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Plane

Plane most commonly refers to: Plane may also refer to: For other uses, see the sections below.

Aviation

Airplane

An airplane is an engine-driven fixed-wing aircraft heavier than air that is supported in flight by the dynamic reaction of the air against its wings, generating lift through forward motion powered by engines such as propellers or jets.^[1] This distinguishes it from lighter-than-air craft like balloons or unpowered gliders, emphasizing its reliance on aerodynamic forces for sustained flight. The history of the airplane began with the first successful powered, controlled flight by Orville and Wilbur Wright on December 17, 1903, at Kitty Hawk, North Carolina, using their Wright Flyer, which covered 120 feet in 12 seconds.^[2] Early designs evolved from biplanes, which dominated World War I-era aviation with their structural stability, to monoplanes in the interwar period for improved speed and efficiency. A pivotal milestone occurred in 1958 when the Boeing 707 entered commercial service with Pan American World Airways, marking the advent of widespread jet travel and enabling transatlantic flights in under eight hours, transforming global transportation.^[3] Airplanes are categorized by purpose, including commercial airliners like the Boeing 737, a narrow-body jet carrying up to 200 passengers on short- to medium-haul routes; military fighters such as the F-16 Fighting Falcon, a multirole supersonic aircraft used for air superiority and ground attack; and general aviation planes, typically small piston-engine models like the Cessna 172, employed for personal transport, training, and recreational flying.^[4] These types share core operational principles governed by four aerodynamic forces: lift, which opposes weight; drag, which resists motion; thrust, provided by engines to propel the aircraft; and weight, the downward force due to gravity.^[5] Lift arises from the airfoil shape of wings, where faster airflow over the curved upper surface creates lower pressure via Bernoulli's principle, while the deflection of air downward imparts an equal upward reaction per Newton's third law.^[5] The magnitude of lift is quantified by the equation

L = \frac{1}{2} \rho v^2 S C_L

where L is lift, \rho is air density, v is the aircraft's velocity relative to the air, S is the wing area, and C_L is the dimensionless lift coefficient depending on wing shape and angle of attack.^[6] In steady flight, lift balances weight, thrust counters drag, enabling efficient cruising. Aviation maintains an exemplary safety record, with the International Air Transport Association reporting seven fatal accidents among 40.6 million flights in 2024, yielding a fatal accident rate of approximately 0.17 per million flights.^[7] This equates to one fatal accident for every roughly 5.8 million flights, underscoring the reliability of modern air travel compared to other transport modes.

Paper plane

A paper plane, also known as a paper airplane, is a toy aircraft constructed by folding a sheet of paper, typically without glue or cuts, to create a glider that relies on a manual launch for flight. The origins of paper planes trace back to ancient China around 2,000 years ago, where early forms emerged from paper kites and folded paper birds made during the Han Dynasty (202 BCE–220 CE), evolving from the invention of paper itself circa 105 CE.^[8] The modern paper plane as a folded glider took shape in the early 20th century, with significant contributions from aviation pioneer Jack Northrop, who in the 1930s used paper models to test wing designs for larger aircraft at Lockheed Corporation, demonstrating their utility in aeronautical experimentation.^[9] These simple models helped refine concepts like wing curvature and stability, influencing early airplane development.^[10] Construction of paper planes involves precise folding techniques using a single uncut sheet of standard printer or origami paper, usually 8.5 by 11 inches, to form wings, fuselage, and control surfaces for aerodynamic efficiency. Basic designs start with folding the paper in half lengthwise to create a centerline, then angling the top corners down to form the nose and wings, as seen in classic models like the dart or glider. The dart style emphasizes a pointed nose for speed, achieved by repeated triangular folds at the leading edge, while the glider prioritizes broad, flat wings for sustained lift, often with trailing edge folds to adjust dihedral angle. These methods ensure structural integrity without adhesives, allowing launches via hand throw at speeds of 10-20 meters per second.^[11] The flight of a paper plane is governed by fundamental aerodynamic principles, where an initial throw imparts forward velocity and upward thrust, countering gravity's downward pull of about 9.8 m/s² on the lightweight craft weighing mere grams. Stability during glide depends on the center of gravity positioned forward of the center of lift—typically 20-30% from the nose—to prevent pitching and ensure level flight, with wings generating lift via Bernoulli's principle as air flows faster over the curved upper surface. Unpowered, these gliders lose altitude gradually due to drag, achieving typical flights of 10-30 meters, though optimized designs have set records; for instance, in 2012, Joe Ayoob threw a paper plane 69.14 meters, the Guinness World Record at the time for farthest flight by a paper aircraft. Paper planes vary from simple single-fold designs for beginners to complex configurations incorporating advanced folds for enhanced performance. Basic types include the fast dart for short, straight trajectories and the stable glider for longer durations aloft, while variations like the Nakamura Lock—designed by Japanese origami expert Eiji Nakamura in 1972—use interlocking folds to create a robust, flat-nosed structure that excels in gentle, circling glides up to 20 seconds. These designs serve an educational role, introducing children to aerodynamics through hands-on experimentation; for example, adjusting wing flaps teaches concepts of lift and drag in classroom activities aligned with STEM curricula.^[12]^[13] Culturally, paper planes symbolize childhood ingenuity and the accessible essence of flight, appearing in art installations like those exploring origami's geometric beauty and serving as metaphors for aviation's foundational simplicity amid complex engineering feats. Global competitions such as Red Bull Paper Wings, held annually since 1994, draw thousands of participants in categories like distance and aerobatics, fostering community and innovation; the 2022 world final in Salzburg, Austria, featured a winning distance of 61.11 meters by Lazar Krstić of Serbia,^[14] while in the same year, a Guinness record of 77.134 meters was set in South Korea by the Shin Kim Chee Team.^[15] The current Guinness World Record for the farthest flight by a paper aircraft is 88.31 meters, achieved by Dillon Ruble (USA) on December 2, 2022.^[16] highlighting their enduring appeal.

