title: Polarization (waves)

text: Just considering electromagnetic waves, we note that the preceding discussion strictly applies to plane waves in a homogeneous isotropic non-attenuating medium, whereas in an anisotropic medium (such as birefringent crystals as discussed below) the electric or magnetic field may have longitudinal as well as transverse components. In those cases the electric displacement "D" and magnetic flux density "B" still obey the above geometry but due to anisotropy in the electric susceptibility (or in the magnetic permeability), now given by a tensor, the direction of "E" (or "H") may differ from that of "D" (or "B"). Even in isotropic media, so-called inhomogeneous waves can be launched into a medium whose refractive index has a significant imaginary part (or "extinction coefficient") such as metals; these fields are also not strictly transverse. Surface waves or waves propagating in a waveguide (such as an optical fiber) are generally "not" transverse waves, but might be described as an electric or magnetic transverse mode, or a hybrid mode.


title: Polarization (waves)

text: Even in free space, longitudinal field components can be generated in focal regions, where the plane wave approximation breaks down. An extreme example is radially or tangentially polarized light, at the focus of which the electric or magnetic field respectively is "entirely" longitudinal (along the direction of propagation).


title: Polarization (waves)

text: For longitudinal waves such as sound waves in fluids, the direction of oscillation is by definition along the direction of travel, so the issue of polarization is normally not even mentioned. On the other hand, sound waves in a bulk solid can be transverse as well as longitudinal, for a total of three polarization components. In this case, the transverse polarization is associated with the direction of the shear stress and displacement in directions perpendicular to the propagation direction, while the longitudinal polarization describes compression of the solid and vibration along the direction of propagation. The differential propagation of transverse and longitudinal polarizations is important in seismology.


title: Polarization (waves)

text: Polarization is best understood by initially considering only pure polarization states, and only a coherent sinusoidal wave at some optical frequency. The vector in the adjacent diagram might describe the oscillation of the electric field emitted by a single-mode laser (whose oscillation frequency would be typically 10 times faster). The field oscillates in the "x-y" plane, along the page, with the wave propagating in the "z" direction, perpendicular to the page.


title: Polarization (waves)

text: The first two diagrams below trace the electric field vector over a complete cycle for linear polarization at two different orientations; these are each considered a distinct "state of polarization" (SOP). Note that the linear polarization at 45° can also be viewed as the addition of a horizontally linearly polarized wave (as in the leftmost figure) and a vertically polarized wave of the same amplitude "in the same phase".


title: Polarization (waves)

text: Now if one were to introduce a phase shift in between those horizontal and vertical polarization components, one would generally obtain elliptical polarization as is shown in the third figure. When the phase shift is exactly ±90°, then "circular polarization" is produced (fourth and fifth figures). Thus is circular polarization created in practice, starting with linearly polarized light and employing a quarter-wave plate to introduce such a phase shift. The result of two such phase-shifted components in causing a rotating electric field vector is depicted in the animation on the right. Note that circular or elliptical polarization can involve either a clockwise or counterclockwise rotation of the field. These correspond to distinct polarization states, such as the two circular polarizations shown above.


title: Polarization (waves)

text: Of course the orientation of the "x" and "y" axes used in this description is arbitrary. The choice of such a coordinate system and viewing the polarization ellipse in terms of the "x" and "y" polarization components, corresponds to the definition of the Jones vector (below) in terms of those basis polarizations. One would typically choose axes to suit a particular problem such as "x" being in the plane of incidence. Since there are separate reflection coefficients for the linear polarizations in and orthogonal to the plane of incidence ("p" and "s" polarizations, see below), that choice greatly simplifies the calculation of a wave's reflection from a surface.


title: Polarization (waves)

text: Moreover, one can use as basis functions "any" pair of orthogonal polarization states, not just linear polarizations. For instance, choosing right and left circular polarizations as basis functions simplifies the solution of problems involving circular birefringence (optical activity) or circular dichroism.


title: Polarization (waves)

text: Consider a purely polarized monochromatic wave. If one were to plot the electric field vector over one cycle of oscillation, an ellipse would generally be obtained, as is shown in the figure, corresponding to a particular state of elliptical polarization. Note that linear polarization and circular polarization can be seen as special cases of elliptical polarization.


title: Polarization (waves)

text: A polarization state can then be described in relation to the geometrical parameters of the ellipse, and its "handedness", that is, whether the rotation around the ellipse is clockwise or counter clockwise. One parameterization of the elliptical figure specifies the orientation angle "ψ", defined as the angle between the major axis of the ellipse and the "x"-axis along with the ellipticity "ε" = "a/b", the ratio of the ellipse's major to minor axis. (also known as the axial ratio). The ellipticity parameter is an alternative parameterization of an ellipse's eccentricity formula_17 or the ellipticity angle, formula_18 formula_19 as is shown in the figure. The angle "χ" is also significant in that the latitude (angle from the equator) of the polarization state as represented on the Poincaré sphere (see below) is equal to ±2"χ". The special cases of linear and circular polarization correspond to an ellipticity "ε" of infinity and unity (or "χ" of zero and 45°) respectively.


title: Polarization (waves)

text: Full information on a completely polarized state is also provided by the amplitude and phase of oscillations in two components of the electric field vector in the plane of polarization. This representation was used above to show how different states of polarization are possible. The amplitude and phase information can be conveniently represented as a two-dimensional complex vector (the Jones vector):


title: Polarization (waves)

text: Here formula_21 and formula_22 denote the amplitude of the wave in the two components of the electric field vector, while formula_23 and formula_24 represent the phases. The product of a Jones vector with a complex number of unit modulus gives a different Jones vector representing the same ellipse, and thus the same state of polarization. The physical electric field, as the real part of the Jones vector, would be altered but the polarization state itself is independent of absolute phase. The basis vectors used to represent the Jones vector need not represent linear polarization states (i.e. be real). In general any two orthogonal states can be used, where an orthogonal vector pair is formally defined as one having a zero inner product. A common choice is left and right circular polarizations, for example to model the different propagation of waves in two such components in circularly birefringent media (see below) or signal paths of coherent detectors sensitive to circular polarization.


title: Polarization (waves)

text: Regardless of whether polarization state is represented using geometric parameters or Jones vectors, implicit in the parameterization is the orientation of the coordinate frame. This permits a degree of freedom, namely rotation about the propagation direction. When considering light that is propagating parallel to the surface of the Earth, the terms "horizontal" and "vertical" polarization are often used, with the former being associated with the first component of the Jones vector, or zero azimuth angle. On the other hand, in astronomy the equatorial coordinate system is generally used instead, with the zero azimuth (or position angle, as it is more commonly called in astronomy to avoid confusion with the horizontal coordinate system) corresponding to due north.


title: Polarization (waves)

text: Another coordinate system frequently used relates to the "plane of incidence". This is the plane made by the incoming propagation direction and the vector perpendicular to the plane of an interface, in other words, the plane in which the ray travels before and after reflection or refraction. The component of the electric field parallel to this plane is termed "p-like" (parallel) and the component perpendicular to this plane is termed "s-like" (from "senkrecht", German for perpendicular). Polarized light with its electric field along the plane of incidence is thus denoted "p-polarized", while light whose electric field is normal to the plane of incidence is called "s-polarized". "P" polarization is commonly referred to as "transverse-magnetic" (TM), and has also been termed "pi-polarized" or "tangential plane polarized". "S" polarization is also called "transverse-electric" (TE), as well as "sigma-polarized" or "sagittal plane polarized".


title: Polarization (waves)

text: Natural light, like most other common sources of visible light, is incoherent: radiation is produced independently by a large number of atoms or molecules whose emissions are uncorrelated and generally of random polarizations. In this case the light is said to be "unpolarized". This term is somewhat inexact, since at any instant of time at one location there is a definite direction to the electric and magnetic fields, however it implies that the polarization changes so quickly in time that it will not be measured or relevant to the outcome of an experiment. A so-called depolarizer acts on a polarized beam to create one which is actually "fully" polarized at every point, but in which the polarization varies so rapidly across the beam that it may be ignored in the intended applications.


title: Polarization (waves)

text: Unpolarized light can be described as a mixture of two independent oppositely polarized streams, each with half the intensity. Light is said to be "partially polarized" when there is more power in one of these streams than the other. At any particular wavelength, partially polarized light can be statistically described as the superposition of a completely unpolarized component and a completely polarized one. One may then describe the light in terms of the degree of polarization and the parameters of the polarized component. That polarized component can be described in terms of a Jones vector or polarization ellipse, as is detailed above. However, in order to also describe the degree of polarization, one normally employs Stokes parameters (see below) to specify a state of partial polarization.


title: Polarization (waves)

text: The transmission of plane waves through a homogeneous medium are fully described in terms of Jones vectors and 2×2 Jones matrices. However, in practice there are cases in which all of the light cannot be viewed in such a simple manner due to spatial inhomogeneities or the presence of mutually incoherent waves. So-called depolarization, for instance, cannot be described using Jones matrices. For these cases it is usual instead to use a 4×4 matrix that acts upon the Stokes 4-vector. Such matrices were first used by Paul Soleillet in 1929, although they have come to be known as Mueller matrices. While every Jones matrix has a Mueller matrix, the reverse is not true. Mueller matrices are then used to describe the observed polarization effects of the scattering of waves from complex surfaces or ensembles of particles, as shall now be presented.


title: Polarization (waves)

text: The Jones vector perfectly describes the state of polarization "and phase" of a single monochromatic wave, representing a pure state of polarization as described above. However any mixture of waves of different polarizations (or even of different frequencies) do "not" correspond to a Jones vector. In so-called partially polarized radiation the fields are stochastic, and the variations and correlations between components of the electric field can only be described statistically. One such representation is the coherency matrix:


title: Polarization (waves)

text: where angular brackets denote averaging over many wave cycles. Several variants of the coherency matrix have been proposed: the Wiener coherency matrix and the spectral coherency matrix of Richard Barakat measure the coherence of a spectral decomposition of the signal, while the Wolf coherency matrix averages over all time/frequencies.


