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41 60 Long Distance (27,800 to 28,500 ft.) Scatter Plot 93 Points 50 40 R2 = 0.91 Rate Site 2 30 20 10 0 0 10 20 30 40 50 60 Rate Site 1 Figure 15. Precipitation rate comparison data for long separation distances. An R2 value was determined for each of the data sets in Fig- The analysis was aimed at determining the effect that any ures 10 to 12: real difference in precipitation between the two sites would have on fluid holdover times. The initial treatment of the · Short separation distance R2=0.98; data thus required calculation of precipitation rates, fol- · Medium separation distance R2=0.93; lowed by calculation of fluid holdover times for a variety of · Long separation distance R2=0.91; and fluids. · Lake-effect data R2=0.31. Subsequently, the calculated fluid holdover times for each precipitation data point were examined statistically to deter- The R2 parameter provides a sense of the variance in the data mine which test sets had differences that could be ascribed to and shows that the variance between the two sites increases as random effects and which had real differences in holdover the distance between the sites is increased. The R2 value for the times generated by each of the two sites. lake-effect snowfall data clearly shows that this type of precip- The analysis is described in detail in the following sections. itation event also increases the variance in precipitation rate. While the variation of the points around the best-fit lines reflects random effects, it may also indicate real differences in Calculation of Precipitation Rates precipitation between sites. The task of the analysis is to iden- The precipitation rate calculation is based on the measured tify which of the data sets result from random effects, and weight of precipitation collected over a measured time span, which reflect real differences, and for those differences that on a surface of known dimensions. are real, to evaluate their operational significance. The rate pans used to collect precipitation had a surface area The next sections describe the approach taken to answer of 14.53 dm2 (1.56 ft2). The duration of test time was deter- these questions. mined from the data test start and end time. For a 10-minute test interval, the precipitation rate is calculated as: Data Analysis The analysis was applied to the consolidated data collected Weight of collected precipitation [ g ] Rate [ g dm 2 h ] = over the two test seasons. 14.53 [ dm 2 ] i 10 60 [ h ]
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42 Any test sets where the average rate calculated for a site The following regression equation is used to calculate hold- exceeded 50 g/dm2/h, were excluded from the analysis. The over times in snow: rationale for this exclusion is as follows. t = 10I R A ( 2 - T ) B The currently published holdover time guidelines for snow have an upper limit on precipitation rates: where: · Very light snow: 4 g/dm2/h; t = time (minutes); · Light snow: 4 and 10 g/dm2/h; and R = rate of precipitation (g/dm2/h); · Moderate snow: 10 and 25 g/dm2/h. T = temperature (°C); and I, A, B = coefficients determined from the regression. During the process of collecting fluid endurance time data to generate HOT guidelines, a good deal of data has been col- This equation substitutes 2-T for the variable T in order to lected during heavy snow events, that is, beyond 25 g/dm2/h. prevent taking the log of a negative number, as natural snow In the past, this data has served to enhance the accuracy of the can occur at temperatures approaching +2°C. regression equations used to develop HOT guidelines for HOTDS produce holdover times by applying the same re- snow at rates up to moderate. However, there has been inter- gression equations and coefficients used to calculate the val- est in extending the guidelines to reflect rates greater than ues in the current holdover time guidelines. moderate. Discussions at the 2006 SAE G-12 HOT subcom- To assess the effect that separate HOTDS sites might have on holdover times, each measured precipitation weight data mittee meeting indicated that an upper limit should not go point was converted to holdover time, using the regression beyond 50 g/dm2/h considering that: equations and coefficients for a selection of fluid brands that are currently in operational use. · The frequency of heavy snow (> 25 g/dm2/h) is about 3%; Those fluid brands and strengths are given in Table 26, along · Most of this occurs in the range 25 to 50 g/dm2/h; and with the regression coefficients used to calculate holdover · Most of the endurance time data in heavy snow was col- times provided in the winter 200708 guidelines. Although dif- lected in the range 25 to 50 g/dm2/h. ferent regression coefficients may apply when ambient temper- atures are lower than -14°C, such temperatures did not occur This analysis has taken the perspective of evaluating the risk during data collection. when holdover times would actually be generated, and thus In accordance with the current practice for HOT table devel- only those test sets are examined. opment for snow, holdover times were capped at 120 minutes. Holdover times for fluid strength of 50/50 concentration Calculation of Fluid Holdover Times are constrained to OAT -3°C and above. This constraint resulted in setting aside some data sets when evaluating the Holdover time guidelines, which are published annually, effect on this fluid's holdover times. provide pilots with tables of the protection times provided by