Latitude Angle Research Articles

Performance of flat plate solar collectors in off-south orientation in India

This paper presents the effect of off-south orientation on the performance of flat plate solar collectors. This study is done, taking into consideration the building's off-south orientation. The present work investigates collector performance and optimum tilt as functions of the off-south angle, collection temperature, latitude and wind velocity. The three latitudes considered are of New Delhi(L = 28.38°N), Bangalore (L = 12.97°N) and Madras (13.0°N). It has been found that, for the best average winter performance, the tilt is latitude angle +15°, whereas, for the best average summer performance, it is latitude angle −15°. It has also been confirmed that, for year round operation, the maximum solar energy is collected when the tilt is 0.9 times the latitude angle. Further, it has been noticed that there is an optimum value of collector tilt for a given azimuthal angle at which yearly effectiveness is a maximum. The effect of increase in off-south angle is to decrease the yearly effectiveness.

HEAO 3 measurements of the atmospheric positron annihilation line

All spectra measured with the High Energy Resolution Gamma‐Ray Spectroscopy Experiment (HEAO C‐1) on the third High Energy Astronomy Observatory (HEAO 3) contain a strong line at 511 keV resulting from positron annihilation. This line originates in the instrument itself, the earth's atmosphere, and cosmic sources, possibly including the diffuse cosmic background. In order to understand the emission from cosmic sources, the atmospheric positron annihilation line emission has been determined as a function of geomagnetic latitude and zenith angle. Although the intensity of the line increases with increasing latitude, it was found that variations with zenith angle can be satisfactorily explained only if the atmospheric emission exhibits significant limb darkening. The atmospheric line has an energy of 511.07±0.10 keV and a net width of 2.29±0.30 keV FWHM. Characteristics of the instrument background have allowed an upper limit of 9.4 × 10−3 photons/cm² ‐sec‐sr to be placed on any narrow (≲3 keV) diffuse cosmic emission at 511 keV.

The Parker spiral configuration of the interplanetary magnetic field between 1 and 8.5 AU

An analysis is presented of the magnetic field data obtained by the Pioneer 10 and 11 spacecraft. The purpose is to provide a quantitative picture of the overall configuration of the interplanetary magnetic field in the outer heliosphere. The field directions observed between 1 and 8.5 AU are found, on average, to conform to the Parker spiral directions within both quiet regions and interaction regions to an overall accuracy of 1.1°. The average latitude angle of the field is shown to be zero within a similar accuracy. The included angle between the inward and outward sectored field directions is found to be very close to 180° and displays no solar cycle dependent trends, such as have been previously reported. The field direction is shown to display greater variability in quiet regions than in interaction regions, a fact which is important in terms of the effect of interaction regions on the propagation of energetic particles. The fractional polarities for observations below 10° heliographic latitude are shown to be dominated by temporal variations; however, dual‐spacecraft studies have allowed a significant latitudinal gradient to be extracted. This result is qualitatively consistent with the almost complete disappearance of the inward sector at 16° heliographic latitude, although it is suggested that the latter effect may be due to a lower than average current sheet inclination in 1976. The sector structure is shown to extend occasionally to these high latitudes during this time, implying a deflection of the equatorial current sheet, in association with individual interaction regions. It is suggested that the fast streams associated with interaction regions may move the current sheet to higher heliographic latitudes when the source of the fast plasma is in the southern solar hemisphere.

Stratospheric free chlorine measured by balloon‐borne in situ resonance fluorescence

