , drag , thrust , and weight . Of these, lift and drag are aerodynamic forces, i.e. forces due to air flow over a solid body. Calculation of these quantities is often founded upon the assumption that the flow field behaves as

1496-438: A fluid, the speed of sound in that fluid can be considered the fastest speed that "information" can travel in the flow. This difference most obviously manifests itself in the case of a fluid striking an object. In front of that object, the fluid builds up a stagnation pressure as impact with the object brings the moving fluid to rest. In fluid traveling at subsonic speed, this pressure disturbance can propagate upstream, changing

SECTION 10

#1733085533068

1632-694: A gimballed system. That is, it must integrate the vehicle's attitude changes in pitch, roll and yaw, as well as gross movements. Gimballed systems could usually do well with update rates of 50–60 Hz. However, strapdown systems normally update about 2000 Hz. The higher rate is needed to let the navigation system integrate the angular rate into an attitude accurately. The data updating algorithms ( direction cosines or quaternions ) involved are too complex to be accurately performed except by digital electronics. However, digital computers are now so inexpensive and fast that rate gyro systems can now be practically used and mass-produced. The Apollo lunar module used

1768-451: A gyroscope system can sometimes also be inferred simply from its position history (e.g., GPS). This is, in particular, the case with planes and cars, where the velocity vector usually implies the orientation of the vehicle body. For example, Honeywell 's Align in Motion is an initialization process where the initialization occurs while the aircraft is moving, in the air or on the ground. This

1904-488: A gyroscopic element (for maintaining an absolute angular reference). Angular accelerometers measure how the vehicle is rotating in space. Generally, there is at least one sensor for each of the three axes: pitch (nose up and down), yaw (nose left and right) and roll (clockwise or counter-clockwise from the cockpit). Linear accelerometers measure non-gravitational accelerations of the vehicle. Since it can move in three axes (up and down, left and right, forward and back), there

2040-627: A long-range drone aircraft that would act as a decoy, distracting Soviet air defenses from the bombers. As new lightweight nuclear weapons emerged in the 1960s, the design was modified with the intent of attacking missile and radar sites at the end of its flight. Further development extended its range so much that it emerged as a weapon allowing the B-52s to launch their attacks while still well outside Soviet airspace, saturating their defenses with hundreds of tiny, low-flying targets that were extremely difficult to see on radar. Entering service in 1982 as part of

2176-599: A mixture of the two remains. In the summer of 1952, Dr. Richard Battin and Dr. J. Halcombe "Hal" Laning, Jr. , researched computational based solutions to guidance and undertook the initial analytical work on the Atlas inertial guidance in 1954. Other key figures at Convair were Charlie Bossart, the Chief Engineer, and Walter Schweidetzky, head of the guidance group. Schweidetzky had worked with von Braun at Peenemünde during World War II. The initial Delta guidance system assessed

2312-410: A range of flow velocities just below and above the local speed of sound (generally taken as Mach 0.8–1.2). It is defined as the range of speeds between the critical Mach number , when some parts of the airflow over an aircraft become supersonic , and a higher speed, typically near Mach 1.2 , when all of the airflow is supersonic. Between these speeds, some of the airflow is supersonic, while some of

2448-634: A result of the Strategic Offensive Reductions Treaty requirement to go below 2,200 deployed nuclear weapons by 2012, with the AGM-129 ACM chosen for disposal because it has reliability problems and high maintenance costs. Even with the SLEP (service life extension program), the remaining AGM-86s were to reach their end of service by 2020, leaving the B-52 without a nuclear mission. However, in 2012,

2584-408: 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 . Lightweight digital computers permit the system to eliminate

2720-458: A strapdown system in its backup Abort Guidance System (AGS). Strapdown systems are nowadays commonly used in commercial and military applications (aircraft, ships, ROVs , missiles , etc.). State-of-the-art strapdown systems are based upon ring laser gyroscopes , fibre optic gyrocopes or hemispherical resonator gyroscopes . They are using digital electronics and advanced digital filtering techniques such as Kalman filter . The orientation of

2856-467: A terrain contour-matching guidance system ( TERCOM ) to fly to its assigned target. It can carry a single W80 thermonuclear warhead, with a yield of 5 or 150 kilotons. A modified variant of the B61 , it was mainly designed for use on ground and air-launched cruise missiles. The AGM-86C/D CALCM carries a conventional high-explosive payload rather than a thermonuclear payload. This is a fragmentation warhead in

SECTION 20

#1733085533068

2992-536: A wide range of applications. These products include "tuning fork gyros". Here, the gyro is designed as an electronically driven tuning fork, often fabricated out of a single piece of quartz or silicon. Such gyros operate in accordance with the dynamic theory that when an angle rate is applied to a translating body, a Coriolis force is generated. This system is usually integrated on a silicon chip. It has two mass-balanced quartz tuning forks, arranged "handle-to-handle" so forces cancel. Aluminum electrodes evaporated onto

3128-681: Is a navigation device that uses motion sensors ( accelerometers ), rotation sensors ( gyroscopes ) and a computer to continuously calculate by dead reckoning the position, the orientation, and the velocity (direction and speed of movement) of a moving object without the need for external references. Often the inertial sensors are supplemented by a barometric altimeter and sometimes by magnetic sensors ( magnetometers ) and/or speed measuring devices. INSs are used on mobile robots and on vehicles such as ships , aircraft , submarines , guided missiles , and spacecraft . Older INS systems generally used an inertial platform as their mounting point to

3264-418: Is a flow in which density is constant in both time and space. Although all real fluids are compressible, a flow is often approximated as incompressible if the effect of the density changes cause only small changes to the calculated results. This is more likely to be true when the flow speeds are significantly lower than the speed of sound. Effects of compressibility are more significant at speeds close to or above

