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Planar Reentry Equations
The planar reentry equations are the equations of motion governing the unpowered reentry of a spacecraft, based on the assumptions of planar motion and constant mass, in an Earth-fixed reference frame. Definition The equations are given by:where the quantities in these equations are: * V is the velocity * \gamma > 0 is the flight path angle * h is the altitude * \rho is the atmospheric density * \beta is the ballistic coefficient * g is the gravitational acceleration * r = r_ + h is the radius from the center of a planet with equatorial radius r_ * L/D is the lift-to-drag ratio * \sigma is the bank angle of the spacecraft. Simplifications Allen-Eggers solution Harry Allen and Alfred Eggers, based on their studies of ICBM trajectories, were able to derive an analytical expression for the velocity as a function of altitude. They made several assumptions: # The spacecraft's entry was purely ballistic (L = 0). # The effect of gravity is small compared to drag, and can be ig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equations Of Motion
In physics, equations of motion are equations that describe the behavior of a physical system in terms of its motion as a function of time. More specifically, the equations of motion describe the behavior of a physical system as a set of mathematical functions in terms of dynamic variables. These variables are usually spatial coordinates and time, but may include momentum components. The most general choice are generalized coordinates which can be any convenient variables characteristic of the physical system. The functions are defined in a Euclidean space in classical mechanics, but are replaced by curved spaces in relativity. If the dynamics of a system is known, the equations are the solutions for the differential equations describing the motion of the dynamics. Types There are two main descriptions of motion: dynamics and kinematics. Dynamics is general, since the momenta, forces and energy of the particles are taken into account. In this instance, sometimes the term ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exponential Atmosphere
The barometric formula is a formula used to model how the air pressure (or air density) changes with altitude. Pressure equations There are two equations for computing pressure as a function of height. The first equation is applicable to the atmospheric layers in which the temperature is assumed to vary with altitude at a non null lapse rate of L_b: P = P_ \left 1 - \frac (h - h_)\right The second equation is applicable to the atmospheric layers in which the temperature is assumed not to vary with altitude (lapse rate is null): P = P_b \exp \left frac\right/math> where: *P_b = reference pressure *T_ = reference temperature ( K) *L_ = temperature lapse rate (K/m) in ISA *h = geopotential height at which pressure is calculated (m) *h_b = geopotential height of reference level ''b'' (meters; e.g., ''hb'' = 11 000 m) *R^* = universal gas constant: 8.3144598 J/(mol·K) *g_0 = gravitational acceleration: 9.80665 m/s2 *M = molar mass of Earth's air: 0.0289644 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hypersonic Flight
Hypersonic flight is flight through the atmosphere below altitudes of about at Hypersonic speed, speeds greater than Mach 5, a speed where Dissociation (chemistry), dissociation of air begins to become significant and high heat loads exist. Speeds over Mach 25 have been achieved below the thermosphere as of 2020. Hypersonic vehicles are able to maneuver through the atmosphere in a #Weapons, non-parabolic trajectory, but their aerodynamic heat loads need to be managed. History The first manufactured object to achieve hypersonic flight was the two-stage RTV-G-4 Bumper, Bumper rocket, consisting of a WAC Corporal second stage set on top of a V-2 rocket, V-2 first stage. In February 1949, at White Sands V-2 Launching Site, White Sands, the rocket reached a speed of , or about Mach 6.7. The vehicle, however, burned on atmospheric re-entry, and only charred remnants were found. In April 1961, Russian Major Yuri Gagarin became the first human to travel at hypersonic speed, dur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Watt
The watt (symbol: W) is the unit of Power (physics), power or radiant flux in the International System of Units (SI), equal to 1 joule per second or 1 kg⋅m2⋅s−3. It is used to quantification (science), quantify the rate of Work (physics), energy transfer. The watt is named in honor of James Watt (1736–1819), an 18th-century Scottish people, Scottish inventor, mechanical engineer, and chemist who improved the Newcomen engine with his own Watt steam engine, steam engine in 1776, which became fundamental for the Industrial Revolution. Overview When an object's velocity is held constant at one meter per second against a constant opposing force of one Newton (unit), newton, the rate at which Work (physics), work is done is one watt. \mathrm. In terms of electromagnetism, one watt is the rate at which electrical work is performed when a current of one ampere (A) flows across an electrical potential difference of one volt (V), meaning the watt is equivalent to the vo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convection
Convection is single or Multiphase flow, multiphase fluid flow that occurs Spontaneous process, spontaneously through the combined effects of material property heterogeneity and body forces on a fluid, most commonly density and gravity (see buoyancy). When the cause of the convection is unspecified, convection due to the effects of thermal expansion and buoyancy can be assumed. Convection may also take place in soft solids or mixtures where particles can flow. Convective flow may be Transient state, transient (such as when a Multiphasic liquid, multiphase mixture of oil and water separates) or steady state (see convection cell). The convection may be due to Gravity, gravitational, Electromagnetism, electromagnetic or Fictitious force, fictitious body forces. Convection (heat transfer), Heat transfer by natural convection plays a role in the structure of Earth's atmosphere, its oceans, and its Earth's mantle, mantle. Discrete convective cells in the atmosphere can be identified by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stagnation Point