Eight balloon‐borne in situ measurements of ClO in the stratosphere are presented. Six of the observations, which were carried out close to local noon, are compared with recent model calculations at the appropriate latitude (32°N), altitude (25–45 km), and solar zenith angle interval (10° < χ < 55°). The ClO mixing ratio by volume observed on four flights between the autumnal equinox and the winter solstice (September 20, October 25, December 2, and December 8, 1977)is found to exhibit little variability, defining an envelope which decreases from 0.5 to 1.1 ppb at 42 km to 10 to 50 ppt at 25 km. Two observations in July (July 28, 1976, and July 14, 1977) indicate significantly higher mixing ratios, the former increasing from 0.8 ppb at 42 km to 1.8 ppb at 36 km and then decreasing to 0.1 ppb at 24 km in reasonable agreement with calculations using 2.2 ppb total chlorine and 8 ppm H2O at the stratopause. The latter summer observation exhibits a serious divergence from calculated densities above 32 km, reaching 7 ppb in a layer between 35 and 40 km. Emphasis is given to a description of laboratory simulation experiments done in parallel with the stratospheric observations and to techniques used for determining the absolute sensitivity of the instrument. Results of the in situ observations are compared with recent results from the laser heterodyne and microwave limb scanning remote sensing methods. The simultaneous observations of [ClO] and [O3] on July 14, 1977, are used in conjunction with a formulation of odd oxygen chemistry in terms of rate limiting steps to deduce that either (a) the [ClO] or [O3] observation is wrong, (b) the observed chlorine was injected into the stratosphere in a period short in comparison with the chemical response time of ozone, or (c) there are important mechanistic steps missing from stratospheric chlorine‐ozone photochemistry.

Mirror enclosures for double-exposure solar collectors

A conventional flat-plate collector panel can be employed in a double-exposure configuration when the panel is glazed on both sides and when mirrors are provided to reflect solar radiation onto the back side of the panel. In this paper, several flat-mirror configurations are evaluated and optimal configurations are determined for different solar energy applications at lat. 35, 40 and 45°. The various mirror configurations are evaluated theoretically by calculating direct-beam and diffuse solar radiation enhancement factors. The enhancement factors are defined as the ratio of the solar flux absorbed by both sides of a double-exposure panel to that absorbed by an identical single-exposure panel tilted at the latitude angle from the horizontal. The enhancement factors are calculated using the method of images and take account of the variation of glazing transmittance with incident angle. Optimal mirror configurations were determined for direct-beam solar radiation for both fixed-mirror configurations and adjustable-mirror configurations with semi-annual mirror rotations. Optimal fixed-mirror configurations were obtained for both winter space-heating and year-round applications. An adjustable-mirror configuration, however, was determined to be optimal for year-round solar collection and overall to be most adaptable to a variety of solar energy applications. The same adjustable-mirror configuration was determined to be optimal at all three latitudes and therefore a single design can be employed at diverse locations.

A New Thermal Rating Approach: The Real Time Thermal Rating System for Strategic Overhead Conductor Transmission Lines Part III Steady State Thermal Rating Program Continued-Solar Radiation Considerations

For the first time, equations and computer programs are developed to show how the solar radiation received by an overhead transmission line is dependent on the conductor sag or slope. In the past, the overhead line has been assumed to lie in a horizontal plane with respect to the earth for the entire span length. Mathematical relationships for determining the sun's position in terms of solar azimuth and solar altitude, as a function of latitude, declination and hour angle are formulated and a polar plot is constructed to show the apparent path of the sun during the day for each month. Two different methods are presented to determine the angle of incidence between the sun's ray and the normal to any sloped cylindrical surface oriented at any azimuth angle. Plots are provided to indicate the variation in the angle of incidence and the direct component of solar radiation absorbed as a function of solar time for four general transmission line azimuths and five slopes at one latitude and declination. In addition, plots are drawn for the total solar radiation received by a conductor on a typical clear day as a function of both the span length and any sag or slope for both minimum and maximum diffuse radiation conditions for four general transmission line azimuths at one latitude and declination. It is shown that the conductor slope can have as much of an effect on the total radiation as does the solar adsorption constant.

