CRRC-1 Method #1: Standard Practice for Measuring Solar Reflectance of a Flat, Opaque, and Heterogeneous Surface Using a Portable Solar Reflectometer

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1 CRRC- Method #: Standad Pactice fo Measuing Sola Reflectance of a Flat, Opaque, and Heteogeneous Suface Using a Potable Sola Reflectomete Scope This standad pactice coves a technique fo estimating the mean sola eflectance of a flat, opaque, and heteogeneous test suface at standad conditions, such as a vaiegated, ganulecoveed asphalt oofing shingle. The mean sola eflectance of the test suface is detemined by aveaging the sola eflectances of andomly located spots (small egions) measued with a commecial potable sola eflectomete in accodance with ASTM C549. This standad pactice must be used in conjunction with ASTM C549. This standad pactice does not pupot to addess all of the safety concens, if any, associated with its use. It is the esponsibility of the use of this standad pactice to establish appopiate safety and health pactices and detemine the applicability of egulatoy limitations pio to use. Refeence Documents ASTM Standads C549, Standad Test Method fo Detemination of Sola Reflectance Nea Ambient Tempeatue Using a Potable Sola Reflectomete. Teminology Estimate of Sample Mean Standad Eo. The sample (athe than population) standad deviation divided by the squae oot of the numbe of samples. Heteogeneous. Consisting of dissimila o divese ingedients o constituents. Population. The goup of sample values about which conclusions ae to be dawn, such as a set of sola eflectance values detemined fom nonovelapping spots (small egions) that cove an entie test suface. Population Mean. The aithmetic mean of the popety values (e.g., sola eflectances) measued fo all membes of a population. Population Standad Deviation. The squae oot of the aithmetic mean of the squaes of the deviation fom the population mean. Reflectomete. A device that measues eflectance.

2 Sample Mean. The aithmetic mean of the popety values (e.g., sola eflectances) measued fo all membes of a sample set. Sample Mean Standad Eo. The population standad deviation divided by the squae oot of the numbe of samples. Sample Set. A subset of the population, such as a set of nonovelapping spots (small egions) on a test suface. Sample Standad Deviation. The squae oot of the atio of the sum of the squaes of the deviation fom the sample mean to a numbe one less than the numbe of samples. Spot. A small egion of a test suface, such as a x squae o a -diamete cicle, whose sola eflectance can be measued. Test Suface. A flat, opaque, and heteogeneous suface, such as that of a vaiegated, ganulecoveed asphalt shingle. Test Suface Mean Sola Reflectance. The atio of sola enegy eflected fom a test suface to the sola enegy incident on a test suface, equal to the atio of aea-integated sola eflectance to aea. Vaiegated. Having discete makings of diffeent colos. Summay of Standad Pactice Fo a flat, opaque, and heteogeneous test suface, sola eflectances ae measued in accodance with ASTM C549 at a seies of andomly located, non-ovelapping spots (small aeas) until the sample mean standad eo is small enough to use the sample mean as an estimate of the mean sola eflectance of the test suface. The algoithm fo selecting measuement locations, computing the sample mean, and computing the sample mean standad eo may be implemented with the assistance of softwae available fom the Cool Roof Rating Council (CRRC). Significance and Use This standad pactice povides a method fo detemining the mean sola eflectance of a flat, opaque, and heteogeneous suface, fom multiple, andom and non-duplicative spot measuements of sola eflectance. Pocedue Set-up. Obtain a epesentative test specimen, as detemined by CRRC.

