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137-592: The AIM-9 Sidewinder ("AIM" for "Air Interception Missile") is a short-range air-to-air missile . Entering service with the United States Navy in 1956 and the Air Force in 1964, the AIM-9 is one of the oldest, cheapest, and most successful air-to-air missiles. Its latest variants remain standard equipment in most Western-aligned air forces. The Soviet K-13 (AA-2 "Atoll"), a reverse-engineered copy of

274-585: A Riemannian manifold , as well as the structure of an abelian Lie group. Perhaps the simplest example of this is when L = Z 2 {\displaystyle \mathbb {Z} ^{2}} : R 2 / Z 2 {\displaystyle \mathbb {R} ^{2}/\mathbb {Z} ^{2}} , which can also be described as the Cartesian plane under the identifications ( x , y ) ~ ( x + 1, y ) ~ ( x , y + 1) . This particular flat torus (and any uniformly scaled version of it)

411-572: A SARH (semi-active radar homing) variant (AIM-9C) and an IR (AIM-9D) in 1963. The AIM-9C's semi-active radar was exclusively tied to the F-8 Crusader 's radar and fire control system (FCS). A total of around 1,000 AIM-9C missiles were launched from 1965 to 1967, but their usage in Vietnam war proved unsuccessful, downing no enemies. A filter modification program for reworked units (to allow high altitude capability up to 18,288m (60,000 feet) This

548-449: A closed path that circles the torus' "hole" (say, a circle that traces out a particular latitude) and then circles the torus' "body" (say, a circle that traces out a particular longitude) can be deformed to a path that circles the body and then the hole. So, strictly 'latitudinal' and strictly 'longitudinal' paths commute. An equivalent statement may be imagined as two shoelaces passing through each other, then unwinding, then rewinding. If

685-514: A fiber bundle over S (the Hopf bundle ). The surface described above, given the relative topology from R 3 {\displaystyle \mathbb {R} ^{3}} , is homeomorphic to a topological torus as long as it does not intersect its own axis. A particular homeomorphism is given by stereographically projecting the topological torus into R 3 {\displaystyle \mathbb {R} ^{3}} from

822-593: A maximal torus ; that is, a closed subgroup which is a torus of the largest possible dimension. Such maximal tori T have a controlling role to play in theory of connected G . Toroidal groups are examples of protori , which (like tori) are compact connected abelian groups, which are not required to be manifolds . Automorphisms of T are easily constructed from automorphisms of the lattice Z n {\displaystyle \mathbb {Z} ^{n}} , which are classified by invertible integral matrices of size n with an integral inverse; these are just

959-752: A product of a Euclidean open disk and a circle. The volume of this solid torus and the surface area of its torus are easily computed using Pappus's centroid theorem , giving: A = ( 2 π r ) ( 2 π R ) = 4 π 2 R r , V = ( π r 2 ) ( 2 π R ) = 2 π 2 R r 2 . {\displaystyle {\begin{aligned}A&=\left(2\pi r\right)\left(2\pi R\right)=4\pi ^{2}Rr,\\[5mu]V&=\left(\pi r^{2}\right)\left(2\pi R\right)=2\pi ^{2}Rr^{2}.\end{aligned}}} These formulas are

1096-534: A solid rocket motor for propulsion, similar to most conventional missiles, a continuous-rod fragmentation warhead , and an infrared seeker . The seeker tracks a difference in temperatures detected and uses proportional guidance to achieve impact. Older variants such as the AIM-9B with uncooled seeker heads could only track the high temperatures of engine exhaust , making them strictly rear aspect. Later variants, however, featured liquid nitrogen coolant bottles in

1233-521: A 1/3 twist (120°): the 3-dimensional interior corresponds to the points on the 3-torus where all 3 coordinates are distinct, the 2-dimensional face corresponds to points with 2 coordinates equal and the 3rd different, while the 1-dimensional edge corresponds to points with all 3 coordinates identical. These orbifolds have found significant applications to music theory in the work of Dmitri Tymoczko and collaborators (Felipe Posada, Michael Kolinas, et al.), being used to model musical triads . A flat torus

1370-678: A combination of any of those three warhead types) is typically used in the attempt to disable or destroy the target aircraft. Warheads are typically detonated by a proximity fuze or by an impact fuze if it scores a direct hit. Less commonly, nuclear warheads have been mounted on a small number of air-to-air missile types (such as the AIM-26 Falcon ) although these are not known to have ever been used in combat. Guided missiles operate by detecting their target (usually by either radar or infrared methods, although rarely others such as laser guidance or optical tracking ), and then "homing" in on

1507-451: A cone shape as the distance from the attacking aircraft increases. This will result in less accuracy for the missile because the beam may actually be larger than the target aircraft when the missile arrives. The missile could be securely within the beam but still not be close enough to destroy the target. Infrared guided (IR) missiles home on the heat produced by an aircraft. Early infra-red detectors had poor sensitivity, so could only track

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1644-663: A contract to support Sidewinder operations through to 2055. Air Force spokeswoman Stephanie Powell said that its relatively low cost, versatility, and reliability mean it is "very possible that the Sidewinder will remain in Air Force inventories through the late 21st century". The AIM-9 was a product of the US Naval Weapons Center at China Lake in the Mojave Desert . It features a lightweight, compact design with cruciform canards and tail fins. It uses

1781-406: A double-covered sphere . If the revolved curve is not a circle, the surface is called a toroid , as in a square toroid. Real-world objects that approximate a torus of revolution include swim rings , inner tubes and ringette rings . A torus should not be confused with a solid torus , which is formed by rotating a disk , rather than a circle, around an axis. A solid torus is a torus plus

1918-492: A flat torus into 3-dimensional Euclidean space R 3 {\displaystyle \mathbb {R} ^{3}} was found. It is a flat torus in the sense that, as a metric space, it is isometric to a flat square torus. It is similar in structure to a fractal as it is constructed by repeatedly corrugating an ordinary torus at smaller scales. Like fractals, it has no defined Gaussian curvature. However, unlike fractals, it does have defined surface normals , yielding

2055-527: A heat-homing rocket. The name Sidewinder was selected in 1950 and is the common name of Crotalus cerastes , a rattlesnake , which uses infrared sensory organs to hunt warm-blooded prey. It did not receive official funding until 1951 when the effort was mature enough to show to Admiral William "Deak" Parsons , the Deputy Chief of the Bureau of Ordnance (BuOrd). It subsequently received designation as

2192-605: A more powerful motor that allows the missile to maneuver against crossing targets and launch at greater ranges, gives the launching aircraft improved tactical freedom. Other members of the 4th generation use focal plane arrays to offer greatly improved scanning and countermeasures resistance (especially against flares). These missiles are also much more agile, some by employing thrust vectoring (typically gimballed thrust ). The latest generation of short-range missiles again defined by advances in seeker technologies, this time electro-optical imaging infrared (IIR) seekers that allow

