Analysis
Tina Lasisi
February 15, 2022
Last updated: 2022-02-15
Checks: 6 1
Knit directory: HairManikin_manuscript/
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1 Preparing data
1.1 Estimating dry heat loss at 30C and solar influx
1.1.1 Solar influx
Here we calculate solar influx and the temperature corrected heat loss for each experiment.
Solar influx (difference between heat loss with radiation on and off) is calculated as:
\[Solar\ influx \ (W/m^2) = heatflux_{(radiation)}- heatflux_{(no \ radiation)}\]
# A tibble: 59 × 7
wig wind wet_dry trial on off influx
<fct> <dbl> <fct> <fct> <dbl> <dbl> <dbl>
1 Nude 0.3 wet 1 90.9 153. 61.9
2 Nude 0.3 wet 2 86.7 151. 64.7
3 Nude 1 wet 1 227. 254. 27.2
4 Nude 2.5 wet 1 276. 288. 11.8
5 Nude 2.5 wet 2 272. 289. 17.1
6 LowCurv 0.3 wet 1 30 71.1 41.1
7 LowCurv 0.3 wet 2 27.6 63.8 36.2
8 LowCurv 1 wet 1 73.3 103. 29.8
9 LowCurv 1 wet 2 80.9 103. 21.9
10 LowCurv 2.5 wet 1 138. 149. 11.9
# … with 49 more rowsHere we plot the solar influx.
A plot of solar influx shows an outlier in the wet experiments where the heat loss with solar radiation was somehow less than the heat loss without solar radiation. We will exclude this outlier.
1.1.2 Temperature correction (to 30 C)
For the dry heat loss experiments (measuring dry heat resistance), we had to run some experiments at different temperatures to create a large enough gradient between skin/surface temperature and ambient temperature. The manikin is only able to produce results by measuring heat loss, and at 0.3 m/s wind speed, we found that the straight hair and nude (no hair) conditions led to overheating of the manikin. Subsequently, we had to adjust the temperatures to create a temperature gradient.
We thus need to bring all the measurements of heat loss to the same temperature. As heat resistance is temperature independent, we can use this to calculate the expected heat loss at various temperatures. We estimate heat loss at 30C with the following calculation.
\[Heat\ loss (W/m^2)_{(30C\ no\ radiation)} = 5/heat\ resistance_{(no \ radiation)} \]
# A tibble: 36 × 5
wig wind wet_dry resistance trial
<fct> <dbl> <fct> <dbl> <fct>
1 Nude 0.3 dry 0.113 1
2 Nude 0.3 dry 0.112 2
3 Nude 0.3 dry 0.112 3
4 Nude 1 dry 0.099 1
5 Nude 1 dry 0.101 2
6 Nude 1 dry 0.101 3
7 Nude 2.5 dry 0.058 1
8 Nude 2.5 dry 0.056 2
9 Nude 2.5 dry 0.058 3
10 LowCurv 0.3 dry 0.42 1
# … with 26 more rows# A tibble: 36 × 7
wig wind wet_dry trial influx resistance off
<fct> <dbl> <fct> <fct> <dbl> <dbl> <dbl>
1 Nude 0.3 dry 1 175. 0.113 44.2
2 Nude 0.3 dry 2 168. 0.112 44.6
3 Nude 0.3 dry 3 176. 0.112 44.6
4 Nude 1 dry 1 176 0.099 50.5
5 Nude 1 dry 2 162. 0.101 49.5
6 Nude 1 dry 3 171. 0.101 49.5
7 Nude 2.5 dry 1 153. 0.058 86.2
8 Nude 2.5 dry 2 169. 0.056 89.3
9 Nude 2.5 dry 3 158. 0.058 86.2
10 LowCurv 0.3 dry 1 62.6 0.42 11.9
# … with 26 more rowsTo calculate the heat loss at 30C with radiation, we subtract the solar influx from the temperature corrected heat loss:
\[Heat\ loss (W/m^2)_{(30C\ with\ radiation)} = Heat\ loss (W/m^2)_{(30C\ no\ radiation)}- solar\ influx(W/m^2) \]