Mathematics

Geometric plane

In Euclidean geometry, a plane is defined as a flat, two-dimensional surface that extends infinitely in all directions and has zero thickness and zero curvature.^[17] One specific construction of a plane is the set of all points equidistant from two fixed points, forming the perpendicular bisector plane to the line segment joining those points.^[18] This abstraction serves as the foundational space for studying geometric figures and relations in two dimensions. Key properties of a plane include its flatness, which ensures no intrinsic curvature, allowing for straight-line paths and Euclidean distances. A line either lies entirely within the plane, intersects it at exactly one point, or remains parallel to it without intersection. Similarly, two distinct planes either intersect along a straight line or are parallel, never intersecting. These intersection behaviors stem from the axioms of Euclidean geometry, as outlined in Euclid's Elements (c. 300 BCE), where postulates enable constructions like drawing lines and circles on the plane but assume its existence implicitly through common notions of equality and order.^[17]^[19]^[20] Planes are visualized through everyday analogies, such as the still surface of a calm lake, which approximates flatness over a local area, or the grid of graph paper extending uniformly. In three-dimensional space, the equation of a plane is given by

ax + by + cz = d,

where a, b, and c are the components of a normal vector perpendicular to the plane, and d is a constant determined by a point on the plane. This form highlights the plane's orientation relative to coordinate axes.^[21] In geometric applications, the plane provides the setting for plane figures like triangles, circles, and polygons, enabling theorems on congruence, similarity, and area. For instance, in Hilbert's axioms for space geometry (1899), any three non-collinear points determine a unique plane, which underpins rigorous proofs in modern axiomatic geometry.^[22] Historically, the concept of the plane was developed in ancient Greece around the 6th–4th centuries BCE, with Euclid synthesizing earlier work into a cohesive system; this flat geometry was later distinguished from curved alternatives, such as spherical geometry, by Bernhard Riemann in his 1854 lecture on hypotheses of geometry, which introduced manifolds with constant positive curvature.^[23]

Plane in linear algebra

In linear algebra, a plane passing through the origin in three-dimensional Euclidean space \mathbb{R}^3 is defined as a two-dimensional subspace, comprising all scalar linear combinations of two linearly independent vectors that span it. This subspace satisfies the vector space axioms, including closure under addition and scalar multiplication, and contains the zero vector. A general affine plane, not necessarily through the origin, is obtained by translating this subspace by a fixed vector \mathbf{r_0}, forming a flat two-dimensional surface parallel to the original subspace.^[24]^[25] The parametric representation provides a convenient way to describe points on the plane:

\mathbf{r} = \mathbf{r_0} + s \mathbf{u} + t \mathbf{v},

where \mathbf{r_0} is a fixed point on the plane, \mathbf{u} and \mathbf{v} are two linearly independent direction vectors lying in the plane, and s, t \in \mathbb{R} are scalar parameters. This form parameterizes the entire affine plane as the set of all such combinations. Alternatively, the normal form equation derives from the perpendicularity condition between the plane and its normal vector \mathbf{n} = (a, b, c): the vector from \mathbf{r_0} = (x_0, y_0, z_0) to any point \mathbf{r} = (x, y, z) on the plane satisfies (\mathbf{r} - \mathbf{r_0}) \cdot \mathbf{n} = 0, which simplifies to the Cartesian equation

a(x - x_0) + b(y - y_0) + c(z - z_0) = 0,

or equivalently ax + by + cz + d = 0 with d = -(ax_0 + by_0 + cz_0). This equation uniquely determines the plane when \mathbf{n} \neq \mathbf{0}.^[26]^[21] Linear transformations involving planes include rotations within the plane and reflections across it. A reflection over a plane preserves vectors in the plane (eigenvalue 1 with multiplicity 2, eigenspace the plane itself) and reverses the normal vector (eigenvalue -1). Rotations in the plane, represented by matrices in the plane's basis, yield complex eigenvalues e^{i\theta} and e^{-i\theta} for a counterclockwise rotation by angle \theta, reflecting the circular nature of the transformation in the real plane. These properties arise from the characteristic polynomial of the transformation matrix restricted to the plane.^[27]^[28] Planes find key applications in computational contexts. In computer graphics, affine planes model flat surfaces for rendering, where projections map 3D points onto 2D screens by intersecting with a view plane, enabling efficient hidden surface removal and shading. In solving systems of linear equations, each independent equation a x + b y + c z = k represents a plane in \mathbb{R}^3; the solution to two such equations is their line of intersection, while three may yield a point, line, plane, or empty set depending on linear dependence. Advanced concepts extend to higher dimensions, where a hyperplane is a codimension-1 affine subspace defined by \sum_{i=1}^n a_i x_i + d = 0, generalizing the 3D plane to \mathbb{R}^n. Computing intersections of hyperplanes underlies algorithms like convex hull construction, where half-spaces bounded by hyperplanes define the feasible region, and dual methods solve for vertices via linear programming.^[29]^[30]^[21]^[31]^[32]