2329-576: A narrow (30-degree) field of view and required the attacker to position himself behind the target ( rear aspect engagement ). This meant that the target aircraft only had to perform a slight turn to move outside the missile seeker's field of view and cause the missile to lose track of the target ("break lock"). The second-generation of short-range missiles utilized more effective seekers that were better cooled than its predecessors while being typically "uncaged"; resulting in improved sensitivity to heat signatures, an increase in field of view as well as allowing

2466-705: A new nose dome and superior optical filtering. Conversions were done to European AIM-9B to upgrade them to the FGW.2 standard. The official designation is the AIM-9B FGW.2 but it is known as the AIM-9F in US nomenclature. The AIM-9G was very similar to the AIM-9D in most aspects, and did not differ externally. The AIM-9G was an AIM-9D that used an improved AIM-9D seeker head with SEAM (Sidewinder Extended Acquisition Mode), this allowed

2603-641: A program in 1952. Originally called the Sidewinder 1 , the first live firing was on 3 September 1952. The missile intercepted a drone for the first time on 11 September 1953. The missile carried out 51 guided flights in 1954, and in 1955 production was authorized. In 1954, the US Air Force carried out trials with the original AIM-9A and the improved AIM-9B at the Holloman Air Development Center. The first operational use of

2740-481: A radio proximity fuze could be used. These improvements were all added into AIM-9D and went into service with the USN. Around 1,000 AIM-9D units were produced from 1965 to 1969. The primary problem of the AIM-9D was breakup during launch. The AIM-9D was eventually developed into AIM-9G. ATM-9D (USN) : AIM-9D used for captive flight target acquisition training. GDU-1/B : AIM-9D used for firing practice. The AIM-9E "Echo"

2877-429: A rectangle together, choosing the other two sides instead will cause the same reversal of orientation. The first homology group of the torus is isomorphic to the fundamental group (this follows from Hurewicz theorem since the fundamental group is abelian ). The 2-torus is a twofold branched cover of the 2-sphere, with four ramification points . Every conformal structure on the 2-torus can be represented as such

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3014-406: A regular torus. For example, in the following map: If R and P in the above flat torus parametrization form a unit vector ( R , P ) = (cos( η ), sin( η )) then u , v , and 0 < η < π /2 parameterize the unit 3-sphere as Hopf coordinates . In particular, for certain very specific choices of a square flat torus in the 3-sphere S , where η = π /4 above, the torus will partition

3151-411: A rocket of some type and the control actuation system or CAS. Dual-thrust solid-fuel rockets are common, but some longer-range missiles use liquid-fuel motors that can "throttle" to extend their range and preserve fuel for energy-intensive final maneuvering. Some solid-fuelled missiles mimic this technique with a second rocket motor which burns during the terminal homing phase. There are missiles, such as

3288-454: A so-called "smooth fractal". The key to obtaining the smoothness of this corrugated torus is to have the amplitudes of successive corrugations decreasing faster than their "wavelengths". (These infinitely recursive corrugations are used only for embedding into three dimensions; they are not an intrinsic feature of the flat torus.) This is the first time that any such embedding was defined by explicit equations or depicted by computer graphics. In

3425-407: A specified range. Towed decoys which closely mimic engine heat and infra-red jammers can also be used. Some large aircraft and many combat helicopters make use of so-called "hot brick" infra-red jammers, typically mounted near the engines. Current research is developing laser devices which can spoof or destroy the guidance systems of infra-red guided missiles. See Infrared countermeasure . Start of

3562-544: A sphere — by adding one additional point that represents the limiting case as a rectangular torus approaches an aspect ratio of 0 in the limit. The result is that this compactified moduli space is a sphere with three points each having less than 2π total angle around them. (Such a point is termed a "cusp", and may be thought of as the vertex of a cone, also called a "conepoint".) This third conepoint will have zero total angle around it. Due to symmetry, M* may be constructed by glueing together two congruent geodesic triangles in

3699-420: A spinning disk with lines painted on it, alternately known as a "reticle" or "chopper". The reticle spun at a fixed speed, causing the output of the photocell to be interrupted in a pattern, and the precise timing of the resulting signal indicated the bearing of the target. Although Hamburg and similar devices like Madrid were essentially complete, the work of mating them to a missile had not been carried out by

3836-565: A target from various angles, not just from behind, where the heat signature from the engines is strongest. Other types rely on radar guidance (either on-board or "painted" by the launching aircraft). In 1999 R-73 missile were adapted by Serb forces for surface to air missiles. The Houthi movement Missile Research and Development Centre and the Missile Force have tried to fire R-27/R-60/R-73/R-77 against Saudi aircraft. Using stockpiles of missiles from Yemeni Air Force stocks. The issue for

3973-461: A torus is a closed surface defined as the product of two circles : S  ×  S . This can be viewed as lying in C and is a subset of the 3-sphere S of radius √2. This topological torus is also often called the Clifford torus . In fact, S is filled out by a family of nested tori in this manner (with two degenerate circles), a fact which is important in the study of S as

4110-425: A torus is punctured and turned inside out then another torus results, with lines of latitude and longitude interchanged. This is equivalent to building a torus from a cylinder, by joining the circular ends together, in two ways: around the outside like joining two ends of a garden hose, or through the inside like rolling a sock (with the toe cut off). Additionally, if the cylinder was made by gluing two opposite sides of

4247-426: A torus is the product of two circles, a modified version of the spherical coordinate system is sometimes used. In traditional spherical coordinates there are three measures, R , the distance from the center of the coordinate system, and θ and φ , angles measured from the center point. As a torus has, effectively, two center points, the centerpoints of the angles are moved; φ measures the same angle as it does in

AIM-9 Sidewinder - Misplaced Pages Continue

4384-563: A torus without stretching the paper (unless some regularity and differentiability conditions are given up, see below). A simple 4-dimensional Euclidean embedding of a rectangular flat torus (more general than the square one) is as follows: where R and P are positive constants determining the aspect ratio. It is diffeomorphic to a regular torus but not isometric . It can not be analytically embedded ( smooth of class C , 2 ≤ k ≤ ∞ ) into Euclidean 3-space. Mapping it into 3 -space requires one to stretch it, in which case it looks like

4521-469: A two-sheeted cover of the 2-sphere. The points on the torus corresponding to the ramification points are the Weierstrass points . In fact, the conformal type of the torus is determined by the cross-ratio of the four points. The torus has a generalization to higher dimensions, the n-dimensional torus , often called the n -torus or hypertorus for short. (This is the more typical meaning of