3400-405: Is a linear accelerometer for each axis. A computer continually calculates the vehicle's current position. First, for each of the six degrees of freedom (x,y,z and θ x , θ y and θ z ), it integrates over time the sensed acceleration, together with an estimate of gravity, to calculate the current velocity. Then it integrates the velocity to calculate the current position. Inertial guidance

3536-448: Is a solution in one dimension to both the momentum and energy conservation equations. The ideal gas law or another such equation of state is often used in conjunction with these equations to form a determined system that allows the solution for the unknown variables. Aerodynamic problems are classified by the flow environment or properties of the flow, including flow speed , compressibility , and viscosity . External aerodynamics

3672-416: Is a subset of the supersonic regime. Hypersonic flow is characterized by high temperature flow behind a shock wave, viscous interaction, and chemical dissociation of gas. The incompressible and compressible flow regimes produce many associated phenomena, such as boundary layers and turbulence. The concept of a boundary layer is important in many problems in aerodynamics. The viscosity and fluid friction in

3808-421: Is accomplished using GPS and an inertial reasonableness test, thereby allowing commercial data integrity requirements to be met. This process has been FAA certified to recover pure INS performance equivalent to stationary alignment procedures for civilian flight times up to 18 hours. It avoids the need for gyroscope batteries on aircraft. Less-expensive navigation systems, intended for use in automobiles, may use

3944-503: Is associated with the frictional forces in a flow. In some flow fields, viscous effects are very small, and approximate solutions may safely neglect viscous effects. These approximations are called inviscid flows. Flows for which viscosity is not neglected are called viscous flows. Finally, aerodynamic problems may also be classified by the flow environment. External aerodynamics is the study of flow around solid objects of various shapes (e.g. around an airplane wing), while internal aerodynamics

4080-407: Is called laminar flow . Aerodynamics is a significant element of vehicle design , including road cars and trucks where the main goal is to reduce the vehicle drag coefficient , and racing cars , where in addition to reducing drag the goal is also to increase the overall level of downforce . Aerodynamics is also important in the prediction of forces and moments acting on sailing vessels . It

4216-409: Is called potential flow and allows the differential equations that describe the flow to be a simplified version of the equations of fluid dynamics , thus making available to the aerodynamicist a range of quick and easy solutions. In solving a subsonic problem, one decision to be made by the aerodynamicist is whether to incorporate the effects of compressibility. Compressibility is a description of

AGM-86 ALCM - Misplaced Pages Continue

4352-516: Is difficult 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

4488-500: Is held annually in October in Germany. The publications of all DGON ISA conferences over the last more than 60 years are accessible. All inertial navigation systems suffer from integration drift: small errors in the measurement of acceleration and angular velocity are integrated into progressively larger errors in velocity, which are compounded into still greater errors in position. Since

4624-500: Is possible to track the position and orientation of a device. An inertial navigation system includes at least a computer and a platform or module containing accelerometers , gyroscopes , or other motion-sensing devices. The INS is initially provided with its position and velocity from another source (a human operator, a GPS satellite receiver, etc.) accompanied with the initial orientation and thereafter computes its own updated position and velocity by integrating information received from

4760-497: Is the study of flow around solid objects of various shapes. Evaluating the lift and drag on an airplane or the shock waves that form in front of the nose of a rocket are examples of external aerodynamics. Internal aerodynamics is the study of flow through passages in solid objects. For instance, internal aerodynamics encompasses the study of the airflow through a jet engine or through an air conditioning pipe. Aerodynamic problems can also be classified according to whether

4896-415: Is the study of flow through passages inside solid objects (e.g. through a jet engine). Unlike liquids and solids, gases are composed of discrete molecules which occupy only a small fraction of the volume filled by the gas. On a molecular level, flow fields are made up of the collisions of many individual of gas molecules between themselves and with solid surfaces. However, in most aerodynamics applications,

5032-426: Is used because gas flows with a Mach number below that value demonstrate changes in density of less than 5%. Furthermore, that maximum 5% density change occurs at the stagnation point (the point on the object where flow speed is zero), while the density changes around the rest of the object will be significantly lower. Transonic, supersonic, and hypersonic flows are all compressible flows. The term Transonic refers to

5168-418: Is used in the design of mechanical components such as hard drive heads. Structural engineers resort to aerodynamics, and particularly aeroelasticity , when calculating wind loads in the design of large buildings, bridges , and wind turbines . The aerodynamics of internal passages is important in heating/ventilation , gas piping , and in automotive engines where detailed flow patterns strongly affect

5304-468: Is used to classify flows according to speed regime. Subsonic flows are flow fields in which the air speed field is always below the local speed of sound. Transonic flows include both regions of subsonic flow and regions in which the local flow speed is greater than the local speed of sound. Supersonic flows are defined to be flows in which the flow speed is greater than the speed of sound everywhere. A fourth classification, hypersonic flow, refers to flows where

5440-452: Is usually used to supplement other navigation systems, providing a higher degree of accuracy than is possible with the use of any single 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 . In aerospace particularly, other measurement systems are used to determine INS inaccuracies, e.g.