Tools and Manufacturing

Woodworking plane

A woodworking plane is a hand-held tool designed for smoothing, shaping, and dimensioning wood by paring away thin layers of material with a sharpened blade secured within a rigid body.^[33] The tool's design allows controlled removal of wood fibers, producing flat surfaces and precise edges essential for joinery and finishing. Early forms trace back to ancient civilizations, with archaeological evidence indicating use in Egypt as early as the 16th century BCE, where simple wooden bodies held iron blades for basic surfacing tasks.^[34] The Romans refined the plane around the 1st century CE, introducing more durable metal components and wedge mechanisms for blade adjustment, as seen in artifacts from Pompeii excavations.^[35] By the Middle Ages, European carpenters adapted Roman designs, adding features like cap irons to break shavings and prevent clogging, though tools remained largely wooden.^[36] In the 19th century, American inventor Leonard Bailey revolutionized the tool with patents from 1855 onward, developing adjustable metal-bodied bench planes featuring a frog for blade angle control and lever caps for secure fastening, which became the basis for modern production.^[37] These innovations improved precision and ease of use, transitioning from artisanal wooden planes to mass-manufactured iron models.^[38] The primary components of a woodworking plane include the body, which provides stability and guides the blade across the wood; the blade, or iron, a thin steel cutter sharpened to remove shavings; the frog, an adjustable wedge-shaped seat that sets the blade's protrusion and bevel angle, typically 45 degrees for bench planes; and the tote, a rear handle for grip during use.^[33] A cap iron, or chipbreaker, attaches to the blade's back to curl and break shavings, reducing tear-out on the wood surface.^[36] The sole, the flat bottom of the body, ensures even planing, while the mouth—an opening at the front—controls shaving thickness. Blade sharpening is critical, involving grinding the primary bevel to approximately 25 degrees and honing a micro-bevel at 30 degrees for optimal cutting without excessive resistance.^[38] Maintenance includes flattening the sole on abrasive stones and ensuring the blade seats squarely against the frog for straight cuts.^[34] Common types of woodworking planes fall into bench and specialized categories, each suited to specific tasks. Bench planes, used at a workbench for general stock preparation, include the jack plane (typically 14-16 inches long), a versatile roughing tool with a slightly cambered blade for rapid material removal; the smoothing plane (about 9 inches), for final surface refinement with a fine mouth opening; and longer jointer planes (22-30 inches) for straightening edges.^[33] Block planes, compact (6-7 inches) and adjustable for low-angle cuts (often 12-20 degrees), excel at trimming end grain and chamfers without tear-out.^[36] The spokeshave, a small handheld plane with twin handles, is ideal for shaping curves on chair legs or bow staves, allowing two-handed control for contoured work.^[35] Effective usage requires planing in the direction of the wood grain—downhill along the fiber slope—to minimize tear-out, where fibers lift instead of shearing cleanly.^[39] Setup involves adjusting the blade for minimal protrusion (0.001-0.003 inches) and a slight lateral camber on jack planes to avoid rounded edges on wide boards.^[38] Safety emphasizes a razor-sharp blade, which reduces pushing force and slippage risk; users should secure workpieces in vises, wear eye protection, and avoid forcing the tool against cross-grain.^[34] Proper stance and body weight distribution enhance control, with diagonal strokes often used initially to level uneven surfaces before straight passes. Hand planes hold enduring cultural significance in carpentry as symbols of craftsmanship, enabling precise, tactile work that fosters skill transmission across generations.^[33] From medieval guilds to modern artisanal traditions, they embody the patience and expertise of woodworkers, contrasting with industrialized planing machines for large-scale production.^[36] Despite the rise of power tools in the 20th century, hand planes remain prized for their role in fine furniture and restoration, preserving techniques that prioritize quality over speed in contemporary maker movements.^[38]

Planing machine

A planing machine is a stationary power tool used in woodworking and metalworking to produce flat surfaces on large workpieces through the action of reciprocating or rotating cutters that remove material in a linear motion.^[40] Unlike jointers, which primarily square edges and flatten one face of a board, planing machines focus on surfacing broad areas or achieving uniform thickness across the material.^[41] These machines evolved from manual woodworking planes as industrial-scale alternatives for efficient processing of lumber and metal parts.^[42] Planing machines emerged during the 19th-century Industrial Revolution, driven by the need to mechanize woodworking for mass production. American inventor William Woodworth patented the first practical steam-powered planing machine in 1828, featuring two long blades mounted in a rotating cylinder to plane, tongue, groove, and dress boards simultaneously.^[43] This innovation, initially developed for flooring and millwork, significantly boosted lumber processing efficiency in emerging factories.^[44] Common types include jointer-planer combinations suitable for small workshops, where a single cutterhead serves dual purposes by flipping the machine between modes for edge jointing and thickness planing.^[45] Thickness planers, also known as surfacers, use a rotating cutterhead to reduce board depth uniformly, producing parallel faces ideal for dimensioning lumber.^[46] In metalworking, open-side planers accommodate oversized parts, employing a reciprocating table and single-point tool for heavy-duty surfacing of castings or forgings.^[47] Operation involves feeding the workpiece through the machine at controlled rates while the cutterhead spins to shear off material; typical feed rates range from 16 to 31 feet per minute, depending on wood hardness and desired finish quality.^[48] Helical cutterheads, equipped with carbide inserts arranged in a spiral pattern, commonly operate at 5,000 RPM to minimize tearout and noise compared to straight-knife designs.^[49] Snipe—unwanted gouges at board ends—is prevented by adjusting infeed and outfeed table heights to maintain consistent contact with the cutterhead, often elevating the outfeed slightly for smoother exits. These machines find primary applications in furniture manufacturing and millwork, where they prepare rough-sawn lumber for assembly by ensuring flat, consistent surfaces on tabletops, panels, and moldings.^[50] Safety features, mandated by OSHA standards established in the 1970s, include integrated dust collection systems to capture fine particulates that pose respiratory and fire hazards, with local exhaust ventilation required at the cutterhead to maintain air quality below permissible exposure limits.^[51] In the 2020s, modern planing machines increasingly incorporate CNC controls for automated precision, enabling programmable feed rates, multi-axis adjustments, and integration with CAD software for complex surfacing in both woodworking and metalworking operations.^[52]