4658-875: A wide variety of missile projects were underway, from huge systems like the Bell Bomi rocket-powered bomber to small systems like air-to-air missiles. By the early 1950s, both the US Air Force and Royal Air Force had started major IR seeker missile projects. The development of the Sidewinder missile began in 1946 at the Naval Ordnance Test Station (NOTS), Inyokern, California, now the Naval Air Weapons Station China Lake , as an in-house research project conceived by William B. McLean . McLean initially called his effort "Local Fuze Project 602" using laboratory funding, volunteer help and fuze funding to develop what they called

4795-459: Is R n {\displaystyle \mathbb {R} ^{n}} modulo the action of the integer lattice Z n {\displaystyle \mathbb {Z} ^{n}} (with the action being taken as vector addition). Equivalently, the n -torus is obtained from the n -dimensional hypercube by gluing the opposite faces together. An n -torus in this sense is an example of an n- dimensional compact manifold . It

4932-413: Is a surface of revolution generated by revolving a circle in three-dimensional space one full revolution about an axis that is coplanar with the circle. The main types of toruses include ring toruses, horn toruses, and spindle toruses. A ring torus is sometimes colloquially referred to as a donut or doughnut . If the axis of revolution does not touch the circle, the surface has a ring shape and

5069-479: Is a compact 2-manifold of genus 1. The ring torus is one way to embed this space into Euclidean space , but another way to do this is the Cartesian product of the embedding of S 1 {\displaystyle S^{1}} in the plane with itself. This produces a geometric object called the Clifford torus , a surface in 4-space . In the field of topology , a torus is any topological space that

5206-461: Is a member of the Lie group SO(4). It is known that there exists no C (twice continuously differentiable) embedding of a flat torus into 3-space. (The idea of the proof is to take a large sphere containing such a flat torus in its interior, and shrink the radius of the sphere until it just touches the torus for the first time. Such a point of contact must be a tangency. But that would imply that part of

5343-411: Is a torus with the metric inherited from its representation as the quotient , R 2 {\displaystyle \mathbb {R} ^{2}} / L , where L is a discrete subgroup of R 2 {\displaystyle \mathbb {R} ^{2}} isomorphic to Z 2 {\displaystyle \mathbb {Z} ^{2}} . This gives the quotient the structure of

5480-473: Is a very limited weapon, but it had no serious competitors and counters when it was introduced, causing it to be adopted by the USAF and NATO as a standard weapon, with around 80,000 units being produced from 1958 to 1962. The viewing angle of the AIM-9B's sensor was a minuscule 4 degrees, So at launch, the pilot had to accurately aim the aircraft's sight over or above the target (to account for drag). The speed of

5617-457: Is also an example of a compact abelian Lie group . This follows from the fact that the unit circle is a compact abelian Lie group (when identified with the unit complex numbers with multiplication). Group multiplication on the torus is then defined by coordinate-wise multiplication. Toroidal groups play an important part in the theory of compact Lie groups . This is due in part to the fact that in any compact Lie group G one can always find

AIM-9 Sidewinder - Misplaced Pages Continue

5754-463: Is called "off- boresight " launch. For example, the Russian Su-27 is equipped with an infra-red search and track (IRST) system with laser rangefinder for its HMS-aimed missiles. A recent advancement in missile guidance is electro-optical imaging. The Israeli Python-5 has an electro-optical seeker that scans designated area for targets via optical imaging. Once a target is acquired,

5891-402: Is called a torus of revolution , also known as a ring torus . If the axis of revolution is tangent to the circle, the surface is a horn torus . If the axis of revolution passes twice through the circle, the surface is a spindle torus (or self-crossing torus or self-intersecting torus ). If the axis of revolution passes through the center of the circle, the surface is a degenerate torus,

6028-1375: Is homeomorphic to a torus. The surface of a coffee cup and a doughnut are both topological tori with genus one. An example of a torus can be constructed by taking a rectangular strip of flexible material such as rubber, and joining the top edge to the bottom edge, and the left edge to the right edge, without any half-twists (compare Klein bottle ). Torus is a Latin word for "a round, swelling, elevation, protuberance". A torus of revolution in 3-space can be parametrized as: x ( θ , φ ) = ( R + r cos ⁡ θ ) cos ⁡ φ y ( θ , φ ) = ( R + r cos ⁡ θ ) sin ⁡ φ z ( θ , φ ) = r sin ⁡ θ {\displaystyle {\begin{aligned}x(\theta ,\varphi )&=(R+r\cos \theta )\cos {\varphi }\\y(\theta ,\varphi )&=(R+r\cos \theta )\sin {\varphi }\\z(\theta ,\varphi )&=r\sin \theta \\\end{aligned}}} using angular coordinates θ , φ ∈ [ 0 , 2 π ) , {\displaystyle \theta ,\varphi \in [0,2\pi ),} representing rotation around

6165-447: Is known as the "square" flat torus. This metric of the square flat torus can also be realised by specific embeddings of the familiar 2-torus into Euclidean 4-space or higher dimensions. Its surface has zero Gaussian curvature everywhere. It is flat in the same sense that the surface of a cylinder is flat. In 3 dimensions, one can bend a flat sheet of paper into a cylinder without stretching the paper, but this cylinder cannot be bent into

6302-581: Is more accurate and somewhat more resistant to countermeasures. The new rocket motor burns longer and the redesigned body makes the R-13M more maneuverable. K-13M1/R-13M1 : Improved R-13M with new forward fins introduced in 1976. The lackluster performance of the AIM-9B caused the Navy to look for successor. And in 1963 the AAM-N-7 Sidewinder IC was designed, It was developed in two variations:

6439-582: Is possible for the system to take missiles straight from an aircraft. After a live-fire test occurred in September 2020 off the coasts of Florida, during which it successfully engaged a simulated cruise missile, in 2022 NASAMS was deployed to Ukraine, where for the first time this missile system was used in real combat conditions, and, according to Ukrainian government, was able to shot down more than 100 aerial targets. A conventional explosive blast warhead, fragmentation warhead, or continuous rod warhead (or

6576-589: Is still a limitation to some degree) and could be distracted by the sun, a reflection of the sun off of a cloud or ground object, or any other "hot" object within its view. More modern infra-red guided missiles can detect the heat of an aircraft's skin, warmed by the friction of airflow, in addition to the fainter heat signature of the engine when the aircraft is seen from the side or head-on. This, combined with greater maneuverability, gives them an " all-aspect " capability, and an attacking aircraft no longer had to be behind its target to fire. Although launching from behind

6713-489: Is subject to a minimum range, before which it cannot maneuver effectively. In order to maneuver sufficiently from a poor launch angle at short ranges to hit its target, some missiles use thrust vectoring , which allow the missile to start turning "off the rail", before its motor has accelerated it up to high enough speeds for its small aerodynamic surfaces to be useful. Short-range air-to-air missiles (SRAAMs), typically used in " dogfighting " or close range air combat compare to