title: Polarization (waves)

text: The coherency matrix contains all second order statistical information about the polarization. This matrix can be decomposed into the sum of two idempotent matrices, corresponding to the eigenvectors of the coherency matrix, each representing a polarization state that is orthogonal to the other. An alternative decomposition is into completely polarized (zero determinant) and unpolarized (scaled identity matrix) components. In either case, the operation of summing the components corresponds to the incoherent superposition of waves from the two components. The latter case gives rise to the concept of the "degree of polarization"; i.e., the fraction of the total intensity contributed by the completely polarized component.


title: Polarization (waves)

text: The coherency matrix is not easy to visualize, and it is therefore common to describe incoherent or partially polarized radiation in terms of its total intensity ("I"), (fractional) degree of polarization ("p"), and the shape parameters of the polarization ellipse. An alternative and mathematically convenient description is given by the Stokes parameters, introduced by George Gabriel Stokes in 1852. The relationship of the Stokes parameters to intensity and polarization ellipse parameters is shown in the equations and figure below.


title: Polarization (waves)

text: Here "Ip", 2ψ and 2χ are the spherical coordinates of the polarization state in the three-dimensional space of the last three Stokes parameters. Note the factors of two before ψ and χ corresponding respectively to the facts that any polarization ellipse is indistinguishable from one rotated by 180°, or one with the semi-axis lengths swapped accompanied by a 90° rotation. The Stokes parameters are sometimes denoted "I", "Q", "U" and "V".


title: Polarization (waves)

text: The four Stokes parameters are enough to describe 2D polarization of a paraxial wave, but not the 3D polarization of a general non-paraxial wave or an evanescent field.


title: Polarization (waves)

text: Neglecting the first Stokes parameter "S" (or "I"), the three other Stokes parameters can be plotted directly in three-dimensional Cartesian coordinates. For a given power in the polarized component given by


title: Polarization (waves)

text: the set of all polarization states are then mapped to points on the surface of the so-called "Poincaré sphere" (but of radius "P"), as shown in the accompanying diagram.


title: Polarization (waves)

text: Often the total beam power is not of interest, in which case a normalized Stokes vector is used by dividing the Stokes vector by the total intensity "S":


title: Polarization (waves)

text: The normalized Stokes vector formula_32 then has unity power (formula_33) and the three significant Stokes parameters plotted in three dimensions will lie on the unity-radius Poincaré sphere for pure polarization states (where formula_34). Partially polarized states will lie "inside" the Poincaré sphere at a distance of formula_35 from the origin. When the non-polarized component is not of interest, the Stokes vector can be further normalized to obtain


title: Polarization (waves)

text: When plotted, that point will lie on the surface of the unity-radius Poincaré sphere and indicate the state of polarization of the polarized component.


title: Polarization (waves)

text: Any two antipodal points on the Poincaré sphere refer to orthogonal polarization states. The overlap between any two polarization states is dependent solely on the distance between their locations along the sphere. This property, which can only be true when pure polarization states are mapped onto a sphere, is the motivation for the invention of the Poincaré sphere and the use of Stokes parameters, which are thus plotted on (or beneath) it.


title: Polarization (waves)

text: Note that the IEEE defines RHCP and LHCP the opposite as those used by Physicists. The IEEE 1979 Antenna Standard will show RHCP on the South Pole of the Poincare Sphere. The IEEE defines RHCP using the right hand with thumb pointing in the direction of transmit, and the fingers showing the direction of rotation of the E field with time. The rationale for the opposite conventions used by Physicists and Engineers is that Astronomical Observations are always done with the incoming wave traveling toward the observer, where as for most engineers, they are assumed to be standing behind the transmitter watching the wave traveling away from them. This article is not using the IEEE 1979 Antenna Standard and is not using the +t convention typically used in IEEE work.


title: Polarization (waves)

text: In a vacuum, the components of the electric field propagate at the speed of light, so that the phase of the wave varies in space and time while the polarization state does not. That is, the electric field vector e of a plane wave in the +"z" direction follows:


title: Polarization (waves)

text: where "k" is the wavenumber. As noted above, the instantaneous electric field is the real part of the product of the Jones vector times the phase factor formula_38. When an electromagnetic wave interacts with matter, its propagation is altered according to the material's (complex) index of refraction. When the real or imaginary part of that refractive index is dependent on the polarization state of a wave, properties known as birefringence and polarization dichroism (or diattenuation) respectively, then the polarization state of a wave will generally be altered.


title: Polarization (waves)

text: In such media, an electromagnetic wave with any given state of polarization may be decomposed into two orthogonally polarized components that encounter different propagation constants. The effect of propagation over a given path on those two components is most easily characterized in the form of a complex 2×2 transformation matrix J known as a Jones matrix:


title: Polarization (waves)

text: The Jones matrix due to passage through a transparent material is dependent on the propagation distance as well as the birefringence. The birefringence (as well as the average refractive index) will generally be dispersive, that is, it will vary as a function of optical frequency (wavelength). In the case of non-birefringent materials, however, the 2×2 Jones matrix is the identity matrix (multiplied by a scalar phase factor and attenuation factor), implying no change in polarization during propagation.


title: Polarization (waves)

text: describing the phase delay and possibly the amplitude attenuation due to propagation in each of the two polarization eigenmodes. T is a unitary matrix representing a change of basis from these propagation modes to the linear system used for the Jones vectors; in the case of linear birefringence or diattenuation the modes are themselves linear polarization states so T and T can be omitted if the coordinate axes have been chosen appropriately.


title: Polarization (waves)

text: In media termed birefringent, in which the amplitudes are unchanged but a differential phase delay occurs, the Jones matrix is a unitary matrix: |"g"| = |"g"| = 1. Media termed diattenuating (or "dichroic" in the sense of polarization), in which only the amplitudes of the two polarizations are affected differentially, may be described using a Hermitian matrix (generally multiplied by a common phase factor). In fact, since "any" matrix may be written as the product of unitary and positive Hermitian matrices, light propagation through any sequence of polarization-dependent optical components can be written as the product of these two basic types of transformations.


title: Polarization (waves)

text: In birefringent media there is no attenuation, but two modes accrue a differential phase delay. Well known manifestations of linear birefringence (that is, in which the basis polarizations are orthogonal linear polarizations) appear in optical wave plates/retarders and many crystals. If linearly polarized light passes through a birefringent material, its state of polarization will generally change, "unless" its polarization direction is identical to one of those basis polarizations. Since the phase shift, and thus the change in polarization state, is usually wavelength-dependent, such objects viewed under white light in between two polarizers may give rise to colorful effects, as seen in the accompanying photograph.


title: Polarization (waves)

text: Circular birefringence is also termed optical activity, especially in chiral fluids, or Faraday rotation, when due to the presence of a magnetic field along the direction of propagation. When linearly polarized light is passed through such an object, it will exit still linearly polarized, but with the axis of polarization rotated. A combination of linear and circular birefringence will have as basis polarizations two orthogonal elliptical polarizations; however, the term "elliptical birefringence" is rarely used.


title: Polarization (waves)

text: One can visualize the case of linear birefringence (with two orthogonal linear propagation modes) with an incoming wave linearly polarized at a 45° angle to those modes. As a differential phase starts to accrue, the polarization becomes elliptical, eventually changing to purely circular polarization (90° phase difference), then to elliptical and eventually linear polarization (180° phase) perpendicular to the original polarization, then through circular again (270° phase), then elliptical with the original azimuth angle, and finally back to the original linearly polarized state (360° phase) where the cycle begins anew. In general the situation is more complicated and can be characterized as a rotation in the Poincaré sphere about the axis defined by the propagation modes. Examples for linear (blue), circular (red), and elliptical (yellow) birefringence are shown in the figure on the left. The total intensity and degree of polarization are unaffected. If the path length in the birefringent medium is sufficient, the two polarization components of a collimated beam (or ray) can exit the material with a positional offset, even though their final propagation directions will be the same (assuming the entrance face and exit face are parallel). This is commonly viewed using calcite crystals, which present the viewer with two slightly offset images, in opposite polarizations, of an object behind the crystal. It was this effect that provided the first discovery of polarization, by Erasmus Bartholinus in 1669.


title: Polarization (waves)

text: Media in which transmission of one polarization mode is preferentially reduced are called "dichroic" or "diattenuating". Like birefringence, diattenuation can be with respect to linear polarization modes (in a crystal) or circular polarization modes (usually in a liquid).


title: Polarization (waves)

text: Devices that block nearly all of the radiation in one mode are known as "polarizing filters" or simply "polarizers". This corresponds to "g"=0 in the above representation of the Jones matrix. The output of an ideal polarizer is a specific polarization state (usually linear polarization) with an amplitude equal to the input wave's original amplitude in that polarization mode. Power in the other polarization mode is eliminated. Thus if unpolarized light is passed through an ideal polarizer (where "g"=1 and "g"=0) exactly half of its initial power is retained. Practical polarizers, especially inexpensive sheet polarizers, have additional loss so that


title: Polarization (waves)

text: "g" < 1. However, in many instances the more relevant figure of merit is the polarizer's degree of polarization or extinction ratio, which involve a comparison of "g" to "g". Since Jones vectors refer to waves' amplitudes (rather than intensity), when illuminated by unpolarized light the remaining power in the unwanted polarization will be ("g"/"g") of the power in the intended polarization.


title: Polarization (waves)

text: In addition to birefringence and dichroism in extended media, polarization effects describable using Jones matrices can also occur at (reflective) interface between two materials of different refractive index. These effects are treated by the Fresnel equations. Part of the wave is transmitted and part is reflected; for a given material those proportions (and also the phase of reflection) are dependent on the angle of incidence and are different for the "s" and "p" polarizations. Therefore, the polarization state of reflected light (even if initially unpolarized) is generally changed.