3 2. Let w and h epesent the width and height of the test suface in units of inches. 3. Place a pai of inch-maked ules at a ight angle on two sides of the test suface to establish a gid of w h squae cells, each x and centeed on intege coodinates. If the aea of the test suface does not exceed 30 squae inches, apply Pocedue A. If the aea is 30 squae inches in aea o geate, apply Pocedue B. Pocedue A (fo test sufaces not exceeding 30 squae inches in aea). Measue the sola eflectance at the cente of each cell with a sola spectum eflectomete in accodance with ASTM C549, centeed ove each cell. 2. Repot the mean value of cell sola eflectance as the mean sola eflectance of the test suface. Pocedue B (fo test sufaces exceeding 30 squae inches in aea) Note: Pocedue B is implemented by softwae available fom the CRRC.. Measue the sola eflectances at the centes of a minimum of 30 diffeent and andomly selected cells with a sola spectum eflectomete centeed ove each cell in accodance with ASTM C Compute the mean, standad deviation, and estimate of standad eo of the sola eflectance of the sample set. These quantities ae defined in Eqs. (3), (4), and (6) of the Appendix, espectively. 3. If the estimate of sample mean standad eo exceeds 0.005, incease the numbe of samples by measuing sola eflectances of additional, diffeent, and andomly selected cells. 4. Repeats steps 2 and 3 until the estimate of sample mean standad eo of the sample set does not exceed Repot the sample mean plus o minus twice the estimate of sample mean standad eo as the mean sola eflectance to within 95% confidence. Repot Include in the epot, in addition to the equiements stated in ASTM C549, the following: Data Requiements. The width, height, and aea of the test suface. 2. The sola eflectance measuement pocedue followed (A o B). 3. The cental coodinates and sola eflectance of each cell measued.

4 4. Fo Pocedue A (applied to test sufaces not exceeding 30 squae inches in aea), the mean sola eflectance of the test suface, equal to the mean value of cell sola eflectance. 5. Fo Pocedue B (applied to test sufaces exceeding 30 squae inches in aea), the mean sola eflectance of the test suface to within 95% confidence, expessed as the sample mean plus o minus twice the estimate of sample mean standad eo. Test Sample Date. Manufactue of the poduct 2. Manufactue-designated poduct name and colo. Date sample was tested. Pecision and Bias Pocedue B was evaluated in a ound obin test fo six poducts (sola eflectance ) by five laboatoies (Table ). Fo five of the six poducts, the spead in epoted values (maximum minimum) did not exceed 0.0. Fo the sixth poduct, the spead was Table Pecision and Bias Sample Numbe Sample A B C D E Mean #2 Black 3 Tab #3 Lt. Gay 3 Tab #4 Contast 3 Tab #5 Bown Laminate #6 Geen Slate # Bown Shake Appendix All eflectances in the following discussion ae sola eflectances. The mean eflectance R A da () of a test suface of aea A is equal to the mean eflectance of the entie population of N = A a suface spots, A

5 N i N i= µ. (2) Each spot i is a subegion of eflectance i and aea a that is small enough to be measued with a eflectomete, and does not ovelap any of its neighbos. If N is lage, it is convenient to estimate the population mean spot eflectance µ, and hence the test suface mean eflectance R, of a lage suface by andomly sampling a population subset. Conside a sample set of n diffeent, non-ovelapping, and andomly located spots that have mean eflectance with standad deviation n i n i = (3) n s ( ) 2 i n (4) n i= By the Cental Limit theoem, the sample mean has a standad eo σ = σ n (5) whee σ is the standad deviation of the spot eflectances of the entie population (Cow et al., 960). The population mean spot eflectance µ (which is also the mean sola eflectance of the test suface, R ) is equal to ± 2σ (95% confidence). If the sample size n is sufficiently lage (say, n 30 ), the population standad deviation σ is well appoximated by the sample standad deviation s, and the estimate of the sample mean standad eo is σ s n (6) The instument used to measue spot eflectance in accodance with C549 has a cicula apetue. Hence, the test suface fomed by a matix of contiguous, non-ovelapping cicula measuement spots will cove a faction π 4 79% of the ectangula egion bounding the matix of cicles. The emaining 2% of the ectangula egion will not be sampled. This should be acceptable if the optical popeties of the aea between each measuement cicle and its bounding squae ae expected to be the same as those of the suface within each measuement cicle. Bibliogaphy Cow, E.L., F.A. Davis, and M.W. Maxfield Statistics Manual: With Examples Taken Fom Odnance Development. New Yok: Dove Publications.

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