5576-428: Is very accurate. However it is still relatively expensive due to the cost of the precision ground and polished hollow quartz hemispheres. Northrop Grumman currently manufactures IMUs ( inertial measurement units ) for spacecraft that use HRGs. These IMUs have demonstrated extremely high reliability since their initial use in 1996. Safran manufactures large numbers of HRG based inertial navigation systems dedicated to

AGM-86 ALCM - Misplaced Pages Continue

5712-520: Is vulnerable to gimbal lock . The primary guidance system of the Apollo spacecraft used a three-axis gyrostabilized platform, feeding data to the Apollo Guidance Computer . Maneuvers had to be carefully planned to avoid gimbal lock. Gimbal lock constrains maneuvering and it would be beneficial to eliminate the slip rings and bearings of the gimbals. Therefore, some systems use fluid bearings or

5848-737: The Cold War led to cutbacks in this program, and its expensive maintenance eventually resulted in it being abandoned in favor of life extensions to the original ALCM. Examples of the AGM-86A and AGM-86B are on display at the Steven F. Udvar-Hazy Center of the National Air and Space Museum , near Washington, D.C. The ALCM traces its history to the ADM-20 Quail missile, which began development in February 1956. Quail

5984-587: The SA-2 Guideline missiles it faced. Flying at Mach 3, it quickly flew out in front of the bombers, reaching the missile site before the bomber flew into the range of the SA-2. While highly capable against known missile locations, SRAM could do nothing to defend against unknown sites, nor help with the problem of interceptor aircraft. To deal with these threats, Quail continued to be carried, typically in pairs, providing some defense against these other threats. However, by

6120-538: The Space Shuttle , open loop guidance was used to guide the Shuttle from lift-off until Solid Rocket Booster (SRB) separation. After SRB separation the primary Space Shuttle guidance is named PEG (Powered Explicit Guidance). PEG takes into account both the Q system and the predictor-corrector attributes of the original "Delta" System (PEG Guidance). Although many updates to the Shuttle's navigation system had taken place over

6256-417: The U.S. Army Research Laboratory reported a method to merge measurements from 10 pairs of MEMS gyroscope and accelerometers (plus occasional GPS), reducing the positional error by two thirds for a projectile. The algorithm can correct for systemic biases in individual sensors, using both GPS and a heuristic based on the gun-firing acceleration force. If one sensor consistently over or underestimates distance,

6392-460: The drift rate of the system was not a serious concern as long as the bomber could feed it accurate information just before launch, to "zero out" the drift. In contrast, SCAD was designed to fly over much longer ranges and slower speeds, resulting in longer flight times and increasing the problem with drift; even with the drift "zeroed out" just before launch, subsequent drift during the longer flight would accumulate to an unacceptable error. To provide

6528-416: The flow speed is below, near or above the speed of sound . A problem is called subsonic if all the speeds in the problem are less than the speed of sound, transonic if speeds both below and above the speed of sound are present (normally when the characteristic speed is approximately the speed of sound), supersonic when the characteristic flow speed is greater than the speed of sound, and hypersonic when

6664-562: The pressure reference system was developed to use one numerical integration of the angular rate measurements. Estimation theory in general and Kalman filtering in particular, provide a theoretical framework for combining information from various sensors. One of the most common alternative sensors is a satellite navigation radio such as GPS , which can be used for all kinds of vehicles with direct sky visibility. Indoor applications can use pedometers , distance measurement equipment, or other kinds of position sensors . By properly combining

6800-499: The AGM-86C and a unitary penetrating warhead in the AGM-86D. The AGM-86C/D uses an onboard Global Positioning System (GPS) coupled with its inertial navigation system (INS) to navigate in flight. This allows the missile to guide itself to the target with pinpoint accuracy. Litton Guidance and Control , and Interstate Electronics Corporation (one of the companies acquired by L3Harris ) were

6936-641: The Air Force and Navy were ordered to collaborate under the "Joint Cruise Missile Project", JCMP, with the intention of using as many parts in common as possible. After considering the two designs, the Air Force agreed to modify the ALCM with the SLCM's McDonnell Douglas AN/DPW-23 TERCOM system, as well as using its Williams F107 turbofan engine. While the JCMP program was taking place, the B-1

SECTION 50

#1733085533068

7072-541: The Air Force had also issued a requirement for a version with a much longer 1,500 nautical miles (2,800 km; 1,700 mi) range. This would allow the bombers to launch their missiles from far off the Russian coast, placing it outside the range of the interceptors as well. To reach the intended range, this new Extended Range Version (ERV) would have to be lengthened to contain more fuel, or external fuel tanks would have to be added. Either change would make it too large to fit on

7208-411: The B model's TERCOM and integrated a GPS capability with the existing inertial navigation system computer . In 1996 and 1997, 200 additional CALCMs were produced from excess ALCMs. These missiles, designated Block I, incorporate improvements such as a larger and improved conventional payload (1,360 kg, 3,000 lb blast class), a multi-channel GPS receiver and integration of the buffer box into

7344-551: The B-52G with the 416th Bombardment Wing / 668th Bombardment Squadron, Griffiss Air Force Base, New York. Eventually, the missile was deployed across the entire B-52G and B-52H fleet throughout Strategic Air Command. Integration and successful flight testing did occur with the B-1B (involving moving the bulkhead between the forward and intermediate stores bay forward one position) - however the AGM-86

7480-805: The C-5A which utilized the triple INS configuration, similar to the 747. The KC-135A fleet was fitted with a single Carousel IV-E system that could operate as a stand-alone INS or can be aided by the AN/APN-81 or AN/APN-218 Doppler radar . Some special-mission variants of the C-135 were fitted with dual Carousel IV-E INSs. ARINC Characteristic 704 defines the INS used in commercial air transport. INSs contain Inertial Measurement Units (IMUs) which have angular and linear accelerometers (for changes in position); some IMUs include

7616-820: The Delco Electronics Div. of General Motors Corp. were awarded the joint contract for design and production of the Apollo Guidance and Navigation systems for the Command Module and the Lunar Module. Delco produced the IMUs ( Inertial Measurement Units ) for these systems, Kollsman Instrument Corp. produced the Optical Systems, and the Apollo Guidance Computer was built by Raytheon under subcontract. For