title: Polarization (waves)

text: Any light striking a surface at a special angle of incidence known as Brewster's angle, where the reflection coefficient for "p" polarization is zero, will be reflected with only the "s"-polarization remaining. This principle is employed in the so-called "pile of plates polarizer" (see figure) in which part of the "s" polarization is removed by reflection at each Brewster angle surface, leaving only the "p" polarization after transmission through many such surfaces. The generally smaller reflection coefficient of the "p" polarization is also the basis of polarized sunglasses; by blocking the "s" (horizontal) polarization, most of the glare due to reflection from a wet street, for instance, is removed.


title: Polarization (waves)

text: In the important special case of reflection at normal incidence (not involving anisotropic materials) there is no particular "s" or "p" polarization. Both the "x" and "y" polarization components are reflected identically, and therefore the polarization of the reflected wave is identical to that of the incident wave. However, in the case of circular (or elliptical) polarization, the handedness of the polarization state is thereby reversed, since by convention this is specified relative to the direction of propagation. The circular rotation of the electric field around the "x-y" axes called "right-handed" for a wave in the "+z" direction is "left-handed" for a wave in the "-z" direction. But in the general case of reflection at a nonzero angle of incidence, no such generalization can be made. For instance, right-circularly polarized light reflected from a dielectric surface at a grazing angle, will still be right-handed (but elliptically) polarized. Linear polarized light reflected from a metal at non-normal incidence will generally become elliptically polarized. These cases are handled using Jones vectors acted upon by the different Fresnel coefficients for the "s" and "p" polarization components.


title: Polarization (waves)

text: Some optical measurement techniques are based on polarization. In many other optical techniques polarization is crucial or at least must be taken into account and controlled; such examples are too numerous to mention.


title: Polarization (waves)

text: In engineering, the phenomenon of stress induced birefringence allows for stresses in transparent materials to be readily observed. As noted above and seen in the accompanying photograph, the chromaticity of birefringence typically creates colored patterns when viewed in between two polarizers. As external forces are applied, internal stress induced in the material is thereby observed. Additionally, birefringence is frequently observed due to stresses "frozen in" at the time of manufacture. This is famously observed in cellophane tape whose birefringence is due to the stretching of the material during the manufacturing process.


title: Polarization (waves)

text: Ellipsometry is a powerful technique for the measurement of the optical properties of a uniform surface. It involves measuring the polarization state of light following specular reflection from such a surface. This is typically done as a function of incidence angle or wavelength (or both). Since ellipsometry relies on reflection, it is not required for the sample to be transparent to light or for its back side to be accessible.


title: Polarization (waves)

text: Ellipsometry can be used to model the (complex) refractive index of a surface of a bulk material. It is also very useful in determining parameters of one or more thin film layers deposited on a substrate. Due to their reflection properties, not only are the predicted magnitude of the "p" and "s" polarization components, but their relative phase shifts upon reflection, compared to measurements using an ellipsometer. A normal ellipsometer does not measure the actual reflection coefficient (which requires careful photometric calibration of the illuminating beam) but the ratio of the "p" and "s" reflections, as well as change of polarization ellipticity (hence the name) induced upon reflection by the surface being studied. In addition to use in science and research, ellipsometers are used in situ to control production processes for instance.


title: Polarization (waves)

text: The property of (linear) birefringence is widespread in crystalline minerals, and indeed was pivotal in the initial discovery of polarization. In mineralogy, this property is frequently exploited using polarization microscopes, for the purpose of identifying minerals. See optical mineralogy for more details.


title: Polarization (waves)

text: Sound waves in solid materials exhibit polarization. Differential propagation of the three polarizations through the earth is a crucial in the field of seismology. Horizontally and vertically polarized seismic waves (shear waves) are termed SH and SV, while waves with longitudinal polarization (compressional waves) are termed P-waves.


title: Polarization (waves)

text: We have seen (above) that the birefringence of a type of crystal is useful in identifying it, and thus detection of linear birefringence is especially useful in geology and mineralogy. Linearly polarized light generally has its polarization state altered upon transmission through such a crystal, making it stand out when viewed in between two crossed polarizers, as seen in the photograph, above. Likewise, in chemistry, rotation of polarization axes in a liquid solution can be a useful measurement. In a liquid, linear birefringence is impossible, however there may be circular birefringence when a chiral molecule is in solution. When the right and left handed enantiomers of such a molecule are present in equal numbers (a so-called racemic mixture) then their effects cancel out. However, when there is only one (or a preponderance of one), as is more often the case for organic molecules, a net circular birefringence (or "optical activity") is observed, revealing the magnitude of that imbalance (or the concentration of the molecule itself, when it can be assumed that only one enantiomer is present). This is measured using a polarimeter in which polarized light is passed through a tube of the liquid, at the end of which is another polarizer which is rotated in order to null the transmission of light through it.


title: Polarization (waves)

text: In many areas of astronomy, the study of polarized electromagnetic radiation from outer space is of great importance. Although not usually a factor in the thermal radiation of stars, polarization is also present in radiation from coherent astronomical sources (e.g. hydroxyl or methanol masers), and incoherent sources such as the large radio lobes in active galaxies, and pulsar radio radiation (which may, it is speculated, sometimes be coherent), and is also imposed upon starlight by scattering from interstellar dust. Apart from providing information on sources of radiation and scattering, polarization also probes the interstellar magnetic field via Faraday rotation. The polarization of the cosmic microwave background is being used to study the physics of the very early universe. Synchrotron radiation is inherently polarized. It has been suggested that astronomical sources caused the chirality of biological molecules on Earth.


title: Polarization (waves)

text: Unpolarized light, after being reflected by a specular (shiny) surface, generally obtains a degree of polarization. This phenomenon was observed in 1808 by the mathematician Étienne-Louis Malus, after whom Malus's law is named. Polarizing sunglasses exploit this effect to reduce glare from reflections by horizontal surfaces, notably the road ahead viewed at a grazing angle.


title: Polarization (waves)

text: Wearers of polarized sunglasses will occasionally observe inadvertent polarization effects such as color-dependent birefringent effects, for example in toughened glass (e.g., car windows) or items made from transparent plastics, in conjunction with natural polarization by reflection or scattering. The polarized light from LCD monitors (see below) is very conspicuous when these are worn.


title: Polarization (waves)

text: Polarization is observed in the light of the sky, as this is due to sunlight scattered by aerosols as it passes through Earth's atmosphere. The scattered light produces the brightness and color in clear skies. This partial polarization of scattered light can be used to darken the sky in photographs, increasing the contrast. This effect is most strongly observed at points on the sky making a 90° angle to the Sun. Polarizing filters use these effects to optimize the results of photographing scenes in which reflection or scattering by the sky is involved.


title: Polarization (waves)

text: Sky polarization has been used for orientation in navigation. The Pfund sky compass was used in the 1950s when navigating near the poles of the Earth's magnetic field when neither the sun nor stars were visible (e.g., under daytime cloud or twilight). It has been suggested, controversially, that the Vikings exploited a similar device (the "sunstone") in their extensive expeditions across the North Atlantic in the 9th–11th centuries, before the arrival of the magnetic compass from Asia to Europe in the 12th century. Related to the sky compass is the "polar clock", invented by Charles Wheatstone in the late 19th century.


title: Polarization (waves)

text: The principle of liquid-crystal display (LCD) technology relies on the rotation of the axis of linear polarization by the liquid crystal array. Light from the backlight (or the back reflective layer, in devices not including or requiring a backlight) first passes through a linear polarizing sheet. That polarized light passes through the actual liquid crystal layer which may be organized in pixels (for a TV or computer monitor) or in another format such as a seven-segment display or one with custom symbols for a particular product. The liquid crystal layer is produced with a consistent right (or left) handed chirality, essentially consisting of tiny helices. This causes circular birefringence, and is engineered so that there is a 90 degree rotation of the linear polarization state. However, when a voltage is applied across a cell, the molecules straighten out, lessening or totally losing the circular birefringence. On the viewing side of the display is another linear polarizing sheet, usually oriented at 90 degrees from the one behind the active layer. Therefore, when the circular birefringence is removed by the application of a sufficient voltage, the polarization of the transmitted light remains at right angles to the front polarizer, and the pixel appears dark. With no voltage, however, the 90 degree rotation of the polarization causes it to exactly match the axis of the front polarizer, allowing the light through. Intermediate voltages create intermediate rotation of the polarization axis and the pixel has an intermediate intensity. Displays based on this principle are widespread, and now are used in the vast majority of televisions, computer monitors and video projectors, rendering the previous CRT technology essentially obsolete. The use of polarization in the operation of LCD displays is immediately apparent to someone wearing polarized sunglasses, often making the display unreadable.


title: Polarization (waves)

text: In a totally different sense, polarization encoding has become the leading (but not sole) method for delivering separate images to the left and right eye in stereoscopic displays used for 3D movies. This involves separate images intended for each eye either projected from two different projectors with orthogonally oriented polarizing filters or, more typically, from a single projector with time multiplexed polarization (a fast alternating polarization device for successive frames). Polarized 3D glasses with suitable polarizing filters ensure that each eye receives only the intended image. Historically such systems used linear polarization encoding because it was inexpensive and offered good separation. However circular polarization makes separation of the two images insensitive to tilting of the head, and is widely used in 3-D movie exhibition today, such as the system from RealD. Projecting such images requires screens that maintain the polarization of the projected light when viewed in reflection (such as silver screens); a normal diffuse white projection screen causes depolarization of the projected images, making it unsuitable for this application.


title: Polarization (waves)

text: Although now obsolete, CRT computer displays suffered from reflection by the glass envelope, causing glare from room lights and consequently poor contrast. Several anti-reflection solutions were employed to ameliorate this problem. One solution utilized the principle of reflection of circularly polarized light. A circular polarizing filter in front of the screen allows for the transmission of (say) only right circularly polarized room light. Now, right circularly polarized light (depending on the convention used) has its electric (and magnetic) field direction rotating clockwise while propagating in the +z direction. Upon reflection, the field still has the same direction of rotation, but now propagation is in the −z direction making the reflected wave "left" circularly polarized. With the right circular polarization filter placed in front of the reflecting glass, the unwanted light reflected from the glass will thus be in very polarization state that is "blocked" by that filter, eliminating the reflection problem. The reversal of circular polarization on reflection and elimination of reflections in this manner can be easily observed by looking in a mirror while wearing 3-D movie glasses which employ left- and right-handed circular polarization in the two lenses. Closing one eye, the other eye will see a reflection in which it cannot see itself; that lens appears black. However the other lens (of the closed eye) will have the correct circular polarization allowing the closed eye to be easily seen by the open one.