Biology and Anatomy

Plane tree

The plane tree, belonging to the genus Platanus in the Platanaceae family, comprises large deciduous trees distinguished by their palmately lobed leaves and distinctive exfoliating bark that reveals a mottled pattern of cream, green, and brown hues.^[53] These trees are primarily native to regions spanning southeastern Europe to Pakistan and Indo-China, as well as eastern Canada to Guatemala, with the majority of species occurring in North and Central America and one in the eastern Mediterranean.^[53]^[54] Prominent species include the American sycamore (P. occidentalis), native to the eastern and central United States and parts of southeastern Canada; the Oriental plane (P. orientalis), indigenous to the eastern Mediterranean and southwestern Asia; and the London plane (P. × acerifolia), a hybrid between P. occidentalis and P. orientalis that originated in 17th-century England.^[55]^[54]^[56] The genus encompasses around seven species, though taxonomic debates suggest up to ten, all sharing adaptations for riparian and floodplain habitats.^[54] Plane trees typically reach heights of 30 to 40 meters, developing broad, irregular crowns with zigzag branching.^[57] They are monoecious, bearing inconspicuous yellowish male and reddish female flowers in separate but co-occurring pendulous spherical heads during spring.^[58] The female flowers develop into spherical fruit clusters containing numerous achenes, each equipped with persistent hairy styles that function as wings for wind dispersal, releasing seeds in autumn.^[57] The bark's exfoliation not only provides aesthetic appeal but also aids in shedding pollutants in urban settings.^[54] Widely cultivated as shade trees in urban environments due to their tolerance of pollution, drought, and compacted soils, plane trees were extensively planted along Paris boulevards during the 19th-century redesign under Georges-Eugène Haussmann, enhancing city aesthetics and providing cooling shade.^[59] Their wood, valued for its fine grain and figuring, is used in veneer production, furniture, and joinery, while historical applications include boiling the bark in vinegar for medicinal extracts to treat ailments like toothaches and diarrhea.^[60]^[61]^[62] Ecologically, plane trees are fast-growing pioneers in wetland and riverine ecosystems, stabilizing banks and supporting biodiversity, though their abundant wind-pollinated flowers produce pollen that triggers allergic reactions in urban populations.^[63]^[64] They face threats from anthracnose (Apiognomonia veneta), a fungal disease causing leaf blight and cankers, with severe outbreaks documented since the early 20th century, exacerbated by cool, wet springs and leading to widespread defoliation in North America and Europe.^[65]^[66]

Anatomical plane

Anatomical planes are imaginary flat surfaces that divide the human body into sections to facilitate the description, location, and orientation of internal structures relative to the standard anatomical position, in which the body stands upright facing forward, with arms at the sides and palms facing forward.^[67] These planes provide a standardized framework for anatomical study, medical imaging, and clinical procedures, ensuring consistent communication among healthcare professionals.^[68] The three cardinal anatomical planes are the sagittal, coronal, and transverse planes. The sagittal plane is a vertical plane that divides the body into left and right portions; when it passes through the midline, it is called the median or midsagittal plane, creating symmetrical halves.^[69] The coronal, or frontal, plane is another vertical plane that separates the body into anterior (front) and posterior (back) sections.^[68] The transverse, also known as horizontal or axial, plane cuts the body horizontally into superior (upper) and inferior (lower) parts.^[68] Additionally, oblique planes intersect the body at angles not aligned with the cardinal planes, allowing for specialized views of structures that do not conform to standard orientations./02:_Medical_Language_Related_to_the_Whole_Body/2.07:_Body_Planes) The use of anatomical planes was standardized during the 19th century as part of broader efforts to systematize human anatomy, with key contributions from texts like the first edition of Gray's Anatomy published in 1858, which helped establish consistent terminology for positions and orientations.^[70] In medical imaging, such as computed tomography (CT) and magnetic resonance imaging (MRI), scans are typically acquired and reconstructed along these planes to provide clear, comparable views of organs and tissues; for example, axial slices align with the transverse plane for whole-body assessments. They also guide surgical planning by enabling precise visualization of target areas, as in preoperative CT or MRI evaluations for tumor resection.^[71] Descriptive terms like "mid-sagittal view" rely on these planes to specify orientations in reports and diagrams. In kinesiology, anatomical planes classify human movements: flexion and extension occur primarily in the sagittal plane, abduction and adduction in the coronal plane, and rotation in the transverse plane, aiding analysis of biomechanics in activities like walking or sports.^[72] In embryology, these planes describe the positioning and development of embryonic structures, such as organ locations within the uterus and the reorganization of cell layers during gastrulation, where the establishment of body axes aligns with sagittal, coronal, and transverse divisions to form the three germ layers.^[73]

Maritime Transport

Planing hull

A planing hull is a boat hull shape designed to generate hydrodynamic lift, allowing the vessel to rise partially out of the water and skim across the surface at higher speeds, where the majority of the boat's weight is supported by dynamic forces rather than static buoyancy.^[74] This contrasts with displacement hulls, which remain fully submerged and rely on buoyancy for support at all speeds. Planing typically begins at speeds exceeding 15 knots, depending on the hull's length, weight, and power, enabling reduced drag and higher velocities compared to displacement modes.^[75] The development of planing hulls emerged in the late 19th century, with early experiments by naval architect Nathanael Herreshoff, who by 1876 had created prototypes featuring a sharp bow and broad, flat aft sections to facilitate lift.^[76] The concept advanced significantly in the early 20th century with the invention of the hydroplane, a specialized planing form credited to American designer William Henry Fauber, whose 1909 designs integrated hard chines and stepped hulls for enhanced speed.^[77] Post-World War II, surplus aircraft engines and materials spurred widespread adoption in powerboating, transforming recreational and racing vessels.^[78] Mechanically, a planing hull transitions from displacement mode—at low speeds, where it plows through the water—to a semi-planing or full planing state as velocity increases, with the bow lifting and the stern settling to create a flatter running surface.^[79] This shift relies on hull geometry, such as V-shaped or flat-bottom designs, which deflect water downward to produce upward lift via Bernoulli's principle and pressure differences.^[80] However, rapid planing can risk propeller cavitation, where low-pressure zones on the blades cause water vapor bubbles to form and collapse, potentially eroding metal and reducing thrust if the propeller is improperly positioned relative to the hull's trim.^[81] Common types include deep-V hulls, which feature a sharp deadrise angle (around 20-24 degrees) for better stability and wave-cutting in rough conditions, ideal for offshore racing, and flat-bottom or warped-plane hulls with minimal deadrise for quick planing on calm waters.^[82] Since the 1950s, fiberglass construction has dominated these designs, offering lightweight strength and ease of molding complex shapes, as pioneered by builders like Hinckley Yachts.^[83] Planing hulls are widely applied in recreational speedboats for efficient high-speed cruising and in competitive racing, such as the APBA Gold Cup (first held in 1904, with hydroplanes first competing successfully from 1911).^[84] At planing speeds, they achieve significant drag reduction—up to 50% less resistance than equivalent displacement hulls—improving fuel efficiency for short, fast transits despite higher overall consumption at idle or transition phases.^[85]