Unexploited Potentials of Loran-C

Current Loran-C radio navigation equipment has demonstrated a repeatable precision index of less than 0.01 μs/km. Thus, two co-located receivers measuring the same time difference will deviate less than this amount as to the standard deviation of their measured time difference. It is therefore concluded that operation of Loran-C in a differential mode is a feasible technique for such practical matters as collision avoidance, instrument landing systems, air traffic control, precise location of surface vessels used out of sight of land in underwater exploration, and ground based vehicle location in the non-urban environment. By differential operation mode, we mean that two vehicles can determine their distance apart, their rate of closing or separation, and indeed their direction of relative motion, if the measured time difference information on each vehicle is relayed between vehicles. Loran-C can be compared quantitatively with other systems such as Omega operating in a differential mode. A comparison of Loran-C data with the Beukers-Nard Omega data reveals a possible 20 to 100 accuracy improvement factor if we use Loran-C instead of Omega in the 0 to 700 km differential separation range. We conclude that the fundamental reason for part of the improvement is the reciprocal phase measurement improvement with frequency. The remainder of the improvement is a consequence of the greater stability of the pulsed ground wave propagation mechanism of Loran-C as compared with the single frequency ionospheric waves of Omega. Frequencies greater than 100 kHz would give greater improvement with a loss of range or coverage area. We have found that Loran-C is an excellent propagation measuring device for the detection and identification of effects of irregular, in-homogeneous terrain in the spatial domain, and the study of meteorological variations in the time domain. Furthermore, the Loran-C skywave signal can be used as a D-region diagnostic to study particle precipitation events and D-region variations with latitude, season and solar zenith angle. We make the observation from our Loran-C studies that the first prerequisite to a capability for prediction of propagation phenomena is the ability to separate, identify, and understand the physical nature of the observed radio measurements. This prediction capability is essential to the successful operation of radio navigation systems in both the normal and the differential mode of operation.

Enhanced solar energy collection using reflector-solar thermal collector combinations

The amount of direct light gathered by a combination of reflector plus flat-plate collector has been analyzed. The calculations were done allowing variable reflector and collector orientation angles, variables latitude, and arbitrary sun hour angle away from solar noon. The effects of reflection and transmission losses and of polarization of the incident light were included. Correction was also made for the finite size of the reflector. It was found that the optimum orientation has the collector plane almost perpendicular to the plane of the reflector. This optimum orientation is approximately independent of the sun's azimuthal dependence. The optimum reflector angle is found to be between 0° and 10° above the horizon for winter solar conditions. For typical winter operating conditions the enhancement in light gathering power for direct solar radiation is about a factor of 1·4–1·7. This results in an effective increase of 100% in the useful winter heat output from a practical reflector-collector combination with a reflector angle of 0°, over the useful heat output obtained with an optimally oriented simple flat-plate collector. An approximate calculation was also made of the overall enhancement in useful heat output for diffuse solar radiation; an increase by a factor of about 1·5 is predicted. Comparison with the preliminary analysis of the performance of the Coos Bay, Oregon solar house shows substantial agreement with the predictions of the present analysis.

Polarization of gravitational geodesic synchrotron radiation

We calculate gravitational radiation as emitted by a test particle moving in a relativistic geodesic circular orbit in the Schwarzschild geometry. For this purpose we first give a compact version of the perturbation technique (using tensor spherical harmonics) for tensor radiation perturbing the Schwarzschild geometry. The polarization properties are analyzed with the help of gravitational Stokes parameters. The radiation is almost totally linearly polarized within the main beam, but the various polarization quantities depend much more strongly on the latitude angle of observation than they do for the analogous electromagnetic radiation at the same frequencies.

Topside ionosphere at sunrise

The sunrise behavior of the midlatitude topside ionosphere at low sunspot numbers was examined by using Alouette 1 electron density and plasma scale height profiles obtained at Stanford University during May and June 1963. Under the assumption that observed variations result from solar control, the data were averaged to form height profiles of plasma scale height and electron density from 450 to 750 km altitude, which vary smoothly with solar zenith angle χ. The first manifestation of sunrise is a sudden and rapid decrease in plasma scale height, beginning between χ=105° and 102° and ending between χ=98° and 96°. Electron densities increase rapidly between χ=98° and 95°. Our interpretation of the observations is that the sudden decrease in plasma scale heights is due to an increase in percentage concentration of O+ ions at all altitudes, due primarily to a thermal expansion of the ionosphere that causes an upward movement of the topside ionization. The velocity of the thermal motion is estimated, and we attempt to resolve conflicting evidence from other observations that the topside ionosphere is controlled by either geomagnetic latitude or solar zenith angle.

