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Elias delta coding

Elias δ code or Elias delta code is a universal code encoding the positive integers developed by Peter Elias.

Encoding
To code a number X ≥ 1:
 * 1) Let N = ⌊log2 X⌋; be the highest power of 2 in X, so 2N ≤ X < 2N+1.
 * 2) Let L = ⌊log2 N+1⌋ be the highest power of 2 in N+1, so 2L ≤ N+1 < 2L+1.
 * 3) Write L zeros, followed by
 * 4) the L+1-bit binary representation of N+1, followed by
 * 5) all but the leading bit (i.e. the last N bits) of X.

An equivalent way to express the same process:
 * 1) Separate X into the highest power of 2 it contains (2N) and the remaining N binary digits.
 * 2) Encode N+1 with Elias gamma coding.
 * 3) Append the remaining N binary digits to this representation of N+1.

To represent a number $$x$$, Elias delta (δ) uses $$\lfloor \log_2(x) \rfloor + 2 \lfloor \log_2 (\lfloor \log_2(x) \rfloor +1) \rfloor + 1$$ bits. This is useful for very large integers, where the overall encoded representation's bits end up being fewer [than what one might obtain using Elias gamma coding] due to the $$\log_2 (\lfloor \log_2(x) \rfloor +1)$$ portion of the previous expression.

The code begins, using $$\gamma'$$ instead of $$\gamma$$:

To decode an Elias delta-coded integer:
 * 1) Read and count zeros from the stream until you reach the first one. Call this count of zeros L.
 * 2) Considering the one that was reached to be the first digit of an integer, with a value of 2L, read the remaining L digits of the integer. Call this integer N+1, and subtract one to get N.
 * 3) Put a one in the first place of our final output, representing the value 2N.
 * 4) Read and append the following N digits.

Example: 001010011 1. 2 leading zeros in 001 2. read 2 more bits i.e. 00101 3. decode N+1 = 00101 = 5 4. get N = 5 − 1 = 4 remaining bits for the complete code i.e. '0011' 5. encoded number = 24 + 3 = 19

This code can be generalized to zero or negative integers in the same ways described in Elias gamma coding.

Generalizations
Elias delta coding does not code zero or negative integers. One way to code all non negative integers is to add 1 before coding and then subtract 1 after decoding. One way to code all integers is to set up a bijection, mapping integers all integers (0, 1, −1, 2, −2, 3, −3, ...) to strictly positive integers (1, 2, 3, 4, 5, 6, 7, ...) before coding. This bijection can be performed using the "ZigZag" encoding from Protocol Buffers (not to be confused with Zigzag code, nor the JPEG Zig-zag entropy coding).

title: Elias delta coding


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Sidney Altman

Sidney Altman (May 7, 1939 – April 5, 2022) was a Canadian-American molecular biologist, who was the Sterling Professor of Molecular, Cellular, and Developmental Biology and Chemistry at Yale University. In 1989, he shared the Nobel Prize in Chemistry with Thomas R. Cech for their work on the catalytic properties of RNA.

Family and education
Altman was born on May 7, 1939, in Montreal, Quebec, Canada. His parents, Ray (Arlin), a textile worker, and Victor Altman, a grocer, were Jewish immigrants to Canada, each coming from Eastern Europe as a young adult, in the 1920s. Altman's mother was from Białystok in Poland, and had come to Canada with her sister at the age of eighteen, learning English and working in a textile factory to earn money to bring the rest of their family to Quebec. Altman's father, born in Ukraine, had been a worker on a collective farm in the Soviet Union. He was sponsored to come to Canada as a farm worker, but later, as a husband and a father of two sons, he supported the family by running a small grocery store in Montreal. Sidney Altman was later to look back on his parents' lives as an illustration of the value of the work ethic: "It was from them I learned that hard work in stable surroundings could yield rewards, even if only in infinitesimally small increments."

As Altman reached adulthood, the family's financial situation had become secure enough that he was able to pursue a college education. He went to the United States to study physics at the Massachusetts Institute of Technology. While at MIT, he was a member of the ice hockey team. After achieving his bachelor's degree from MIT in 1960, Altman spent 18 months as a graduate student in physics at Columbia University. Due to personal concerns and the lack of opportunity for beginning graduate students to participate in laboratory work, he left the program without completing the degree. Some months later, he enrolled as a graduate student in biophysics at the University of Colorado Medical Center. His project was a study of the effects of acridines on the replication of bacteriophage T4 DNA. He received his Ph.D. in biophysics from the University of Colorado in 1967 with thesis advisor Leonard Lerman; Lerman went in 1967 to Vanderbilt University, where Altman worked briefly as a researcher in molecular biology before leaving for Harvard.

Altman was married to Ann M. Körner (daughter of Stephan Körner) in 1972. They are the parents of two children, Daniel and Leah. Having lived primarily in the United States since departing Montreal to attend MIT in 1958, Altman became a U.S. citizen in 1984, maintaining dual citizenship as a Canadian citizen as well.

Career
After receiving his Ph.D., Altman embarked upon the first of two research fellowships. He joined Matthew Meselson's laboratory at Harvard University to study a DNA endonuclease involved in the replication and recombination of T4 DNA. Later, at the MRC Laboratory of Molecular Biology in Cambridge, England, Altman started the work that led to the discovery of RNase P and the enzymatic properties of the RNA subunit of that ribozyme. John D. Smith, as well as several postdoctoral colleagues, provided Altman with very good advice that enabled him to test his ideas. "The discovery of the first radiochemically pure precursor to a tRNA molecule enabled me to get a job as an assistant professor at Yale University in 1971, a difficult time to get any job at all".

Altman's career at Yale followed a standard academic pattern with promotion through the ranks until he became Professor in 1980. He was Chairman of his department from 1983 to 1985 and in 1985 became the Dean of Yale College for four years. On July 1, 1989, he returned to the post of Professor on a full-time basis. His doctoral students include Ben Stark.

While at Yale, Altman's Nobel Prize work came with the analysis of the catalytic properties of the ribozyme RNase P, a ribonucleoprotein particle consisting of both a structural RNA molecule and one (in prokaryotes) or more (in eukaryotes) proteins. Originally, it was believed that, in the bacterial RNase P complex, the protein subunit was responsible for the catalytic activity of the complex, which is involved in the maturation of tRNAs. During experiments in which the complex was reconstituted in test tubes, Altman and his group discovered that the RNA component, in isolation, was sufficient for the observed catalytic activity of the enzyme, indicating that the RNA itself had catalytic properties, which was the discovery that earned him the Nobel Prize. Although the RNase P complex also exists in eukaryotic organisms, his later work revealed that in those organisms, the protein subunits of the complex are essential to the catalytic activity, in contrast to the bacterial RNase P.

Recognition
Altman was elected a Fellow of the American Academy of Arts and Sciences in 1988 and a member of both the National Academy of Sciences and the American Philosophical Society in 1990.

Death
Altman died on April 5, 2022, in Rockleigh, New Jersey, after a long illness.

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

title: Sidney Altman


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Hydrostatic equilibrium

In fluid mechanics, hydrostatic equilibrium (hydrostatic balance, hydrostasy) is the condition of a fluid or plastic solid at rest, which occurs when external forces, such as gravity, are balanced by a pressure-gradient force. In the planetary physics of Earth, the pressure-gradient force prevents gravity from collapsing the planetary atmosphere into a thin, dense shell, whereas gravity prevents the pressure-gradient force from diffusing the atmosphere into outer space. In general, it is what causes objects in space to be spherical.

Hydrostatic equilibrium is the distinguishing criterion between dwarf planets and small solar system bodies, and features in astrophysics and planetary geology. Said qualification of equilibrium indicates that the shape of the object is symmetrically rounded, mostly due to rotation, into an ellipsoid, where any irregular surface features are consequent to a relatively thin solid crust. In addition to the Sun, there are a dozen or so equilibrium objects confirmed to exist in the Solar System.

Mathematical consideration

For a hydrostatic fluid on Earth: $$dP = - \rho(P) \, g(h) \, dh$$

Derivation from force summation
Newton's laws of motion state that a volume of a fluid that is not in motion or that is in a state of constant velocity must have zero net force on it. This means the sum of the forces in a given direction must be opposed by an equal sum of forces in the opposite direction. This force balance is called a hydrostatic equilibrium.

The fluid can be split into a large number of cuboid volume elements; by considering a single element, the action of the fluid can be derived.