de/anti-icing fluids in winter conditions. The values in the Statistical Analysis to Compute HOT Difference holdover time tables are developed through regression analy- Between Sites sis of recorded fluid endurance time data. Aircraft de/anti-icing fluid holdover time is a function of Each test set consisted of data collected simultaneously at fluid dilution, precipitation rate, precipitation type, and am- two separate sites. At each site, precipitation was measured bient temperature. All the tests reported here were conducted simultaneously on four rate pans. Thus, each test set usually in snow conditions. comprised a total of eight data points. The foregoing analy- Table 26. Fluid holdover time regression coefficients. Clariant Octagon Kilfrost Kilfrost Safewing MP IV Coefficients SAE Type I MaxFlo ABC-S ABC-S 2012 Protect 100/0 75/25 50/50 100/0 I 2.0072 2.9261 3.0846 2.5569 2.3232 A -0.5752 -0.6725 -0.8545 -0.7273 -0.8869 B -0.5585 -0.5399 -0.3781 -0.1092 -0.2936
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43 sis then produced eight values of fluid holdover time for each t-test. These data sets are then analyzed using a separate test set. In several cases, only three data points were recorded variances t-test. at one of the sites, and the statistical analysis took this into account. For ease of description, the following refers to tests com- The objective then was to examine the difference in HOTs prised of four HOTs for each site. The actual analysis exam- for the two sites. ined the real number of samples recorded. Because a maximum of four HOT values existed for each of The t-test for those test sets that passed the F-test was the two sites for each test, the comparison was conducted applied, as follows: using small sample theory. This complies with the general rule that statistical analysis of samples with size less than 30 must · Calculate standard deviation (SD) for each site; and be corrected for sample size. The Student--t distribution, · Calculate a combined variance for the two sites and its which corrects for sample size, was applied to learn if there was square root for a combined SD. The combination is a statistically significant difference between the holdover times weighted by degrees of freedom: generated at the two site locations, for each test set. In tests such as these, where a small number of data points Combined Variance = (( n 1 - 1) SD12 + ( n 2 - 1) SD22 ) exist for each of two conditions and the objective is to deter- ( n1 + n 2 - 2) mine whether there is a difference between the two, the com- where: SD = standard deviation mon analytical approach is to apply a null hypothesis, which SD2 = variance assumes that there is no difference between the two sets. This n1 = number of tests in test set from site 1 assumption enables the two databases for each test set to be combined, which produces a better estimate of the popula- · Calculate t: tion standard deviation. The analysis then examines the data to statistically test the null hypothesis. ( mean holdover time1 - mean holdover time 2 ) t= Before the t-test can be used in this way, the two sets of four [combined SD sqrt (1 n1 + 1 n2 )] HOTs must first be examined to see if their variances are suf- ficiently alike to justify the assumption that they each could · Compare calculated t-value to t-table value for t at a signif- be estimates of the same population variance. This examina- icance level of 0.025, for 6 degrees of freedom (n1 + n2 - 2). tion of statistical variance uses the F-distribution. This is a two-tailed test, thus the resulting level of signifi- If there is a significant difference in statistical variance, cance is 0.05; and then those test sets cannot be combined. For those test sets, a · If the calculated t is less than the t-table value, then accept different statistical approach using separate variances t-test is the hypothesis that there is no difference between the two applied. tests. The F-test was applied to the HOTs for each test set in the following manner: The t-test for those test sets that failed the F-test was ap- plied, as follows: · Calculate F-value, which is the ratio of the statistical variance of the two sets of HOTs, with the highest in the numerator; · Calculate t: · Retrieve the appropriate F-value from an F-distribution table ( mean holdover time1 - mean holdover time 2 ) calculated for a 0.05 significance level. The tables are format- t= ted by number of degrees of freedom for the numerator and sqrt ( variance1 n1 + variance 2 n 2 ) denominator, with the highest number in the numerator. · Calculate degrees of freedom: The number of degrees of freedom is the site test sample size minus 1 (nx - 1); · Compare the calculated F-value to the table F-value; D. F. = (SD 1 2 n1 + SD22 n 2 ) 2 · If the calculated F-value is less than the table F-value, then (SD1 2 n1 ) + (SD 2 2 2 n2 ) 2 one can assume that the variances of the two sets are not sig- ( n1 - 1) ( n 2 - 1) nificantly different, and the data from the two sites can be combined for the t-test using the null hypothesis approach; · Compare calculated t-value to t-table value for t at a signif- and icance level of 0.025, for the calculated number of degrees · If the calculated F-value is greater than the table F-value, of freedom; and then the variances of the two sets are significantly different, · If the calculated t is less than the t-table value, then accept the and the data from the two sites cannot be combined for the hypothesis that there is no difference between the two tests.