Hydroplane

A hydroplane is a lightweight, high-speed planing boat characterized by minimal displacement and a specialized hull shape optimized for extreme velocities, often exceeding 200 miles per hour on straightaways.^[86] These vessels operate on the principle of planing hulls, lifting onto the water surface to reduce drag. The hull typically incorporates steps—transverse notches that trap air and minimize the wetted surface area, enhancing lift and efficiency at high speeds.^[87] The origins of the hydroplane trace back to the 1870s, when British engineer Sir John Isaac Thornycroft developed the first experimental planing craft, such as his 1877 design, to achieve higher speeds by reducing hull immersion.^[88] Modern unlimited-class hydroplanes emerged in 1911 during the APBA Gold Cup race, where early step-hydro designs like MIT II competed, marking the shift to dedicated racing forms.^[89] The iconic Miss America series, built by Garfield Wood in the 1920s and 1930s, further advanced the type; starting with Miss America I in 1920 powered by Liberty engines, the fleet evolved to multi-engine configurations, setting multiple speed records and popularizing the stepped, sponson-equipped layout.^[90] Key design features include the three-point configuration, where the hull contacts the water only at the tips of two forward sponsons and the stern pad, minimizing resistance while providing stability.^[91] Powerplants transitioned from supercharged piston engines, such as Liberty and Allison V-12s in the mid-20th century, to gas turbines introduced competitively in the 1970s, with the first turbine victory in 1982 offering greater reliability and power output up to 2,500 horsepower.^[92] Following a series of driver fatalities in the 1980s, including the death of Dean Chenoweth in 1982, safety enhancements were implemented, including fully enclosed cockpits with integrated roll cages bonded to the chassis for occupant protection during flips and impacts.^[93]^[94] Hydroplane racing centers on the APBA Unlimited Hydroplane Championship, sanctioned by the American Power Boat Association, featuring oval-course events on rivers and lakes with heats determining national points.^[95] Chip Hanauer holds multiple records, including a one-lap course speed of 154.573 miles per hour set in 1990 during qualifying at Las Vegas, exemplifying the sport's emphasis on precision at high velocities.^[96] While racing hydroplanes prioritize unlimited power and speed, recreational variants include smaller runabouts designed for personal use, such as three-point hydroplanes seating four with outboard motors for leisurely high-speed outings on lakes.^[97] In the 2020s, environmental adaptations have emerged with electric prototypes, like the E1 Series Racebird, an all-electric foiling hydroplane developed for sustainable racing with hydrofoil-assisted planing and battery-powered propulsion, which launched its inaugural season in 2023 and held events through 2025.^[98]^[99]

Arts and Entertainment

Film and television

Plane is a 2023 American action thriller film directed by Jean-François Richet.^[100] The story follows pilot Brodie Torrance (Gerard Butler), who crash-lands a passenger plane on a remote island in the fictional Mutara region of the Philippines' Sulu archipelago after an electrical storm disables the aircraft, stranding passengers in hostile territory amid a separatist conflict.^[101] Teaming with convicted passenger Louis Gaspard (Mike Colter), Torrance fights to protect survivors from militants while awaiting rescue.^[100] The film was released theatrically in the United States on January 13, 2023, by Lionsgate, and grossed $74.5 million worldwide against a $25 million budget.^[100] Principal photography took place primarily in Puerto Rico, with locations in the San Juan metropolitan area doubling for the island setting, alongside some scenes in California.^[102] Critics praised its high-octane action sequences and Butler's performance, earning a 78% approval rating on Rotten Tomatoes based on 176 reviews.^[103] Planes is a 2013 American 3D computer-animated sports comedy film produced by Disneytoon Studios and released by Walt Disney Pictures.^[104] Directed by Klay Hall, it serves as a spin-off from Pixar's Cars franchise, centering on Dusty Crophopper (voiced by Dane Cook), a small-town crop-dusting plane with a fear of heights who dreams of competing in the around-the-world Leg of the Sky Rally race.^[104] Supported by a mentor naval aviator (voiced by Val Kilmer) and friends, Dusty overcomes his limitations to pursue his passion.^[104] The voice cast includes Carlos Alazraqui, Priyanka Chopra, and John Ratzenberger.^[104] A sequel, Planes: Fire & Rescue (2014), directed by Bobs Gannaway, follows Dusty transitioning to aerial firefighting after discovering engine damage, joining a team led by helicopter Blade Ranger (voiced by Ed Harris).^[105] While Planes received mixed reviews from critics (26% on Rotten Tomatoes from 121 reviews), it appealed to families for its uplifting underdog story and vibrant animation, garnering a 49% audience score.^[106] In television, aviation peril tropes involving planes are recurrent motifs, often exploring survival, time anomalies, and isolation. The second-season episode "The Odyssey of Flight 33" from The Twilight Zone (1961), written by Rod Serling, depicts Global Airlines Flight 33 en route from London to New York encountering mysterious turbulence that propels it back through time to the prehistoric era, forcing the crew to decide whether to attempt a return to 1961 at the risk of further displacement.^[107] The episode aired on February 24, 1961, and is noted for its tense, dialogue-driven suspense without a traditional resolution.^[107] The ABC series Lost (2004–2010) prominently features a plane crash as its central inciting incident and recurring motif across multiple episodes. In the pilot episodes "Pilot, Part 1" and "Pilot, Part 2," Oceanic Airlines Flight 815 breaks apart mid-air due to electromagnetic interference from a nearby island, scattering survivors across a mysterious tropical location where they confront supernatural elements and interpersonal conflicts.^[108] The crash wreckage recurs in later episodes, such as the season 2 finale "Live Together, Die Alone," symbolizing the characters' entrapment and the show's themes of fate and redemption, with the event depicted from varying perspectives to reveal inconsistencies in the narrative.^[109] Created by J.J. Abrams, Damon Lindelof, and Jeffrey Lieber, Lost uses the plane crash to launch its ensemble survival drama, influencing subsequent aviation-themed storytelling in media.