There are three forces: the force downwards onto the top of the cuboid from the pressure, P, of the fluid above it is, from the definition of pressure, $$F_\text{top} = - P_\text{top} A$$ Similarly, the force on the volume element from the pressure of the fluid below pushing upwards is $$F_\text{bottom} = P_\text{bottom} A$$

Finally, the weight of the volume element causes a force downwards. If the density is ρ, the volume is V and g the standard gravity, then: $$F_\text{weight} = -\rho g V$$ The volume of this cuboid is equal to the area of the top or bottom, times the height – the formula for finding the volume of a cube. $$F_\text{weight} = -\rho g A h$$

By balancing these forces, the total force on the fluid is $$\sum F = F_\text{bottom} + F_\text{top} + F_\text{weight} = P_\text{bottom} A - P_\text{top} A - \rho g A h$$ This sum equals zero if the fluid's velocity is constant. Dividing by A, $$0 = P_\text{bottom} - P_\text{top} - \rho g h$$ Or, $$P_\text{top} - P_\text{bottom} = - \rho g h$$ Ptop − Pbottom is a change in pressure, and h is the height of the volume element—a change in the distance above the ground. By saying these changes are infinitesimally small, the equation can be written in differential form. $$dP = - \rho g \, dh$$ Density changes with pressure, and gravity changes with height, so the equation would be: $$dP = - \rho(P) \, g(h) \, dh$$

Derivation from Navier–Stokes equations
Note finally that this last equation can be derived by solving the three-dimensional Navier–Stokes equations for the equilibrium situation where $$u = v = \frac{\partial p}{\partial x} = \frac{\partial p}{\partial y} = 0$$ Then the only non-trivial equation is the $$z$$-equation, which now reads $$\frac{\partial p}{\partial z} + \rho g = 0$$ Thus, hydrostatic balance can be regarded as a particularly simple equilibrium solution of the Navier–Stokes equations.

Derivation from general relativity
By plugging the energy–momentum tensor for a perfect fluid $$T^{\mu\nu} = \left(\rho c^{2} + P\right) u^\mu u^\nu + P g^{\mu\nu}$$ into the Einstein field equations $$R_{\mu\nu} = \frac{8\pi G}{c^4} \left(T_{\mu\nu} - \frac{1}{2} g_{\mu\nu} T\right)$$ and using the conservation condition $$\nabla_\mu T^{\mu\nu} = 0$$ one can derive the Tolman–Oppenheimer–Volkoff equation for the structure of a static, spherically symmetric relativistic star in isotropic coordinates: $$\frac{dP}{dr} = -\frac{G M(r)\rho(r)}{r^2} \left(1+\frac{P(r)}{\rho(r)c^2}\right) \left(1+\frac{4\pi r^3 P(r)}{M(r) c^2}\right) \left(1 - \frac{2GM(r)}{r c^2}\right)^{-1}$$ In practice, Ρ and ρ are related by an equation of state of the form f(Ρ,ρ) = 0, with f specific to makeup of the star. M(r) is a foliation of spheres weighted by the mass density ρ(r), with the largest sphere having radius r: $$M(r) = 4\pi \int_0^r dr' \, r'^2 \rho(r').$$ Per standard procedure in taking the nonrelativistic limit, we let c → ∞, so that the factor $$\left(1+\frac{P(r)}{\rho(r)c^2}\right) \left(1+\frac{4\pi r^3P(r)}{M(r)c^2}\right) \left(1-\frac{2GM(r)}{r c^2} \right)^{-1} \rightarrow 1$$ Therefore, in the nonrelativistic limit the Tolman–Oppenheimer–Volkoff equation reduces to Newton's hydrostatic equilibrium: $$\frac{dP}{dr} = -\frac{GM(r)\rho(r)}{r^2} = -g(r)\,\rho(r)\longrightarrow dP = - \rho(h)\,g(h)\, dh$$ (we have made the trivial notation change h = r and have used f(Ρ,ρ) = 0 to express ρ in terms of P). A similar equation can be computed for rotating, axially symmetric stars, which in its gauge independent form reads: $$\frac{\partial_i P}{P+\rho} - \partial_i \ln u^t + u_t u^\varphi\partial_i\frac{u_\varphi}{u_t}=0$$ Unlike the TOV equilibrium equation, these are two equations (for instance, if as usual when treating stars, one chooses spherical coordinates as basis coordinates $$(t,r,\theta,\varphi)$$, the index i runs for the coordinates r and $$\theta$$).

Fluids
The hydrostatic equilibrium pertains to hydrostatics and the principles of equilibrium of fluids. A hydrostatic balance is a particular balance for weighing substances in water. Hydrostatic balance allows the discovery of their specific gravities. This equilibrium is strictly applicable when an ideal fluid is in steady horizontal laminar flow, and when any fluid is at rest or in vertical motion at constant speed. It can also be a satisfactory approximation when flow speeds are low enough that acceleration is negligible.

Astrophysics and planetary science
From the time of Isaac Newton much work has been done on the subject of the equilibrium attained when a fluid rotates in space. This has application to both stars and objects like planets, which may have been fluid in the past or in which the solid material deforms like a fluid when subjected to very high stresses. In any given layer of a star there is a hydrostatic equilibrium between the outward-pushing pressure gradient and the weight of the material above pressing inward. One can also study planets under the assumption of hydrostatic equilibrium. A rotating star or planet in hydrostatic equilibrium is usually an oblate spheroid, that is, an ellipsoid in which two of the principal axes are equal and longer than the third. An example of this phenomenon is the star Vega, which has a rotation period of 12.5 hours. Consequently, Vega is about 20% larger at the equator than from pole to pole.

In his 1687 Philosophiæ Naturalis Principia Mathematica Newton correctly stated that a rotating fluid of uniform density under the influence of gravity would take the form of a spheroid and that the gravity (including the effect of centrifugal force) would be weaker at the equator than at the poles by an amount equal (at least asymptotically) to five fourths the centrifugal force at the equator. In 1742, Colin Maclaurin published his treatise on fluxions, in which he showed that the spheroid was an exact solution. If we designate the equatorial radius by $$r_e,$$ the polar radius by $$r_p,$$ and the eccentricity by $$\epsilon,$$ with
 * $$\epsilon=\sqrt{1-r_p^2/r_e^2},$$

he found that the gravity at the poles is

\begin{align} g_p & =4\pi\frac{r_p}{r_e}\frac{\epsilon r_e-r_p\arctan(\epsilon r_e/r_p)}{\epsilon^3}G\rho \\ &=3\frac{\epsilon r_e-r_p\arctan(\epsilon r_e/r_p)}{\epsilon^3 r_e^3}GM \\ \end{align} $$ where $$G$$ is the gravitational constant, $$\rho$$ is the (uniform) density, and $$M$$ is the total mass. The ratio of this to $$g_0,$$ the gravity if the fluid is not rotating, is asymptotic to
 * $$g_p/g_0\sim 1+\frac 1{15}\epsilon^2\sim 1+\frac 2 {15} f $$

as $$\epsilon$$ goes to zero, where $$f$$ is the flattening:
 * $$f=\frac{r_e-r_p}{r_e}.$$

The gravitational attraction on the equator (not including centrifugal force) is

\begin{align} g_e &=\frac 32\left(\frac 1{r_e r_p}-\frac{\epsilon r_e-r_p\arctan(\epsilon r_e/r_p)}{\epsilon^3 r_e^2 r_p}\right)GM\\ & =\frac 32\frac{r_e\arctan(\epsilon r_e/r_p)-\epsilon r_p}{\epsilon^3 r_e^3} GM \\ \end{align} $$

Asymptotically we have:
 * $$g_e/g_0\sim 1-\frac 1{30}\epsilon^2\sim 1-\frac 1 {15} f $$

Maclaurin showed (still in the case of uniform density) that the component of gravity toward the axis of rotation depended only on the distance from the axis and was proportional to that distance, and the component in the direction toward the plane of the equator depended only on the distance from that plane and was proportional to that distance. Newton had already pointed out that the gravity felt on the equator (including the lightening due to centrifugal force) has to be $$\frac{r_p}{r_e}g_p$$ in order to have the same pressure at the bottom of channels from the pole or from the equator to the centre, so the centrifugal force at the equator must be
 * $$g_e-\frac{r_p}{r_e}g_p\sim \frac 25\epsilon^2g_e\sim\frac 45fg_e.$$

Defining the latitude to be the angle between a tangent to the meridian and axis of rotation, the total gravity felt at latitude $$\phi$$ (including the effect of centrifugal force) is
 * $$g(\phi)=\frac{g_p(1-f)}{\sqrt{1-(2f-f^2)\sin^2\phi}}.$$

This spheroid solution is stable up to a certain (critical) angular momentum (normalized by $$M\sqrt{G\rho r_e}$$), but in 1834 Carl Jacobi showed that it becomes unstable once the eccentricity reaches 0.81267 (or $$f$$ reaches 0.3302). Above the critical value the solution becomes a Jacobi, or scalene, ellipsoid (one with all three axes different). Henri Poincaré in 1885 found that at still higher angular momentum it will no longer be ellipsoidal but piriform or oviform. The symmetry drops from the 8-fold D$2h$ point group to the 4-fold C$2v$, with its axis perpendicular to the axis of rotation. Other shapes satisfy the equations beyond that, but are not stable, at least not near the point of bifurcation. Poincaré was unsure what would happen at higher angular momentum, but concluded that eventually the blob would split in two.

The assumption of uniform density may apply more or less to a molten planet or a rocky planet, but does not apply to a star or to a planet like the earth which has a dense metallic core. In 1737 Alexis Clairaut studied the case of density varying with depth. Clairaut's theorem states that the variation of the gravity (including centrifugal force) is proportional to the square of the sine of the latitude, with the proportionality depending linearly on the flattening ($$f$$) and the ratio at the equator of centrifugal force to gravitational attraction. (Compare with the exact relation above for the case of uniform density.) Clairaut's theorem is a special case, for an oblate spheroid, of a connexion found later by Pierre-Simon Laplace between the shape and the variation of gravity.