title: Polarization (waves)

text: All radio (and microwave) antennas used for transmitting or receiving are intrinsically polarized. They transmit in (or receive signals from) a particular polarization, being totally insensitive to the opposite polarization; in certain cases that polarization is a function of direction. Most antennas are nominally linearly polarized, but elliptical and circular polarization is a possibility. As is the convention in optics, the "polarization" of a radio wave is understood to refer to the polarization of its electric field, with the magnetic field being at a 90 degree rotation with respect to it for a linearly polarized wave.


title: Polarization (waves)

text: The vast majority of antennas are linearly polarized. In fact it can be shown from considerations of symmetry that an antenna that lies entirely in a plane which also includes the observer, can "only" have its polarization in the direction of that plane. This applies to many cases, allowing one to easily infer such an antenna's polarization at an intended direction of propagation. So a typical rooftop Yagi or log-periodic antenna with horizontal conductors, as viewed from a second station toward the horizon, is necessarily horizontally polarized. But a vertical "whip antenna" or AM broadcast tower used as an antenna element (again, for observers horizontally displaced from it) will transmit in the vertical polarization. A turnstile antenna with its four arms in the horizontal plane, likewise transmits horizontally polarized radiation toward the horizon. However, when that same turnstile antenna is used in the "axial mode" (upwards, for the same horizontally-oriented structure) its radiation is circularly polarized. At intermediate elevations it is elliptically polarized.


title: Polarization (waves)

text: Polarization is important in radio communications because, for instance, if one attempts to use a horizontally polarized antenna to receive a vertically polarized transmission, the signal strength will be substantially reduced (or under very controlled conditions, reduced to nothing). This principle is used in satellite television in order to double the channel capacity over a fixed frequency band. The same frequency channel can be used for two signals broadcast in opposite polarizations. By adjusting the receiving antenna for one or the other polarization, either signal can be selected without interference from the other.


title: Polarization (waves)

text: Especially due to the presence of the ground, there are some differences in propagation (and also in reflections responsible for TV ghosting) between horizontal and vertical polarizations. AM and FM broadcast radio usually use vertical polarization, while television uses horizontal polarization. At low frequencies especially, horizontal polarization is avoided. That is because the phase of a horizontally polarized wave is reversed upon reflection by the ground. A distant station in the horizontal direction will receive both the direct and reflected wave, which thus tend to cancel each other. This problem is avoided with vertical polarization. Polarization is also important in the transmission of radar pulses and reception of radar reflections by the same or a different antenna. For instance, back scattering of radar pulses by rain drops can be avoided by using circular polarization. Just as specular reflection of circularly polarized light reverses the handedness of the polarization, as discussed above, the same principle applies to scattering by objects much smaller than a wavelength such as rain drops. On the other hand, reflection of that wave by an irregular metal object (such as an airplane) will typically introduce a change in polarization and (partial) reception of the return wave by the same antenna.


title: Polarization (waves)

text: The effect of free electrons in the ionosphere, in conjunction with the earth's magnetic field, causes Faraday rotation, a sort of circular birefringence. This is the same mechanism which can rotate the axis of linear polarization by electrons in interstellar space as mentioned below. The magnitude of Faraday rotation caused by such a plasma is greatly exaggerated at lower frequencies, so at the higher microwave frequencies used by satellites the effect is minimal. However medium or short wave transmissions received following refraction by the ionosphere are strongly affected. Since a wave's path through the ionosphere and the earth's magnetic field vector along such a path are rather unpredictable, a wave transmitted with vertical (or horizontal) polarization will generally have a resulting polarization in an arbitrary orientation at the receiver.


title: Polarization (waves)

text: Many animals are capable of perceiving some of the components of the polarization of light, e.g., linear horizontally polarized light. This is generally used for navigational purposes, since the linear polarization of sky light is always perpendicular to the direction of the sun. This ability is very common among the insects, including bees, which use this information to orient their communicative dances. Polarization sensitivity has also been observed in species of octopus, squid, cuttlefish, and mantis shrimp. In the latter case, one species measures all six orthogonal components of polarization, and is believed to have optimal polarization vision. The rapidly changing, vividly colored skin patterns of cuttlefish, used for communication, also incorporate polarization patterns, and mantis shrimp are known to have polarization selective reflective tissue. Sky polarization was thought to be perceived by pigeons, which was assumed to be one of their aids in homing, but research indicates this is a popular myth.


title: Polarization (waves)

text: The naked human eye is weakly sensitive to polarization, without the need for intervening filters. Polarized light creates a very faint pattern near the center of the visual field, called Haidinger's brush. This pattern is very difficult to see, but with practice one can learn to detect polarized light with the naked eye.


title: Polarization (waves)

text: It is well known that electromagnetic radiation carries a certain linear momentum in the direction of propagation. In addition, however, light carries a certain angular momentum if it is circularly polarized (or partially so). In comparison with lower frequencies such as microwaves, the amount of angular momentum in light, even of pure circular polarization, compared to the same wave's linear momentum (or radiation pressure) is very small and difficult to even measure. However it was utilized in an experiment to achieve speeds of up to 600 million revolutions per minute.


title: 7.92×57mm Mauser

text: The 7.92×57mm Mauser (designated as the 8mm Mauser or 8×57mm by the SAAMI and 8 × 57 IS by the C.I.P.) is a rimless bottlenecked rifle cartridge. The 7.92×57mm Mauser cartridge was adopted by the German Empire in 1903–1905, and was the German service cartridge in both World Wars. In its day, the 7.92×57mm Mauser cartridge was one of the world's most popular military cartridges. In the 21st century it is still a popular sport and hunting cartridge that is factory-produced in Europe and the United States.


title: 7.92×57mm Mauser

text: The parent cartridge, upon which the 7.92×57mm Mauser is based, was adopted by Germany in 1888 as the "Patrone 88" (cartridge 88) or "M/88" (along with the Gewehr 1888 service rifle). It was a first-generation smokeless propellant cartridge designed by the German "Gewehr-Prüfungskommission" (G.P.K.) (Rifle Testing Commission), as the new smokeless propellant introduced as Poudre B in the 1886 pattern 8mm Lebel had started a military rifle ammunition revolution. The M/88 cartridge was loaded with of single-base (based on nitrocellulose) smokeless powder and a relatively heavy, , round-nosed ball bullet with a diameter of . The M/88 bore originally had lands diameter and grooves diameter. The M/88 barrel bore specification was changed by 1894–1895 to lands diameter and grooves diameter to improve accuracy and reduce barrel wear in M/88 chambered arms.


title: 7.92×57mm Mauser

text: German government driven efforts to further improve on the performance of the military M/88 ammunition and the service arms in which the M/88 was used after several development steps eventually resulted in the official adoption on 3 April 1903 by the "Gewehr-Prüfungskommission" of the dimensionally redesigned 7.92×57mm Mauser chambering. Besides the chambering, the bore (designated as "S-bore") was also dimensionally redesigned because the new bullet with a shorter cylindrical part had reduced bearing surface, which necessitated increasing its diameter and deepening barrel grooves (as a result the new cartridge was not fully interchangeable with the old one).


title: 7.92×57mm Mauser

text: The 1903 pattern "S Patrone" (S ball cartridge) was loaded with a lighter , pointed "Spitzgeschoß" (spire point bullet) of diameter and more powerful double-base (based on nitrocellulose and nitroglycerin) smokeless powder resulting in nearly 38% higher muzzle velocity and 27% more muzzle energy. The operating pressure was . With the improved ballistic coefficient – (G1 BC) of approximately 0.321 to 0.337 (ballistic coefficients are somewhat debatable) – of the new bullet, the 1903 pattern cartridge had an improved maximum effective range and a flatter trajectory, and was therefore less critical of range estimation compared to the M/88 cartridge.


title: 7.92×57mm Mauser

text: In German military service the "Patrone 88" was replaced in 1904 and 1905 by the "S Patrone". As the bolt thrust of the 7.92×57mm Mauser is relatively low compared to many other service rounds used in the early 20th century, many arms originally chambered for the "Patrone 88" could be and were adapted for chambering the "S Patrone" by reaming out metal from the chamber as it required a wider chamber throat to take the differently shaped and thicker brass of the new "S Patrone".


title: 7.92×57mm Mauser

text: The rimless cartridge cases have been used as the parent cases for several other necked-down and necked-up cartridges and a rimmed variant.


title: 7.92×57mm Mauser

text: Due to restrictions imposed by the Treaty of Versailles, the Germans were not able to develop or sell any military equipment after World War I. In the post-war years, 7.92×57mm Mauser chambered Gewehr 98 pattern rifles were produced in Belgium, Czechoslovakia, Poland, Mexico, Austria and China. This, and the cartridge's high performance and versatility, led to the 7.92×57mm Mauser being adopted by the armed forces of various governments. These included: Spain, Poland, Czechoslovakia, Romania, Iran, Turkey, China, Egypt, Yugoslavia, former German African colonies. This made the round the most widely used military rifle cartridge in the world during the inter-war years.


title: 7.92×57mm Mauser

text: During World War II it was one of the few cartridges used by both the Axis and Allied powers, a distinction it shared with the 9×19mm Parabellum pistol round. Apart from being the standard rifle cartridge of the German and Polish armed forces, it was also used by the armed forces of Great Britain in the Besa machine gun, which was mounted in some of their tanks and other armoured vehicles, as well as being extensively used by the Chinese, especially early in the war. After World War II it was used by the early Bundeswehr of West Germany. It saw limited uses by the various (police and paramilitary) units in East Germany before being completely phased out of service in the 1960s. Later, when Egypt decided to manufacture the Hakim rifle, a licensed copy of the Swedish Ag m/42, they redesigned the breech to accept the 7.92×57mm Mauser cartridge rather than use the original 6.5×55mm Ag m/42 cartridge. Its military use continues today (2012) in some former Yugoslavia republics. The Zastava M76 sniper rifle, M48 bolt-action rifle and the license-built copy of the MG 42, the M53 "Šarac" machine gun use this cartridge.