Music

In music, the term "plane" appears in various song titles, band names, and niche theoretical contexts, often evoking themes of flight, escape, or spatial abstraction. One prominent example is "Paper Planes," a 2007 single by British-Sri Lankan artist M.I.A. (Mathangi Arulpragasam) from her album Kala. The track blends alternative hip hop and electro elements, sampling the guitar riff from The Clash's 1982 song "Straight to Hell" to underscore its critique of immigration stereotypes and economic aspirations among refugees.^[110]^[111] Lyrics like "I fly like paper, get high like planes" juxtapose playful imagery with darker undertones of border crossings and visa struggles, reflecting M.I.A.'s own experiences as a Tamil refugee.^[112] The song achieved commercial success, peaking at No. 4 on the Billboard Hot 100 in 2008 and earning a Grammy nomination for Record of the Year in 2009.^[110] Its cultural resonance extended to media, notably featuring in the 2008 film Pineapple Express, which amplified its reach in popular soundtracks.^[113] Other compositions with "plane" motifs include variants like "Aeroplane" by Red Hot Chili Peppers, a 1995 funk rock track from their album One Hot Minute that uses aviation as a metaphor for personal liberation and hedonism, with lyrics penned by Anthony Kiedis drawing from his recovery journey.^[114] In ambient music, Brian Eno's 1978 album Ambient 1: Music for Airports incorporates ethereal soundscapes designed to evoke the serenity of flight and airport environments, originally conceived as installation pieces to calm passengers amid the anxiety of travel.^[115] Eno's generative approach, using looped tapes of piano and synths, creates immersive "planes" of sound that mimic the drift of aircraft, influencing subsequent ambient works focused on spatial and aerial themes.^[116] Band names incorporating "plane" also contribute to the motif, such as Planes Mistaken for Stars, an American post-hardcore and emo outfit formed in Peoria, Illinois, in 1997 and later based in Denver, Colorado. Active until the death of vocalist/guitarist Gared O'Donnell in 2021, after which the band went on hiatus, the band released albums like Mercy (2006) and Prey (2016), blending raw emotional lyrics with aggressive riffs to explore themes of loss and resilience, often evoking transient journeys akin to mistaken aerial sightings.^[117] In 2024, the band released a final posthumous album, Do You Still Love Me?, featuring recordings by O'Donnell. Their discography, spanning punk and hardcore influences, garnered a cult following in underground scenes.^[118] In musical terminology, "plane" occasionally refers to conceptual layers in harmonic or structural analysis, such as the "harmonic plane" denoting levels of consonance and dissonance in composition, though this usage is rare and not standardized in mainstream theory.^[119] For instance, some analyses model harmonic hierarchies as geometric planes or trees to visualize pitch relationships, prioritizing relational depth over linear progression.^[120] This abstract application underscores "plane" as a tool for understanding multidimensional sound organization in experimental and academic contexts.

Places

Settlements

Plane is a small village in the Plzeň-North District of the Plzeň Region in the Czech Republic. Comprising the hamlets of Vrážné, Ondřejov, Korýtka, and Pláně itself, it lies approximately 20 km north of Plzeň in the scenic Plaská pahorkatina landscape. The population was approximately 261 as of the 2021 census.^[121]^[122]^[123] The name "Pláně" derives from the Czech word for flat terrain. Post-1990s migration patterns have led to gradual depopulation, reflecting broader rural decline in the Czech Republic, with residents moving to urban centers like Plzeň for employment opportunities.^[121]

Natural features

Plane Table is a flat-topped plateau in the Wright Valley of Victoria Land, Antarctica, rising to an elevation of approximately 1,531 m above sea level. Mapped during U.S. Antarctic expeditions in the 1960s using plane-table surveying methods, it forms part of the rugged terrain of the McMurdo Dry Valleys region, characterized by minimal precipitation and extreme cold. A short, tapering glacier descends from its north side, extending partway down the south wall of Wright Valley, highlighting the area's glacial geomorphology.^[124] In geographical nomenclature, "plane" occasionally denotes flat or level landforms, akin to plains or plateaus shaped by long-term erosion processes. Terrestrial planes, such as those formed by glacial or fluvial action, represent low-relief surfaces resulting from the wearing down of higher terrain over millions of years; for instance, glacial plains emerge from the deposition of till and outwash materials during ice age retreats. These features contrast with more elevated plateaus, which maintain greater height due to resistant bedrock layers. In hydrology, floodplains are the flat areas adjacent to rivers that are periodically inundated, facilitating sediment deposition and nutrient cycling essential for ecosystem health. Formation of such floodplains occurs through repeated flooding that levels the landscape, with examples including the broad alluvial plains along major river systems where erosion and deposition balance over geological time scales.

