Effects of overhang shading of windows having arbitrary azimuth

A method is presented for calculating either nonthly average or clear-day insolation on overhang shaded windows of arbitrary azimuth. This technique is based on an extension to a totally arbitrary orientation of the methods of Liu and Jordan[1] and of Klein[2] for estimating the radiation on tilted surfaces.     

A method of estimating monthly average solar radiation on shaded receivers

The geometry of vertical solar radiation receivers shaded by overhangs is described. The instantaneous mean solar radiation on a shaded receiver is defined leading to a method of estimating , the monthly average daily radiation on a shaded receiver. Values of the monthly average beam irradiated fraction of the receiver area, , are presented in a series of figures. The effects of overhang extension and receiver azimuth on are considered. Example calculations are presented and the overall effect of an overhang as a shading device is discussed.     

Effect of manual tilt adjustments on incident irradiance on fixed and tracking solar panels

Hourly typical meteorological year (TMY3) data was utilized with the Perez radiation model to simulate solar radiation on fixed, azimuth tracking and two axis tracking surfaces at 217 geographically diverse temperate latitude sites across the contiguous United States of America. The optimum tilt angle for maximizing annual irradiation on a fixed south-facing panel varied from being equal to the latitude at low-latitude, high clearness sites, to up to 14° less than the latitude at a north-western coastal site with very low clearness index. Across the United States, the optimum tilt angle for an azimuth tracking panel was found to be on average 19° closer to vertical than the optimum tilt angle for a fixed, south-facing panel at the same site. Azimuth tracking increased annual solar irradiation incident on a surface by an average of 29% relative to a fixed south-facing surface at optimum tilt angle. Two axis tracking resulted in an average irradiation increase of 34% relative to the fixed surface. Introduction of manual surface tilt changes during the year produced a greater impact for non-tracking surfaces than it did for azimuth tracking surfaces. Even monthly tilt changes only resulted in an average annual irradiation increase of 5% for fixed panels and 1% for azimuth tracked surfaces, relative to using a single optimized tilt angle in each case. In practice, the decision whether to manually tilt panels requires balancing the added cost in labor and the panel support versus the extra energy generation and the cost value of that energy. A Supplementary spreadsheet file is available that gives individual results for each of the 217 simulated sites.     

Calculation of monthly average daily insolation on tilted, variously oriented surfaces using analytically weighted factors

A new, analytic method for calculating monthly average daily insolation on surfaces with various tilts and orientations is proposed. Beside the usual geometrical expressions concerning diurnal sun path, this method also takes into account changes in atmospheric transmissivity. Results are compared with those obtained by the widely accepted Klein's method also based on daily radiation data, as well as with more detailed and more accurate hourly calculations. Our results for two climatically very different locations in Yugoslavia stand in close agreement with hourly calculations for surfaces of arbitrary orientation and tilt, whereas Klein's method leads to significant error for large azimuth angles.     

Calculation of monthly average daily insolation on tilted,variously oriented surfaces using analytically weighted Rb factors

A new, analytic method for calculating monthly average daily insolation on surfaces with various tilts and orientations is proposed. Beside the usual geometrical expressions concerning diurnal sun path, this method also takes into account changes in atmospheric transmissivity. Results are compared with those obtained by the widely accepted Klein's method also based on daily radiation data, as well as with more detailed and more accurate hourly calculations. Our results for two climatically very different locations in Yugoslavia stand in close agreement with hourly calculations for surfaces of arbitrary orientation and tilt, whereas Klein's method leads to significant error for large azimuth angles.     

Shading effect of eggcrate devices on vertical windows of arbitrary orientation

A combination of horizontal and vertical elements forming an eggcrate-type shading system is often used in the architectural design of building facades. An analytical-numerical method is presented to estimate the shading effect of such a structure on vertical windows of arbitrary azimuthal orientation. The effect of reflections from aggregate walls is accounted for in the analysis. Daily and monthly average solar radiation data are presented for shaded windows in Venice (45.40° northen latitude). The effects of the window geometry and the eggcrate projection are discussed.     