title: 7.92×57mm Mauser

text: Rifles formerly manufactured for the "Wehrmacht", captured by the Allies and acquired by Israel were important in the 1948 Arab–Israeli War. Israel did not have a domestic arms industry and could not manufacture rifles but it could produce replacement parts and refurbish weapons. Israel only used its Mauser rifles in their original configuration for a short period, when NATO countries adopted a standard rifle cartridge, the 7.62×51mm NATO, Israel replaced all of the 7.92×57mm Mauser barrels on its Mauser rifles with barrels chambered for the new 7.62×51mm NATO cartridge.


title: 7.92×57mm Mauser

text: After World War I the Treaty of Versailles imposed comprehensive and complex restrictions upon the post-war German armed forces (the "Reichswehr"). According to the treaty the "Reichswehr" could, on a limited scale, continue using the 7.92×57mm Mauser as their service cartridge. The Treaty of Versailles however effectively nixed the civilian use of 7.92×57mm Mauser chambered rifles by German hunters and sport shooters. During the mid-1930s Germany stopped obeying the restrictions imposed by the Treaty of Versailles and gradually the civilian use of 7.92×57mm Mauser chambered rifles by German hunters and sport shooters was resumed. In 1939 the "Normalisierungsverordnung" (Normalization regulation) effectively prohibited the production of non S-bore/7.92×57mm Mauser chambered arms in Nazi Germany. In post-World War 2 Germany, the production of the various preceding chamberings is allowed again, but these chamberings have become rare in post-1939 produced arms.


title: 7.92×57mm Mauser

text: The 7.92×57mm Mauser is a common chambering offering in rifles marketed for European and North American sportsmen, alongside broadly similar cartridges such as the 5.6×57mm, 6.5×55mm, 6.5×57mm, and the 6.5×68mm and 8×68mm S magnum hunting cartridges. Major European manufacturers like Zastava Arms, Blaser, Česká Zbrojovka firearms, Heym, Mauser Jagdwaffen GmbH and Steyr Mannlicher produce factory new 7.92×57mm Mauser hunting rifles and European ammunition manufacturers like Blaser, Lapua, RUAG Ammotec/RWS, Prvi Partizan, Sako and Sellier & Bellot produce factory new ammunition. In 2004 Remington Arms offered a limited-edition Model 700 Classic bolt action hunting rifle chambered for the 7.92×57mm Mauser.


title: 7.92×57mm Mauser

text: The 7.92×57mm Mauser cartridge's performance makes it suitable for the hunting all medium-sized game such as the deer family, chamois, mouflon, bighorn sheep, wild boar and bear. The 7.92×57mm Mauser can offer very good penetrating ability due to a fast twist rate that enables it to fire long, heavy bullets with a high sectional density.


title: 7.92×57mm Mauser

text: The 7.92×57mm Mauser cannot be used in countries that ban civil use of former or current military rifle cartridges, though since 2013 is no longer restricted in France.


title: 7.92×57mm Mauser

text: The rimmed variant of the 7.92×57mm Mauser, the 8×57mm IRS, was developed later for break-barrel rifles and combination guns. The 8×57mm IRS is commercially offered as a chambering option in European break-action rifles.


title: 7.92×57mm Mauser

text: The 7.92 naming convention is often used by English speaking sources for the military issued 7.92×57mm Mauser and 7.92×33mm Kurz cartridges. Remarkably, both the 7.92 and 7,9 used in these and alike designations do not exactly comply to the actual C.I.P. or SAAMI cartridge, chamber and bore dimensions. All other non-military issued rimless and rimmed rifle cartridges originating from Germany having approximately 8 mm bullet diameter are connected to 8 mm namings.


title: 7.92×57mm Mauser

text: The widespread use in German military Gewehr 98 and Karabiner 98k service rifles designed and manufactured by Mauser caused the "Mauser" tag, though the Mauser company had nothing to do with the development of this cartridge.


title: 7.92×57mm Mauser

text: The letter "J" often mentioned by English speaking sources is actually an "I" for "Infanterie" (German for "infantry"). A stamped "I" at the cartridge bottom in writing styles used in the past in Germany could be easily mistaken for a "J". Even in the 21st century the "I" is often substituted by a "J" in English speaking communities and German ammunition manufacturers often write "JS" instead of "IS" to avoid confusing customers. The letter "S" stands for "Spitzgeschoß" ("pointed bullet"), and the English designation "spitzer" for that style of bullet is derived from this German term.


title: 7.92×57mm Mauser

text: The mainly European arms standards body "Commission Internationale Permanente pour l'Epreuve des Armes à Feu Portatives" (Permanent International Commission for portable firearms testing) (C.I.P.)—an organisation for standards in ammunition for civilian use—currently (2012) designates the 7.92×57mm Mauser as the 8 × 57 IS. This designation has the power of law for civil use in C.I.P. member states like the United Kingdom.


title: 7.92×57mm Mauser

text: The United States standardizing body for sporting cartridges Sporting Arms and Ammunition Manufacturers' Institute (SAAMI) currently (2012) designates the 7.92×57mm Mauser cartridge as the 8mm Mauser, also known as 8×57mm.


title: 7.92×57mm Mauser

text: Since the SAAMI has no authority to issue nomenclature rulings, the nomenclature used for this cartridge can vary in the United States.


title: 7.92×57mm Mauser

text: The German military used 7,9mm as designation or omitted any diameter reference and only printed the exact type of loading on ammunition boxes during World War II.


title: 7.92×57mm Mauser

text: The Norwegian military used the designation 7,92×57 mm, sometimes "7,92 Lett" ("lett" meaning "light") to differentiate it from the similar but not interchangeable 7,92×61 Tung ("heavy"). Ammunition produced by Raufoss after the war was designated 7,92x57.


title: 7.92×57mm Mauser

text: The British military's Besa machine gun was chambered for the 7.92×57mm Mauser, and was used in armoured vehicles during World War II. The British referred to this ammunition as Cartridge SA, 7.92.


title: 7.92×57mm Mauser

text: United States intelligence documents from World War II refer to the cartridge as 7.92 or 7.92 mm or 7.92-mm.


title: 7.92×57mm Mauser

text: The 7.92×57mm Mauser cartridge has a cartridge case capacity of 4.09 ml (63 grains) HO. The exterior shape of the case was designed to promote reliable case feeding and extraction in bolt-action rifles and machine guns alike, under extreme conditions.


title: 7.92×57mm Mauser

text: Americans would define the shoulder angle at alpha/2 ≈ 19.1 degrees. The common rifling twist rate for this cartridge is 240 mm (1 in 9.45 in), 4 grooves, Ø of the lands = , Ø grooves = , land width = and the primer type is large rifle.


title: 7.92×57mm Mauser

text: According to the official C.I.P. (Commission Internationale Permanente pour l'Epreuve des Armes à Feu Portatives) rulings the 7.92×57mm Mauser can handle up to P piezo pressure. In C.I.P. regulated countries every rifle cartridge combo has to be proofed at 125% of this maximum C.I.P. pressure to certify for sale to consumers.


title: 7.92×57mm Mauser

text: This means that 7.92×57mm Mauser chambered arms in C.I.P. regulated countries are currently (2013) proof tested at PE piezo pressure.


title: 7.92×57mm Mauser

text: The SAAMI (voluntary) Maximum Average Pressure (MAP) for this cartridge is piezo pressure or (37,000 CUP). This is considerably lower than the C.I.P. pressure limit and is done for liability reasons, in case a 7.92×57mm Mauser "S-bore" cartridge is fired in an "I-bore" rifle that has a narrower throat and barrel diameter. Most European ammunition manufacturers load to a lower C.I.P. pressure limit - P piezo pressure for the 8×57mm I civilian "Patrone 88" offspring - for I-bore cartridges and use diameter projectiles; while the US based manufacturer Hornady followed their lead in their (now discontinued) EuroSpec brand 8×57 JS load.


title: 7.92×57mm Mauser

text: Germany produced many military versions of the cartridge, and continued the development of different variations until the end of World War II. The bullet lengths substantially varied between the different cartridge types, but all were loaded to an overall length of . The Germans had started using steel cases in World War I, and by the end of 1943, most German ammunition had that type of case. The weights and case capacities of the World War II military cartridge cases varied somewhat. The German military ammunition manufacturer Polte produced brass cartridge cases weighing 10.32 g (159 gr) with 4.03 ml (62 gr) HO case capacity and steel cartridge cases weighing 10.90 g (168 gr) with 3.95 ml (61 gr) HO case capacity. The steel cartridge cases were produced in copper plated and lacquered executions. Some military cartridge cases were made with the aim to use less material and their ammunition boxes were marked Für Gewehr ("for rifle") use. Other military cartridge cases were made extra sturdy and their ammunition boxes were marked Für MG ("for machine gun") use.


title: 7.92×57mm Mauser

text: The German standard s.S. Patrone ("s.S. ball cartridge") was originally designed for long range machine gun use. It was loaded with a long, boat-tailed, "s.S. - schweres Spitzgeschoß" ("heavy pointed or spitzer bullet") full metal jacket bullet and very well made. It was lead filled, had a gilding-metal-plated jacket, and weighed . The "s.S. Patrone" had a muzzle velocity of fired from a long barrel and an operating pressure of . From a long barrel the muzzle velocity increased to . From its 1914 introduction the "s.S. Patrone" was mainly issued for aerial combat and as of 1918 in the later stages of World War I to infantry machine gunners.