6850-414: Is that it enables a " fire-and-forget " mode of attack, where the attacking aircraft is free to pursue other targets or escape the area after launching the missile. Semi-active radar homing (SARH) guided missiles are simpler and more common. They function by detecting radar energy reflected from the target. The radar energy is emitted from the launching aircraft's own radar system. However, this means that

6987-545: Is the n -fold product of the circle, the n -torus is the configuration space of n ordered, not necessarily distinct points on the circle. Symbolically, T n = ( S 1 ) n {\displaystyle \mathbb {T} ^{n}=(\mathbb {S} ^{1})^{n}} . The configuration space of unordered , not necessarily distinct points is accordingly the orbifold T n / S n {\displaystyle \mathbb {T} ^{n}/\mathbb {S} _{n}} , which

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7124-512: Is the "home on jam" mode which, when installed, allows a radar-guided missile to home in on the jammer of the target aircraft if the primary seeker is jammed by the electronic countermeasures of the target aircraft. Air-to-air missiles are typically long, thin cylinders in order to reduce their cross section and thus minimize drag at the high speeds at which they travel. Missiles are divided into five primary systems (moving forward to aft): seeker, guidance, warhead, motor, and control actuation. At

7261-491: Is the quotient of the torus by the symmetric group on n letters (by permuting the coordinates). For n = 2, the quotient is the Möbius strip , the edge corresponding to the orbifold points where the two coordinates coincide. For n = 3 this quotient may be described as a solid torus with cross-section an equilateral triangle , with a twist ; equivalently, as a triangular prism whose top and bottom faces are connected with

7398-400: Is the standard 2-torus, T 2 {\displaystyle \mathbb {T} ^{2}} . And similar to the 2-torus, the n -torus, T n {\displaystyle \mathbb {T} ^{n}} can be described as a quotient of R n {\displaystyle \mathbb {R} ^{n}} under integral shifts in any coordinate. That is, the n -torus

7535-537: The R-60M or the Python-3 . The R-73 (missile) ( AA-11 Archer ) entered service in 1985 and marked a new generation of dogfight missile. It had a wider field of view and could be cued onto a target using a helmet mounted sight . This allowed it to be launched at targets that would otherwise not be seen by older generation missiles that generally stared forward while waiting to be launched. This capability, combined with

7672-513: The AIM-95 Agile and SRAAM that were intended to replace it. The Sidewinder is the most widely used air-to-air missile in the West, with more than 110,000 missiles produced for the U.S. and 27 other nations, of which perhaps one percent have been used in combat. It has been built under license by Sweden and other nations. The AIM-9 has an estimated 270 aircraft kills. In 2010, Boeing won

7809-686: The ASRAAM and Sea Ceptor . The air-to-air missile grew out of the unguided air-to-air rockets used during the First World War . Le Prieur rockets were sometimes attached to the struts of biplanes and fired electrically, usually against observation balloons , by such early pilots as Albert Ball and A. M. Walters. Facing the Allied air superiority, Germany in World War II invested limited effort into missile research, initially adapting

7946-454: The Euler characteristic of the n -torus is 0 for all n . The cohomology ring H ( T n {\displaystyle \mathbb {T} ^{n}} ,  Z ) can be identified with the exterior algebra over the Z - module Z n {\displaystyle \mathbb {Z} ^{n}} whose generators are the duals of the n nontrivial cycles. As the n -torus

8083-480: The beyond-visual-range missiles . Most of the short-range air-to-air missiles are infrared guided and few are active radar guided . Those missiles usually classified into five "generations" according to the historical technological advances. Most of these advances were in infrared seeker technology (later combined with digital signal processing ). Early short-range missiles such as the early Sidewinders and K-13 (missile) ( AA-2 Atoll ) had infrared seekers with

8220-418: The conical scan was very slow, additionally, the uncooled missile had a low sensitivity and was liable to extraneous heat. The AIM-9B was recommended for use on non-threatening targets (like bombers), only from behind (so it can lock on the thermal radiation from the target engines) and only with the sun behind or to the side of your aircraft (as the missile would lock onto it due to its thermal radiation). It

8357-478: The hyperbolic plane along their (identical) boundaries, where each triangle has angles of π/2, π/3, and 0. (The three angles of a hyperbolic triangle T determine T up to congruence.) As a result, the Gauss-Bonnet theorem shows that the area of each triangle can be calculated as π - (π/2 + π/3 + 0) = π/6, so it follows that the compactified moduli space M* has area equal to π/3. The other two cusps occur at

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8494-454: The square root gives a quartic equation , ( x 2 + y 2 + z 2 + R 2 − r 2 ) 2 = 4 R 2 ( x 2 + y 2 ) . {\displaystyle \left(x^{2}+y^{2}+z^{2}+R^{2}-r^{2}\right)^{2}=4R^{2}\left(x^{2}+y^{2}\right).} The three classes of standard tori correspond to

8631-427: The volume inside the torus. Real-world objects that approximate a solid torus include O-rings , non-inflatable lifebuoys , ring doughnuts , and bagels . In topology , a ring torus is homeomorphic to the Cartesian product of two circles : S 1 × S 1 {\displaystyle S^{1}\times S^{1}} , and the latter is taken to be the definition in that context. It

8768-433: The " moduli space " of the torus to contain one point for each conformal equivalence class, with the appropriate topology. It turns out that this moduli space M may be identified with a punctured sphere that is smooth except for two points that have less angle than 2π (radians) around them: One has total angle = π and the other has total angle = 2π/3. M may be turned into a compact space M* — topologically equivalent to

8905-492: The 21st century missiles such as the ASRAAM use an " imaging infrared " seeker which "sees" the target (much like a digital video camera), and can distinguish between an aircraft and a point heat source such as a flare. They also feature a very wide detection angle, so the attacking aircraft does not have to be pointing straight at the target for the missile to lock on. The pilot can use a helmet mounted sight (HMS) and target another aircraft by looking at it, and then firing. This

9042-406: The 3-sphere into two congruent solid tori subsets with the aforesaid flat torus surface as their common boundary . One example is the torus T defined by Other tori in S having this partitioning property include the square tori of the form Q ⋅ T , where Q is a rotation of 4-dimensional space R 4 {\displaystyle \mathbb {R} ^{4}} , or in other words Q

9179-560: The AIM-9B, but is worse than the "D". The canard design was changed to a squared tip double delta planform, this helped improve canard behaviour at higher angles of attack (AOA). Over 5,000 AIM-9B's were rebuilt into AIM-9E's. The AIM-9E appeared in Vietnam after the conclusion of the Operation Rolling Thunder in 1968, with the U.S. Air Force (USAF), becoming one of their main missile armaments. Up until Operation Linebacker in 1972 intense air-to-air activity in Vietnam

