Showing papers on "Tilt (optics) published in 2012"

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

Abstract: 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 ).

Myopic optic disc tilt and the characteristics of peripapillary retinal nerve fiber layer thickness measured by spectral-domain optical coherence tomography.

Abstract: PURPOSE To investigate the correlation between myopic optic disc tilt and the characteristics of peripapillary retinal nerve fiber layer (RNFL) thickness measured by Cirrus HD spectral-domain optical coherence tomography (Cirrus HD OCT; Carl Zeiss Meditec, Dublin, CA). METHODS A total of 255 eyes of 255 healthy young male participants with various degrees of refractive errors (mean spherical equivalent, -3.17 ± 2.40 D; range, -11.00 to 0.00 D) underwent ophthalmic examinations, including refractive error, axial length, and optic disc area measurement. The degree of horizontal/vertical optic disc tilt was evaluated by cross-sectional images obtained by the Cirrus HD OCT. The average, superior, nasal, inferior, and temporal quadrant thickness and superior/inferior peak locations of the peripapillary RNFL were also measured with the Cirrus HD OCT. RESULTS On the univariate analysis, eyes with more temporally tilted optic discs (horizontal tilt) had higher myopia, greater axial length, a thinner average, superior, nasal, and inferior RNFL, thicker temporal RNFL, and more temporally positioned superior/inferior peak locations (all P values <0.001). The degree of inferior optic disc tilt (vertical tilt) was associated with high myopia and a more temporally positioned inferior peak location (all P values <0.05). On multivariate analysis, eyes with more temporally tilted optic discs had a thicker temporal RNFL and more temporally positioned superior/inferior peak locations. CONCLUSIONS The characteristics of the peripapillary RNFL thickness were associated with the degree of myopic optic disc tilt, especially in the temporal area. The degree of myopic optic disc tilt should be considered when interpreting the RNFL thickness measured by the Cirrus HD OCT.

System and method for navigating a mobile device user interface with a directional sensing device

Abstract: An electronic mobile device includes a display for displaying a graphical element. A tilt sensor is configured to sense first and second tilt angles of the mobile device. A processor is coupled to the display and the tilt sensor and configured to move the graphical element relative to the display in a first direction based on the first tilt angle, and to move the graphical element relative to the display in a second direction based on the second tilt angle.

Tilt displays: designing display surfaces with multi-axis tilting and actuation

Abstract: We present a new type of actuatable display, called Tilt Displays, that provide visual feedback combined with multi-axis tilting and vertical actuation. Their ability to physically mutate provides users with an additional information channel that facilitates a range of new applications including collaboration and tangible entertainment while enhancing familiar applications such as terrain modelling by allowing 3D scenes to be rendered in a physical-3D manner. Through a mobile 3x3 custom built prototype, we examine the design space around Tilt Displays, categorise output modalities and conduct two user studies. The first, an exploratory study examines users' initial impressions of Tilt Displays and probes potential interactions and uses. The second takes a quantitative approach to understand interaction possibilities with such displays, resulting in the production of two user-defined gesture sets: one for manipulating the surface of the Tilt Display, the second for conducting everyday interactions.

Characteristics of peripapillary retinal nerve fiber layer thickness in eyes with myopic optic disc tilt and rotation.

Abstract: Purpose:The purpose of the study was to investigate the effects of myopic optic disc tilt and rotation on peripapillary retinal nerve fiber layer (RNFL) thickness characteristics measured by Cirrus HD spectral-domain optical coherence tomography (Cirrus HD OCT).Methods:A total of 93 right eyes from

Long-term measurements of sunspot magnetic tilt angles

Abstract: Tilt angles of close to 30,600 sunspots are determined using Mount Wilson daily averaged magnetograms taken from 1974 to 2012, and SOHO/MDI magnetograms taken from 1996 to 2010. Within a cycle, more than 90% of sunspots have a normal polarity alignment along the east-west direction following Hale's law. The median tilts increase with increasing latitude (Joy's law) at a rate of ~05 per degree of latitude. Tilt angles of spots appear largely invariant with respect to time at a given latitude, but they decrease by ~09 per year on average, a trend that largely reflects Joy's law following the butterfly diagram. We find an asymmetry between the hemispheres in the mean tilt angles. On average, the tilts are greater in the Southern than in the Northern Hemisphere for all latitude zones, and the differences increase with increasing latitude.