title: 7.92×57mm Mauser

text: The desire for adopting new shorter barreled rifles and the introduction of the Karabiner 98k were reasons for changing the standard German service ball rifle cartridge. The 1903 pattern 7.92×57mm Mauser "S Patrone" produced excessive muzzle flash when fired from arms that did not have a long barrel like the Gewehr 98. It was found that the "s.S. Patrone", originally designed for long range machine gun use, produced less muzzle flash out of rifles that had a shorter barrel and also provided better accuracy. Because of this the "S Patrone" was phased out in 1933 and the "s.S. Patrone" became the standard German service ball cartridge in the 1930s when the German rearmament program started.


title: 7.92×57mm Mauser

text: The s.S. ball projectile with a long 6° 25′ 51″ boat tail was designed for long range use and offered the best aerodynamic efficiency and external ballistic performance of any standard rifle bullet used during World War II, with a G1 ballistic coefficient between 0.593 and 0.557 (ballistic coefficients are somewhat debatable) or a ballistic coefficient of approximately 0.295 (G7). When fired at the typical muzzle velocity of out of a barrel the s.S. bullet retained supersonic velocity up to and past (V ≈ Mach 1.07) under International Standard Atmosphere conditions at sea level (air density ρ = 1.225 kg/m). Mounted to a "Lafette" tripod and aimed through the MG Z 34 or MG Z 40 telescopic sight, the effective range of the MG 34 and MG 42 general-purpose machine guns in long-range indirect fire support roles could be extended out to , though plunging fire or indirect fire methods were not as commonly used by machine gunners during World War II as they were during World War I. This indirect firing method exploits the "s.S. Patrone" useful maximum range, that is defined by the maximum range of a small-arms projectile while still maintaining the minimum kinetic energy required to put unprotected personnel out of action, which is generally believed to be 15 kilogram-meters (147 J / 108 ft⋅lbf). The "s.S. Patrone" had a maximum range of approximately . Even by contemporary (2012) standards 1000 m (1,094 yards) effective supersonic range is quite remarkable for a standard military rifle round. For recognition the primer sealant was green, and it had a yellow-tip marked bullet.


title: 7.92×57mm Mauser

text: The regular s.S. projectile had the following penetration performance: of dry pine wood at , at , at and at , of iron at , at , of steel at and at .


title: 7.92×57mm Mauser

text: During World War II German snipers were issued with purpose-manufactured sniping ammunition, known as the 'effect-firing' s.S. round. The 'effect-firing' s.S. round featured an extra carefully measured propellant charge and seated an sS full-metal-jacketed boat-tail projectile of match-grade build quality, lacking usual features such as a cannelure, to further improve the already high G1 ballistic coefficient to approximately 0.595 (G1) or 0.300 (G7). The 'effect-firing' s.S. projectile had a form factor (G7 "i") of 0.869, which indicates good aerodynamic efficiency and external ballistic performance for the bullet diameter.


title: 7.92×57mm Mauser

text: The S.m.E. ammunition was developed to replace the s.S. ammunition to save on lead and other metals that became scarce in Germany during World War II. The projectile core was covered by a relatively thin layer of lead. Muzzle velocity was and the operating pressure was . For recognition the primer annulus or whole primers were colored blue. S.m.E. bullets were long, boat-tailed, and weighed . The mild steel core weights varied between the four production sub-executions from . From 1942 onwards S.m.E. ammunition practically replaced the s.S. ammunition.


title: 7.92×57mm Mauser

text: In 1943 the lead content of the S.m.E. bullet was further reduced. To compensate for the lead reduction the mild steel core was redesigned resulting in a projectile lengthened to to retain the original S.m.E. bullet weight of . This ammunition was designated ("spitzer with iron core long") and lacked recognition marks. The S.m.E. lg external ballistic characteristics were practically identical to s.S. ammunition up to and the lengthened S.m.E. lg projectile was more accurate compared to the shorter S.m.E. projectile.


title: 7.92×57mm Mauser

text: British cartridges included "ball", "armour-piercing", "tracer", and "incendiary". Blanks and a drill round were also available for instruction purposes. The drill round was an aluminium bullet fixed in a chromium-plated case which had three deep lengthwise recesses painted red to identify it. Ammunition was supplied in belted form with 225 rounds per belt.


title: 7.92×57mm Mauser

text: The British cartridge was used in only one weapon—the Besa machine gun. This was a Czechoslovak ZB-53 design adopted shortly before the war as a move towards rimless ammunition across the armed service. However the move was disrupted by the lead up to war. The BESA was only fitted to tanks and armoured cars of British design (the original Czech design was also produced for German use following the occupation of Czechoslovakia) and captured German ammunition was used when available.


title: 7.92×57mm Mauser

text: The cartridges manufactured in Poland during the interwar period were mainly copies or modifications of the corresponding original German cartridge designs. The standard rifle cartridge was loaded with the S bullet ("Spiczasty", "Pointed [Ball]"), a copy of the 1905 pattern German "S Patrone". For machine guns a cartridge variant loaded with the heavier SC bullet ("Spiczasty Ciężki", "Pointed, Heavy [Ball]") — a copy of the German 1934 pattern s.S. cartridge — was used. The variant loaded with the armor-piercing P bullet ("przeciwpancerny") was a copy of the German SmK cartridge. The armor-piercing-with-tracer PS ("przeciwpancerny smugowy") and incendiary Z ("zapalający") cartridges were Polish modifications of the original German counterpart designs. The Polish designed a machine gun cartridge loaded with the long-range D bullet ("dalekosiężny"), which offered a maximum plunging fire range of to .


title: 7.92×57mm Mauser

text: The Romanian military used the 7.92×57mm Mauser cartridge as standard issue from its independence. It gradually converted over in the 1950s and 1960s to using Warsaw Pact standard calibers.


title: 7.92×57mm Mauser

text: The 7.92 LPS gs MD71 (7.92×56mm) cartridge was manufactured in Romania by their Factory 22 ("UM Sadu") from 1972 to 1978. It had a Semi-Armor-Piercing bullet with a copper jacket and mild steel core, corrosive VT stick propellant, and a Berdan-primed steel case with a green lacquer coating. The case mouth and primer pocket were sealed with a red sealant. It is unusual in that it has a uniform 56mm-long case, perhaps for cleaner extraction when used in belt-fed 8mm machine guns. Since it is from the portion after the neck, it chambers and feeds safely and extracts positively. It has sometimes been confused with the rather different Hungarian 8×56mmR Mannlicher cartridge. Some experts mistakenly believed it to be an experimental rimless pointed-bullet Hungarian "sniper rifle cartridge" developed by Hungary's Factory 22 ("Andezit Muvek") until it became available as surplus.


title: 7.92×57mm Mauser

text: It is not clear why the cartridge was manufactured, as the Romanian military used the standard Communist-Bloc 7.62mm M91 Mosin-Nagant rifle round. Some believe it may have been for an experimental self-loading rifle or for a Communist Bloc client. It was most likely for use in the obsolete 8mm vz 24 rifles and MG 42 machine guns used by the Romanian "Garzile Patriotice" ("Patriotic Guards") from 1968 to the early 1980s.


title: 7.92×57mm Mauser

text: After World War II the Socialist Federal Republic of Yugoslavia used the 7.92×57mm Mauser as a military service round. The Yugoslav National Army (JNA) designated their 7.92×57mm Mauser ammunition as 7.9 mm. At the end of the 1940s the Yugoslav National Army adopted a 7.9 mm cartridge, ball M49 variant, designated M49, as infantry ammunition for use in Mauser-type bolt-action rifles and MG 42 general-purpose machinegun clones like the M53. Yugoslavian state arms manufacturers like Prvi Partizan started making 7.92×57mm Mauser ammunition for export to the Middle East in the 1950s and 1960s. In the 1970s the JNA started to develop a new more accurate 7.9 mm ammunition, sniper universal ball M75, variant, designated M75. This was done to support the new Zastava M76 sniper/designated marksman rifle for the JNA. Other adoption of the ammunition where tracer round 7.9 mm cartridge, ball with tracer, designated M70. The M70 tracer round burns out to . For training and ceremonial use a 7.9 mm cartridge, blank was adopted. By the mid-1980s the JNA started to push toward adopting Soviet / Warsaw Pact 7.62×54mm R ammunition. This process was interrupted by the fall of Yugoslavia and brought the 7.9 mm back into military service with the onset of the Yugoslav wars.


title: National debt of the United States

text: The national debt of the United States is the total national debt owed by the federal government of the United States to Treasury security holders. The national debt at any point in time is the face value of the then-outstanding Treasury securities that have been issued by the Treasury and other federal agencies. The terms "national deficit" and "national surplus" usually refer to the federal government budget balance from year to year, not the cumulative amount of debt. In a deficit year the national debt increases as the government needs to borrow funds to finance the deficit, while in a surplus year the debt decreases as more money is received than spent, enabling the government to reduce the debt by buying back some Treasury securities. In general, government debt increases as a result of government spending and decreases from tax or other receipts, both of which fluctuate during the course of a fiscal year. There are two components of gross national debt:


title: National debt of the United States

text: Historically, the U.S. public debt as a share of gross domestic product (GDP) increases during wars and recessions and then subsequently declines. The ratio of debt to GDP may decrease as a result of a government surplus or via growth of GDP and inflation. For example, debt held by the public as a share of GDP had peaked just after World War II (113% of GDP in 1945), but has since reached new highs of up to 134.84% of GDP during the second quarter of 2020. In recent decades, aging demographics and rising healthcare costs have led to concern about the long-term sustainability of the federal government's fiscal policies. The aggregate, gross amount that Treasury can borrow is limited by the United States debt ceiling.


title: National debt of the United States

text: As of November 2022, federal debt held by the public was $31 trillion. Debt held by the public was estimated at 96.19% of GDP, and approximately 33% of this public debt was owned by foreigners. The United States has the largest external debt in the world. The total number of U.S. Treasury securities held by foreign countries in December 2021 was $7.7 trillion, up from $7.1 trillion in December 2020. As of February 2022, total US federal government debt breached $30 trillion mark for the first time in history.