In fluid dynamics, a stagnation point is a point in a flow field where the local velocity of the fluid is zero.Clancy, L.J. (1975), ''Aerodynamics'', Pitman Publishing Limited, London. The Bernoulli equation shows that the static pressure is highest when the velocity is zero and hence static pressure is at its maximum value at stagnation points: in this case static pressure equals stagnation pressure. The Bernoulli equation applicable to incompressible flow shows that the stagnation pressure is equal to the dynamic pressure and static pressure combined.Clancy, L.J. (1975), ''Aerodynamics'', Pitman Publishing Limited, London. In compressible flows, stagnation pressure is also equal to total pressure as well, provided that the fluid entering the stagnation point is brought to rest isentropically. A plentiful, albeit surprising, example of such points seem to appear in all but the most extreme cases of fluid dynamics in the form of the "no-slip condition" - the assumption that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
G-force
The g-force or gravitational force equivalent is a Specific force, mass-specific force (force per unit mass), expressed in Unit of measurement, units of standard gravity (symbol ''g'' or ''g''0, not to be confused with "g", the symbol for grams). It is used for sustained accelerations that cause a perception of weight. For example, an object at rest on Earth's surface is subject to 1 ''g'', equaling the conventional value of gravitational acceleration on Earth, about . More transient acceleration, accompanied with significant jerk (physics), jerk, is called Shock (mechanics), ''shock''. When the g-force is produced by the surface of one object being pushed by the surface of another object, the reaction force to this push produces an equal and opposite force for every unit of each object's mass. The types of forces involved are transmitted through objects by interior Stress (mechanics), mechanical stresses. Gravitational acceleration is one cause of an object's accelera ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mach Number
The Mach number (M or Ma), often only Mach, (; ) is a dimensionless quantity in fluid dynamics representing the ratio of flow velocity past a boundary to the local speed of sound. It is named after the Austrian physicist and philosopher Ernst Mach. \mathrm = \frac, where: * is the local Mach number, * is the local flow velocity with respect to the boundaries (either internal, such as an object immersed in the flow, or external, like a channel), and * is the speed of sound in the medium, which in air varies with the square root of the thermodynamic temperature. By definition, at Mach1, the local flow velocity is equal to the speed of sound. At Mach0.65, is 65% of the speed of sound (subsonic), and, at Mach1.35, is 35% faster than the speed of sound (supersonic). The local speed of sound, and hence the Mach number, depends on the temperature of the surrounding gas. The Mach number is primarily used to determine the approximation with which a flow can be treated as an i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hypersonic Speed
In aerodynamics, a hypersonic speed is one that exceeds five times the speed of sound, often stated as starting at speeds of Mach 5 and above. The precise Mach number at which a craft can be said to be flying at hypersonic speed varies, since individual physical changes in the airflow (like molecular dissociation and ionization) occur at different speeds; these effects collectively become important around Mach 5–10. The hypersonic regime can also be alternatively defined as speeds where specific heat capacity changes with the temperature of the flow as kinetic energy of the moving object is converted into heat. Characteristics of flow While the definition of hypersonic flow can be quite vague and is generally debatable (especially because of the absence of discontinuity between supersonic and hypersonic flows), a hypersonic flow may be characterized by certain physical phenomena that can no longer be analytically discounted as in supersonic flow. The peculiarities in hyperso ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scale Height
In atmospheric, earth, and planetary sciences, a scale height, usually denoted by the capital letter ''H'', is a distance ( vertical or radial) over which a physical quantity decreases by a factor of e (the base of natural logarithms, approximately 2.718). Scale height used in a simple atmospheric pressure model For planetary atmospheres, scale height is the increase in altitude for which the atmospheric pressure decreases by a factor of ''e''. The scale height remains constant for a particular temperature. It can be calculated by H = \frac, or equivalently, H = \frac, where : ''k''B = Boltzmann constant = : ''R'' = molar gas constant = 8.31446 J⋅K−1⋅mol−1 : ''T'' = mean atmospheric temperature in kelvins = 250 K for Earth : ''m'' = mean mass of a molecule : ''M'' = mean molar mass of atmospheric particles = 0.029 kg/mol for Earth : ''g'' = acceleration due to gravity at the current location The pressure (force per unit area) at a given altitu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intercontinental Ballistic Missile
An intercontinental ballistic missile (ICBM) is a ballistic missile with a range (aeronautics), range greater than , primarily designed for nuclear weapons delivery (delivering one or more Thermonuclear weapon, thermonuclear warheads). Conventional weapon, Conventional, Chemical weapon, chemical, and Biological agent, biological weapons can also be delivered with varying effectiveness, but have never been deployed on ICBMs. Most modern designs support multiple independently targetable reentry vehicle (MIRVs), allowing a single missile to carry several warheads, each of which can strike a different target. The Nuclear weapons of the United States, United States, Russia and weapons of mass destruction, Russia, China and weapons of mass destruction, China, France and weapons of mass destruction, France, India and weapons of mass destruction, India, the United Kingdom and weapons of mass destruction, United Kingdom, Nuclear weapons and Israel, Israel, and North Korea and weapons of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