Esotericism and Philosophy

Plane of existence

In philosophical and metaphysical traditions, a plane of existence refers to a hierarchical realm of being, ranging from the material and physical to increasingly subtle spiritual levels, where reality emanates from a singular divine source. This concept originated in Neoplatonism, developed by Plotinus in the 3rd century CE, who described a structured cosmos emerging through emanation from the One—an ineffable, transcendent unity beyond all multiplicity. In Plotinus' system, as outlined in the Enneads, the hierarchy descends from the One to the Intellect (Nous), the World Soul, and finally the sensible world of matter, forming interconnected levels of reality where lower planes participate in the higher ones without diminishing the source.^[125]^[126] Hindu cosmology elaborates this idea through the concept of lokas, fourteen distinct planes or worlds described in ancient texts such as the Puranas (composed circa 300–1500 CE), which divide existence into seven upper realms (vyahrtis) and seven lower ones (patalas). The physical plane, known as Bhuloka, represents the earthly realm inhabited by humans, while the highest plane, Brahmaloka, is the abode of Brahma, characterized by ultimate spiritual purity and proximity to the divine. These lokas form a vertical axis of cosmic order, with beings ascending or descending based on karma and spiritual merit, as detailed in scriptures like the Bhagavata Purana.^[127]^[128] In Western esotericism, Helena Blavatsky's Theosophy (founded 1875) synthesized Eastern and Western ideas into a system of seven fundamental planes of existence, each subdivided into seven subplanes, progressing from the densest to the most ethereal. These include the physical plane (material world), astral plane (realm of emotions and forms), and mental plane (world of thought and intellect), with higher planes like the buddhic and atmic inaccessible to ordinary consciousness. Blavatsky posited that spiritual evolution involves raising one's vibrational frequency to ascend these planes, allowing alignment with subtler realities and ultimate enlightenment, as articulated in works like The Secret Doctrine.^[129] Modern interpretations often draw speculative analogies between these metaphysical planes and concepts in quantum physics, such as multiverses or parallel realities, suggesting hidden dimensions beyond empirical observation, though such links remain unverified and criticized for overextending scientific principles. In New Age self-help contexts, the idea of "raising your plane" emphasizes personal practices like meditation to elevate vibrational states and access higher realms of consciousness and well-being.^[130]^[131] Critics argue that the notion of planes of existence lacks empirical evidence, relying instead on subjective experiences and ancient texts unverifiable by scientific methods, which undermines claims of objective reality. Additionally, the syncretic blending of diverse cultural traditions—such as Hindu lokas with Neoplatonic emanation in Theosophy—raises concerns about diluting original contexts and imposing Western frameworks on Eastern philosophies, potentially leading to misrepresentations.^[132]

Astral plane

The astral plane is a concept in Western esotericism and occultism referring to a non-physical dimension of reality, posited as an intermediate realm between the physical world and higher spiritual planes. It is closely associated with the astral body, a subtle counterpart to the physical form, through which consciousness can travel via astral projection or after death. This plane is characterized by its responsiveness to thought and emotion, where mental impressions manifest as tangible forms, creating a dynamic environment shaped by the perceiver's inner state.^[133] In Theosophical doctrine, as articulated by C.W. Leadbeater in his 1895 monograph The Astral Plane: Its Scenery, Inhabitants, and Phenomena, the astral plane serves as the repository of human desires, passions, and subconscious impulses. Leadbeater describes it as a vast, interpenetrating realm enveloping the Earth, divided into seven sub-planes of increasing refinement: the lowest sub-planes teem with gross, chaotic energies tied to material vices, while the higher ones exhibit greater harmony and luminosity, approaching the mental plane. He emphasizes its fluid scenery, where landscapes, structures, and natural features can dissolve and reform instantaneously, unlike the relative stability of the physical world. For instance, Leadbeater describes the scenery of the astral plane, particularly its lower sub-planes, as resembling the physical world but fluid and responsive to thought and emotion, allowing landscapes to form and dissolve rapidly.^[133]^[134] The inhabitants of the astral plane, according to Leadbeater and other Theosophical sources, include a diverse array of entities beyond human souls. These encompass the astral bodies of living individuals during sleep or projection, the disembodied spirits of the recently deceased navigating their post-mortem experiences, artificial thought-forms created by strong emotions or rituals, and non-human beings such as nature spirits (elementals) or devas that oversee natural processes. Phenomena on this plane include clairvoyant visions, apparitions, and interactions with these entities, often experienced as vivid dreams or out-of-body travels. Leadbeater warns of the plane's deceptive qualities, where illusions born of fear or desire can mislead the unprepared traveler, underscoring the need for spiritual discipline to navigate it effectively.^[133]^[135] This Theosophical framework draws from earlier occult traditions, including Neoplatonism and medieval mysticism, but gained widespread influence through the works of Helena Blavatsky, who integrated Eastern concepts like the subtle realms (sūkṣma-loka) from Hindu and Buddhist cosmology into Western esotericism. Blavatsky's The Secret Doctrine (1888) portrays the astral plane as the "astral light," a universal etheric medium recording all human actions and thoughts, akin to Akasha in Vedic traditions. In contemporary scholarship, the concept has been re-examined through South Asian lenses, highlighting its parallels to non-dualistic planes in Tantra and Yoga, where it facilitates spiritual ascent beyond dualistic perception.^[136]