title: National debt of the United States

text: During the COVID-19 pandemic, the federal government spent trillions in virus aid and economic relief. The CBO estimated that the budget deficit for fiscal year 2020 would increase to $3.3 trillion or 16% GDP, more than triple that of 2019 and the largest as % GDP since 1945.


title: National debt of the United States

text: On April 28, 2022, the Congressional Budget Office released a report which stated that in order to stabilize the $30 trillion in national debt (i.e. stop the debt from growing relative to the United States economy), it will require that "income tax receipts or benefit payments change substantially from their currently projected path." In other words, taxes will likely increase and government services will likely have to be reduced.


title: National debt of the United States

text: The United States federal government has continuously had a fluctuating public debt since its formation in 1789, except for about a year during 1835–1836, a period in which the nation, during the presidency of Andrew Jackson, completely paid the national debt. To allow comparisons over the years, public debt is often expressed as a ratio to GDP. The United States public debt as a percentage of GDP reached its highest level during Harry Truman's first presidential term, during and after World War II. Public debt as a percentage of GDP fell rapidly in the post-World War II period and reached a low in 1974 under Richard Nixon. Debt as a share of GDP has consistently increased since then, except during the presidencies of Jimmy Carter and Bill Clinton.


title: National debt of the United States

text: Public debt rose sharply during the 1980s, as Ronald Reagan negotiated with Congress to cut tax rates and increase military spending. It fell during the 1990s because of decreased military spending, increased taxes and the 1990s boom. Public debt rose sharply during George W Bush's presidency and in the wake of the 2007–2008 financial crisis, with resulting significant tax revenue declines and spending increases, such as the Emergency Economic Stabilization Act of 2008 and the American Recovery and Reinvestment Act of 2009.


title: National debt of the United States

text: In their September 2018 monthly report published on October 5 and based on data from the Treasury Department's "Daily Treasury Statements" (DTS), the Congressional Budget Office (CBO) wrote that the federal budget deficit was c.$782 billion for the fiscal year 2018—which runs from October 2017 through September 2018. This is $116 billion more than in FY2017. The Treasury statements as summarized by in the CBO report that corporate taxes for 2017 and 2018 declined by $92 billion representing a drop of 31%. The CBO added that "about half of the decline ... occurred since June" when some of the provisions of the Tax Cuts and Jobs Act of 2017 took effect, which included the "new lower corporate tax rate and the expanded ability to immediately deduct the full value of equipment purchases".


title: National debt of the United States

text: According to articles in "The Wall Street Journal" and "Business Insider", based on documents released on October 29, 2018, by the Treasury Department, the department's projection estimated that by the fourth quarter of the FY2018, it would have issued c. $1.338 trillion in debt. This would have been the highest debt issuance since 2010, when it reached $1.586 trillion. The Treasury anticipated that the total "net marketable debt"—net marketable securities—issued in the fourth quarter would reach $425 billion; which would raise the 2018 "total debt issuance" to over a trillion dollars of new debt, representing a "146% jump from 2017". According to the "Journal" that is the highest fourth quarter issuance "since 2008, at the height of the financial crisis." As cited by the "Journal" and the "Business Insider", the primary drivers of new debt issuance are "stagnant", "sluggish tax revenues", a decrease in "corporate tax revenue", due to the GOP Tax Cuts and Jobs Act of 2017, the "bipartisan budget agreement", and "higher government spending".


title: National debt of the United States

text: As of July 20, 2020, debt held by the public was $20.57 trillion, and intragovernmental holdings were $5.94 trillion, for a total of $26.51 trillion. Debt held by the public was approximately 77% of GDP in 2017, ranked 43rd highest out of 207 countries. The CBO forecast in April 2018 that the ratio will rise to nearly 100% by 2028, perhaps higher if current policies are extended beyond their scheduled expiration date.


title: National debt of the United States

text: The national debt can also be classified into marketable or non-marketable securities. Most of the marketable securities are Treasury notes, bills, and bonds held by investors and governments globally. The non-marketable securities are mainly the "government account series" owed to certain government trust funds such as the Social Security Trust Fund, which represented $2.82 trillion in 2017.


title: National debt of the United States

text: The non-marketable securities represent amounts owed to program beneficiaries. For example, in the cash upon receipt but spent for other purposes. If the government continues to run deficits in other parts of the budget, the government will have to issue debt held by the public to fund the Social Security Trust Fund, in effect exchanging one type of debt for the other. Other large intragovernmental holders include the Federal Housing Administration, the Federal Savings and Loan Corporation's Resolution Fund and the Federal Hospital Insurance Trust Fund (Medicare).


title: National debt of the United States

text: Only debt held by the public is reported as a liability on the consolidated financial statements of the United States government. Debt held by US government accounts is an asset to those accounts but a liability to the Treasury; they offset each other in the consolidated financial statements. Government receipts and expenditures are normally presented on a cash rather than an accrual basis, although the accrual basis may provide more information on the longer-term implications of the government's annual operations. The United States public debt is often expressed as a ratio of public debt to GDP. The ratio of debt to GDP may decrease as a result of a government surplus as well as from growth of GDP and inflation.


title: National debt of the United States

text: Under normal accounting rules, fully owned companies would be consolidated into the books of their owners, but the large size of Fannie Mae and Freddie Mac has made the U.S. government reluctant to incorporate them into its own books. When the two mortgage companies required bail-outs, White House Budget Director Jim Nussle, on September 12, 2008, initially indicated their budget plans would not incorporate the government-sponsored enterprise (GSE) debt into the budget because of the temporary nature of the conservator intervention. As the intervention has dragged out, pundits began to question this accounting treatment, noting that changes in August 2012 "makes them even more permanent wards of the state and turns the government's preferred stock into a permanent, perpetual kind of security".


title: National debt of the United States

text: The federal government controls the Public Company Accounting Oversight Board, which would normally criticize inconsistent accounting practices, but it does not oversee its own government's accounting practices or the standards set by the Federal Accounting Standards Advisory Board. The on- or off-balance sheet obligations of those two independent GSEs was just over $5 trillion at the time the conservatorship was put in place, consisting mainly of mortgage payment guarantees and agency bonds. The confusing "independent but government-controlled" status of the GSEs resulted in investors of the legacy common shares and preferred shares launching various activist campaigns in 2014.


title: National debt of the United States

text: U.S. federal government guarantees were not included in the public debt total as they were not drawn against. In late 2008, the federal government had guaranteed large amounts of obligations of mutual funds, banks, and corporations under several programs designed to deal with the problems arising from the late-2000s financial crisis. The guarantee program lapsed at the end of 2012, when Congress declined to extend the scheme. The funding of direct investments made in response to the crisis, such as those made under the Troubled Asset Relief Program, was included in the debt totals.


title: National debt of the United States

text: The U.S. federal government is obligated under current law to make mandatory payments for programs such as Medicare, Medicaid and Social Security. The Government Accountability Office (GAO) projects that payouts for these programs will significantly exceed tax revenues over the next 75 years. The Medicare Part A (hospital insurance) payouts already exceed program tax revenues, and social security payouts exceeded payroll taxes in fiscal year 2010. These deficits require funding from other tax sources or borrowing. The present value of these deficits or unfunded obligations is an estimated $45.8 trillion. This is the amount that would have had to be set aside in 2009 in order to pay for the unfunded obligations which, under current law, will have to be raised by the government in the future. Approximately $7.7 trillion relates to Social Security, while $38.2 trillion relates to Medicare and Medicaid. In other words, health care programs will require nearly five times more funding than Social Security. Adding this to the national debt and other federal obligations would bring total obligations to nearly $62 trillion. However, these unfunded obligations are not counted in the national debt, as shown in monthly Treasury reports of the national debt.


title: National debt of the United States

text: GDP is a measure of the total size and output of the economy. One measure of the debt burden is its size relative to GDP, called the "debt-to-GDP ratio." Mathematically, this is the debt divided by the GDP amount. The Congressional Budget Office includes historical budget and debt tables along with its annual "Budget and Economic Outlook." Debt held by the public as a percentage of GDP rose from 34.7% GDP in 2000 to 40.5% in 2008 and 67.7% in 2011. Mathematically, the ratio can decrease even while debt grows if the rate of increase in GDP (which also takes account of inflation) is higher than the rate of increase of debt. Conversely, the debt to GDP ratio can increase even while debt is being reduced, if the decline in GDP is sufficient.


title: National debt of the United States

text: According to the "CIA World Factbook", during 2015, the U.S. debt to GDP ratio of 73.6% was the 39th highest in the world. This was measured using "debt held by the public." However, $1 trillion in additional borrowing since the end of FY 2015 raised the ratio to 76.2% as of April 2016 [See Appendix#National debt for selected years]. Also, this number excludes state and local debt. According to the OECD, general government gross debt (federal, state, and local) in the United States in the fourth quarter of 2015 was $22.5 trillion (125% of GDP); subtracting out $5.25 trillion for intragovernmental federal debt to count only federal "debt held by the public" gives 96% of GDP.


title: National debt of the United States

text: The ratio is higher if the total national debt is used, by adding the "intragovernmental debt" to the "debt held by the public." For example, on April 29, 2016, debt held by the public was approximately $13.84 trillion or about 76% of GDP. Intra-governmental holdings stood at $5.35 trillion, giving a combined total public debt of $19.19 trillion. U.S. GDP for the previous 12 months was approximately $18.15 trillion, for a total debt to GDP ratio of approximately 106%.


title: National debt of the United States

text: Conceptually, an annual deficit (or surplus) should represent the change in the national debt, with a deficit adding to the national debt and a surplus reducing it. However, there is complexity in the budgetary computations that can make the deficit figure commonly reported in the media (the "total deficit") considerably different from the annual increase in the debt. The major categories of differences are the treatment of the Social Security program, Treasury borrowing, and supplemental appropriations outside the budget process.


title: National debt of the United States

text: Social Security payroll taxes and benefit payments, along with the net balance of the U.S. Postal Service, are considered "off-budget", while most other expenditure and receipt categories are considered "on-budget". The total federal deficit is the sum of the on-budget deficit (or surplus) and the off-budget deficit (or surplus). Since FY1960, the federal government has run on-budget deficits except for FY1999 and FY2000, and total federal deficits except in FY1969 and FY1998–FY2001.


