So~ Ea¢~ Vol. 25, p. 91 Petpnma Press Ltd., 1~0. Printed in Great Britain

LETTERS TO T H E EDITOR

Comments on "Calculating the position of the sun"

Dear Sir, The procedure for calculating the position of the sun, given by

Walraven[l], can perhaps be improved at two points: 1. In the algorithm for TIME, the quantity DAY has to be

entered directly as the day-of-year, with an adjustment required in leap years. This tends to be inconvenient. The following algorithm allows the day-of-year N to be found simply and naturally, by entering the year, month and day-of-month (Y, M,/). It includes a correction for leap years, and is valid for almost two centuries, 1901-2099. It was designed for use in a microprocessor, and is thus given in BASIC.

I INPUT "YEAR, MONTH, DAY", Y, M, J 2 I = 1 3 B=0.5 4 K = 0 5 IFM<3THEN 10 6 1 = 3 7 B = 59.5

8 X = Y / 4 9 K = INT (X - INT (X -0.1))

10 P = M - I II L = I N T ( P * 3 0 . 6 + B ) 12 N = J + K + L

2. Atmospheric refraction is mentioned only briefly under "Sunrise and Sunset" (where it is incorrectly termed diffraction). Since refraction can amount to several tenths of a degree, it must be allowed for in order to approach Walraven's claimed accuracy. The standard refraction formulae of Cassini and of Bradley are unsuitable, as they break down at large zenith distances. The following procedure applies a refraction correction to the cal- culated value of cos Z, where Z is the zenith distance, to find cos ZI, Zl being the required apparent zenith distance.

CI = cos Z D = 1/(0.955 + (20.267 × CI)) - 0.047121 C = C1 +0.0083 × D

ZI = arccos C

This method agrees with Bessel's standard tables of mean refrac- tion within 0.02 degree near the horizon, and very much closer at higher elevations; this is comparable to the day-to-<lay variations in refraction due to changes in air density.

REFERENCE I. R. Walraven, Calculating the position of the sun. Solar Energy

20, 393 (1978).

Note that N is always the true day-of-year, whereas DAY is equal to N - 1 in January and February of a leap year. However, only a small modification to this algorithm, or to Walraven's, would be needed to make them compatible.

Department'o/Meteorological Services Belvedere Salisbury Zimbabwe

C. B. ARCHER

Dear Sk, In a 1921 article on power hanks[l] the Canadian-American

inventor R. A. Fessenden mentions an interesting method of generating power which he called negative radiation. In the section on power generators from solar heat he wrote: "As I have pointed out elsewhere, this method is not limited to day- time, as negative radiation may be used at night time, cooling the vapor from sea water after passing it through a low pressure steam turbine. Some calculations I made show that a negative radiation plant operating in Alaska in winter would have about the same power output per dollar of plant as a positive radiation plant operating in summer in the tropics".

I have been unable to find the material referred to or any other analysis of this type of power generation and it is hard to believe that a system operating at such a low pressure level would be cost effective. However the basic idea is interesting and it might be possible to obtain a reasonable power output if a source of warm water is available or a more volatile working fluid is used.

If a system could be designed to use the same equipment as a conventional low pressure solar system the combined system might be of considerable interest as it would utilize the invested capital more effectively and provide power for a much larger part of the day. It is well known that some sunny regions have clear nights in which considerable radiative cooling occurs.

If any reader knows of past or present work on power generating systems using such radiative cooling I would ap- preciate being informed.

REFERENCE

1. R. A. Fressenden, "Banking" electricity for universal use. Sci. Am. 124, 348 (1921).

Department o~ Aerospace Engineering West Virginia University Morgantown WV 26506 U.S.A.

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