Comparison of Different Techniques of Tilt Testing and Basic Friction Angle Variability Assessment

Abstract: A relevant parameter for estimating discontinuity shear strength is the basic friction angle, usually derived from different types of tilt tests. However, the tilt tests described in the literature produce varying basic friction angle values. From a large number of different types of tilt tests on different kinds of rocks, it was possible to conclude that the mechanisms of sliding along cylinder generatrixes and planar surfaces are quite different, and that tests based on sliding along generatrixes are not appropriate for determining reliable basic friction angle values for discontinuity planes. Tests on small specimens are also not recommended, for geometry reasons and because ensuring reliable stress conditions is difficult. To quantify the natural variability in tilt testing, large specimens of the same granite were tested. The results revealed coefficients of variation for the basic friction angle in the range of 5–10 %, a variability which is no greater than that found for other rock mechanics parameters. This observation enables to forward some recommendations concerning the appropriate number of tests needed to obtain reliable results.

Intuitive analysis of space-time focusing with double-ABCD calculation

Abstract: We analyze the structure of space-time focusing of spatially-chirped pulses using a technique where each frequency component of the beam follows its own Gaussian beamlet that in turn travels as a ray through the system. The approach leads to analytic expressions for the axially-varying pulse duration, pulse-front tilt, and the longitudinal intensity profile. We find that an important contribution to the intensity localization obtained with spatial-chirp focusing arises from the evolution of the geometric phase of the beamlets.

Determining tilt angle and tilt direction using image processing

Abstract: A survey instrument includes a surveying device configured to perform survey measurements and an imaging device coupled to the surveying device and having a known spatial relationship with the surveying device. The imaging device may be configured to obtain image information. The survey instrument also includes a processor in electrical communication with the imaging device. The processor may be configured to receive the image information from the imaging device, process the image information to determine a pose of the imaging device, and determine a tilt angle of the survey instrument and a tilt direction of the survey instrument in a reference frame. Tilt angle and the tilt direction of the survey instrument may be determined using the pose of the imaging device.

FittsTilt: the application of Fitts' law to tilt-based interaction

Abstract: We evaluated tilt as an input method for devices with built-in accelerometers, such as touchscreen phones and tablet computers. The evaluation was empirical and experimental. Sixteen participants performed a tilt-based position-select task, similar to the multi-directional Fitts' law task in ISO 9241-9. Four levels of tilt gain (25, 50, 100, and 200) and two selection modes (first-entry and 500 ms dwell) were used. Movement times were lowest with tilt gain = 50 and first-entry selection. Maximum tilt angles ranged from about 2° to 13°, depending on condition. Tilt as an input primitive is shown to conform to Fitts' law. Throughput is low, however, about 2.3 bits/s for first-entry and 1.2 bits/s for dwell.

The optimum tilt angle for flat-plate solar collectors in Iran

Abstract: This paper aims at determining the optimum tilt angle for south facing flat-plate solar collectors in Iran. Solar radiation on a horizontal surface was estimated by applying an empirical method and employing meteorological data from 80 selected cities. A mathematical model was used for estimating the solar radiation at different tilt angles. Daily, monthly, seasonally, bi-annually, and yearly optimum tilt angles and solar radiations were determined for 80 selected cities. Recommendations were made on the optimum tilt angle adjustment for different places in the country in order to benefit the best solar radiation available. The averaged benefits of annual solar radiation for 80 cities were 21.3% for daily, 21% for monthly, 19.6% for seasonal, 19.3% for bi-annual, and 13.3% for yearly adjustments compared with the radiation on the horizontal collector. Based on these results, adjusting tilt angles, at least twice a year, is recommended. Optimum tilt angles for cloudy sky cities with a low clearness index are lower than those for cities at the same latitude angle having a higher clearness index. In addition to latitude angle, the climate conditions are also important for determining the optimum tilt angle.