9316-554: The AIM-9B, was also widely adopted. Low-level development started in the late 1940s, emerging in the early 1950s as a guidance system for the modular Zuni rocket . This modularity allowed for the introduction of newer seekers and rocket motors, including the AIM-9C variant, which used semi-active radar homing and served as the basis of the AGM-122 Sidearm anti-radar missile . Due to the Sidewinder's infrared guidance system,

9453-494: The MBDA Meteor, that "breathe" air (using a ramjet , similar to a jet engine) in order to extend their range. Modern missiles use "low-smoke" motors – early missiles produced thick smoke trails, which were easily seen by the crew of the target aircraft alerting them to the attack and helping them determine how to evade it. The CAS is typically an electro-mechanical, servo control actuation system, which takes input from

9590-487: The Navy opted for a different approach after Walt Freitag, a USN engineer proposed a full change to solid-state in one missile. The "H" variant had major changes over the AIM-9D/G, which had multiple issues with reliability. One of the issues was the intolerance of the vacuum tubes to repeated 20ft/sec sink rate landings by US Navy aircraft on carrier decks. The "H" was the first Sidewinder to be fully solid state, replacing

9727-538: The R-27 and R-77 is the lack of a radar to support their guidance to the target. However the R-73 and R-60 are infra-red heat seeking missiles. They only require, power, liquid nitrogen "to cool the seeker head" and a pylon to launch the missile. These missiles have been paired with a "US made FLIR Systems ULTRA 8500 turrets". Only one near miss has been verified and that was a R-27T fired at Royal Saudi Air Force F-15SA. However

9864-652: The Taiwan strait resulted in a AIM-9B becoming lodged in a MiG-17 without exploding, allowing it to be removed after landing. The Soviets later became aware that the Chinese had at least one Sidewinder, and after some wrangling, were able to persuade the Chinese to send them one of the captured missiles. K-13/R-3 (AA-2) Variants : K-13/R-3 (Object 300) (AA-2 Atoll): It was the standard variant and entered limited service only two years later in 1960. K-13A/R-3S (Object 310) (AA-2A Atoll) : This entered service in 1962. The R-3S

10001-598: The US that early F-4 variants were armed only with missiles in the 1960s. High casualty rates during the Vietnam War caused the US to reintroduce autocannon and traditional dogfighting tactics but the missile remains the primary weapon in air combat. In the Falklands War British Harriers , using AIM-9L missiles were able to defeat faster Argentinian opponents. Since the late 20th century all-aspect heat-seeking designs can lock-on to

10138-575: The USAF did not use) ATM-9G (USN) : AIM-9G used for captive flight target acquisition training. Within December 1965, two designers McLean and LaBerge (who were employed by Philco-Ford) came together to create ways to improve the AIM-9G's reliability. One submission was to advance all the remaining missile electronic components from vacuum to solid-state gradually.The US Air Force adhered to this steady replacement of their AIM-9's to solid-state, however

10275-488: The USN's AIM-7 Sparrow and AIM-9 Sidewinder . Post-war research led the Royal Air Force to introduce Fairey Fireflash into service in 1957 but their results were unsuccessful. The Soviet Air Force introduced its K-5 into service in 1957. As missile systems have continued to advance, modern air warfare consists almost entirely of missile firing. The use of beyond-visual-range combat became so pervasive in

10412-404: The aircraft, rendering it inoperable. The continuous rod warhead features rods welded together to form a cylindrical outer shell, with explosive filler inside. Upon detonation, the rods are scattered in a toroidal shape, ensuring that at least some portion of the shrapnel hits enemy aircraft. Newer models of the AIM-9 sought to increase the range that the seeker head's gimbal can turn, allowing

10549-446: The amount of energy devoted to actuating control surfaces, the AIM-9 does not use active roll stabilization. Instead, it uses rollerons , small metal discs protruding out of the aft end of the tips of the tail fins which spin as the missile flies through the air, providing gyroscopic stabilization. The AIM-9 uses a passive infrared proximity fuze to detonate its warhead near an enemy aircraft, scattering shrapnel that aims to damage

10686-683: The anti-radiation missile (ARM) design, pioneered during Vietnam and used to home in against emitting surface-to-air missile (SAM) sites, to an air intercept weapon. Current air-to-air passive anti-radiation missile development is thought to be a countermeasure to airborne early warning and control (AEW&C – also known as AEW or AWACS) aircraft which typically mount powerful search radars. Due to their dependence on target aircraft radar emissions, when used against fighter aircraft passive anti-radiation missiles are primarily limited to forward-aspect intercept geometry. For examples, see Vympel R-27 and Brazo . Another aspect of passive anti-radiation homing

10823-657: The attack radar to illuminate the target during part or all of the missile interception itself. Radar guidance is normally used for medium- or long-range missiles, where the infra-red signature of the target would be too faint for an infra-red detector to track. There are three major types of radar-guided missile – active, semi-active, and passive. Radar-guided missiles can be countered by rapid maneuvering (which may result in them "breaking lock", or may cause them to overshoot), deploying chaff or using electronic counter-measures . Active radar (AR)-guided missiles carry their own radar system to detect and track their target. However,

10960-556: The brevity code " Fox two " is used when firing the AIM-9. Originally a tail-chasing system, early models saw extensive use during the Vietnam War , but had a low success rate (8% hit rate with the AIM-9E variant). This led to all-aspect capability in the L (Lima) version, which proved an effective weapon during the 1982 Falklands War and Operation Mole Cricket 19 in Lebanon. Its adaptability has kept it in service over newer designs like

11097-424: The category of beyond-visual-range missiles (BVRAAMs), tend to rely upon radar guidance, of which there are many forms. Some modern ones use inertial guidance and/or "mid-course updates" to get the missile close enough to use an active homing sensor. The concepts of air-to-air missiles and surface-to-air missiles are closely related, and in some cases versions of the same weapon may be used for both roles, such as

11234-620: The designation AIM-9E-2 As the Sidewinder was being acquired by NATO forces, licensed production was given to West Germany and they would produce around 15,000 units. Like the Americans, the West Germans sought to improve the AIM-9B design due to its limitations. The only visible exterior difference is a greenish sensor window, but many tech improvements were added beneath the shell. Unnoticed improvements include solid state electronics (instead of vacuum tubes), carbon dioxide seeker cooling,

11371-558: The drawback is that these missiles are intended to be fired from one jet fighter against another. So the motors and fuel load are smaller than a purpose built surface to air missile. On the Western side, the Norwegian-American made NASAMS air defense system has been developed for using AIM-9 Sidewinder , IRIS-T and AMRAAM air-to-air missiles to intercept targets. None of these missiles require modifications and hence it

11508-528: The early AIM-9A & B was that a non-propulsive attachment (NPA) for their MK 15 motor was provided, assuming an assembled missile would be less dangerous to ground crew and material if the rocket motor was ignited. This same NPA was used in the AIM-9B Sidewinder as well. The AIM-9B is very similar to the AIM-9A, but the "B" has a more sophisticated rear and more aerodynamical front fins. The AIM-9B