The optimisation of the angle of inclination of a solar collector to maximise the incident solar radiation

Irradiation data, recorded on vertical surfaces facing north, south, east and west and on a horizontal surface every ten minutes during daylight hours from January–December 1992 in Valencia, Spain, have been compared with estimated solar irradiation from inclined-surface models. Results show that Hays model most accurately reproduces the variation in irradiation on all vertical surfaces.Hays model has been used to find the hourly variation in the optimum tilt angle for a South-facing solar collector in Valencia, Spain, and also to calculate the yearly average of this angle. This method has been compared with the results provided by another model that uses average monthly values of daily irradiation derived from the same experimental data, to calculate average monthly values of the optimum tilt angle. The results show that the method involving monthly averages is more accurate and easier to work with.     

Estimation of monthly average daily and hourly solar radiation impinging on a sloped surface using the isotropic sky model for Dhahran, Saudi Arabia

In this paper the isotropic sky method of Liu and Jordan is used to theoretically estimate the monthly average daily and hourly solar radiation impinging on an unshaded tilted surface in Dhahran, Saudi Arabia. The surface receiving solar radiation is assumed to be fixed at a tilt angle, β, equal to the latitude of Dhahran, Ø and oriented such that it is facing south with zero azimuth angle, γ. The calculation of total radiation on a sloped surface from measurements on a horizontal surface is discussed. Monthly average daily and hourly solar radiation values are then tabulated. The results obtained can be effectively employed in solar process design calculations.     

Calculation of monthly average insolation on tilted surfaces

Several simplified design procedures for solar energy systems require monthly average meteorological data. Monthly average daily totals of the solar radiation incident on a horizontal surface are available. However, radiation data on tilted surfaces, required by the design procedures, are generally not available. A simple method of estimating the average daily radiation for each calendar month on surfaces facing directly towards the equator has been presented by Liu and Jordan [1]. This method is verified with experimental measurements and extended to allow calculation of monthly average radiation on surfaces of a wide range of orientations.     

Solar radiation on variously oriented sloping surfaces

Monthly average daily irradiation on surfaces tilted towards the equator and also inclined at various azimuth angles are estimated for two locations in Lesotho and the results are presented. The isotropic model suggested by Liu and Jordan (Trans. of Ashrae, 526, 1962) along with the modified equation of Klein (Solar Energy, 19, 4, 1977) are employed for the estimation purposes. Surface orientations are selected at three inclinations for six different azimuth angles. Conclusions are reached for optimum tilt and orientation for summer, winter and annual collection. Total annual radiation values are computed for all the slopes and orientations.     

Radiation modelling and performance evaluations of fixed,single- and double-axis tracking surfaces: a case study for Dhahran city,Saudi Arabia

This work overviews the solar radiation basics and insolation of different surfaces is presented. A complete solar radiation modelling and investigation on the effect of horizontal plate, yearly tilt, monthly tilt, and single-axis and double-axis tracking surface on the insolation are carried out to conduct performance evaluation using the case study in Dhahran city of Saudi Arabia. The increments received by insolation for the yearly tilt, monthly tilt, and single-axis and dual-axis tracking surface with respect to traditional flat-plate collector is estimated. The results show that the yearly optimal tilt angle due to the south is close to the 0.913 time latitude of Dhahran. It is found that the yearly irradiation gains using yearly and monthly optimal tilts relative to flat panel installation are 7% and 14%, respectively. The yearly insulation gains made by single-axis and dual-axis continuous tracking surfaces are 33% and 48%, respectively.     

A study on the intercepted insolation as a function of slope and azimuth of the surface

Monthly average daily global radiation on surfaces tilted towards the equator and also inclined at various azimuth angels are estimated for three locations in the Southern African region from reported global and diffuse radiation on a horizontal surface. The anisotropic model suggested by Hay is used in obtaining daily radiation at various slopes and orientations. Total annual radiation data are also computed for various tilt and azimuth angles and optimum tilt and azimuth angels corresponding to maximum insolation are obtained for winter, summer and annual collection. The optimum tilt and orientation reported here show some variation from those reported earlier by other investigators and the results are discussed.     