If the star has a massive nearby companion object then tidal forces come into play as well, distorting the star into a scalene shape when rotation alone would make it a spheroid. An example of this is Beta Lyrae.

Hydrostatic equilibrium is also important for the intracluster medium, where it restricts the amount of fluid that can be present in the core of a cluster of galaxies.

We can also use the principle of hydrostatic equilibrium to estimate the velocity dispersion of dark matter in clusters of galaxies. Only baryonic matter (or, rather, the collisions thereof) emits X-ray radiation. The absolute X-ray luminosity per unit volume takes the form $$\mathcal{L}_X=\Lambda(T_B)\rho_B^2$$ where $$T_B$$ and $$\rho_B$$ are the temperature and density of the baryonic matter, and $$\Lambda(T)$$ is some function of temperature and fundamental constants. The baryonic density satisfies the above equation $dP = -\rho g \, dr$: $$p_B(r+dr)-p_B(r)=-dr\frac{\rho_B(r)G}{r^2}\int_0^r 4\pi r^2\,\rho_M(r)\, dr.$$ The integral is a measure of the total mass of the cluster, with $$r$$ being the proper distance to the center of the cluster. Using the ideal gas law $$p_B=kT_B\rho_B/m_B$$ ($$k$$ is the Boltzmann constant and $$m_B$$ is a characteristic mass of the baryonic gas particles) and rearranging, we arrive at $$\frac{d}{dr}\left(\frac{kT_B(r)\rho_B(r)}{m_B}\right)=-\frac{\rho_B(r)G}{r^2}\int_0^r 4\pi r^2\,\rho_M(r)\, dr.$$ Multiplying by $$r^2/\rho_B(r)$$ and differentiating with respect to $$r$$ yields $$\frac{d}{dr}\left[\frac{r^2}{\rho_B(r)}\frac{d}{dr}\left(\frac{kT_B(r)\rho_B(r)}{m_B}\right)\right]=-4\pi Gr^2\rho_M(r).$$ If we make the assumption that cold dark matter particles have an isotropic velocity distribution, then the same derivation applies to these particles, and their density $$\rho_D=\rho_M-\rho_B$$ satisfies the non-linear differential equation $$\frac{d}{dr}\left[\frac{r^2}{\rho_D(r)}\frac{d}{dr}\left(\frac{kT_D(r)\rho_D(r)}{m_D}\right)\right]=-4\pi Gr^2\rho_M(r).$$ With perfect X-ray and distance data, we could calculate the baryon density at each point in the cluster and thus the dark matter density. We could then calculate the velocity dispersion $$\sigma^2_D$$ of the dark matter, which is given by $$\sigma^2_D=\frac{kT_D}{m_D}.$$ The central density ratio $$\rho_B(0)/\rho_M(0)$$ is dependent on the redshift $$z$$ of the cluster and is given by $$\rho_B(0)/\rho_M(0)\propto (1+z)^2\left(\frac{\theta}{s}\right)^{3/2}$$ where $$\theta$$ is the angular width of the cluster and $$s$$ the proper distance to the cluster. Values for the ratio range from 0.11 to 0.14 for various surveys.

Planetary geology
The concept of hydrostatic equilibrium has also become important in determining whether an astronomical object is a planet, dwarf planet, or small Solar System body. According to the definition of planet adopted by the International Astronomical Union in 2006, one defining characteristic of planets and dwarf planets is that they are objects that have sufficient gravity to overcome their own rigidity and assume hydrostatic equilibrium. Such a body will often have the differentiated interior and geology of a world (a planemo), though near-hydrostatic or formerly hydrostatic bodies such as the proto-planet 4 Vesta may also be differentiated and some hydrostatic bodies (notably Callisto) have not thoroughly differentiated since their formation. Often the equilibrium shape is an oblate spheroid, as is the case with Earth. However, in the cases of moons in synchronous orbit, nearly unidirectional tidal forces create a scalene ellipsoid. Also, the purported dwarf planet is scalene due to its rapid rotation, though it may not currently be in equilibrium.

Icy objects were previously believed to need less mass to attain hydrostatic equilibrium than rocky objects. The smallest object that appears to have an equilibrium shape is the icy moon Mimas at 396 km, whereas the largest icy object known to have an obviously non-equilibrium shape is the icy moon Proteus at 420 km, and the largest rocky bodies in an obviously non-equilibrium shape are the asteroids Pallas and Vesta at about 520 km. However, Mimas is not actually in hydrostatic equilibrium for its current rotation. The smallest body confirmed to be in hydrostatic equilibrium is the dwarf planet Ceres, which is icy, at 945 km, whereas the largest known body to have a noticeable deviation from hydrostatic equilibrium is Iapetus being made of mostly permeable ice and almost no rock. At 1,469 km Iapetus is neither spherical nor ellipsoid. Instead, it is rather in a strange walnut-like shape due to its unique equatorial ridge. Some icy bodies may be in equilibrium at least partly due to a subsurface ocean, which is not the definition of equilibrium used by the IAU (gravity overcoming internal rigid-body forces). Even larger bodies deviate from hydrostatic equilibrium, although they are ellipsoidal: examples are Earth's Moon at 3,474 km (mostly rock), and the planet Mercury at 4,880 km (mostly metal).

In 2024, Kiss et al. found that has an ellipsoidal shape incompatible with hydrostatic equilibrium for its current spin. They hypothesised that Quaoar originally had a rapid rotation and was in hydrostatic equilibrium, but that its shape became "frozen in" and did not change as it spun down due to tidal forces from its moon Weywot. If so, this would resemble the situation of Iapetus, which is too oblate for its current spin. Iapetus is generally still considered a planetary-mass moon nonetheless, though not always.

Solid bodies have irregular surfaces, but local irregularities may be consistent with global equilibrium. For example, the massive base of the tallest mountain on Earth, Mauna Kea, has deformed and depressed the level of the surrounding crust, so that the overall distribution of mass approaches equilibrium.

Atmospheric modeling
In the atmosphere, the pressure of the air decreases with increasing altitude. This pressure difference causes an upward force called the pressure-gradient force. The force of gravity balances this out, keeping the atmosphere bound to Earth and maintaining pressure differences with altitude.

title: Hydrostatic equilibrium


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Fleet Air Arm

The Fleet Air Arm (FAA) is the naval aviation component of the United Kingdom's Royal Navy (RN). The FAA is one of five RN fighting arms. it is a primarily helicopter force, undertaking roles once performed by biplanes such as the Fairey Swordfish. It operates the F-35 Lightning II for maritime strike and the AW159 Wildcat and AW101 Merlin for commando and anti-submarine warfare.

The RAF was formed by the 1918 merger of the RN's Royal Naval Air Service with the British Army's Royal Flying Corps. The FAA did not come under the direct control of the Admiralty until mid-1939. During the Second World War, the FAA operated aircraft on ships as well as land-based aircraft that defended the Royal Navy's shore establishments and facilities.

Beginnings
British naval flying started in 1909, with the construction of an airship for naval duties. In 1911 the Royal Navy graduated its first aeroplane pilots at the Royal Aero Club flying ground near Eastchurch, Isle of Sheppey under the tutelage of pioneer aviator George Bertram Cockburn. In May 1912, naval and army aviation were combined to become the Royal Flying Corps (RFC). The Naval Wing of the RFC lasted until July 1914 when the Royal Navy reformed its air branch, under the Air Department of the Admiralty, naming it the Royal Naval Air Service (RNAS). By the outbreak of the First World War, in August 1914, the RNAS had more aircraft under its control than the remaining RFC. The roles of the RNAS were fleet reconnaissance, patrolling coasts for enemy ships and submarines, attacking enemy coastal territory and defending Britain from enemy air raids, along with deployment along the Western Front. In April 1918 the RNAS, which at this time had 67,000 officers and men, 2,949 aircraft, 103 airships and 126 coastal stations, merged with the RFC to form the Royal Air Force.

Fleet Air Arm
On 1 April 1924, the Fleet Air Arm of the Royal Air Force was formed, encompassing those RAF units that normally embarked on aircraft carriers and fighting ships. The year was significant for British naval aviation as only weeks before the founding of the Fleet Air Arm, the Royal Navy had commissioned HMS Hermes (95), the world's first ship to be designed and built as an aircraft carrier. Over the following months RAF Fleet Air Arm Fairey IIID reconnaissance biplanes operated off Hermes, conducting flying trials.

On 24 May 1939 the Fleet Air Arm was returned to Admiralty control under the "Inskip Award" (named after the Minister for Co-ordination of Defence overseeing the British re-armament programme) and renamed the Air Branch of the Royal Navy. At the onset of the Second World War, the Fleet Air Arm consisted of 20 squadrons with only 232 frontline aircraft, and 191 additional trainers. By the end of the war the strength of the Fleet Air Arm was 59 aircraft carriers, 3,700 aircraft, 72,000 officers and men and 56 Naval air stations.

During the war, the FAA operated fighters, torpedo bombers and reconnaissance aircraft. Following the Dunkirk evacuation and the commencement of the Battle of Britain, the Royal Air Force soon found itself critically short of fighter pilots. In the summer of 1940, the RAF had just over 800 fighter pilots and as personnel shortages worsened; the RAF turned to the Admiralty to ask for help from the Fleet Air Arm. Fleet Air Arm crews under RAF Fighter Command were either seconded individually to RAF fighter squadrons or entire as with 804 and 808 Naval Air Squadrons. The former provided dockyard defence during the Battle of Britain with Sea Gladiators.