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Planes: Fire & Rescue (2014) - IMDb
Rating 5.9/10 (21,280) Planes: Fire and Rescue is about second chances. Dusty is a hot shot plane until one day he is at a crossroads in life, so he decides to join the world of fire ...Full cast & crew · Planes · Plot · Awards
[110]
Planes | Rotten Tomatoes
Rating 26% (121) Dusty is a small-town plane who dreams of one day competing as a high-flying air racer. However, poor Dusty has two strikes against him.Planes: Fire & Rescue · Cast and Crew · 121 Reviews
[111]
"The Twilight Zone" The Odyssey of Flight 33 (TV Episode 1961)
Rating 7.8/10 (3,773) John Anderson stars as the captain of Global Jetliner 33, which is a passenger jet en route from London to New York in what was a routine flight.Full cast & crew · John Anderson · Mr. Dingle, the Strong
[112]
"Lost" Pilot: Part 1 (TV Episode 2004) - IMDb
Rating 9.1/10 (17,793) Forty-eight survivors of an airline flight from Australia, bound for the U.S., crash-land on an unknown island 1000 miles off course and struggle to survive.
[113]
Lost (TV Series 2004–2010) - Episode list - IMDb
S1.E1 ∙ Pilot: Part 1 ... Forty-eight survivors of an airline flight originating from Australia, bound for the U.S., which crash-lands onto an unknown island 1000 ...Pilot: Part 2 · "Lost" Pilot · Lost · The Constant
[114]
Diplo on Why M.I.A.'s "Paper Planes" Is One of His Favorites - Billboard
Mar 13, 2020 · Diplo adds that “Paper Planes” was one of his favorite records to produce, and that it even earned him a Grammy nomination for record of the ...
[115]
The Meaning Behind M.I.A.'s Punk-Rock Influenced Hit "Paper Planes"
Nov 7, 2023 · For the eleventh song “Paper Planes,” though, which peaked at No. 4 on the Billboard Hot 100, the multi-dimensional artist drew influence from ...
[116]
Paper Planes by M.I.A. - Songfacts
Paper Planes by M.I.A. song meaning, lyric interpretation, video and chart position. ... performed the song on the David Letterman Show in September 2007, when ...
[117]
https://www.discogs.com/artist/255492-Planes-Mistaken-For-Stars
[118]
The 46 Best Songs About Flying And Planes - uDiscover Music
The 46 Best Songs About Flying And Planes · 46: Dierks Bentley: Drunk on a Plane · 45: Red Hot Chilli Peppers – The Zephyr Song · 44: Bowling for Soup – Turbulence.
[119]
The 50 Best Ambient Albums of All Time | Pitchfork
Sep 26, 2016 · Field recordings—planes high overhead, children laughing, the gentle ... Brian Eno: Ambient 1: Music for Airports (1978). Eno may not ...
[120]
Unsettling Brian Eno's Music for Airports | Twentieth-Century Music
Jul 25, 2017 · ... planes take off through the smoked windows'.Footnote Yet Eno's ... Although he continued to use Ambient music in site-specific audiovisual ...
[121]
https://www.obec-plane.cz/
[122]
Rank Your Records: Planes Mistaken For Stars' Gared O'Donnell
May 7, 2020 · Throughout the early 2000s, Planes were hard partying road dogs, hopping on tours with anyone who would have them, from Mastodon to The Ataris.Missing: history | Show results with:history
[123]
https://www.britannica.com/place/Plzen
[124]
[PDF] The Geometry of Melodic, Harmonic, and Metrical Hierarchy
Property (1) for musical hierarchies implies that they correspond more specifically to plane trees, trees in which the children of each node are ordered from ...
[125]
Obec Pláně - Oficiální stránka obce Pláně
Obec Pláně. Obec Pláně, kterou tvoří čtyři vesnice Vrážné, Ondřejov, Korýtka a vlastní Pláně, leží 20 km severně od Plzně v krásné krajině Plaské pahorkatiny.Missing: počet obyvatel 2021
[126]
Pláně - Počet obyvatel - Obyvatelé Česka
Počet obyvatel v obci Pláně, Plzeň-sever ; 2022, 268 ; 2021, 261 ; 2020, 262 ; 2019, 267.
[127]
Plzen | Brewing, Beer Culture, & Architecture | Britannica
Oct 7, 2025 · Plzen is a city in western Czech Republic. It is famous for its industrial and brewing traditions.Missing: Plane village
[128]
Explore the Plzeň Region from the skies! | Radio Prague International
May 6, 2024 · Area: 7,561 km2, Czechia's third-largest region; Population: approx. 600,000; Regional capital: Plzeň, population around 180,000; Pilsner ...Missing: Plane village
[129]
Vratsa | Balkan Mountains, Danube River, History | Britannica
Vratsa, town, northwestern Bulgaria. It is situated in the northern foothills of the western Balkan Mountains at the point where the Leva River emerges.
[130]
SCAR Composite Gazetteer - Australian Antarctic Data Centre
A short, tapering glacier on the N side of Plane Table that extends part way down the S wall of Wright Valley, Victoria Land. Named in 1997 by US-ACAN in ...
[131]
Plotinus - Stanford Encyclopedia of Philosophy
Sep 25, 2024 · Plotinus is generally regarded as the founder of Late Antique Platonism, sometimes termed “Neoplatonism”, a school of thought that, while ...Missing: planes | Show results with:planes
[132]
[PDF] Plotinus' Sympatheia and Its Philosophical Foundations
accidental but the natural expressions of the One's emanation into all levels of existence. ... For Plotinus, the cosmos is an emanation of the One, and ...
[133]
(DOC) Hindu cosmology - Academia.edu
" Lower seven Lokas in Puranas Puranas: 14 lokas The later Puranic view asserts that the Universe is created, destroyed, and re-created in an eternally ...
[134]
[PDF] Towards the Systematic Cross-Civilizational Comparison
Image Description: Showing 14 Lokas (Worlds) as per Hindu beliefs. Source ... Indologist and scholar of Hindu studies Rajiv Malhotra, in his work “Being Different ...
[135]
Planes in Theosophy
The word “plane” means an extension of space. There are multiple planes of nature, such as physical, astral, mental, buddhic, ātmic, and other finer planes.
[136]
Toward a Transformative Hermeneutics of Quantum Gravity
26 New Age interpretations of these insights from quantum physics have often gone overboard in unwarranted speculation, but the general soundness of the ...<|separator|>
[137]
The Spiritual Awakening of the Third Eye - Theosophical Society
We cannot see or seek the soul with our normal vision, but with our inner vision, we can know and experience its existence on higher planes. Quantum physics ...
[138]
Physics in Metaphysics -A Conceptual Framework for the Cosmos
Aug 24, 2024 · 1. Lack of Empirical Evidence. Response: The lack of empirical evidence in theories that bridge physical and metaphysical · 2. Ambiguity in ...
[139]
https://www.gutenberg.org/ebooks/21080
[140]
The astral plane : its scenery, inhabitants, and phenomena
May 16, 2006 · The astral plane : its scenery, inhabitants, and phenomena. by ... FULL TEXT download · download 1 file · HOCR download · download 1 file.
[141]
The Astral Light - The Theosophical Society
The astral light is with regard to the material realms of the solar system the copy or reflection of what the akasa is in the spiritual realms.
[142]
Re-orienting the Astral Plane | Center for the Study of World Religions
Sep 24, 2024 · The astral plane refers to non-physical worlds or planes, where astral beings inhabit infinite planes. South Asian sources suggest re-orienting ...