OPTIMUM TILT ANGLE FOR SOLAR COLLECTION SYSTEMS

For non-tracking solar collection systems, the tilt angle has a predominant effect on the quantity of energy that the system can intercept. In the present work, a computational algorithm is developed for the calculation of the optimum tilt angle that would orient a non-tracking solar collection system (concentrating or non-concentrating) in its best position for the maximum average daily, monthly seasonal or yearly intercepted radiation. The optimum tilt angles were obtained for latitudes ranging from l0–50oN on monthly, seasonal and yearly bases. A case study is applied on Riyadh City (latitude 24.9°N) to investigate the sensitivity of intercepted radiation when the tilt angle varies from that of the optimum value. The results show that, on a monthly basis when the collector is mounted at the yearly optimum tilt angle, the loss of radiation intercepted is less than 10% as compared to the monthly optimum tilt angle. The optimum seasonal tilt angle reduces the incident radiation by less than 2% from that of the monthly optimum tilt angle.     

A simple formula for estimating global solar radiation in central arid deserts of Iran

Over the last two decades, using simple radiation models has been an interesting task to estimate daily solar radiation in arid and semi-arid deserts such as those in Iran, where the number of solar observation sites is poor. In Iran, most of the models used so far, have been validated for a few specific locations based on short-term solar observations. In this work, three different radiation models (Sabbagh, Paltridge, Daneshyar) have been revised to predict the climatology of monthly average daily solar radiation on horizontal surfaces in various cities in central arid deserts of Iran. The modifications are made by the inclusion of altitude, monthly total number of dusty days and seasonal variation of Sun–Earth distance. A new height-dependent formula is proposed based on MBE, MABE, MPE and RMSE statistical analysis. It is shown that the revised Sabbagh method can be a good estimator for the prediction of global solar radiation in arid and semi-arid deserts with an average error of less than 2%, that performs a more accurate prediction than those in the previous studies. The required data for the suggested method are usually available in most meteorological sites. For the locations, where some of the input data are not reported, an alternative approach is presented.     

General models for optimum tilt angles of solar panels: Turkey case study

This paper deals with finding the optimum tilt angle of solar panels for solar energy applications. The optimization of tilt angles was performed using solar radiation data measured for eight big provinces in Turkey. The optimum angle for tilted surfaces varying from 0° to 90° in steps of 1° was calculated by searching for the values of which the daily total solar radiation was at a maximum for a specific period. It was found that the optimum tilt angle changed between 0° and 65° throughout the year in Turkey. It was seen that the optimum tilt angle reached a minimum of 0° in June and July and, the monthly average daily total radiation at this angle was generally at a maximum. In addition, the optimum tilt angle increased during the winter months and reached a maximum in December in all provinces. Likewise, general correlations were developed to estimate the optimum tilt angle of solar collectors used in Turkey and their accuracies were compared on the basis of statistical error tests of Mean Bias Error (MBE), Root Mean Square Error (RMSE), t-statistic (t-stat) and correlation coefficient (r).     

Model evaluation and optimum collector slope for a tropical country

Various models proposed in the literature, viz. the Beam method, proposed by Morse & Czarnecki; two methods proposed by Liu & Jordan, using hourly values and average daily values of solar radiation: and Klucher's method are compared in this paper using measured hourly values of global and diffuse radiation on a horizontal surface and the total radiation on a tilted surface. It was observed that the model proposed by Klucher estimates the radiation more consistently with the experimental observations for clear as well as cloudy sky conditions.

This method was used for predicting the year round radiation availability on (i) a fixed collector inclined at an optimum tilt, (ii) a partially tracking collector in which the slope is fixed but following the sun's azimuth angle, and (iii) a fully tracking collector. In this analysis, measured values of hourly global and diffuse solar radiation on a horizontal plane for four widely separated Indian stations, viz. Delhi (28°38′N), Poona (18°29′N), Calcutta (22°36′N), and Madras (13°8′N) as per India Meteorological Department classification for climatic analysis, have been used.