7752-639: The Department of Defense has awarded both Lockheed Martin and Raytheon Corporations with $ 900 million ($ 1.12 billion in 2023) to develop the LRSO. Contracts end in 2022, when the Department of Defense will select one design to continue further developments. The CALCM was retired on 20 November 2019, replaced in the conventional standoff strike role by the AGM-158B JASSM-ER . Aerodynamics#Incompressible aerodynamics Modern aerodynamics only dates back to

7888-460: The Earth, since they did not know what direction the car was facing relative to the Earth when they felt the accelerations. However, by tracking both the current angular velocity of the system and the current linear acceleration of the system measured relative to the moving system, it is possible to determine the linear acceleration of the system in the inertial reference frame. Performing integration on

8024-561: The GPS receiver. The upgraded avionics package was retrofitted into all existing CALCM (Block 0) so all AGM-86C missiles are electronically identical. All variants of the AGM-86 missile are powered by a Williams F107 turbofan jet engine that propels it at sustained subsonic speeds and can be launched from aircraft at both high and low altitudes. The missile deploys its folded wings, tail surfaces and engine inlet after launch. AGM-86B/C/D missiles increase flexibility in target selection. AGM-86B missiles can be air-launched in large numbers by

8160-507: The Honeywell LaseRefV inertial navigation systems uses GPS and air data computer outputs to maintain required navigation performance . The navigation error rises with the lower sensitivity of the sensors used. Currently, devices combining different sensors are being developed, e.g. attitude and heading reference system . Because the navigation error is mainly influenced by the numerical integration of angular rates and accelerations,

8296-557: The SRAM launchers and the extended-fuselage version would be too large to fit in the bomb bay of the new B-1 Lancer bomber. The Air Force intended to replace the original ALCM with the new version at some future date. The Navy was also in the midst of its own cruise missile project, the Sea-Launched Cruise Missile (SLCM), which ultimately emerged as the BGM-109 Tomahawk , which was similar to ALCM in many ways. In 1977,

SECTION 60

#1733085533068

8432-574: The USAF announced plans to extend the useful life of the missiles until at least 2030. To replace the ALCM, the USAF planned to award a contract for the development of the new Long-Range Stand-Off (LRSO) weapon in 2015. Unlike the AGM-86, the LRSO will be carried on multiple aircraft, including the B-52, the B-2 Spirit , and the Northrop Grumman B-21 . Like the AGM-86, the LRSO can be armed with either

8568-546: The V2 provided many innovations as an integrated platform with closed loop guidance. At the end of the war von Braun engineered the surrender of 500 of his top rocket scientists, along with plans and test vehicles, to the Americans. They arrived at Fort Bliss, Texas in 1945 under the provisions of Operation Paperclip and were subsequently moved to Huntsville, Alabama , in 1950 where they worked for U.S. Army rocket research programs. In

8704-510: The accuracy needed to attack the SAM sites with a small warhead, some system was needed to zero out the drift in-flight, and for this need, a radar-based TERCOM system was added. Development was approved in July 1970, and it was given the designation ZAGM-86A, the Z indicating its initial development status. As SCAD moved from the pure-decoy role to decoy-and-attack, this meant it would be able to carry out

8840-410: The adoption of low-level attacks, where the bombers would fly below the radar horizon so they could not be seen on ground-based radars. Quail, originally designed for the high-altitude mission, was modified with the addition of a barometric altimeter to allow it to fly at lower altitudes. Doing so seriously limited its effective range and flight time. In the early 1960s, the Air Force began to question

8976-429: The advent of spacecraft , guided missiles , and commercial airliners . Early German World War II V2 guidance systems combined two gyroscopes and a lateral accelerometer with a simple analog computer to adjust the azimuth for the rocket in flight. Analog computer signals were used to drive four graphite rudders in the rocket exhaust for flight control. The GN&C (Guidance, Navigation, and Control) system for

9112-412: The air is approximated as being significant only in this thin layer. This assumption makes the description of such aerodynamics much more tractable mathematically. In aerodynamics, turbulence is characterized by chaotic property changes in the flow. These include low momentum diffusion, high momentum convection, and rapid variation of pressure and flow velocity in space and time. Flow that is not turbulent

9248-563: The airflow is not supersonic. Supersonic aerodynamic problems are those involving flow speeds greater than the speed of sound. Calculating the lift on the Concorde during cruise can be an example of a supersonic aerodynamic problem. Supersonic flow behaves very differently from subsonic flow. Fluids react to differences in pressure; pressure changes are how a fluid is "told" to respond to its environment. Therefore, since sound is, in fact, an infinitesimal pressure difference propagating through

9384-576: The amount of change of density in the flow. When the effects of compressibility on the solution are small, the assumption that density is constant may be made. The problem is then an incompressible low-speed aerodynamics problem. When the density is allowed to vary, the flow is called compressible. In air, compressibility effects are usually ignored when the Mach number in the flow does not exceed 0.3 (about 335 feet (102 m) per second or 228 miles (366 km) per hour at 60 °F (16 °C)). Above Mach 0.3,

9520-435: The angular displacement, the system's current orientation is known at all times. This can be thought of as the ability of a blindfolded passenger in a car to feel the car turn left and right or tilt up and down as the car ascends or descends hills. Based on this information alone, the passenger knows what direction the car is facing, but not how fast or slow it is moving, or whether it is sliding sideways. Accelerometers measure

9656-586: The bomber force. B-52H bombers carry six AGM-86B or AGM-86C missiles on each of two externally mounted pylons and eight internally on a rotary launcher, giving the B-52H a maximum capacity of 20 missiles per aircraft. An enemy force would have to counterattack each of the missiles individually, making defense against them costly and complicated. The enemy's defenses are further hampered by the missiles' small size and low-altitude flight capability, which makes them difficult to detect on radar . The nuclear armed AGM-86B uses