In British home waters and out into the Atlantic Ocean, operations against Axis shipping and submarines in support of the RN were mounted by RAF Coastal Command with large patrol bombers, flying boats and land-based fighter-bombers. The aircraft carrier had replaced the battleship as the capital ship of the RN and its aircraft were now its principal offensive weapons. The top scoring fighter ace with 17 victories was Commander Stanley Orr, the Royal Marine ace was Ronald Cuthbert Hay with 13 victories. A number of Royal Marines were FAA pilots during the war.

Notable Fleet Air Arm operations during the war included the Battle of Taranto, the sinking of the Bismarck, the attempt to prevent the Channel Dash, Operation Tungsten against the Tirpitz and Operation Meridian against oil plants in Sumatra.

Post-war history
After the war the FAA needed to fly jet aircraft from their carriers. The jet aircraft of the era were considerably less effective at low speeds than propeller aircraft, but propeller aircraft could not effectively fight jets at the high speeds flown by jet aircraft. The FAA took on its first jet, the Sea Vampire, in the late 1940s. The Sea Vampire was the first jet credited with taking off and landing on a carrier. The Air Arm continued with high-powered prop aircraft alongside the new jets resulting in the FAA being woefully outpowered during the Korean War. Nevertheless, jets were not yet wholly superior to propeller aircraft and a flight of ground attack Hawker Sea Furies downed a MiG-15 and damaged others in an engagement.

As jets became larger, more powerful and faster they required more space to take off and land. The US Navy simply built much larger carriers. The Royal Navy had a few large carriers built and completed after the end of the war but another solution was sought. This was partly overcome by the introduction of a Royal Navy idea to angle the flight deck away from the centre line so that the aircraft landing had a clear run away from the usual forward deck park. An associated British invention, intended to provide more precise optical guidance to aircraft on final approaching the deck, was the Fresnel lens optical landing aid. Another Royal Navy invention was the use of a steam-powered catapult to cater for the larger and heavier aircraft (both systems were adopted by the US Navy).

Defence cuts across the British armed forces during the 1960s and 1970s led to the withdrawal of existing Royal Navy aircraft carriers, transfer of Fleet Air Arm fixed-wing jet strike aircraft such as the F-4K (FG.1) Phantom II and Buccaneer S.2 to the Royal Air Force, and cancellation of large replacement aircraft carriers, including the CVA-01 design. The last conventional carrier to be retired was HMS Ark Royal (R09) in 1978. When HMS Hermes was converted in 1980/81 to a STOVL carrier to operate Sea Harriers, a 'Ski-jump ramp' was fitted to aid take-off. A new series of small carriers, the Invincible-class aircraft carrier anti-submarine warfare ships (known as "through deck cruisers") were built and equipped with the Sea Harrier a derivative of the Hawker Siddeley Harrier VTOL aircraft. These carriers incorporated an upswept forward section of the flight deck that deflected the aircraft upward on launch and permitted heavier loads to be carried by the Harrier, for example in weaponry, and the system was used extensively in the Falklands War, with both Hermes and Invincible part of the Task Force. At the end of the Cold War in 1989 the Fleet Air Arm was under the command of the Flag Officer Naval Air Command, a rear admiral based at RNAS Yeovilton.
 * Flag Officer Naval Air Command (FONAC), at RNAS Yeovilton
 * RNAS Prestwick:
 * 819 Naval Air Squadron, (Anti-submarine, 12× Sea King HAS.5)
 * 826 Naval Air Squadron, (Anti-submarine, 12× Sea King HAS.6)
 * HMS Gannet SAR Flight, (Search & Rescue, 8× Sea King HU.5)
 * RNAS Yeovilton:
 * 707 Naval Air Squadron, (Air Assault, 10× Sea King HC.4)
 * 800 Naval Air Squadron, (12× Sea Harrier FA.2)
 * 801 Naval Air Squadron, (12× Sea Harrier FA.2)
 * 845 Naval Air Squadron, (Air Assault, 10× Sea King HC.4)
 * 846 Naval Air Squadron, (Air Assault, 10× Sea King HC.4)
 * 899 Naval Air Squadron, (Training, 24× Sea Harrier FA.2)
 * Fleet Requirements and Aircraft Direction Unit, (Aggressor Squadron, Canberra TT.18, Hawker Hunter GA.11)
 * RNAS Culdrose:
 * 705 Naval Air Squadron, (Basic Helicopter Training, 38× Gazelle HT.2)
 * 706 Naval Air Squadron, (Sea King Training, 12× various types of Sea King)
 * 750 Naval Air Squadron, (Observer Training, Jetstream T2)
 * 771 Naval Air Squadron, (Search & Rescue, 12× Sea King HU.5)
 * 814 Naval Air Squadron, (Anti-submarine, 12× Sea King HAS.5)
 * 820 Naval Air Squadron, (Anti-submarine, 12× Sea King HAS.6)
 * 824 Naval Air Squadron, (Anti-submarine, 12× Sea King HAS.6) (disbanded August 1989)
 * 849 Naval Air Squadron, (Airborne early warning and control, 10× Sea King AEW.2A, 4× Sea King AEW.5)
 * RNAS Portland:
 * 702 Naval Air Squadron, (Aircrew & Maintenance Training, 24× Lynx HAS.3S)
 * 772 Naval Air Squadron, (Air Assault, 10× Sea King HC.4)
 * 810 Naval Air Squadron, (Anti-submarine, 12× Sea King HAS.6)
 * 815 Naval Air Squadron, (Frigate & Destroyer Helicopters, 32× Lynx HAS.3S, most deployed on frigates and destroyers at sea)
 * 829 Naval Air Squadron, (Frigate & Destroyer Helicopters, 32× Lynx HAS.3S, most deployed on frigates and destroyers at sea)

Fleet Air Arm inventory 1989
The inventory of the Fleet Air Arm in 1989 consisted of the following aircraft:
 * Combat aircraft:
 * 42× Sea Harrier FRS.1/F(A).2
 * 2×/2× Sea Harrier T.4A/T.4N
 * Helicopters:
 * 60+ Sea King HAS.5
 * 31+ Sea King HAS.6
 * 10× Sea King AEW.2A
 * 33× Sea King HC.4
 * 80+ Lynx HAS.3S
 * 23×/8× Gazelle HT.2/HT.3
 * Trainers:
 * 3× Canberra TT.18
 * 14× Chipmunk T.10
 * 5× Hunter T.8M
 * 12×/9× Hunter GA.11/T8
 * 19× Jetstream T.2
 * Liaison:
 * 16× Dassault Falcon 20 (Civil-registered)

Post Cold War

In 2000 the Sea Harrier force was merged with the RAF's Harrier GR7 fleet to form Joint Force Harrier. The Fleet Air Arm began withdrawing the Sea Harrier from service in 2004 with the disbandment of 800 NAS. 801 NAS disbanded on 28 March 2006 at RNAS Yeovilton (HMS Heron). 800 and 801 NAS were then combined to form the Naval Strike Wing, flying ex-RAF Harrier GR7 and GR9s. On 1 April 2010, NSW reverted to the identity of 800 Naval Air Squadron. The Harrier GR7 and GR9 retired from service in December 2010 following the Strategic Defence and Security Review 2010.

Two new Queen Elizabeth-class aircraft carrier carriers able to operate the F-35B short take-off and landing variant of the US Lockheed Martin Lightning II aircraft were constructed. In the Strategic Defence and Security Review 2015, it was announced that the carriers would enter service "from 2018". The procurement plan is for a force of 138 F-35 aircraft, which are intended to be operated by both the RAF and FAA from a common pool, in the same manner as the Joint Force Harrier. With the introduction of the F-35, the Fleet Air Arm will return to the operation of fixed-wing strike aircraft at sea. In 2013, an initial cadre of Royal Air Force and Royal Navy pilots and aircraft maintenance personnel were assigned to the U.S. Marine Corps' Marine Fighter Attack Training Squadron 501 (VMFAT-501), part of the U.S. Air Force's 33rd Fighter Wing at Eglin Air Force Base, Florida, for training on the F-35B. 809 Naval Air Squadron will be the first FAA unit to operate the F-35B and will be based at RAF Marham.

Helicopters
Helicopters also became important combat platforms since the Second World War. Initially used in the search and rescue role, they were later developed for anti-submarine warfare and troop transport; during the 1956 Suez Crisis they were used to land Royal Marine Commando forces, the first time this had ever been done in combat. Originally operated only from carriers, the development of the Westland Wasp in the 1960s allowed helicopters to operate on all ships of frigate size or larger. Wasps, Sea Kings and Wessex helicopters all played an active part in the 1982 Falklands War, while Lynx helicopters played an attack role against Iraqi patrol boats in the 1991 Gulf War and Commando Sea King HC4s as well as the Lynx HMA Mk 8 from HMS Argyll, assisted in suppressing rebel forces in the British intervention in the Sierra Leone Civil War in 2000.