11645-414: The front is the seeker, either a radar system, radar homer, or infra-red detector. Behind that lies the avionics which control the missile. Typically after that, in the centre of the missile, is the warhead, usually several kilograms of high explosive surrounded by metal that fragments on detonation (or in some cases, pre-fragmented metal). The rear part of the missile contains the propulsion system, usually

11782-422: The front or side aspects, as opposed to just the hotter engine nozzle(s) from rear-aspect, allowing for a true all-aspect capability. This significantly expanded potential attacking envelopes, allowing the attacker to fire at a target which was side-on or front-on to itself as opposed to just the rear. While the field-of-view was still restricted to a fairly narrow cone, the attack at least did not have to be behind

11919-488: The guidance system and manipulates the airfoils or fins at the rear of the missile that guide or steers the weapon to target. Nowadays, countries start developing hypersonic air-to-air missile using scramjet engines (such as R-37 , or AIM-260 JATM ), which not only increases efficiency for BVR battles, but it also makes survival chances of target aircraft drop to nearly zero. A number of terms frequently crop up in discussions of air-to-air missile performance. A missile

12056-426: The hot exhaust pipes of an aircraft. This meant an attacking aircraft had to maneuver to a position behind its target before it could fire an infra-red guided missile. This also limited the range of the missile as the infra-red signature soon become too small to detect with increasing distance and after launch the missile was playing "catch-up" with its target. Early infrared seekers were unusable in clouds or rain (which

12193-406: The integral matrices with determinant ±1. Making them act on R n {\displaystyle \mathbb {R} ^{n}} in the usual way, one has the typical toral automorphism on the quotient. The fundamental group of an n -torus is a free abelian group of rank n . The k -th homology group of an n -torus is a free abelian group of rank n choose k . It follows that

12330-472: The internal wiring harnesses. These improvements facilitated a better 100 Hz reticle rate, and a 16.5 deg/sec tracking rate. The most significant design change was the addition of cooling for the PbS detector, adding Peltier (thermoelectric) cooling, giving the advantage of unlimited cooling when positioned on the launch rail, but is only active when electrical power is present. The AIM-9E gives greater range over

12467-400: The last sighting. So if the target remained at 5 degrees left between two rotations of the mirror, the electronics would not output any signal to the control system. Consider a missile fired at right angles to its target; if the missile is flying at the same speed as the target, it should "lead" it by 45 degrees, flying to an impact point far in front of where the target was when it was fired. If

12604-417: The launch aircraft has to maintain a "lock" on the target (keep illuminating the target aircraft with its own radar) until the missile makes the interception. This limits the attacking aircraft's ability to maneuver, which may be necessary should threats to the attacking aircraft appear. An advantage of SARH-guided missiles is that they are homing on the reflected radar signal, so accuracy actually increases as

12741-479: The launchers, allowing the missile to track any part of the aircraft heated by air resistance due to high speed flight, giving modern Sidewinders all-aspect capabilities. The nose canards provide maneuverability for the AIM-9, with the AIM-9X using thrust vectoring to augment this. The hot gases generated were used to actuate the nose canards in older models, while newer variants use thermal batteries . To minimize

12878-528: The little-used US Navy AIM-9C Sidewinder. This took longer to develop, and did not enter service until 1966. K-13M/R-13M (Object 380) (AA-2D Atoll) : The R-13M is a much improved version of the R-3S and has capabilities similar to the AIM-9G Sidewinder. The R-13M is still a tail engagement missile only but is far more capable than the R-3S due to its new seeker and rocket motor. The new cooled seeker

13015-422: The missile automatically got pre-launch instructions. The conical scanning speed was also increased greatly. The seeker head was now able to seek in a 25˚ circular scan. This allowed the AIM-9G to have an improved chance of acquiring the target than earlier models. This, along with other upgraded solid-state modules, culminated in the AIM-9G. The improvement was substantial enough that an order of 5,000 AIM-9D seekers

13152-482: The missile close to the target. At a predetermined point (frequently based on time since launch or arrival near the predicted target location) the missile's radar system is activated (the missile is said to "go active"), and the missile then homes in on the target. If the range from the attacking aircraft to the target is within the range of the missile's radar system, the missile can "go active" immediately upon launch. The great advantage of an active radar homing system

13289-500: The missile gets closer because the reflection comes from a "point source": the target. Against this, if there are multiple targets, each will be reflecting the same radar signal and the missile may become confused as to which target is its intended victim. The missile may well be unable to pick a specific target and fly through a formation without passing within lethal range of any specific aircraft. Newer missiles have logic circuits in their guidance systems to help prevent this problem. At

13426-506: The missile is traveling four times the speed of the target, it should follow an angle about 11 degrees in front. In either case, the missile should keep that angle all the way to interception, which means that the angle that the target makes against the detector is constant. It was this constant angle that the Sidewinder attempted to maintain. This " proportional pursuit " system is straightforward to implement and offers high-performance lead calculation almost for free and can respond to changes in

13563-408: The missile that allows it to home in on the jamming signal. An early form of radar guidance was " beam-riding " (BR). In this method, the attacking aircraft directs a narrow beam of radar energy at the target. The air-to-air missile was launched into the beam, where sensors on the aft of the missile controlled the missile, keeping it within the beam. So long as the beam was kept on the target aircraft,

13700-457: The missile to track aircraft at greater angles from its direct line of sight, or boresight. Models such as the AIM-9L, AIM-9M, and AIM-9X feature high off-boresight capabilities, meaning they are able to track targets at high seeker gimbal angles, or highly distant from its boresight. The Sidewinder is not guided by the actual position recorded by the detector, but by the change in position since

13837-546: The missile was by Grumman F9F-8 Cougars and FJ-3 Furies of the United States Navy in the middle of 1956. Nearly 100,000 of the first generation (AIM-9B/C/D/E) of the Sidewinder were produced with Raytheon and General Electric as major subcontractors. Philco-Ford produced the guidance and control sections of the early missiles. The NATO version of the first-generation missile was built under license in Germany by Bodenseewerk Gerätetechnik ; 9,200 examples were built. AIM-9A

13974-403: The missile will lock-on to it for the kill. Electro-optical seekers can be programmed to target vital area of an aircraft, such as the cockpit. Since it does not depend on the target aircraft's heat signature, it can be used against low-heat targets such as UAVs and cruise missiles . However, clouds can get in the way of electro-optical sensors. Evolving missile guidance designs are converting

14111-405: The missile would ride the beam until making the interception. While conceptually simple, the move is hard because of the challenge of simultaneously keeping the beam solidly on the target (which could not be relied upon to cooperate by flying straight and level), continuing to fly one's own aircraft, and monitoring enemy countermeasures. An added complication was that the beam will spread out into