9792-452: The car has turned and how it has accelerated and decelerated since, then they can accurately know the current orientation, position, and velocity of the car at any time. Inertial navigation is used in a wide range of applications including the navigation of aircraft, tactical and strategic missiles, spacecraft, submarines and ships. It is also embedded in some mobile phones for purposes of mobile phone location and tracking. Recent advances in

9928-690: The choice between statistical mechanics and the continuous formulation of aerodynamics. The assumption of a fluid continuum allows problems in aerodynamics to be solved using fluid dynamics conservation laws . Three conservation principles are used: Together, these equations are known as the Navier–Stokes equations , although some authors define the term to only include the momentum equation(s). The Navier–Stokes equations have no known analytical solution and are solved in modern aerodynamics using computational techniques . Because computational methods using high speed computers were not historically available and

10064-460: The construction of microelectromechanical systems (MEMS) have made it possible to manufacture small and light inertial navigation systems. These advances have widened the range of possible applications to include areas such as human and animal motion capture . Inertial navigation systems are used in many different moving objects. However, their cost and complexity place constraints on the environments in which they are practical for use. To support

10200-457: The continuum assumption is reasonable. The continuum assumption is less valid for extremely low-density flows, such as those encountered by vehicles at very high altitudes (e.g. 300,000 ft/90 km) or satellites in Low Earth orbit . In those cases, statistical mechanics is a more accurate method of solving the problem than is continuum aerodynamics. The Knudsen number can be used to guide

10336-463: The desire to improve the aerodynamic efficiency of current aircraft and propulsion systems, continues to motivate new research in aerodynamics, while work continues to be done on important problems in basic aerodynamic theory related to flow turbulence and the existence and uniqueness of analytical solutions to the Navier–Stokes equations. Understanding the motion of air around an object (often called

10472-515: The difference in position from a reference trajectory. A velocity to be gained (VGO) calculation is made to correct the current trajectory with the objective of driving VGO to zero. The mathematics of this approach were fundamentally valid, but dropped because of the challenges in accurate inertial guidance and analog computing power. The challenges faced by the Delta efforts were overcome by the Q system (see Q-guidance ) of guidance. The Q system's revolution

10608-437: The discrete molecular nature of gases is ignored, and the flow field is assumed to behave as a continuum . This assumption allows fluid properties such as density and flow velocity to be defined everywhere within the flow. The validity of the continuum assumption is dependent on the density of the gas and the application in question. For the continuum assumption to be valid, the mean free path length must be much smaller than

10744-736: The early 1950s, the US government wanted to insulate itself against over-dependency on the German team for military applications, including the development of a fully domestic missile guidance program. The MIT Instrumentation Laboratory (later to become the Charles Stark Draper Laboratory , Inc.) was chosen by the Air Force Western Development Division to provide a self-contained guidance system backup to Convair in San Diego for

10880-462: The end of 2012. In March 2014 a further three-year delay in the project was announced by the Department of Defense, delaying a contract award until fiscal year 2018. The House Armed Services Committee moved to reject this delay. The delay was caused by financial pressures and an uncertain acquisition plan, and allowed by the long remaining service life left for the AGM-86 and lack of urgent necessity compared to other defense needs. As of August 24, 2017,

11016-445: The first person to develop a theory of air resistance, making him one of the first aerodynamicists. Dutch - Swiss mathematician Daniel Bernoulli followed in 1738 with Hydrodynamica in which he described a fundamental relationship between pressure, density, and flow velocity for incompressible flow known today as Bernoulli's principle , which provides one method for calculating aerodynamic lift. In 1757, Leonhard Euler published

11152-504: The first person to identify the four aerodynamic forces of flight ( weight , lift , drag , and thrust ), as well as the relationships between them, and in doing so outlined the path toward achieving heavier-than-air flight for the next century. In 1871, Francis Herbert Wenham constructed the first wind tunnel , allowing precise measurements of aerodynamic forces. Drag theories were developed by Jean le Rond d'Alembert , Gustav Kirchhoff , and Lord Rayleigh . In 1889, Charles Renard ,

11288-669: The first powered airplane on December 17, 1903. During the time of the first flights, Frederick W. Lanchester , Martin Kutta , and Nikolai Zhukovsky independently created theories that connected circulation of a fluid flow to lift. Kutta and Zhukovsky went on to develop a two-dimensional wing theory. Expanding upon the work of Lanchester, Ludwig Prandtl is credited with developing the mathematics behind thin-airfoil and lifting-line theories as well as work with boundary layers . As aircraft speed increased designers began to encounter challenges associated with air compressibility at speeds near

11424-483: The first production Carousel systems for the early models (-100, -200 and -300) of the 747 aircraft. The 747 utilized three Carousel systems operating in concert for reliability purposes. The Carousel system and derivatives thereof were subsequently adopted for use in many other commercial and military aircraft. The USAF C-141 was the first military aircraft to utilize the Carousel in a dual system configuration, followed by

11560-525: The first time in March 1976, and its new guidance system was first tested that September. In January 1977, the missile was ordered into full-scale production. Compared to the models that entered service in the 1980s, the A-model had a distinctive look; the nose tapered sharply to a triangular point giving it a shark-like appearance, compared to the later models which had a more rounded conventional appearance. Meanwhile,

11696-477: The flow pattern ahead of the object and giving the impression that the fluid "knows" the object is there by seemingly adjusting its movement and is flowing around it. In a supersonic flow, however, the pressure disturbance cannot propagate upstream. Thus, when the fluid finally reaches the object it strikes it and the fluid is forced to change its properties – temperature , density , pressure , and Mach number —in an extremely violent and irreversible fashion called