Museums
The Fleet Air Arm has a museum near RNAS Yeovilton (HMS Heron) in Somerset, England, at which many of the great historical aircraft flown by the Service are on display, along with aircraft from other sources. There is also a Fleet Air Arm museum inside the Museum of Transport & Technology in Auckland, New Zealand. On display there is a full-size replica Fairey Swordfish, along with historic items and memorabilia.

Personnel
In 1938, Admiralty Fleet Orders 2885 announced the formation of an Air Branch of the Royal Naval Reserve. Thirty three unmarried men signed up for eighteen months full-time flying training; however, before these first volunteers were able to gain their wings Britain was at war. At the end of hostilities in 1945 the RNVR(A) was 46,000 strong, with over 8,000 aircrew. Post war the RNVR(A) comprised 12 dedicated reserve squadrons, grouped regionally into Air Divisions. However, defence cuts in 1957 disbanded the five Air Divisions, and the following year the RNVR was merged with the RNR.

Today
As of 1 December 2013, the Regular Fleet Air Arm has a reported strength of 5,000 personnel, which represents approximately 20% of the Royal Navy's total strength (excluding Royal Marines).

The Assistant Chief of the Naval Staff (Aviation & Carriers), the professional head (and also Rear Admiral Fleet Air Arm), is Rear Admiral Martin Connell as of February 2019. Under First Sea Lord Admiral Tony Radakin’s plans, the professional head of the Fleet Air Arm is set to shortly change to a one-star role, headed by a Commodore.

Members of the Fleet Air Arm continue to be known as WAFUs. WAFU ("wet and f**king useless") is said to actually derive from "Weapon and Fuel Users", a stores category for clothing.

Reserve Air Branch
The RNR Air Branch was commissioned at RNAS Yeovilton on 16 July 1980, and shortly afterwards 38 ex-regular aircrew began refresher training. Today the RNR Air Branch comprises approximately 250 ex-regular service Officers and Ratings, covering all aviation trades, tasked to support the Fleet Air Arm.

The Air Branch has its roots in the Royal Naval Volunteer Reserve Air Branch, whose members served with distinction between 1937 through the Second World War until 1950 when it was disbanded. Formed on 3 April 1980, the Air Branch was initially established to provide additional Pilots and Observers to the Royal Navy, but later expanded to include all trades and specialisations of the Fleet Air Arm. Currently comprising some 320 personnel, HMS Pegasus is one of the biggest Units in the Royal Naval Reserve.

The name HMS Pegasus has a long and interesting history in the Royal Navy, dating back to 1585. The second HMS Pegasus was commanded by Prince William Henry, who later became King William IV, known as the Sailor King. In late 1786, the third HMS Pegasus was stationed in the West Indies under then Captain Horatio Nelson, earning three of her four Battle Honours. The fourth and last HMS Pegasus served as a prototype fighter catapult ship, originally commissioned as HMS Ark Royal, serving primarily on convoy duty in the Second World War.

The name Pegasus has associations outside of the Royal Navy, including the Bristol Aeroplane Company engine that powered the Fairey Swordfish and the Rolls Royce engine that powered the BAE Sea Harrier. And, of course, the Parachute Regiment use Pegasus as their emblem.

Insignia

The FAA is known for its use of the 'Fleet Air Arm Zig Zag': a light blue zig zag on a dark blue background.

The pattern is thought to have belonged to the "Perch Club", membership of which was restricted to those who had completed 100 deck landings without an accident. The zig zag was thought to have been taken from a Creeping Line Ahead, a parallel search pattern performed by FAA aircraft in a carrier task group.

Today, the dark blue background represents the Royal Navy; the colour of the zigzag represents the Royal Flying Corps, from which the Royal Naval Air Service was born; and the zigzag shape represents a nod to the Royal Artillery (red zigzag on blue background), given that the first people sent aloft in tethered balloons to spot the fall of shot were Royal Artillery observers. It was these observers who became early members of the Royal Flying Corps.

Aircrew wear flying badges, such as pilots wearing a pair of gold albatross wings. The wings badges also feature a crown and fouled anchor in the centre, to reflect the maritime element of the flying undertaken. Wings are worn on the left sleeve of naval aviators, unlike their other service counterparts.

Aircraft
The FAA operates fixed wing and rotary wing aircraft. It uses the same aircraft designation system as the RAF.

F-35B Lightning II

The introduction of the F-35B Lightning II saw a restoration of fixed wing, front-line operations to the FAA after the retirement of Joint Force Harrier in 2010. The Lightning Force is a joint RAF-Fleet Air Arm formation with all F-35Bs capable of operating from the Royal Navy's Queen Elizabeth-class aircraft carriers. The first Fleet Air Arm squadron to operate the F-35B is 809 Naval Air Squadron which formally stood-up in December 2023, joining other F-35B squadrons within the RAF that are formally part of No. 1 Group RAF.

An initial order of 48 airframes was made in 2012 to equip the air wings of the two Queen Elizabeth-class aircraft carriers, with the operation split between the FAA and the Royal Air Force, as was the case with Joint Force Harrier. 809 Naval Air Squadron was announced as the second UK unit to fly the F-35B (the first being 617 Squadron RAF) and is the first FAA unit to operate the aircraft. It is understood that at least two further frontline squadrons will stand up in the future alongside 809, 617, 17(R) Test and Evaluation Squadron and an RAF-numbered Operational Conversion Unit, creating a total of six squadrons including the OCU and OEU. Under the Strategic Defence and Security Review of November 2015, the UK Government made a commitment to buying 138 F-35B, with at least 24 available for carrier use by 2023. Subsequently, following on the 2021 defence review, the First Sea Lord indicated that the new envisaged number was to be 60 aircraft initially and "then maybe more", up to a maximum of around 80 to hopefully equip four "deployable squadrons". In April 2022, the Deputy Chief of Defence Staff, Air Marshal Richard Knighton, told the House of Commons Defence Select Committee that the MoD was in discussions to purchase a second tranche of 26 F-35B fighters. Plans for frontline F-35B squadrons had been modified and now envisaged a total of three squadrons (rather than four) each deploying 12-16 aircraft. In surge conditions 24 F-35s might be deployed on the Queen Elizabeth-class carriers but a routine deployment would likely involve 12 aircraft.

In January 2019, initial operating capability for the UK's F-35B was announced with 18 F-35Bs jointly delivered to the UK. As of December 2022, 26 aircraft were operational in the UK and were based at RAF Marham. These aircraft regularly deployed for operations on the Queen Elizabeth-class aircraft carriers. Another 3 F-35s remained in the US for testing and evaluation purposes.

While 33 F-35B aircraft (including 3 or 4 based in the U.S.) were in the U.K. inventory by March 2024, former U.K. Defence Secretary Ben Wallace reported that the RAF and Royal Navy faced a considerable challenge in providing even the existing modest F-35B fleet with qualified pilots. As of late 2022 there were only 30 qualified British pilots (plus three exchange pilots from the United States and Australia) for the F-35. The average wait time for RAF trainee Typhoon and F-35 pilots, after completing the Military Flying Training System, was approximately 11 and 12 months respectively. A further gap of 68 weeks existed between completing Basic Flying Training and beginning Advanced Fast Jet Training. The resulting pilot shortage was a factor in delaying the ability to stand up the first Fleet Air Arm Squadron (809 Squadron) on a timely basis. In February 2023, the Chief of the Air Staff, Air Chief Marshal Sir Mike Wigston, reported that the number of F-35 pilots had grown to 34 UK pilots with a further 7 to complete training by August 2023.

Training
Four types of fixed wing aircraft are operated by the FAA for training purposes: Pilot Grading is carried out using the Grob Tutor T1. Elementary flying training is then conducted on the Grob Prefect T1. From there, pilots are streamed to either Rotary or Fast-Jet. Observer grading and training is done using four Beechcraft Avenger T1 before observers join their frontline aircraft.

Rotary
Today the largest section of the FAA is the rotary wing section. Pilots designated for rotary wing service train under No. 1 Flying Training School at RAF Shawbury. The school is a tri-Service organisation consisting of civilian and military instructors (including Naval instructors and a Naval Air Squadron) that take the student from basic flying through to more advanced flying such as instrument flying, navigation, formation and captaincy.

Its aviators fly one of four types of helicopters:

Commando Merlin
The HC4/4A AW101 Merlin (nicknamed "Junglie Merlin") serves as a medium lifter and troop transporter in support of the Royal Marines. The FAA received the Merlin HC3/HC3A fleet from the RAF, replacing the Commando Sea King in September 2014. These have been marinised and replaced with HC4s/HC4As, under the Merlin Life Sustainment Programme (MLSP) that was placed on contract in December 2013.

Commando Wildcat AH1

The AW159 Wildcat: the BRH (Battlefield Reconnaissance Helicopter) replaces the Westland Lynx as the Battlefield Reconnaissance Helicopter of the FAA. Along with the Commando Merlin, these squadrons operate under Commando Helicopter Force, which provides airborne support to 3 Commando Brigade of the Royal Marines.

Wildcat HMA2
The Wildcat HMA2 became the standard small ship borne helicopter in the FAA, with 28 Wildcats replacing the Lynx HMA8 in 2017. 28 AW159 Wildcat HMA2 helicopters perform a range of roles including anti-surface and anti-submarine warfare and airborne surveillance.