Scattering of radio waves from the ionosphere in presence of time varying random irregularities

In this paper the modified formula for scattering cross-section of radio waves from the ionosphere has been deduced in presence of time-varying random irregularities. The anisotropic behaviour of the medium which arises due to the presence of the geomagnetic field along with the time-varying irregularities of the medium has been considered. The derived expression for the dielectric tensor for the above medium has been utilised to obtain the required cross-section. The latitude, altitude, azimuth and polarisation angle dependence of scattering of radio waves from the ionosphere has been shown. The evaluated formula may be verified experimentally and the importance of the geomagnetic field and irregularities may then be analysed.

Broad Band Micropulsation Activity at a Geomagnetic Midlatitude Station

The relationships of broad band geomagnetic micropulsations (periods from 20-300sec.) at Strawberry Hill, Concord, Mass, to some magnetospheric, interplanetary, and solar phenomena are examined to ascertain possible locations of energy sources for their excitation. The micropulsation activity is characterized by a one-hour, quasi-logarithmic index, M, which is chiefly a measure of hydromagnetic (HM) wave amplitudes. The strong diurnal variation in the HM wave energy continues to elude adequate explanation. However, it is apparent that the excitation of these waves is favored in the daylight hemisphere. High micropulsation activity levels generally obtain during periods of sustained magnetic disturbance, but several exceptions preclude the existence of a direct cause-and-effect relationship. Indirect evidence suggests the importance of magnetospheric convection in controlling the micropulsation activity level. Daily micropulsation activity levels are more closely related to interplanetary magnetic field variability than to daily averages of the solar wind velocity. No significant relationship between the sign of θ (the latitude angle of the interplanetary magnetic field vector in solar ecliptic coordinates) and micropulsation activity is indicated by the present study. Superposed epoch analysis reveals an association of highly disturbed micropulsation days with the central meridian passage (CMP), 3 to 5 days earlier, of solar regions characterized by low levels of calcium plage activity. It is suggested that high micropulsation activity levels are more closely associated with the CMP of unipolar magnetic regions (UMR) than are high geomagnetic activity levels.

On Certain Truncation Errors Associated with Spherical Coordinates

Excessive errors are committed in grids, in which mesh-lengths in the longitudinal direction are preserved in polar regions, if the hydrodynamic equations written in spherical coordinates are directly transformed into finite differences. The errors arise from the curvilinearity of the coordinate system. One alternative is the abandonment of spherical coordinates, with the retention of the constant mesh-length grid, an alternative which is not economical. The errors can be reduced by at least two orders of magnitude by adoption of a grid regular in latitude and longitude angle, with the consequent great space resolution in polar regions. Even the latter alternative may result in unacceptable truncation errors in finite-difference equations in spherical co-ordinates. It turns out, however, that if one departs from spherical coordinates to the extent of expressing velocity components in Cartesian coordinates on locally tangent planes, a further reduction of error by an order of magnitude is achieved, a reduction to perhaps acceptable levels.

Latitude, altitude, azimuth and polarization angle dependence of scattering of radio waves in the ionosphere considering anisotropy

This paper describes the latitude, altitude, azimuth and polarization angle dependence of scattering of radio waves in the ionosphere. The anisotropic behaviour which arises due to the presence of the geomagnetic field has been taken into account. The formula obtained for scattering cross-section may be verified experimentally and the importance of the geomagnetic field in the production of anisotropy may then be analysed.

On the anomalous component of low-energy geomagnetically trapped protons

The energy spectrum of trapped protons shows a pronounced variation with latitude at energies <30 Mev. An anomalous, low-energy component is found on relatively high magnetic shells in the inner zone. The interpretation in terms of the decay of albedo neutrons generated in the polar caps by solar cosmic rays is examined. This interpretation requires that the inner shells, where a normal spectrum is seen, should be shielded from the polar source. The intensity of albedo neutrons as a function of energy, latitude, and zenith angle is computed. The injection rate into specific trapped orbits is then evaluated, and it is shown that those orbits where no anomalous component exists cannot be populated by the solar cosmic-ray mechanism, whereas the orbits where the anomalous component is seen can be populated. Assuming adiabatic trapping in this low-energy region, lifetimes are long compared with the average intervals between large injection events. Therefore, the anomalous component may represent an equilibrium phenomenon rather than a transient. This component should extend into the outer belt.