How changes in the tilt angle of the geomagnetic dipole affect the coupled magnetosphere-ionosphere-thermosphere system

Abstract: [1] The orientation of the Earth's magnetic field has changed dramatically during the geological past. We have investigated the effects of changes in dipole tilt angle on the magnetosphere, ionosphere, and thermosphere, using the Coupled Magnetosphere-Ionosphere-Thermosphere (CMIT) model. The dipole tilt angle modulates the efficiency of solar wind-magnetosphere coupling, by influencing the diurnal variation in the angleμ between the dipole axis and the GSM z axis. This influences how much Joule heating occurs at high magnetic latitudes. The dipole tilt angle also controls the geographic distribution of the Joule heating, as it determines the geographic latitude of the magnetic poles. Changes in the amount and distribution of Joule heating with tilt an`gle produce further changes in temperature and neutral winds. The latter affect the O/N2 ratio, which in turn modifies the peak electron density of the F2 layer, NmF2. All these effects are most important when the Interplanetary Magnetic Field (IMF) is southward, while being almost negligible under northward IMF. However, a change in dipole tilt also changes the inclination of the magnetic field, which affects the vertical component of ionospheric plasma diffusion along the magnetic field, regardless of the IMF direction. Changes in vertical plasma diffusion are responsible for ∼2/3 of the changes in NmF2 and most of the low to midlatitude changes in hmF2under southward IMF and for most of the changes in both variables under northward IMF. Thermal contraction may be responsible for high-latitude decreases in hmF2 with increasing tilt angle under southward IMF.

Long-Term Measurements of Sunspot Magnetic Tilt Angles

Abstract: Tilt angles of close to 30,600 sunspots are determined using Mount Wilson daily averaged magnetograms taken from 1974 to 2012, and SOHO/MDI magnetograms taken from 1996 to 2010. Within a cycle, more than 90% of sunspots have a normal polarity alignment along the east-west direction following Hale's law. The median tilts increase with increasing latitude (Joy's law) at a rate of ~05 per degree of latitude. Tilt angles of spots appear largely invariant with respect to time at a given latitude, but they decrease by ~09 per year on average, a trend that largely reflects Joy's law following the butterfly diagram. We find an asymmetry between the hemispheres in the mean tilt angles. On average, the tilts are greater in the Southern than in the Northern Hemisphere for all latitude zones, and the differences increase with increasing latitude.

GALACSI system design and analysis

Abstract: GALACSI is one of the Adaptive Optics (AO) systems part of the ESO Adaptive Optics Facility (AOF). It will use the VLT 4-Laser Guide Stars system, high speed and low noise WaveFront Sensor cameras (<1e-, 1000Hz) the Deformable Secondary Mirror (DSM) and the SPARTA Real Time Computer to sharpen images and enhance faint object detectability of the MUSE Instrument. MUSE is an Integral Field Spectrograph working at wavelengths from 465nm to 930nm. GALACSI implements 2 different AO modes; in Wide Field Mode (WFM) it will perform Ground Layer AO correction and enhance the collected energy in a 0.2" by 0.2" pixel by a factor 2 at 750nm over a Field of View (FoV) of 1' by 1'. The 4 LGSs and one tip tilt reference star (R-mag <17.5) are located outside the MUSE FoV. Key requirements are to provide this performance and a very good image stability for a 1hour long integration time. In Narrow Field Mode (NFM) Laser Tomography AO will be used to reconstruct and correct the turbulence for the center field using the 4 LGSs at 15" off axis and the Near Infra Red (NIR) light of one reference star on axis for tip tilt and focus sensing. In NFM GALACSI will provide a moderate Strehl Ratio of 5% (goal 10%) at 650nm. The NFM hosts several challenges and many subsystems will be pushed to their limits. The opto mechanical design and error budgets of GALACSI is described here.