Merlin HM2
The Merlin HM2 ("Grey Merlin") is the FAA's primary anti-submarine warfare (ASW) helicopter, having replaced the Sea King HAS6 in the role. It is presently deployed with various ships of the Royal Navy.

Merlin HM2 also incorporates an airborne early warning and surveillance (AEW) variant, known as Crowsnest, which replaced the ASaC7 variant of the Sea King. The first Merlin HM2 test flight with Crowsnest was completed in April 2019. However, initial operating capability of the system was significantly delayed. While Crowsnest was deployed with the U.K. carrier strike group in 2021, it experienced operating challenges and finally achieved initial operating capability in July 2023. Full operating capability is expected in 2024/25. While all Merlins in the Royal Navy will be equipped to operate Crowsnest, only ten kits for the system are being acquired. It has been reported that initially five Merlins will be equipped with Crowsnest, three of these being normally assigned to the "high readiness" aircraft carrier. Challenges involved in the Crowsnest program have led the Royal Navy to seek a replacement for its helicopter-based AEW platform with a new fixed-wing UAV, under Project Vixen, by 2030.

Unmanned
The Royal Navy operates the AeroVironment Puma AE as of 2020.

Future
A number of unmanned systems are under development for the Fleet Air Arm including the Peregrine rotary-wing UAV which is scheduled to enter service beginning in mid-2024. Other fixed-wing UAVs, envisaged for potential operation from the Queen Elizabeth-class carriers, are in the conceptual or planning stages under a program known as Project Vixen.

Squadrons and flights
A Fleet Air Arm flying squadron is formally titled Naval Air Squadron (NAS), a title used as a suffix to the squadron number. The FAA assigns numbers in the 700–799 range to training and operational conversion squadrons and numbers in the 800–899 range to operational squadrons. Exceptions to the 700–799 include operational conversion squadrons which also hold some form of operational commitment where they are then titled 800–899. During WWII the 1700 and 1800 ranges were also used for operational squadrons.

An additional flying unit of the Royal Navy is the FOST Helicopter Support Unit based at HMS Raleigh in Cornwall. This unit is not part of the Fleet Air Arm, but is directly under the control of Fleet Operational Sea Training, operated by British International Helicopters (BIH). BIH also support various Royal Navy and NATO exercises with passenger and freight transfer services and transfers by hoist, for ships exercising both in the Atlantic and the North Sea.

The Royal Navy share both operational and training duties on the Lightning II with the RAF under a banner organisation called the Lightning Force, which will operate in the same manner as Joint Force Harrier.

Until March 2019, the Fleet Air Arm had responsibility for the Royal Navy Historic Flight, a heritage unit of airworthy aircraft representing the history of aviation in the Royal Navy. The Historic Flight was disbanded on 31 March 2019, with responsibility for maintaining and operating the aircraft transferred to Navy Wings, a charitable body that also runs the Fly Navy Heritage Trust.

Notable members

 * Vice-Admiral Richard Bell Davies (1886–1966): the first naval aviator to receive the VC and the first naval aviator of the Fleet Air Arm to reach flag rank
 * Vice-Admiral Sir Lumley Lyster (1888–1957): drew up attack plan in 1935 that was used for the Battle of Taranto five years later
 * Admiral Sir Reginald Portal (1894–1983): naval aviator who was the younger brother of Marshal of the Royal Air Force Lord Portal (1893–1971)
 * Captain Henry Fancourt (1900–2004): a pioneering aviator, he had a distinguished career in naval aviation until 1949. Worked for Short Bros and Hartland.
 * Ralph Richardson (1902–1983): English stage and screen actor, volunteered as a navy pilot during Second World War and rose to the rank of lieutenant-commander in the Air Branch.
 * Admiral of the Fleet Sir Caspar John (1903–1984): First Sea Lord 1960–63 and the first British naval aviator to reach the highest rank within the RN.
 * Admiral Sir Walter Couchman (1905–1981): naval observer who earned his pilot's wings too, he led the fly-past for the Coronation Fleet Review in June 1953.
 * Laurence Olivier (1907–1989): English stage and screen actor and director, volunteered as a navy pilot during the Second World War and rose to the rank of lieutenant in the Air Branch.
 * Duncan Hamilton: English Grand Prix driver and winner of the 1953 24 Hours of Le Mans.
 * Lieutenant Commander (A) Eugene Esmonde (1909–1942): posthumously awarded the Victoria Cross for leading 825 Naval Air Squadron Swordfish torpedo bombers in an attack on German capital ships during the "Channel Dash".
 * Lieutenant Commander Roy Sydney Baker-Falkner (1916-1944): awarded the Distinguished Service Order for leading Operation Tungsten attack on the German battleship Tirpitz.
 * Michael Hordern (1911–1995): actor, served as fighter controller during World War II.
 * Jeffrey Quill (1913–1996): RAF officer and Spitfire test pilot (Vickers-Armstrongs) who served five months with Fleet Air Arm as T/Lt.Cdr RNVR in 1944–1945, helping to develop better carrier deck-landings with the Supermarine Seafire, the naval version of the Spitfire.
 * Kenneth More (1914–1982): actor, including films such as Reach for the Sky and Sink the Bismarck.
 * Commander Charles Lamb (1914–1981): author of the Second World War Fleet Air Arm autobiography War in a Stringbag.
 * Vice-Admiral Sir Peter Compston (1915–2000): served briefly in the British Army, then in the RAF for two years, before transferring as a pilot to the Royal Navy in 1938.
 * Admiral Sir (Leslie) Derek Empson (1918–1997): naval pilot who joined the Royal Navy as a naval rating. In his flying career, executed 782 aircraft carrier landings without a mishap.
 * Rear-Admiral Cedric Kenelm Roberts (1918–2011): (always known as 'Chico') a distinguished naval pilot who joined the Royal Navy as a naval rating in 1940. He was personal pilot to Vice-Admiral Lumley Lyster in 1943, commanded three Naval Air Squadrons and was shot down during the Korean War. Later, he commanded three Naval Air Stations and ended his naval flying career as Flag Officer Naval Flying Training 1968–71.
 * Lieutenant-Commander Charles Wines ("Charlie Wines") (1917–1991): joined the Royal Navy as a Supply Assistant, flew Swordfish torpedo bomber as a rating pilot in the Second World War. Commissioned as a pilot in 1944 he later spent more than twenty years, in the same job as a serving and retired officer, as the FAA Drafting Officer and as such the career manager for thousands of FAA ratings.
 * Rear-Admiral Dennis Cambell (1907–2000): inventor of the angled flight deck for aircraft carriers in 1951.
 * Rear-Admiral Nick Goodhart (1919–2011): inventor of the mirror-sight deck landing system for aircraft carriers in 1951.
 * Captain Eric "Winkle" Brown (1919–2016): holds the world record for the most types of aircraft flown by an individual (487 types). As a test pilot he made the first-ever jet landing on an aircraft carrier in December 1945.
 * Lieutenant Commander John Moffat (1919–2016): crippled the GERMAN BATTLESHIP Bismarck on 26 May 1941.
 * Admiral Sir John Treacher (1924–2018): naval pilot who was promoted rear-admiral at the age of 45 and held four important flag appointments before leaving the Royal Navy in 1977, despite many expecting him to become First Sea Lord, for a career in business. Was at the helm of Westland during the political drama of the 1980s.
 * Admiral Sir Ray Lygo (1924–2012): naval pilot who joined the Royal Navy as a naval rating in 1942 and who reached First Sea Lord in 1978, led a successful career in industry and was chief executive and deputy chairman of British Aerospace in the 1980s.
 * Sir George Martin (1926–2016): record producer for The Beatles.
 * Admiral of the Fleet Sir Ben Bathurst (1936–): First Sea Lord 1993–95 and the last Royal Navy officer to be promoted to five-star rank.
 * Rear-Admiral Sir Robert Woodard KCVO (c.1939–): naval aviator commanded two Naval Air Squadrons, two warships, a Naval Air Station, the Clyde submarine base and ended his career as the Flag Officer Royal Yachts 1990–95, the only aviator to command the Royal Yacht HMY Britannia.
 * Commander Nigel David "Sharkey" Ward (1943–2024): commanded 801 Naval Air Squadron during the 1982 Falklands War.
 * Rear-Admiral Iain Henderson (c. 1948–): the first officer, and first naval officer, to hold the modern appointment of Air Officer Commanding 3 Group 2000–01.
 * Vice-Admiral Sir Adrian Johns (c. 1952–) is the first naval aviator to hold the post of Governor of Gibraltar.
 * Commander Prince Andrew, Duke of York (1960–): served during the Falklands War 1982 and for some years afterwards.
 * Captain Brian Young (1930–2009): former Sea Hawk pilot, later commanded the task group for Operation Paraquet during the Falklands War.
 * John Cecil Moore English pilot, author and conservationist. Born in Tewksbury 1907 died Bristol 1967. Served in WW2

Some 64 naval pilots and nine observers have reached flag rank in the Royal Navy and four Royal Marines pilots general rank in the Royal Marines. Four of these admirals with pilot's 'wings' were air engineering officers (test pilots) and two were supply officers; two of the non-executive officers reached four-star rank: a supply officer, Admiral Sir Brian Brown (1934–), and a Royal Marine, General Sir Peter Whiteley (1920–2016).
 * At least 21 naval Air Engineer Officers (AEOs) have reached flag rank (including the four test pilots (see above)).

title: Fleet Air Arm


text:
Church of Satan

The Church of Satan (CoS) is a religious organization dedicated to the religion of Satanism as defined by Anton Szandor LaVey. Founded in San Francisco in 1966, by LaVey, it is considered the "oldest satanic religion in continual existence", and more importantly the most influential, inspiring "numerous imitator and breakaway groups". According to the Church, Satanism has been "codified" as "a religion and philosophy" by LaVey and his church. Founded in an era when there was much public interest in the occult, witchcraft and Satanism, the  church enjoyed a heyday for  several years after its founding. Celebrities attended LaVey's satanic parties and he was invited on talk shows. His Satanic Bible sold nearly a million copies.