11832-458: The flow speed is much greater than the speed of sound. Aerodynamicists disagree on the precise definition of hypersonic flow. Compressible flow accounts for varying density within the flow. Subsonic flows are often idealized as incompressible, i.e. the density is assumed to be constant. Transonic and supersonic flows are compressible, and calculations that neglect the changes of density in these flow fields will yield inaccurate results. Viscosity

11968-570: The flow speed is much greater than the speed of sound. Aerodynamicists disagree over the precise definition of hypersonic flow; a rough definition considers flows with Mach numbers above 5 to be hypersonic. The influence of viscosity on the flow dictates a third classification. Some problems may encounter only very small viscous effects, in which case viscosity can be considered to be negligible. The approximations to these problems are called inviscid flows . Flows for which viscosity cannot be neglected are called viscous flows. An incompressible flow

12104-419: 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 can be accurate. 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

12240-449: The gimbals, creating strapdown systems, so called because their sensors are simply strapped to the vehicle. This reduces the cost, eliminates gimbal lock , removes the need for some calibrations and increases the reliability by eliminating some of the moving parts. Angular rate sensors called rate gyros measure the angular velocity of the vehicle. A strapdown system needs a dynamic measurement range several hundred times that required by

12376-505: The guidance contractors for the C model. The CALCM became operational in January 1991 at the onset of Operation Desert Storm . Seven B-52Gs from Barksdale AFB launched 35 missiles at designated launch points in the U.S. Central Command 's area of responsibility to attack high-priority targets in Iraq . These "round-robin" missions marked the beginning of the operation's Air Force component and were

12512-465: The high computational cost of solving these complex equations now that they are available, simplifications of the Navier–Stokes equations have been and continue to be employed. The Euler equations are a set of similar conservation equations which neglect viscosity and may be used in cases where the effect of viscosity is expected to be small. Further simplifications lead to Laplace's equation and potential flow theory. Additionally, Bernoulli's equation

12648-451: The inertial accelerations (using the original velocity as the initial conditions) using the correct kinematic equations yields the inertial velocities of the system and integration again (using the original position as the initial condition) yields the inertial position. In our example, if the blindfolded passenger knew how the car was pointed and what its velocity was before they were blindfolded, and if they are able to keep track of both how

12784-563: The information from an INS and other systems ( GPS ), the errors in position and velocity are stable . Furthermore, INS can be used as a short-term fallback while GPS signals are unavailable, for example when a vehicle passes through a tunnel. In 2011, GPS jamming at the civilian level became a governmental concern. The relative ease in ability to jam these systems has motivated the military to reduce navigation dependence on GPS technology. Because inertial navigation sensors do not depend on radio signals unlike GPS, they cannot be jammed. In 2012,

12920-504: The last 30 years (ex. GPS in the OI-22 build), the guidance core of the Shuttle GN&;C system had evolved little. Within a crewed system, there is a human interface needed for the guidance system. As astronauts are the customer for the system, many new teams were formed that touch GN&C as it is a primary interface to "fly" the vehicle. One example of a popular INS for commercial aircraft

13056-550: The late 1960s the Air Force concluded "that the Quail was only slightly better than nothing." In January 1968, a new requirement emerged for a modern version of Quail for this new mission, the Subsonic Cruise Aircraft Decoy, or SCAD. SCAD was designed specifically to fit onto the same rotary launcher used by SRAM, allowing a single aircraft to carry multiple SRAM and SCAD and launch either at any time. This led to it being

13192-433: The length scale of the application in question. For example, many aerodynamics applications deal with aircraft flying in atmospheric conditions, where the mean free path length is on the order of micrometers and where the body is orders of magnitude larger. In these cases, the length scale of the aircraft ranges from a few meters to a few tens of meters, which is much larger than the mean free path length. For such applications,

13328-410: The linear acceleration and angular velocity applied to the system. Since it requires no external reference (after initialization), it is immune to jamming and deception. Gyroscopes measure the angular displacement of the sensor frame with respect to the inertial reference frame . By using the original orientation of the system in the inertial reference frame as the initial condition and integrating

13464-512: The linear acceleration of the moving vehicle in the sensor or body frame, but in directions that can only be measured relative to the moving system (since the accelerometers are fixed to the system and rotate with the system, but are not aware of their own orientation). This can be thought of as the ability of a blindfolded passenger in a car to feel themself pressed back into their seat as the vehicle accelerates forward or pulled forward as it slows down; and feel themself pressed down into their seat as

13600-607: The longest known aircraft combat sorties in history at the time (more than 14,000 miles (23,000 km) and 35 hours of flight). CALCM's next employment occurred in September 1996 during Operation Desert Strike . In response to Iraq's continued hostilities against the Kurds in northern Iraq, the Air Force launched 13 CALCMs in a joint attack with the Navy . This mission has put the CALCM program in

13736-456: The more general Euler equations which could be applied to both compressible and incompressible flows. The Euler equations were extended to incorporate the effects of viscosity in the first half of the 1800s, resulting in the Navier–Stokes equations . The Navier–Stokes equations are the most general governing equations of fluid flow but are difficult to solve for the flow around all but the simplest of shapes. In 1799, Sir George Cayley became

13872-413: The motion sensors. The advantage of an INS is that it requires no external references in order to determine its position, orientation, or velocity once it has been initialized. An INS can detect a change in its geographic position (a move east or north, for example), a change in its velocity (speed and direction of movement) and a change in its orientation (rotation about an axis). It does this by measuring

14008-534: The new Atlas intercontinental ballistic missile (Construction and testing were completed by Arma Division of AmBosch Arma). The technical monitor for the MIT task was engineer Jim Fletcher, who later served as NASA Administrator. The Atlas guidance system was to be a combination of an on-board autonomous system and a ground-based tracking and command system. The self-contained system finally prevailed in ballistic missile applications for obvious reasons. In space exploration,