title: National debt of the United States

text: For example, in January 2009 the CBO reported that for FY2008, the "on-budget deficit" was $638 billion, offset by an "off-budget surplus" (mainly due to Social Security revenue in excess of payouts) of $183 billion, for a "total deficit" of $455 billion. This latter figure is the one commonly reported in the media. However, an additional $313 billion was required for "the Treasury actions aimed at stabilizing the financial markets," an unusually high amount because of the subprime mortgage crisis. This meant that the "debt held by the public" increased by $768 billion ($455B + $313B = $768B). The "off-budget surplus" was borrowed and spent (as is typically the case), increasing the "intra-governmental debt" by $183 billion. So the total increase in the "national debt" in FY2008 was $768B +$183B = $951 billion. The Treasury Department reported an increase in the national debt of $1,017B for FY2008. The $66 billion difference is likely from "supplemental appropriations" for the War on Terror, some of which were outside the budget process entirely until President Obama began including most of them in his FY2010 budget.


title: National debt of the United States

text: In other words, spending the "off budget" Social Security surplus adds to the total national debt (by increasing the intragovernmental debt) while the "off-budget" surplus reduces the "total" deficit reported in the media. Certain spending called "supplemental appropriations" is outside the budget process entirely but adds to the national debt. Funding for the Iraq and Afghanistan wars was accounted for this way prior to the Obama administration. Certain stimulus measures and earmarks were also outside the budget process. The federal government publishes the total debt owed (public and intragovernmental holdings) daily.


title: National debt of the United States

text: Since 2010, the U.S. Treasury has been obtaining negative real interest rates on government debt, meaning the inflation rate is greater than the interest rate paid on the debt. Such low rates, outpaced by the inflation rate, occur when the market believes that there are no alternatives with sufficiently low risk, or when popular institutional investments such as insurance companies, pensions, or bond, money market, and balanced mutual funds are required or choose to invest sufficiently large sums in Treasury securities to hedge against risk. Economist Lawrence Summers states that at such low interest rates, government borrowing actually saves taxpayer money and improves creditworthiness.


title: National debt of the United States

text: In the late 1940s through the early 1970s, the U.S. and UK both reduced their debt burden by about 30% to 40% of GDP per decade by taking advantage of negative real interest rates, but there is no guarantee that government debt rates will continue to stay this low. Between 1946 and 1974, the U.S. debt-to-GDP ratio fell from 121% to 32% even though there were surpluses in only eight of those years which were much smaller than the deficits.


title: National debt of the United States

text: Two economists, Jaromir Benes and Michael Kumhof, working for the International Monetary Fund, published a working paper called "The Chicago Plan Revisited" suggesting that the debt could be eliminated by raising bank reserve requirements and converting from fractional-reserve banking to full-reserve banking. Economists at the Paris School of Economics have commented on the plan, stating that it is already the "status quo" for coinage currency, and a Norges Bank economist has examined the proposal in the context of considering the finance industry as part of the real economy. A Centre for Economic Policy Research paper agrees with the conclusion that "no real liability is created by new fiat money creation and therefore public debt does not rise as a result."


title: National debt of the United States

text: The debt ceiling is a legislative mechanism to limit the amount of national debt that can be issued by the Treasury. In effect, it restrains the Treasury from paying for expenditures after the limit has been reached, even if the expenditures have already been approved (in the budget) and have been appropriated. If this situation were to occur, it is unclear whether Treasury would be able to prioritize payments on debt to avoid a default on its debt obligations, but it would have to default on some of its non-debt obligations.


title: National debt of the United States

text: Because a large variety of people own the notes, bills, and bonds in the "public" portion of the debt, the Treasury also publishes information that groups the types of holders by general categories to portray who owns United States debt. In this data set, some of the public portion is moved and combined with the total government portion, because this amount is owned by the Federal Reserve as part of United States monetary policy. (See Federal Reserve System.)


title: National debt of the United States

text: As is apparent from the chart, a little less than half of the total national debt is owed to the "Federal Reserve and intragovernmental holdings". The foreign and international holders of the debt are also put together from the notes, bills, and bonds sections. To the right is a chart for the data as of June 2008:


title: National debt of the United States

text: As of October 2018, foreigners owned $6.2 trillion of U.S. debt, or approximately 39% of the debt held by the public of $16.1 trillion and 28% of the total debt of $21.8 trillion. In December 2020, foreigners held 33% ($7 trillion out of $21.6 trillion) of publicly held US debt; of this $7 trillion, $4.1 trillion (59.2%) belonged to foreign governments and $2.8 trillion (40.8%) to foreign investors. Including both private and public debt holders, the top three December 2020 national holders of American public debt are Japan ($1.2 trillion or 17.7%), China ($1.1 trillion or 15.2%), and the United Kingdom ($0.4 trillion or 6.2%).


title: National debt of the United States

text: Historically, the share held by foreign governments had grown over time, rising from 13% of the public debt in 1988 to 34% in 2015. In more recent years, foreign ownership has retreated both in percent of total debt and total dollar amounts. China's maximum holding of 9.1% or $1.3 trillion of U.S. debt occurred in 2011, subsequently reduced to 5% in 2018. Japan's maximum holding of 7% or $1.2 trillion occurred in 2012, subsequently reduced to 4% in 2018.


title: National debt of the United States

text: According to Paul Krugman, "America actually earns more from its assets abroad than it pays to foreign investors." Nonetheless, the country's net international investment position represents a debt of more than $9 trillion.


title: National debt of the United States

text: The CBO estimated the impact of the Tax Cuts and Jobs Act and separate spending legislation over the 2018–2028 period in their annual "Budget & Economic Outlook", released in April 2018:


title: National debt of the United States

text: The CBO estimated that the budget deficit for fiscal year 2020 would increase to $3.3 trillion or 16% GDP, more than triple that of 2019 and the largest as % GDP since 1945, because of the impact of the COVID-19 pandemic. CBO also forecast the debt held by the public would rise to 98% GDP in 2020, compared with 79% in 2019 and 35% in 2007 before the Great Recession.


title: National debt of the United States

text: The CBO reports its "Long-Term Budget Outlook" annually, providing at least two scenarios for spending, revenue, deficits, and debt. The 2019 Outlook mainly covers the 30-year period through 2049. The CBO reported:


title: National debt of the United States

text: Large budget deficits over the next 30 years are projected to drive federal debt held by the public to unprecedented levels—from 78 percent of gross domestic product (GDP) in 2019 to 144 percent by 2049. That projection incorporates CBO’s central estimates of various factors, such as productivity growth and interest rates on federal debt. CBO’s analysis indicates that even if values for those factors differed from the agency’s projections, debt several decades from now would probably be much higher than it is today.


title: National debt of the United States

text: If lawmakers changed current laws to maintain certain major policies now in place—most significantly, if they prevented a cut in discretionary spending in 2020 and an increase in individual income taxes in 2026—then debt held by the public would increase even more, reaching 219 percent of GDP by 2049. By contrast, if Social Security benefits were limited to the amounts payable from revenues received by the Social Security trust funds, debt in 2049 would reach 106 percent of GDP, still well above its current level.


title: National debt of the United States

text: Over the long-term, the CBO projects that interest expense and mandatory spending categories (e.g., Medicare, Medicaid and Social Security) will continue to grow relative to GDP, while discretionary categories (e.g., Defense and other Cabinet Departments) continue to fall relative to GDP. Debt is projected to continue rising relative to GDP under the above two scenarios, although the CBO did also offer other scenarios that involved austerity measures that would bring the debt to GDP ratio down.


title: National debt of the United States

text: The CBO reported several types of risk factors related to rising debt levels in a July 2010 publication:


title: National debt of the United States

text: According to a 2013 Forbes article, many American and other economic analysts have expressed concerns on account of the People's Republic of China's "extensive" holdings of United States government debt as part of their reserves. The National Defense Authorization Act of FY2012 included a provision requiring the Secretary of Defense to conduct a "national security risk assessment of U.S. federal debt held by China." The department issued its report in July 2012, stating that "attempting to use U.S. Treasury securities as a coercive tool would have limited effect and likely would do more harm to China than to the United States. An August 19, 2013 Congressional Research Service report said that the threat is not credible and the effect would be limited even if carried out. The report said that the threat would not offer "China deterrence options, whether in the diplomatic, military, or economic realms, and this would remain true both in peacetime and in scenarios of crisis or war."


title: National debt of the United States

text: A 2010 article by James K. Galbraith in "The Nation", defends deficits and dismisses concerns over foreign holdings of United States government debt denominated in U.S. dollars, including China's holdings. In 2010, Warren Mosler, wrote that "When[ever] the Chinese redeem those T-securities, the money is transferred back to China's checking account at the Fed. During the entire purchase and redemption process, the dollars never leave the Fed." Australian economist Bill Mitchell argued that the United States government had a "nearly infinite capacity...to spend." An August 2020 "Kyodo News" report from Beijing, says that, against the backdrop of an escalation in Sino-U.S. tensions, financial markets are concerned that China might weaponize its holdings of over a $1 trillion of United States debt. If China undertakes a massive sales of its U.S. Treasury bonds, it would result in a decrease in the price of debt and an increase in interest rates in the United States, that would stifle American domestic "investment and consumer spending." However, a massive Chinese selloff, resulting in a drop in the price of debt, will also adversely impact China's proceeds on sale as well as the value of its remaining holdings.


title: National debt of the United States

text: In 2009 the Government Accountability Office (GAO) reported that the United States was on a "fiscally unsustainable" path because of projected future increases in Medicare and Social Security spending. According to the Treasury report in October 2018, summarized by "Business Insider"'s Bob Bryan, the U.S. federal budget deficit rose as a result of the Tax Cuts and Jobs Act of 2017 signed into law by President Donald Trump on December 22, 2017 and the Consolidated Appropriations Act, 2018 signed into law on March 23, 2018.