LaVey was the church's High Priest until his death in 1997. In 2001, Peter H. Gilmore was appointed to the position of high priest, and the church's headquarters were moved to Hell's Kitchen, Manhattan, New York City. Members do not believe that Satan literally exists and do not worship him. Instead, Satan is viewed as a positive archetype embracing the Hebrew root of the word "Satan" as "adversary", who represents pride, carnality, and enlightenment, humanity's natural instincts which Abrahamic faiths have wrongly suppressed. According to High Priest Peter H. Gilmore, Satan is "a name for the reservoir of power inside each human to be tapped at will" . In LaVey's book, The Satanic Bible, the Satanist's concept of a god is described as the Satanist's true "self"— a projection of his or her own personality, not an external deity. Satan is used as a representation of personal liberty and individualism.

The Church dismisses the idea of a “Satanic Community” and does not share membership lists with its members, arguing members are "radical individualists" who "may share very little in common beyond" being Satanists. The Church rejects the legitimacy of any other organizations who claim to be Satanists. Scholars agree that there is no reliably documented case of Satanic continuity prior to the founding of the Church of Satan. It was the first organized church in modern times to be devoted to the figure of Satan, and according to Faxneld and Petersen, the Church represented "the first public, highly visible, and long-lasting organization which propounded a coherent satanic discourse".

Beliefs
LaVey described his religion as "just Ayn Rand's philosophy with ceremony and ritual added"; similarly, sociologist of religion James R. Lewis described it as "a blend of Epicureanism and Ayn Rand's philosophy, flavored with a pinch of ritual magic." There is no belief in or worship of the Devil or a Christian notion of Satan. High priest Peter Gilmore describes its members as "skeptical atheists", indicating the Hebrew root of the word "Satan" as "adversary" or "opposer." Gilmore rejects the legitimacy of theistic Satanists, who believe Satan to be a supernatural being or force that may be contacted or supplicated to, dubbing them "devil worshipers". In an interview with David Shankbone, High Priest Peter Gilmore stated "My real feeling is that anybody who believes in supernatural entities on some level is insane. Whether they believe in the Devil or God, they are abdicating reason." He added, "Satanism begins with atheism. We begin with the universe and say, 'It’s indifferent. There’s no God, there’s no Devil. No one cares!'" According to Gilmore, "[W]e do not believe in the supernatural. To the Satanist, he is his own God. Satan is a symbol of Man living as his prideful, carnal nature dictates. Some Satanists extend this symbol to encompass the evolutionary 'force' of entropy that permeates all of nature and provides the drive for survival and propagation inherent in all living things. To the Satanist, Satan is not a conscious entity to be worshiped, rather it is a name for the reservoir of power inside each human to be tapped at will ." The church has stated its contention that they are the first formally organized religion to adopt the term "Satanism" and describes the term "Theistic Satanism" as "oxymoronic". LaVey's views on magic were ambiguous. He insisted Satanism was a "materialist philosophy" but also often talked of magic. He included this rule in his "Rules of the Earth": "Acknowledge the power of magic if you have employed it successfully to obtain your desires. If you deny the power of magic after having called upon it with success, you will lose all you have obtained.”"

LaVey also often talked of a "Satanic magical formula" of  "nine parts respectability to one part outrageousness",  satanism requiring  some element of sinisterness, but not so much as to put off potential congregants. The "Rules of the Earth" in LaVey's Satanic Bible specifically prohibited unwanted sexual advances and harming animals or children, but the Church also  "often featured a nude woman serving as an altar" in its black masses.

Though not emphasizing social or political causes, like Ayn Rand, LaVey explicitly opposed egalitarianism and supported social stratification, calling for the end of the “myth of ‘equality’”, which only “supports the weak at the expense of the strong”. But he also suggested that in loving themselves, hedonists developed the ability to love others. He was quoted as saying, “If Satanists didn’t care, they wouldn’t be so dark and pessimistic.”

Early years
In the 1960s Anton Szandor LaVey formed a group called the Order of the Trapezoid, which later became the governing body of the Church of Satan. The group included: "The Baroness" Carin de Plessen, Dr. Cecil Nixon, Kenneth Anger, San Francisco city assessor Russell Wolden, and Donald Werby. According to the Church of Satan historiography, other LaVey associates from this time include noted science fiction and horror writers Anthony Boucher, August Derleth, Robert Barbour Johnson, Reginald Bretnor, Emil Petaja, Stuart Palmer, Clark Ashton Smith, Forrest J. Ackerman, and Fritz Leiber Jr.

The Church of Satan was established at the Black House in San Francisco, California, on Walpurgisnacht, April 30, 1966, by LaVey, who was the church's High Priest until his death in 1997.

In the first year of its foundation, LaVey and the Church of Satan publicly performed a Satanic marriage of Judith Case and journalist John Raymond. The ceremony was attended by Joe Rosenthal. LaVey performed the first publicly recorded Satanic baptism in history for his youngest daughter Zeena, which garnered worldwide publicity and was originally recorded on The Satanic Mass LP. A Satanic funeral for naval machinist-repairman, third-class Edward Olsen, was performed at the request of his wife, complete with an honor guard.

The Church of Satan was the subject of a number of books, magazine and newspaper articles during the 1960s and 1970s. It is also the subject of a documentary, Satanis (1970). LaVey appeared in Kenneth Anger's film Invocation of My Demon Brother, acted as technical adviser on The Devil's Rain, which starred Ernest Borgnine, William Shatner, and introduced John Travolta. The Church of Satan was also featured in a segment of Luigi Scattini's film Angeli Bianchi, Angeli Neri, released in the United States as Witchcraft '70.

One attempt to establish the church abroad was done in connection with Maarten Lamers of the Netherlands who read The Satanic Bible and in 1971 flew to San Francisco to meet LaVey. Back in Amsterdam, Lamers established the first CoS grotto outside the U.S. -- the Magistralis Grotto or the Kerk van Satan. The "Kerk" was in the Red Light District and connected to club called Walpurga Abbey where customers could paid by the minute to observe “monastic sisters” of the Abbey masturbate on stage. Lamers insisted that since the sisters were "performing religious acts of sexual magic", Walpurga Abbey was tax-exempt. The Dutch government disagreed and in 1987, "after a decade of police raids and legal battles", Lamers was compelled to pay 10 million guilders in back taxes.

In 1972, LaVey stopped holding weekly rituals at the Black House and announced these would be done at the local grottos. Then on September 27, 1974, he declared the end of all regional organizations and that individual members and grottos should report to the Church's Central Grotto in San Francisco. LaVey called this move “Phase IV of his master plan”

Schisms
Starting in the early 1970s, the Church faced internal dissent and a series of schisms. The first breakaway was by the Babylonian Grotto and its leader Wayne West, who LaVey excommunicated. A bigger schism happened with the excommunication of the Stygian Grotto, whose leader established the Church of Satanic Brotherhood in 1973 with units in Dayton, Indianapolis, Louisville, New York City, and St. Petersburg (FL). From the Church's Belphegor Grotto, another splinter group created the Order of the Black Goat, which was allegedly neo-Nazi in orientation, led by Michael Grumbowski. A later, more resilient offshoot was the World Church of Satanic Liberation, which ran from 1986 to 2011.

In 1975, the Church of Satan underwent a significant fracture. Michael Aquino, the editor of the church newsletter and a fairly high level leader in the church, who disagreed with LaVey's changes, left to found the Temple of Set, taking a significant portion of the CoS leadership with him. This schism involved the largest Church branch, the Nineveh Grotto in NJ, and the Lilith Grotto in NY, among others. The Temple of Set reportedly had more than 500 members at its founding, although Anton LaVey claimed that only 29 people left.

LaVey announced that the Temple of Set schism was not a setback but "Phase V" of his master plan, however, according to author Amina Lap, from this point on Satanism became a "splintered and disorganized movement".

Schisms from the Church were caused by several factors, according to sociologist Foertsch. He focused on differences in costliness or barriers to entry for members, disputes over authority and doctrine, and opportunities for niche development in the American counter-culture world of occultism, and persecution of alleged Satanists during the moral panic (described below) of the 1980s.

The same year LaVey painted the Black House beige to lessen unwanted attention and "largely retired from public life". (In 1986, the Black House was repainted black.) According to at least one critic, James R. Lewis, LaVey was not instituting "a Master Plan" but demonstrating that he “was not up to making the necessary personal sacrifices that being a founding prophet and leader required" because his motives for founding the Church were personal enrichment and self-aggrandizement, not spreading some religious truth.