14144-489: The new position is calculated from the previous calculated position and the measured acceleration and angular velocity, these errors accumulate roughly proportionally to the time since the initial position was input. Even the best accelerometers, with a standard error of 10 micro-g, would accumulate a 50-meter (164-ft) error within 17 minutes. Therefore, the position must be periodically corrected by input from some other type of navigation system. Accordingly, inertial navigation

14280-579: The performance of the engine. Urban aerodynamics are studied by town planners and designers seeking to improve amenity in outdoor spaces, or in creating urban microclimates to reduce the effects of urban pollution. The field of environmental aerodynamics describes ways in which atmospheric circulation and flight mechanics affect ecosystems. Aerodynamic equations are used in numerical weather prediction . Sports in which aerodynamics are of crucial importance include soccer , table tennis , cricket , baseball , and golf , in which most players can control

14416-401: The platform keep the same orientation while the vehicle rotates around it). 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 torque. By mounting a pair of gyroscopes (of the same rotational inertia and spinning at the same speed in opposite directions) at right angles

14552-502: 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

14688-485: The point where entire aircraft can be designed using computer software, with wind-tunnel tests followed by flight tests to confirm the computer predictions. Understanding of supersonic and hypersonic aerodynamics has matured since the 1960s, and the goals of aerodynamicists have shifted from the behaviour of fluid flow to the engineering of a vehicle such that it interacts predictably with the fluid flow. Designing aircraft for supersonic and hypersonic conditions, as well as

14824-492: 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

14960-421: The problem flow should be described using compressible aerodynamics. According to the theory of aerodynamics, a flow is considered to be compressible if the density changes along a streamline . This means that – unlike incompressible flow – changes in density are considered. In general, this is the case where the Mach number in part or all of the flow exceeds 0.3. The Mach 0.3 value is rather arbitrary, but it

15096-664: The renewed American arms buildup during the Late Cold War , the ALCM so improved the capabilities of the US bomber force that the Soviets developed new technologies to counter the weapon. Among these were airborne early warning aircraft and new weapons like the MiG-31 and Tor missile system specifically to shoot down the AGM-86. The Air Force responded with the development of the AGM-129 ACM , which included stealth capabilities. The ending of

15232-490: The same 14 foot (4.3 m) length as SRAM, and the use of a fuselage with a triangular cross-section, which maximized the usable volume on the rotary launchers. The system was otherwise similar to Quail, using a simple inertial navigation system (INS) allowing the missile to fly a pre-programmed course. Soon after development began, it was noted that the very small nuclear warheads being developed at that time could be fit to SCAD without seriously affecting its performance as

15368-542: The same mission as SRAM, but from much longer range. This would reduce the need for a decoy. Accordingly, in June 1973, SCAD was canceled in favor of a system dedicated purely to the long-range attack mission. The original designation number remained, but the name changed to reflect the new mission, becoming the Air Launched Cruise Missile, or ALCM. The first example, similar to the original SCAD in most ways, flew for

15504-618: The satellite signals. If a standing wave is induced in a hemispheric resonant structure and then the resonant structure is rotated, the spherical harmonic standing wave rotates through an angle different from the quartz resonator structure due to the Coriolis force. The movement of the outer case with respect to the standing wave pattern is proportional to the total rotation angle and can be sensed by appropriate electronics. The system resonators are machined from fused quartz due to its excellent mechanical properties. The electrodes that drive and sense

15640-478: The seventeenth century, but aerodynamic forces have been harnessed by humans for thousands of years in sailboats and windmills, and images and stories of flight appear throughout recorded history, such as the Ancient Greek legend of Icarus and Daedalus . Fundamental concepts of continuum , drag , and pressure gradients appear in the work of Aristotle and Archimedes . In 1726, Sir Isaac Newton became

15776-450: The speed of sound. The Mach number is used to evaluate whether the incompressibility can be assumed, otherwise the effects of compressibility must be included. Subsonic (or low-speed) aerodynamics describes fluid motion in flows which are much lower than the speed of sound everywhere in the flow. There are several branches of subsonic flow but one special case arises when the flow is inviscid , incompressible and irrotational . This case

15912-459: The speed of sound. The differences in airflow under such conditions lead to problems in aircraft control, increased drag due to shock waves , and the threat of structural failure due to aeroelastic flutter . The ratio of the flow speed to the speed of sound was named the Mach number after Ernst Mach who was one of the first to investigate the properties of the supersonic flow. Macquorn Rankine and Pierre Henri Hugoniot independently developed

16048-409: 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

16184-585: The spotlight for future modifications. Operation Desert Strike was also the combat debut of the B-52H and the carriage of the CALCM on the weapons bay-mounted Common Strategic Rotary Launcher (CSRL). During the Operation Desert Storm, the CALCM had been carried on the B-52G and wing-mounted pylons. The CALCM was also used in Operation Desert Fox in 1998, Operation Allied Force in 1999, and Operation Iraqi Freedom in 2003. Operation Iraqi Freedom

16320-404: The standing waves are deposited directly onto separate quartz structures that surround the resonator. These gyros can operate in either a whole angle mode (which gives them nearly unlimited rate capability) or a force rebalance mode that holds the standing wave in a fixed orientation with respect to the gyro housing (which gives them much better accuracy). This system has almost no moving parts and

16456-433: 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. 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 about any rotational axis (or, rather, they let

16592-400: The system can adjust the corrupted sensor's contributions to the final calculation. Inertial navigation systems were originally developed for rockets . American rocketry pioneer Robert Goddard experimented with rudimentary gyroscopic systems. Goddard's systems were of great interest to contemporary German pioneers including Wernher von Braun . The systems entered more widespread use with