Effects of non-primary cosmic radiation on the number-energy relation and geomagnetic correlations near the top of the atmosphere

Experimental results for flights at the geomagnetic latitudes 10 deg and 55 deg North in 1953 are presented. The data are presented in total flux as a function of atmospheric depth, pulse height distributions during ascent, and fast albedo and slow proton intensities at 0 and 60 deg zenith angles. The character of the splash albedo is illustrated by plots of its dependence on geomagnetic latitude, zenith and azimuthal angle, and on atmospheric depth. (M.H.R.)

A One-Body Fix

In U.S. Naval Institute Proceedings for June 1957 (page 680), Captain P. V. H. Weems and Captain R. E. Jasperson outline a method for finding a position by observing one celestial body only. The principle of the method is to use the observed rate of change of altitude, together with the observed altitude itself, to solve directly for latitude and hour angle, and thus to obtain the position. The authors point out that the parallactic angle, C (the angle at the observed body), in the usual navigational spherical triangle is obtainable from:sin C = sec (declination) × rate of change of altitude with hour angle.

Precomputed Altitudes

P. F. Everitt (Journal, Vol. 2, No. 1, p. 49) has discussed the problem of precomputing sights but gives the impression that the A.N.T.s cannot be used for this purpose; this is not the case, provided of course that the accuracy of 1 or 2 miles obtainable from A.N.T.s is acceptable. My experience of the method described below is confined to marine use with Hughes' Tables, but the same limitation of being confined to integral degrees of latitude and hour angle applies, so the method is clearly applicable in the air. Provided that the observation is actually obtained, the extra work involved in computing the sight in advance is trifling, and there are often appreciable advantages.

The Willis Navigating Machine

AT a recent meeting of the Royal Astronomical Society, the capabilities of this ingenious instrument (aviation type), designed by Mr. E. Willis for the solution of spherical triangles, were demonstrated by Dr. L. J. Comrie, Superintendent, H.M. Nautical Almanac Office. Mechanically, the instrument is a combination of an alt-azimuth and equatorial with five graduated circles corresponding to altitude, azimuth, latitude, declination, and hour angle. The principal problem in nautical astronomy is the calculation of the altitude and azimuth of a heavenly body from given values of the latitude, declination, and hour angle. These quantities are set on the corresponding circles and the machine at once gives the appropriate altitude and azimuth, which can then be used, in conjunction with the altitude from a sextant observation, to give the position line on the chart. This is only one of the many problems that the instrument can solve. In the type of instrument designed for aeronautical navigation, the circles read to five minutes of arc, which is sufficiently accurate in practice, being of the same order of accuracy as readings made with a bubble-sextant. The instrument designed for marine purposes is larger and more accurate; in this type the graduated circles read to one minute of arc. In æronautical navigation, the quick reduction of observations is an essential desideratum, and the Willis machine gives complete satisfaction in this respect. The instruments are manufactured by Messrs. Heath and Co., New Eltham, London, S.E.9.

Lead Hydrogen Arsenate as a Mineral

A SPECIMEN from the Tsumeb mines in the Otavi district, South-West Africa, recently acquired for the Mineral Collection of the British Museum, shows colourless transparent crystal plates with brilliant lustre, which had been labelled lanarkite. The largest of these are 1 cm. across with a thickness of 1 mm. They rest on a crust of bayldonite pseudomorphous after mimetite (chloro-arsenate of lead), chessylite, and large crystals of anglesite (PbSO4). The crystals are monoclinic (a:b:c = 0.8643:1:0.7181, = 84° 36′) and show a development of sixteen crystal-forms. These forms have been listed to show the angles from each to the three axial planes; and it is believed that such a method of tabulation may effect a compromise between the method of giving interfacial angles in zones and that of longitude and latitude (ϕ and ρ) angles employed in two - circle goniometry. The crystals are optically positive, and the optic axial plane is perpendicular to the plane of symmetry and direction of good cleavage. The refraction (nγ = 1.9765 for sodium-light), birefringence, and dispersion are all high.