With the model proposed, the radiation availability on different slopes for all the twelve months of the year for a fixed and partially tracking collector have been evaluated and optimum tilts for various seasons of a year for different solar energy applications for all the four Indian stations have been determined. For a typical winter month at New Delhi in the semi-arid zone of India, a fixed collector, a partially tracking collector and a fully tracking collector receive 60, 80 and 95% more radiation compared to that received on a horizontal plane respectively. Another observation is that the variation of the insolation received on inclined surfaces is not at all sensitive to the angle of tilt in the neighbourhood of the optimum angle of operation.     

Determining optimum tilt angles and orientations of photovoltaic panels in Sanliurfa, Turkey

The performance of a photovoltaic (PV) panel is affected by its orientation and its tilt angle with the horizontal plane. This is because both of these parameters change the amount of solar energy received by the surface of the PV panel. A mathematical model was used to estimate the total solar radiation on the tilted PV surface, and to determine optimum tilt angles for a PV panel installed in Sanliurfa, Turkey. The optimum tilt angles were determined by searching for the values of angles for which the total radiation on the PV surface was maximum for the period studied. The study also investigated the effect of two-axis solar tracking on energy gain compared to a fixed PV panel. This study determined that the monthly optimum tilt angle for a PV panel changes throughout the year with its minimum value as 13° in June and maximum value as 61° in December. The results showed that the gains in the amount of solar radiation throughout the year received by the PV panel mounted at monthly optimum tilt angles with respect to seasonal optimum angles and tilt angel equal to latitude were 1.1% and 3.9%, respectively. Furthermore, daily average of 29.3% gain in total solar radiation results in an daily average of 34.6% gain in generated power with two-axis solar tracking compared to a south facing PV panel fixed at 14° tilt angle on a particular day in July in Sanliurfa, Turkey.     

Overhang shading factor values for windows of general azimuthal angle evaluated under extraterrestrial and terrestrial conditions

An Erratum has been published for this article in International Journal of Energy Research 1999; 23(9):831. This article deals with assessing the differences between the values of the shading factors for windows with overhangs calculated under extraterrestrial and terrestrial conditions. It has been shown that the shading factor can be estimated under terrestrial conditions employing the available algorithms for the monthly average daily tilt factor for beam radiation. The present results have been validated by comparing with the values obtained by hour‐by‐hour calculations employing solar radiation data. The shading factor values evaluated under terrestrial conditions can differ by 25% compared to the extraterrestrial value for non‐south facing windows shaded by overhangs. Copyright © 1999 John Wiley & Sons, Ltd.     

Mean daily averages of beam radiation received by tilted surfaces as affected by the atmosphere

A method to compare the values of the monthly average beam radiation tilt factor, , obtained if atmospheric effects are accounted for or not, is presented. It is found that the difference between the two determinations may vary greatly with declination, latitude and ratio of daily averaged diffuse to global irradiation. In cases when this ratio is not obtained via direct measurement and its value is large enough, the accuracy of the “atmospheric” may be seriously affected. By comparison with measured radiation data from Montreal, Canada, the “atmospheric” as calculated by the proposed method appears very accurate for south vertical surfaces, and of acceptable accuracy for east or west vertical surfaces. In the latter case, a part of the discrepancy is attributed to various experimental errors, which are discussed.     

Solar irradiance on non-horizontal surfaces at the East-Mediterranean coastal plain of Israel

A large volume of global, diffuse and direct solar radiation observed at the National Radiation Center in Bet-Dagan (the East-Mediterranean coastal plain of Israel) has been analysed to evaluate the solar irradiance climatology on non-horizontal surfaces of various slope aspects and tilt angles. The isotropic approximation was used with respect to the diffuse sky radiation, as well as with regard to the reflected radiation from the ground. The feasibility of applying this approximation for the assessment of the insolation climate on non-horizontal surfaces is discussed. The monthly curves of daily total insolation on inclined surfaces were drawn, and their characteristic patterns for the various slope aspects and seasons are examined.