14248-429: The missiles to "see" images rather than single "points" of infrared radiation (heat). The sensors combined with more powerful digital signal processing provide the following benefits: Examples of fifth generation short-range missiles include: For each missile, short notes are given, including an indication of its range and guidance mechanism. Torus In geometry , a torus ( pl. : tori or toruses )

14385-430: The north pole of S . The torus can also be described as a quotient of the Cartesian plane under the identifications or, equivalently, as the quotient of the unit square by pasting the opposite edges together, described as a fundamental polygon ABA B . The fundamental group of the torus is just the direct product of the fundamental group of the circle with itself: Intuitively speaking, this means that

14522-458: The original vacuum tubes. The AIM-9H also included a new lead sulphide detector, using nitrogen cooling. The new guidance package was built using semiconductors. When the engineers redesigned these electronics, they essentially kept the AIM-9G's optical system, but the tracking rate increased further, from the original 12˚ to 20˚ degrees per second, this complementing the more powerful 120 lb.ft actuators that had been installed. They also replaced

14659-473: The other 7 were MiG-21s. This was due to the missile design and USN fighter pilot training at TOPGUN . The United States Air Force attempted to attain AIM-9Gs from the USN, due to bad experience with their AIM-9 Sidewinders models (B, E, and J), but they were incompatible with US Air Force's Sidewinder launchers due to the different cooling mechanisms. (the USN used a nitrogen gas container on the launcher, which

14796-481: The possibility of leading a missile within its FOV for an increased probability of kill against a maneuvering target. In some cases, the improved sensitivity to heat signatures allows for a very limited side and even all-aspect tracking, as is the case with the Red Top missile . In conjunction with improved control surfaces and propulsion motors over the first generation of dogfight missiles, the technological advances of

14933-513: The projectile of the unguided 21 cm Nebelwerfer 42 infantry barrage rocket system into the air-launched BR 21 anti-aircraft rocket in 1943; leading to the deployment of the R4M unguided rocket and the development of various guided missile prototypes such as the Ruhrstahl X-4 . The US Navy and US Air Force began equipping guided missiles in 1956, deploying the USAF's AIM-4 Falcon and

15070-431: The same as for a cylinder of length 2π R and radius r , obtained from cutting the tube along the plane of a small circle, and unrolling it by straightening out (rectifying) the line running around the center of the tube. The losses in surface area and volume on the inner side of the tube exactly cancel out the gains on the outer side. Expressing the surface area and the volume by the distance p of an outermost point on

15207-402: The same time, jamming the missile lock-on is easier because the launching aircraft is further from the target than the missile, so the radar signal has to travel further and is greatly attenuated over the distance. This means that the missile may be jammed or "spoofed" by countermeasures whose signals grow stronger as the missile gets closer. One counter to this is a "home on jam" capability in

15344-471: The second-generation short-range missiles allowed them to be used not just on non-maneuvering bombers, but also actively maneuvering fighters. Examples include advanced derivatives of the K-13 (missile) and AIM-9 such as K-13M ( R-13M , Object 380) or AIM-9D / G / H . This generation introduced much more sensitive seekers that are capable of locking onto the warm heat irradiated by the skins of aircraft from

15481-409: The size of the radar antenna is limited by the small diameter of missiles, limiting its range which typically means such missiles are launched at a predicted future location of the target, often relying on separate guidance systems such as Global Positioning System , inertial guidance , or a mid-course update from either the launching aircraft or other system that can communicate with the missile to get

15618-412: The slewing of the optics through a search pattern to acquire the enemy (most likely using a rosette scan ), it also allowed the slaving of the optics to a radar or helmet sight. This was connected to the onboard computer of the aircraft, which gave the capability of capturing the target using the data coming from the airborne radar. This meant that the target could be locked without being in the sights, and

15755-491: The spherical system, but is known as the "toroidal" direction. The center point of θ is moved to the center of r , and is known as the "poloidal" direction. These terms were first used in a discussion of the Earth's magnetic field, where "poloidal" was used to denote "the direction toward the poles". In modern use, toroidal and poloidal are more commonly used to discuss magnetic confinement fusion devices. Topologically ,

15892-449: The study of Riemann surfaces , one says that any two smooth compact geometric surfaces are "conformally equivalent" when there exists a smooth homeomorphism between them that is both angle-preserving and orientation-preserving. The Uniformization theorem guarantees that every Riemann surface is conformally equivalent to one that has constant Gaussian curvature . In the case of a torus, the constant curvature must be zero. Then one defines

16029-1057: The surface of the torus to the center, and the distance q of an innermost point to the center (so that R = ⁠ p + q / 2 ⁠ and r = ⁠ p − q / 2 ⁠ ), yields A = 4 π 2 ( p + q 2 ) ( p − q 2 ) = π 2 ( p + q ) ( p − q ) , V = 2 π 2 ( p + q 2 ) ( p − q 2 ) 2 = 1 4 π 2 ( p + q ) ( p − q ) 2 . {\displaystyle {\begin{aligned}A&=4\pi ^{2}\left({\frac {p+q}{2}}\right)\left({\frac {p-q}{2}}\right)=\pi ^{2}(p+q)(p-q),\\[5mu]V&=2\pi ^{2}\left({\frac {p+q}{2}}\right)\left({\frac {p-q}{2}}\right)^{2}={\tfrac {1}{4}}\pi ^{2}(p+q)(p-q)^{2}.\end{aligned}}} As

16166-410: The target increases the probability of a hit, the launching aircraft usually has to be closer to the target in such a tail-chase engagement . An aircraft can defend against infra-red missiles by dropping flares that are hotter than the aircraft, so the missile homes in on the brighter, hotter target. In turn, IR missiles may employ filters to enable it to ignore targets whose temperature is not within

16303-440: The target on a collision course. Although the missile may use radar or infra-red guidance to home on the target, the launching aircraft may detect and track the target before launch by other means. Infra-red guided missiles can be "slaved" to an attack radar in order to find the target and radar-guided missiles can be launched at targets detected visually or via an infra-red search and track (IRST) system, although they may require

16440-474: The target's flight path, which is much more efficient and makes the missile "lead" the target. During World War II , various researchers in Germany designed infrared guidance systems of various complexity. The most mature development of these, codenamed Hamburg , was intended for use by the Blohm & Voss BV 143 glide bomb in an anti-ship role. Hamburg used a single IR photocell as its detector along with

16577-446: The target. Also typical of the third generation of short-range missiles are further improved agility over the previous generation as well as their ability to radar-slave; which is acquiring tracking data from the launching aircraft's radar or IRST systems, allowing attackers to launch missiles without ever pointing the nose of the aircraft at an enemy prior to leading the missile. Examples of this generation of dogfight missiles include