1980s, early 1990s, and "Satanic Panic"
In the 1980s a phenomenon that became known as the "Satanic Panic" arose and the media reported concerns of criminal conspiracies by the Church of Satan. According to a report released in 2020, LaVey indicated to FBI agents who interviewed him on October 31, 1980 that he had lost interest in the Church. "“LAVEY STATED THAT HE IS WELL AWARE THAT MOST PEOPLE ASSOCIATED WITH THE CHURCH OF SATAN ARE IN FACT ‘FANATICS, CULTISTS, AND WEIRDOES.’ HE STATED HIS INTEREST IN THE CHURCH OF SATAN IS STRICTLY FROM A MONETARY POINT OF VIEW AND SPENDS HIS TIME FURNISHING INTERVIEWS, WRITING MATERIALS, AND LATELY HAS BECOME INTERESTED IN PHOTOGRAPHY.”" (Kenneth Lanning, an FBI expert in investigating child sexual abuse, produced a report on Satanic Ritual Abuse (SRA) in 1994 aimed at child protection authorities, in which wrote that despite hundreds of investigations, no corroboration of SRA had been found. Following this report, several convictions based on SRA allegations were overturned and the defendants released.)

During the 1980s and 90s, LaVey was no longer interested in making media appearances, and began a "long period of silence", becoming "increasingly reclusive", he began sending his daughter Zeena to represent the CoS. She appeared on television and radio broadcasts, (including The Phil Donahue Show, Nightline with Ted Koppel, Entertainment Tonight, The Late Show, Secrets & Mysteries and the Sally Jesse Raphael Show), in part to educate about the Church, and in part to debunk Satanic ritual abuse and any connection between it and true Satanism, and specifically the Church of Satan. She also became a High Priestess in the Church during this time and in 1988, married Nikolas Schreck, a prominent CoS member and changed her name to Zeena Schreck.

In the 1980s and 1990s remaining members of the Church of Satan became active in media appearances to refute allegations of criminal activity. Members of the Church who were active in producing movies, music, films, and magazines devoted to Satanism include Adam Parfrey's Feral House publishing, the musician Boyd Rice, musician King Diamond, and the filmmaker Nick Bougas (a.k.a. A. Wyatt Mann).

On Walpurgisnacht 30 April 1990, Zeena formally renounced any association with the Church or LaVey, whom she now called her “unfather.” She and her husband joined the Temple of Set for a time but in 2002 formed the Sethian Liberation Movement, their own occult left-hand path group. Not long after, Zeena testified against LaVey on behalf of her mother, Diane Hegarty. The court awarded Hegarty half of LaVey’s property, bankrupting him.

After LaVey
After Anton Szandor LaVey's death on October 29, 1997, the role of High Priest was empty for some time. On November 7, 1997 Karla LaVey made a press release about continuing the church with fellow high priestess Blanche Barton. Barton eventually received ownership of the organization, which she held for 4 years. Karla LaVey ultimately left the Church of Satan and founded First Satanic Church. On October 16, 2001, the Black House, the original home of the Church, was demolished after a fundraising effort failed to raise enough to buy it. (In 1992, LaVey had sold the house to a real estate developer to raise money to settle a divorce but the developer allowed LaVey to continue to live in the house for free.)

In 2001, Blanche ceded her position to longtime members Peter H. Gilmore and Peggy Nadramia, the current High Priest and High Priestess and publishers of The Black Flame, the official magazine of The Church of Satan, who managed an active CoS group in New York. The Central Office of the Church of Satan has also moved from San Francisco to New York City's Hell's Kitchen neighborhood, where the couple resides. The Church of Satan does not recognize any other organizations as holding legitimate claim to Satanism and its practice, though it does recognize that one need not be a member of the Church of Satan to be a Satanist.

In October 2004, the Royal Navy officially recognised its first registered Satanist, 24-year-old Chris Cranmer, as a technician aboard HMS Cumberland (F85).

6/6/06 High Mass
On June 6, 2006, the Church of Satan held the first public ritual Satanic Mass in 40 years at the Steve Allen Theater in the Center for Inquiry in Los Angeles. The date corresponds to the number of the Beast, 666, from the biblical Book of Revelation. The ritual, based on the rites outlined in The Satanic Bible and The Satanic Rituals, was conducted by Reverend Bryan Moore and Priestess Heather Saenz.

The event was by invitation only, and over one hundred members of the Church of Satan from around the world filled the theatre to capacity. Many members of the Church of Satan were interviewed by the BBC with permission. The music for the mass was created and performed by Lustmord and was subsequently released on his album Rising.

Example of law abidingness
In December 2007 the Associated Press reported on a story concerning the Church of Satan, in which a teenager had sent an email to High Priest Gilmore stating he wanted to "kill in the name of our unholy lord Satan". Gilmore then reported the message to the Federal Bureau of Investigation, who informed local police, who arrested the teenager.

Realm of Satan documentary
In January 2024, the film Realm of Satan was shown at the Sundance Film Festival. The film is similar to a documentary, though it consists primarily of scenes staged with members of the Church of Satan. One reviewer described it as "an 80-minute art installation in which Satanists are rendered—and deliberately render themselves—performative characters in a diabolical play of their own making." The film is directed by Scott Cummings and it shows a variety of satanic rituals, which may been performed for the film alone.

Membership
The Church of Satan claims they do not solicit memberships nor proselytize. Individuals seeking membership must be legally defined as adults in their nation of residence. As of at least January 2023, no one "under the legal age of consent" may join the Church of Satan, with the exception those whose "parents or legal guardians are already members in good standing".

Active Members begin at the First Degree. One must apply and be approved for an Active Membership, and this is subject to one's answers to a lengthy series of questions. One cannot apply for higher Degrees, and the requirements for each degree are not open to the public. Promotion to a higher degree is by invitation only. Members of the Third through Fifth degrees constitute the Priesthood and may be addressed as "Reverend" (although the titles of "Magister/Magistra" and "Magus/Maga" are more often used when referring to members of the Fourth and Fifth Degrees, respectively). Members of the Fifth degree may also be known as "Doctor", although "The Doctor" usually refers to LaVey. Memberships may be terminated at the discretion of the ruling body of the Church of Satan consisting of the High Priest, the High Priestess and the Council of Nine.

The church emphasizes that one does not have to join the organization to consider themselves a Satanist, and that one only needs to recognize themselves in The Satanic Bible and live according to the tenets outlined therein.

As the Church of Satan does not publicly release membership information, it is not known how many members belong to the Church. However, according to an interview with the Church of Satan, "interest in the Church of Satan and Satanism is growing all the time if our mailboxes, answering and fax machines, and e-mail is any indication." Another source (The Washington Post) states the church claimed to have "hundreds of thousands" of members. However, according to Joseph Laycock, the Church grew rapidly in its first five years before declining, and had an estimated 250 members (according to one source). According to The Washington Post, up until at least 1998, Church membership was never totaled "more than 300".

Hierarchy
The church follows a formulated system of degrees based on meritocracy. These degrees are not open to application or to request and are only awarded to those who demonstrate excellence in the understanding and communication of Satanic Theory coupled with personal achievements in the outside world.

These degrees are:
 * Registered Member (no degree)
 * Active Member/Satanist (first degree)
 * Witch/Warlock (second degree)
 * Priestess/Priest (third degree)
 * Magistra/Magister (fourth degree)
 * Maga/Magus (fifth degree)

Agents of the Church of Satan are individuals who have been trained to serve as contacts for local media and other interested parties.

Priesthood of Mendes and Council of Nine
Members of the Priesthood make up the Council of Nine, which is the ruling body of the Church of Satan, of which Magistra Templi Rex Blanche Barton is the chair-mistress. Individuals who are part of the priesthood are those who act as spokespersons of the Church of Satan. The priesthood is exclusive to third-, fourth-, and fifth-degree members. Members of the priesthood may be referred to as "reverend". The High Priest and Priestess act as administrative chiefs and primary public representatives; each position (High Priest and High Priestess) is held by a single individual at a time. The current High Priest is Peter H. Gilmore, the current High Priestess is Peggy Nadramia.

The Church of Satan evaluates active members for the Priesthood by their accomplishment in society—mastered skills and peer recognition within a profession—rather than by mastery of irrelevant occult trivia. While expected to be experts in communicating the Satanic philosophy, members of the Priesthood are not required to speak on behalf of the Church of Satan and may even choose to keep their affiliation and rank secret in order to better serve their personal goals, as well as those of the organization. Membership in the Priesthood is by invitation only.

The Grotto System
Within Satanism, a Grotto is a clandestine association or gathering of Satanists within geographical proximity for means of social, ritual, and special interest activities. The Church of Satan no longer formally recognizes or charters grottos. The primary reason for the end of the Grotto system is that only a small minority of members ever participated. This was further compounded by the fact that a publicly listed Grotto defeated the ability to remain secret and unknown to the larger populace. The Grotto system was in practice replaced by social media, private online forums, and other methods for members to interact with one another outside of the need for a so-called Grotto Master and annual reports to the central office of the Church of Satan.

title: Church of Satan