Tilt prior to explosions and the effect of topography on ultra-long-period seismic records at Fuego volcano, Guatemala

Abstract: [1] Ground tilt is measured from broadband seismic records prior to frequent explosions at Fuego volcano, Guatemala We are able to resolve tilt beginning 20–30 minutes prior to explosions, followed by a rapid reversal in deformation coincident with explosion onsets The tilt amplitude and polarity recorded on the horizontal channels vary from station to station such that the steep and unusual topography of the upper cone of Fuego appears to affect the ultra-long-period signals We account for the effect of topography and attempt to constrain the tilt source depth and geometry through finite-difference modeling The results indicate a shallow spherical pressure source, and that topography must be considered when attempting to model tilt sources at volcanoes with steep topography The tilt signals are interpreted as pressurization of the shallow conduit beneath a crystallized plug followed by elastic deflation concurrent with explosive pressure release

System and method for controlling unmanned aerial vehicle

Abstract: An unmanned aerial vehicle (UAV) includes a driving unit and a control unit. The control unit detects a human figure in an image of a scene of a monitored area, determines coordinate differences between the scene image's center and the figure image's center, and determines a tilt direction and a tilt angle of a lens of the image capture unit based on the coordinate differences. If the tilt angle falls within an allowable rotation range of the lens, the control unit controls the driving unit to directly rotate the lens by the tilt angle along the tilt direction. Otherwise, the control unit controls the driving unit to rotate the lens by a threshold angle along the tilt direction, and further controls the driving unit to adjust a flight orientation and a flight height of the UAV until the figure image's center superposes the scene image's center.

A new traveltime approximation for TI media

Abstract: In a transversely isotropic (TI) medium, the trade-off between inhomogeneity and anisotropy can dramatically reduce our capability to estimate anisotropy parameters. By expanding the TI eikonal equation in power series in terms of the aneliptic parameter η, we derive an efficient tool to estimate (scan) for η in a generally inhomogeneous, elliptically anisotropic background medium. For a homogeneoustilted transversely isotropic medium, we obtain an analytic nonhyperbolic moveout equation that is accurate for large offsets. In the common case where we do not have well information and it is necessary to resolve the vertical velocity, the background medium can be assumed isotropic, and the traveltime equations becomes simpler. In all cases, the accuracy of this new TI traveltime equation exceeds previously published formulations and demonstrates how η is better resolved at small offsets when the tilt is large.

Dynamic control of directional asymmetry observed in ultrafast laser direct writing

Abstract: A liquid crystal spatial light modulator (SLM) is used to control the focal symmetry and the associated directional “quill” effect encountered when using a femtosecond laser for direct laser writing of fused silica. Applying a blazed grating to the SLM effectively introduces pulse front tilt to the fabrication beam and a spatiotemporal asymmetry at the focus. As a result different fabricated features are generated when moving the substrate in opposite directions relative to the tilt. It is additionally shown that inhomogeneous pupil illumination can cause similar directionality in the fabrication via a spatial asymmetry in the focus.

A simple, low-cost, high-sensitivity fiber-optic tilt sensor

Abstract: The paper presents a simple, low-cost and high-sensitivity fiber-optic tilt sensor. The sensor consists of two optical fibers and a container filled with transparent liquid to the half of the total volume of the container. The sensor principle is based on the change in angle of the liquid surface with respect to the fibers with the tilt angle. The achieved sensor sensitivity and resolution are 1 V/° and 0.02°, respectively.

Tip-tilt estimation and correction using FQPM coronagraphic images

Abstract: Context Direct imaging of exoplanets located a few AU from their hosting star requires angular resolution at the diffraction limit of large telescopes and a contrast level in the image of 105 to 1010 Simultaneous use of adaptive optics and coronagraphy is mandatory to fulfil these requirementsAims Coronagraphs are usually very sensitive to pointing errors upstream of their focal plane mask Approaches to measuring these errors in conventional adaptive optics systems consist in setting a wavefront sensor in an additional channel Differential aberrations between the coronagraphic channel and the additional one induce a loss in performance To tackle this limitation, we propose a new technique for measuring the tip-tilt errors directly from the coronagraphic imageMethods Our method uses the relations between the intensity distribution in the coronagraphic image and upstream tip-tilt errors We also propose a method of estimating the tip-tilt errors downstream of the focal plane mask We validate at visible wavelength our upstream and downstream tip-tilt estimation and compensation techniques with numerical simulation images and on laboratory imagesResults Numerical simulations predict that our techniques correct for the tip-tilt errors to a 13 × 10-2 λ /D level when considering a λ /40 wavefront error upstream of the coronagraph In laboratory, where the coronagraph is mostly limited by wavefront errors, we correct for the tip-tilt errors with an accuracy better than 65 × 10-2 λ /D Conclusions We demonstrate in numerical simulations and in laboratory that our technique can efficiently estimate the tip-tilt errors directly from the coronagraphic image with no additional channel It is robust and can be used with small wavefront errors It should be applicable to planet imager systems currently in preparation, such as SPHERE and MIRI/JWST