16714-439: The term " n -torus", the other referring to n holes or of genus n . ) Just as the ordinary torus is topologically the product space of two circles, the n -dimensional torus is topologically equivalent to the product of n circles. That is: The standard 1-torus is just the circle: T 1 = S 1 {\displaystyle \mathbb {T} ^{1}=\mathbb {S} ^{1}} . The torus discussed above

16851-617: The thermal battery with a turbo-alternator. The AIM-9H also included a continuous-rod bundle warhead, improving its destructive capability. The AIM-9H was the last and most manoeuvrable of the rear-aspect USN Sidewinders, with USN moving to the all-aspect AIM-9L. The AIM-9H was actually used at the very end of the Vietnam war, with it being introduced into the US navy service in 1972 and being used in Operation Linebacker . A total of around 7,700 AIM-9H units would be manufactured from 1972-1974 by Philco-Ford and Raytheon. The AIM-9H

16988-426: The three possible aspect ratios between R and r : When R ≥ r , the interior ( x 2 + y 2 − R ) 2 + z 2 < r 2 {\displaystyle {\textstyle {\bigl (}{\sqrt {x^{2}+y^{2}}}-R{\bigr )}^{2}}+z^{2}<r^{2}} of this torus is diffeomorphic (and, hence, homeomorphic) to

17125-403: The time the war ended. In the immediate post-war era, Allied military intelligence teams collected this information, along with many of the engineers working on these projects. Several lengthy reports on the various systems were produced and disseminated among the Western aircraft firms, while a number of the engineers joined these companies to work on various missile projects. By the late 1940s

17262-484: The torus, since it has zero curvature everywhere, must lie strictly outside the sphere, which is a contradiction.) On the other hand, according to the Nash-Kuiper theorem , which was proven in the 1950s, an isometric C embedding exists. This is solely an existence proof and does not provide explicit equations for such an embedding. In April 2012, an explicit C (continuously differentiable) isometric embedding of

17399-534: The torus. The typical doughnut confectionery has an aspect ratio of about 3 to 2. An implicit equation in Cartesian coordinates for a torus radially symmetric about the z {\displaystyle z} - axis is ( x 2 + y 2 − R ) 2 + z 2 = r 2 . {\displaystyle {\textstyle {\bigl (}{\sqrt {x^{2}+y^{2}}}-R{\bigr )}^{2}}+z^{2}=r^{2}.} Algebraically eliminating

17536-420: The tube and rotation around the torus' axis of revolution, respectively, where the major radius R {\displaystyle R} is the distance from the center of the tube to the center of the torus and the minor radius r {\displaystyle r} is the radius of the tube. The ratio R / r {\displaystyle R/r} is called the aspect ratio of

17673-502: Was a pre-production of the Sidewinder, first fired successfully in September 1953. Missile production began in 1955, and the first models entered the Navy's fleet service in 1956. Generally, it was a prototype production run, with 240 pieces being produced, and mainly intended for training pilots in air combat techniques. The AIM-9A was initially called the AAM-N-7 before the tri-service designation change in 1962. An interesting fact about

17810-453: Was added for the fuze, being the first in the world. This enhanced the missile's head sensitivity. Maneuverability was also improved with a faster tracking rate, as well as a new actuator system. The Sidewinder's range was improved as well, with the new Hercules MK 36 solid-fuel rocket motor allowing the missile to fly up to 18km. Finally, a new Mk 48 continuous-rod warhead was fitted to the missile for increased damage; this also meant infrared or

17947-432: Was famously the first Sidewinder variant to be fired in anger as on 24 September 1958, it achieved the world's first successful kill with a air-to-air missiles, when Taiwanese F-86Fs shot down Communist Chinese MiG-15s using AIM-9Bs supplied and fitted by the U.S. Navy (USN). RB24 : A Swedish AIM-9B Sidewinder. K-13/R-3 (AA-2) : The K-13/R-3 was a reversed engineered AIM-9B Sidewinder, A engagement on 28 September 1958 in

18084-550: Was not present. There were 71 AIM-9E launch attempts from January to October 1972, however, only 6 missiles managed to down an aircraft, with 1 other hitting an aircraft, but not causing complete destruction. Reasons for the poor success rate was listed as "poor air crew training, launches out of the envelope, the tactical situation, marginal tone, tone discrimination, the missile going ballistic, and other malfunctions". AIM-9E : Standard production model. AIM-9E-2 : Some "E" models are equipped with reduced-smoke rocket motors and have

18221-525: Was stopped at 1,850 units, with the rest being ordered to AIM-9G seeker specifications instead. Around 2120 AIM-9G were built by Raytheon from 1970 to 1972. The AIM-9G would be used with its predecessor, the AIM-9D, during the Vietnam War, as the US Navy's choice of IR missile. A 46% hit rate with the AIM-9G during Operation Linebackers I and II in 1972 was achieved, of which 14 aircraft were MiG-17s and

18358-860: Was the basis for the all-aspect USAF/USN AIM-9L. ATM-9H : Was a training version of the AIM-9H for captive flight target acquisition. The AIM-9K was a planned U.S. Navy (USN) upgrade to the AIM-9H, but the development was abandoned in favour of USAF/USN joint AIM-9L. Air-to-air missile Air-to-air missiles are broadly put in two groups. Those designed to engage opposing aircraft at ranges of around 30 km to 40 km maximum are known as short-range or "within visual range" missiles (SRAAMs or WVRAAMs) and are sometimes called " dogfight " missiles because they are designed to optimize their agility rather than range. Most use infrared guidance and are called heat-seeking missiles. In contrast, medium- or long-range missiles (MRAAMs or LRAAMs), which both fall under

18495-491: Was the first version developed solely by the U.S. Air Force (USAF). The AIM-9E allows the expansion of the weapons acquisition envelope, especially at low-altitude, increasing its Probability of Kill (P[k]). It achieved this using a new low-drag conical nose head, being a distinguishing feature of USAF Sidewinders. A magnesium fluoride seeker dome was introduced, along with a more compact optical assembly, an improved guidance control system, new electronics, and significant changes to

18632-441: Was the first version to enter widespread production, in spite of a very long seeker settling time around 22 seconds, as opposed to 11 seconds for the original version. PL-2 : Chinese produced R-3S. A-91 : Romanian produced R-3S. K-13R/R-3R (Object 320) (AA-2B/C Atoll) : While the R-3S was being introduced in 1961, work started on a semi-active radar homing (SARH) version for high-altitude use, with 8 km range, similar to

18769-427: Was the only planned modification. Recognizing the limitations of the initial AIM-9B, the US Navy (USN) worked to improve the missile's performance. They changed the missile nose to an aerodynamical ogival nose. The seeker was improved with a wider field of view beyond 25 degrees and a reduced instantaneous field of view of 2.5 degrees, to reduce foreign thermal interference (from flares). A better nitrogen cooling system

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