![]() ![]() ![]() ![]() at θ equal to 87°, the uncertainty in cos θ is 0.7%, which can result in an uncertainty of 0.35% in calculating G because at such large zenith angles the normal incidence irradiance is approximately equal to half the value of G). 1 shows that the uncertainty in cos θ exponentially increases as θ reaches 90° (e.g. 1 shows the magnitude of errors that the 0.01° uncertainty in θ can contribute to the calculation of cos θ, and consequently G that is used to calculate the responsivity. During the calibration, the responsivity of the pyranometer is calculated at zenith angles from 0° to 90° by dividing its output voltage by the reference global solar irradiance ( G), which is a function of the cosine of the zenith angle (cos θ). For example, Michalsky’s calculations are limited to the period from 1950 to 2050 with uncertainty of greater than ☐.01° (Michalsky, 1988), and the calculations of Blanco-Muriel et al.’s are limited to the period from 1999 to 2015 with uncertainty greater than >☐.01° (Blanco-Muriel et al., 2001).Īn example emphasizing the importance of reducing the uncertainty of calculating the solar position to lower than ☐.01°, is the calibration of pyranometers that measure the global solar irradiance. Many methods to calculate the solar position have been published in the solar radiation literature, nevertheless, their uncertainties have been greater than ☐.01° in solar zenith and azimuth angle calculations, and some are only valid for a specific number of years (Blanco-Muriel et al., 2001). With the continuous technological advancements in solar radiation applications, there will always be a demand for smaller uncertainty in calculating the solar position. This report also includes the calculation of incidence angle for a surface that is tilted to any horizontal and vertical angle, as described by Iqbals in 1983. The changes include changing the direction of measuring azimuth angles to be measured from north and eastward instead of being measured from south and eastward, and the direction of measuring the observer’s geographical longitude to be measured as positive eastward from Greenwich meridian instead of negative. It also introduces some changes to accommodate for solar radiation applications. This report is written in a step by step format to simplify the complicated steps described in the book, with a focus on the sun instead of the planets and stars in general. The algorithm is described in a book written by Jean Meeus in 1998. This report is a step by step procedure for implementing an algorithm to calculate the solar zenith and azimuth angles in the period from the year −2000 to 6000, with uncertainties of ☐.0003°. For some, the algorithm is valid for a limited number of years varying from 15 years to a hundred years. The best uncertainty achieved in most of these articles is greater than ☐.01° in calculating the solar zenith and azimuth angles. There have been many published articles describing solar position algorithms for solar radiation applications. ![]()
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![]() ![]() In a major-diameter fit spline, the major diameter of the internal part and the outside diameter of the external part act like pilots to each other, and there is only a small amount of difference between these two values, which is the radial clearance. This difference is called the backlash or clearance. The fit for a side-fit spline is the difference between the circular-tooth thickness of the external splined part and the circular-space width of the internal part. Also, there is clearance between the outside diameter of the external part and the major diameter of the internal part. A side-fit spline has clearance between the root diameter of the external part and the inside diameter of the internal part. Splines are specified as either side fit or major-diameter fit. Standard cutting tools are available for both types in a range of standard DPs. The root diameter of a flat root external spline is typically larger than a fillet root spline, but the stresses are close to being the same because the fillet root with the smaller root diameter offsets the sharper corner but larger root diameter of the flat-root spline. ![]() Splines are made with either a fillet root or a flat root at the interface of the tooth flank and the root diameter. The 30-degree splines are by far the most common, so that is what will be considered here. Involute splines are available in several different pressure angles: 30 degrees, 37.5 degrees, and 45 degrees. Thus an 8/16 spline has the tooth thickness of 8 DP and a tooth height (whole depth) of 16 DP. Typical involute SAE/ANSI spline teeth are specifies as two numbers: a numerator that specifies the tooth thickness in diametral pitch (DP) and the second number that specified the tooth height in diametral pitch (DP). They have the same number of teeth and fit together as one. 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