Dipole tilt control of the magnetopause for southward IMF from global magnetohydrodynamic simulations

Abstract: [1] Numerical results from a physics-based global magnetohydrodynamic (MHD) model are used to examine the effect of the dipole tilt angle (ψ) on the location and shape of the magnetopause. Identification of the magnetopause location in the simulation domain is automated using criteria based on the current density and the shape of the streamlines. These data are fitted with a three-dimensional surface controlled by 10 configuration parameters which allow description of the cusp geometry as well as the asymmetry in the Z direction and the azimuthal asymmetry of the magnetopause. Effects of dipole tilt angle on the configuration parameters are analyzed from a series of simulations for southward IMF and different dipole tilt angle values. It is found that dipole tilt angle has little impact on the equatorial magnetopause but significantly affects the cusp locations and the degree of asymmetry between the Northern and Southern hemispheres and the equatorial/meridional plane. The results are shown to be consistent with three frequently used empirical models derived from satellite observations.

MEMS mirrors based on a curved concentric electrothermal actuator

Abstract: A curved concentric electrothermal actuator has been designed and developed to actuate circular micromirrors with improved area efficiency, while at the same time achieving large scan range at low voltage. This actuator consists of three curved concentric Aluminum/Tungsten bimorphs for fast thermal response and high responsivity, and two rigid frames connected in between for scan range amplification. A tip–tilt–piston micromirror with a circular mirror plate based on this actuator design has been proposed and fabricated. The mirror is capable of scanning ±11° at 0.6 V, and generating a 227 μm piston displacement at only 0.8 V. The measured lateral shift and tilt angle of the mirror plate are less than 7 μm and 0.7°, respectively, through the entire piston displacement. A piston-only micromirror has also been demonstrated, and it has even smaller lateral shift of less than 3 μm and tilt of less than 0.4° through the piston scan range. This mirror generates large vertical displacement of about 200 μm at only 0.9 V.

Effect of compression paddle tilt correction on volumetric breast density estimation.

Abstract: For the acquisition of a mammogram, a breast is compressed between a compression paddle and a support table. When compression is applied with a flexible compression paddle, the upper plate may be tilted, which results in variation in breast thickness from the chest wall to the breast margin. Paddle tilt has been recognized as a major problem in volumetric breast density estimation methods. In previous work, we developed a fully automatic method to correct the image for the effect of compression paddle tilt. In this study, we investigated in three experiments the effect of paddle tilt and its correction on volumetric breast density estimation. Results showed that paddle tilt considerably affected accuracy of volumetric breast density estimation, but that effect could be reduced by tilt correction. By applying tilt correction, a significant increase in correspondence between mammographic density estimates and measurements on MRI was established. We argue that in volumetric breast density estimation, tilt correction is both feasible and essential when mammographic images are acquired with a flexible compression paddle.

Display device and method of switching display direction

Abstract: A portable display device comprises: a tilt detection unit detecting an angle of rotation, measured between a vertical plane component of a tilt vector of a predetermined reference line in the display and a gravitational vector, as a display tilt; a facial orientation specification unit recognizing a face of a person facing the display and specifying an upright orientation of the face; a terminal orientation determination unit establishing a plurality of angle ranges, and determining whether the display tilt newly detected by the tilt detection unit exceeds a given angle range and enters another angle range, the given angle range including the angle detected by the tilt detection unit upon updating a previous display orientation; and a control unit causing the facial orientation specification unit to begin the specification when the terminal orientation determination unit makes an affirmative determination, and updating the display orientation according to the specified upright orientation.