# A tibble: 36 × 5
wig wind wet_dry resistance trial
<fct> <dbl> <fct> <dbl> <fct>
1 Nude 0.3 dry 0.237 1
2 Nude 0.3 dry 0.224 2
3 Nude 0.3 dry 0.234 3
4 Nude 1 dry 0.324 1
5 Nude 1 dry 0.292 2
6 Nude 1 dry 0.318 3
7 Nude 2.5 dry 0.088 1
8 Nude 2.5 dry 0.089 2
9 Nude 2.5 dry 0.091 3
10 LowCurv 0.3 dry 1.46 1
# … with 26 more rows# A tibble: 36 × 7
wig wind wet_dry trial influx off on
<fct> <dbl> <fct> <fct> <dbl> <dbl> <dbl>
1 Nude 0.3 dry 1 175. 44.2 -131.
2 Nude 0.3 dry 2 168. 44.6 -124.
3 Nude 0.3 dry 3 176. 44.6 -131.
4 Nude 1 dry 1 176 50.5 -125.
5 Nude 1 dry 2 162. 49.5 -113.
6 Nude 1 dry 3 171. 49.5 -122.
7 Nude 2.5 dry 1 153. 86.2 -66.7
8 Nude 2.5 dry 2 169. 89.3 -79.9
9 Nude 2.5 dry 3 158. 86.2 -72.2
10 LowCurv 0.3 dry 1 62.6 11.9 -50.7
# … with 26 more rows# A tibble: 94 × 7
wig wind wet_dry trial influx off on
<fct> <dbl> <fct> <fct> <dbl> <dbl> <dbl>
1 Nude 0.3 dry 1 175. 44.2 -131.
2 Nude 0.3 dry 2 168. 44.6 -124.
3 Nude 0.3 dry 3 176. 44.6 -131.
4 Nude 1 dry 1 176 50.5 -125.
5 Nude 1 dry 2 162. 49.5 -113.
6 Nude 1 dry 3 171. 49.5 -122.
7 Nude 2.5 dry 1 153. 86.2 -66.7
8 Nude 2.5 dry 2 169. 89.3 -79.9
9 Nude 2.5 dry 3 158. 86.2 -72.2
10 LowCurv 0.3 dry 1 62.6 11.9 -50.7
# … with 84 more rows# A tibble: 246 × 6
wig wind wet_dry trial var heatloss
<fct> <dbl> <fct> <fct> <chr> <dbl>
1 Nude 0.3 dry 1 influx 175.
2 Nude 0.3 dry 1 off 44.2
3 Nude 0.3 dry 1 on -131.
4 Nude 0.3 dry 2 influx 168.
5 Nude 0.3 dry 2 off 44.6
6 Nude 0.3 dry 2 on -124.
7 Nude 0.3 dry 3 influx 176.
8 Nude 0.3 dry 3 off 44.6
9 Nude 0.3 dry 3 on -131.
10 Nude 1 dry 1 influx 176
# … with 236 more rows2 Exploratory plots
3 Analyses
4 Analyses
4.1 Solar influx
4.1.1 Dry
Here, we model the effect of the wig variable on influx while correcting for wind. In case of solar influx, having hair will decrease solar influx when the hair is dry. The curvature of hair will decrease more solar influx.
Call:
lm(formula = influx ~ wind + wig, data = df_dry)
Residuals:
Min 1Q Median 3Q Max
-8.106 -3.844 1.099 2.763 9.053
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 175.4796 1.3680 128.275 < 2e-16 ***
wind -6.1330 0.6134 -9.998 6.46e-15 ***
wigLowCurv -110.1778 1.5923 -69.195 < 2e-16 ***
wigMidCurv -132.2778 1.5923 -83.075 < 2e-16 ***
wigHighCurv -152.0333 1.5923 -95.482 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 4.777 on 67 degrees of freedom
Multiple R-squared: 0.994, Adjusted R-squared: 0.9936
F-statistic: 2755 on 4 and 67 DF, p-value: < 2.2e-16
4.1.2 Wet
Here, we repeat the same modelling process for the wet data.
When the hair is sweaty, having curliest hair would decrease solar influx.
Call:
lm(formula = influx ~ wind + wig, data = df_wet)
Coefficients:
(Intercept) wind wigLowCurv wigMidCurv wigHighCurv
53.511 -12.857 -9.392 -15.259 -10.537 
Call:
lm(formula = influx ~ wind + wig, data = df_wet)
Residuals:
Min 1Q Median 3Q Max
-13.4541 -4.2173 -0.8525 3.9887 15.0463
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 53.511 4.577 11.690 1.50e-09 ***
wind -12.857 1.969 -6.529 5.15e-06 ***
wigLowCurv -9.392 5.102 -1.841 0.08318 .
wigMidCurv -15.259 5.102 -2.991 0.00822 **
wigHighCurv -10.537 5.361 -1.966 0.06591 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 8.425 on 17 degrees of freedom
Multiple R-squared: 0.7498, Adjusted R-squared: 0.6909
F-statistic: 12.74 on 4 and 17 DF, p-value: 5.664e-054.2 Heat loss
4.2.1 Dry
4.2.1.1 Radiation off
Here, we model the effect of the wig variable on the off (heat loss without radiation) variable while correcting for wind.
when the radiation is off, having straight or curly hair will decrease the heat loss.