16728-446: The theory for flow properties before and after a shock wave , while Jakob Ackeret led the initial work of calculating the lift and drag of supersonic airfoils. Theodore von Kármán and Hugh Latimer Dryden introduced the term transonic to describe flow speeds between the critical Mach number and Mach 1 where drag increases rapidly. This rapid increase in drag led aerodynamicists and aviators to disagree on whether supersonic flight

16864-543: The trajectory of the ball using the " Magnus effect ". General aerodynamics Subsonic aerodynamics Transonic aerodynamics Supersonic aerodynamics Hypersonic aerodynamics History of aerodynamics Aerodynamics related to engineering Ground vehicles Fixed-wing aircraft Helicopters Missiles Model aircraft Related branches of aerodynamics Aerothermodynamics Inertial navigation system An inertial navigation system ( INS ; also inertial guidance system , inertial instrument )

17000-504: The use of inertial technology in the best way, already in 1965 a technical working group for Inertial Sensors had been established in Germany to bring together the users, the manufacturers and the researchers of inertial sensors. This working group has been continuously developed and today it is known as DGON ISA Inertial Sensors and Application Symposium, the leading conference for inertial technologies for more than 60 years. This Symposium DGON / IEEE ISA with about 200 international attendees

17136-557: The usefulness of Quail in the face of improving Soviet defenses. Looking for another solution to the Soviet SAM problem, in 1964 the Air Force began developing a new system that would directly attack the missile sites rather than confuse them. This emerged as the AGM-69 SRAM , with a range of about 50 nautical miles (93 km; 58 mi), allowing it to be launched from outside the roughly 20 nautical miles (37 km; 23 mi) range of

17272-420: The vehicle accelerates up a hill or rise up out of their seat as the car passes over the crest of a hill and begins to descend. Based on this information alone, they know how the vehicle is accelerating relative to itself; that is, whether it is accelerating forward, backward, left, right, up (toward the car's ceiling), or down (toward the car's floor), measured relative to the car, but not the direction relative to

17408-661: The vehicle and the terms are sometimes considered synonymous. Integrals in the time domain implicitly demand a stable and accurate clock for the quantification of elapsed time. Inertial navigation is a self-contained navigation technique in which measurements provided by accelerometers and gyroscopes are used to track the position and orientation of an object relative to a known starting point, orientation and velocity. Inertial measurement units (IMUs) typically contain three orthogonal rate-gyroscopes and three orthogonal accelerometers, measuring angular velocity and linear acceleration respectively. By processing signals from these devices it

17544-485: Was achievable until the sound barrier was broken in 1947 using the Bell X-1 aircraft. By the time the sound barrier was broken, aerodynamicists' understanding of the subsonic and low supersonic flow had matured. The Cold War prompted the design of an ever-evolving line of high-performance aircraft. Computational fluid dynamics began as an effort to solve for flow properties around complex objects and has rapidly grown to

17680-494: Was also the combat debut of the AGM-86D, a further development of the missile which replaced the blast/fragmentation warhead of the AGM-86C with a penetrating warhead. In 2007 the USAF announced its intention to retire all of its AGM-129 ACMs and to reduce the ALCM fleet by more than 500 missiles, leaving 528 nuclear cruise missiles. The ALCM force will be consolidated at Minot Air Force Base , North Dakota , and all excess cruise missile bodies will be destroyed. The reductions are

17816-712: Was canceled. This eliminated the need for ALCM to fit in the B-1's bomb bay, and the length limitations that implied. The Air Force decided to cancel production of the A-model ALCM, and replace it with either an air-launched version of the SLCM, or the ERV. The ERV flew in August 1979, and was declared the winner of the head-to-head fly-off against the SLCM in March 1980. Production of the initial 225 AGM-86B missiles began in fiscal year 1980. The AGM-86B reached operational status in December 1982, on

17952-523: Was never operationally deployed on the B-1. Production of a total 1,715 missiles was completed in October 1986. More than 100 launches have taken place since then, with a 90% approximate success rate. In June 1986 a limited number of AGM-86B missiles were converted to carry a high-explosive blast/fragmentation warhead and an internal GPS. They were redesignated as the AGM-86C CALCM (Conventional Air-Launched Cruise Missile). This modification also replaced

18088-536: Was presented at the first Technical Symposium on Ballistic Missiles held at the Ramo-Wooldridge Corporation in Los Angeles on 21 and 22 June 1956. The Q system was classified information through the 1960s. Derivations of this guidance are used for today's missiles. In February 1961 NASA awarded MIT a contract for preliminary design study of a guidance and navigation system for the Apollo program . MIT and

18224-479: Was the Delco Carousel , which provided partial automation of navigation in the days before complete flight management systems became commonplace. The Carousel allowed pilots to enter 9 waypoints at a time and then guided the aircraft from one waypoint to the next using an INS to determine aircraft position and velocity. Boeing Corporation subcontracted the Delco Electronics Div. of General Motors to design and build

18360-531: Was the ultimate outcome of several similar programs to develop a small decoy aircraft that would be launched from bombers during their approach to targets, presenting false targets to saturate the defenses and allow the bombers to escape an attack. The small jet-powered drone aircraft had a simple inertial navigation system (INS) that allowed it to fly a pre-programmed course that would make it visible to known Soviet defensive sites. A number of radar jammers and radar reflectors were intended to make it appear like

18496-420: Was to bind the challenges of missile guidance (and associated equations of motion) in the matrix Q. The Q matrix represents the partial derivatives of the velocity with respect to the position vector. A key feature of this approach allowed for the components of the vector cross product (v, xdv, /dt) to be used as the basic autopilot rate signals—a technique that became known as cross-product steering . The Q-system

#67932