High performance tilt rotor aircraft in which nacelle tilt angle and flaperon angle mechanically interwork with each other

Abstract: Provided is a high performance tilt rotor aircraft in which a nacelle tilt angle and a flaperon angle mechanically interlock with each other. In the tilt rotor aircraft having nacelles in which rotors are mounted in left and right main wings and configured so that the nacelles rotate according to whether the tilt rotor aircraft conducts forward flight or vertical take-off and landing flight, each of the main wings is provided with a flaperon, and the nacelle and the flaperon are connected to each other by a power transfer unit, such that the flaperon also rotates together with the nacelle at the time of rotation of the nacelle, thereby allowing a change in a nacelle tilt angle to lead to a change in a flaperon angle.

Optimum Tilt Angles for Photovoltaic Panels during Winter Months in the Vaal Triangle, South Africa

Abstract: Optimizing the output power of a photovoltaic panel improves the efficiency of a solar driven energy system. The maximum output power of a photovoltaic panel depends on atmospheric conditions, such as (direct solar radiation, air pollution and cloud movements), load profile and the tilt and orientation angles. This paper describes an experimental analysis of maximizing output power of a photovoltaic panel, based on the use of existing equations of tilt angles derived from mathematical models and simulation packages. Power regulation is achieved by the use of a DC-DC converter, a fixed load resistance and a single photovoltaic panel. A data logger is used to make repeated measurements which ensure reliability of the results. The results of the paper were taken over a four month period from April through July. The photovoltaic panel was set to an orientation angle of 0? with tilt angles of 16?, 26? and 36?. Preliminary results indicate that tilt angles between 26? and 36? provide optimum photovoltaic output power for winter months in South Africa.

Analytical and experimental analysis of optimal tilt angle of solar photovoltaic systems

Abstract: Performance of PV panel depends on the tilt angle of the panel with respect to the horizontal plane The tilt angle determines the amount of solar insolation on panel surface and intern determines quantity of energy collected Conventionally the best tilt angle is equivalent to latitude of the location at which panel is installed The value of optimal tilt angle at defined location depends on local atmospheric condition, altitude of region, movement of sun etc So the value of optimal tilt angle varies over each month In this paper the values of optimal tilt angle over each month for a PV panel installed in Kerala, India (955°N, 7681°E) was theoretically estimated using geographic factor method, clearness index method and declination angle method The results showed that the gain 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 angle equal to latitude were 34% and 7%, respectively The theoretically estimated values of optimal tilt angles are used as a base for experimental investigation Experimental investigation was done for three months and it is found that the geographic factor method is the best method among three methods

On the monthly optimum tilt angle of solar panel for five sites in Malaysia

Abstract: In this research, an optimization of monthly tilt angle for solar panels for five main sites in Malaysia is conducted. The optimization method is based on the Liu and Jordan model for solar energy incident on a tilt surface. As a result, applying the monthly optimum tilt angle, increases the collected yields of the PV module/array in Kuala Lumpur, Johor Bharu, Ipoh, Kuching and Alor Setar by 5.03%, 5.02%, 5.65%, 7.96% and 6.13%, respectively. Such recommendations help in increasing the productively of PV systems in Malaysia and nearby country.

Comparative Approach For The Optimization Of Tilt Angle To Receive Maximum Radiation

Abstract: India is both densely populated and has high solar insolation, providing an ideal combination for solar power in India. As the angle between the sun and a fixed surface is continually changing, the power density on a fixed PV module is less than that of the incident sunlight. Since the flat plate solar collectors are placed at an angle to the horizontal, it is necessary to calculate the optimum tilt angle which maximizes the amount of collected energy. The best way to collect the maximum solar energy is by using solar tracking systems, and thus to maximize the collected beam radiation. In this paper a mathematical model was used for estimating the total (global) solar radiation on a tilted surface, and to determine the optimum tilt angle and orientation (surface azimuth angle) for the solar collector in India at four different locations on a monthly basis, as well as for a specific period. The results reveal that changing the tilt angle 12 times in a year (i.e. using the monthly-averaged optimum tilt angle) maintains approximately the total amount of solar radiation near the maximum value that is found by changing the tilt angle daily to its optimum value. This achieves a yearly gain in solar radiation of 4.56% more than the case of a solar collector fixed on a horizontal surface.