# A tibble: 72 × 7
wig wind wet_dry trial influx off on
<fct> <dbl> <fct> <fct> <dbl> <dbl> <dbl>
1 Nude 0.3 dry 1 175. 44.2 -131.
2 Nude 0.3 dry 2 168. 44.6 -124.
3 Nude 0.3 dry 3 176. 44.6 -131.
4 Nude 1 dry 1 176 50.5 -125.
5 Nude 1 dry 2 162. 49.5 -113.
6 Nude 1 dry 3 171. 49.5 -122.
7 Nude 2.5 dry 1 153. 86.2 -66.7
8 Nude 2.5 dry 2 169. 89.3 -79.9
9 Nude 2.5 dry 3 158. 86.2 -72.2
10 LowCurv 0.3 dry 1 62.6 11.9 -50.7
# … with 62 more rows
Call:
lm(formula = off ~ wind + wig, data = df_dry_off[1:36, ])
Residuals:
Min 1Q Median 3Q Max
-8.0046 -4.0646 0.1855 2.7241 14.8000
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 46.192 2.279 20.27 < 2e-16 ***
wind 11.317 1.022 11.07 2.65e-12 ***
wigLowCurv -40.449 2.653 -15.25 5.91e-16 ***
wigMidCurv -40.838 2.653 -15.39 4.54e-16 ***
wigHighCurv -38.445 2.653 -14.49 2.37e-15 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 5.627 on 31 degrees of freedom
Multiple R-squared: 0.9373, Adjusted R-squared: 0.9292
F-statistic: 115.8 on 4 and 31 DF, p-value: < 2.2e-164.2.1.2 Radiation on
when radiation is on and hair is dry, the heat loss would increase given the presence of hair. The curvature of hair would increase the heat loss.
Call:
lm(formula = on ~ wind + wig, data = df_dry_on[1:36, ])
Residuals:
Min 1Q Median 3Q Max
-13.6579 -4.8720 -0.0048 3.3664 18.9682
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -129.287 2.854 -45.29 < 2e-16 ***
wind 17.450 1.280 13.63 1.23e-14 ***
wigLowCurv 69.729 3.322 20.99 < 2e-16 ***
wigMidCurv 91.439 3.322 27.52 < 2e-16 ***
wigHighCurv 113.588 3.322 34.19 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 7.048 on 31 degrees of freedom
Multiple R-squared: 0.9798, Adjusted R-squared: 0.9771
F-statistic: 375 on 4 and 31 DF, p-value: < 2.2e-164.2.2 Wet
4.2.2.1 Radiation off
Here, we model the effect of the wig variable on the off (heat loss without radiation) variable while correcting for wind.
when the radiation is off, having straight or curly hair will decrease the heat loss.
Call:
lm(formula = off ~ wind + wig, data = df_wet_off)
Residuals:
Min 1Q Median 3Q Max
-32.423 -5.988 2.672 5.875 40.867
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 171.047 9.142 18.71 8.88e-13 ***
wind 42.586 3.933 10.83 4.77e-09 ***
wigLowCurv -116.039 10.191 -11.39 2.24e-09 ***
wigMidCurv -129.155 10.191 -12.67 4.35e-10 ***
wigHighCurv -134.404 10.707 -12.55 5.04e-10 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 16.83 on 17 degrees of freedom
Multiple R-squared: 0.955, Adjusted R-squared: 0.9444
F-statistic: 90.24 on 4 and 17 DF, p-value: 3.238e-114.2.2.2 Radiation on
when the radiation is on, having straight or curly hair will decrease the heat loss.
Call:
lm(formula = on ~ wind + wig, data = df_wet_on)
Residuals:
Min 1Q Median 3Q Max
-47.469 -11.283 4.403 6.848 54.322
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 117.536 12.729 9.234 4.91e-08 ***
wind 55.442 5.476 10.124 1.29e-08 ***
wigLowCurv -106.646 14.189 -7.516 8.45e-07 ***
wigMidCurv -113.896 14.189 -8.027 3.49e-07 ***
wigHighCurv -123.867 14.908 -8.309 2.17e-07 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 23.43 on 17 degrees of freedom
Multiple R-squared: 0.9255, Adjusted R-squared: 0.9079
F-statistic: 52.77 on 4 and 17 DF, p-value: 2.307e-09
R version 4.1.2 (2021-11-01)
Platform: x86_64-apple-darwin17.0 (64-bit)
Running under: macOS Big Sur 10.16
Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/4.1/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/4.1/Resources/lib/libRlapack.dylib
locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] ggstatsplot_0.9.0 fs_1.5.0 kableExtra_1.3.4 knitr_1.36
[5] forcats_0.5.1 stringr_1.4.0 dplyr_1.0.7 purrr_0.3.4
[9] readr_2.0.2 tidyr_1.1.4 tibble_3.1.5 ggplot2_3.3.5
[13] tidyverse_1.3.1 workflowr_1.6.2
loaded via a namespace (and not attached):
[1] bit64_4.0.5 lubridate_1.8.0 RColorBrewer_1.1-2
[4] insight_0.14.5 webshot_0.5.2 httr_1.4.2
[7] rprojroot_2.0.2 tools_4.1.2 backports_1.2.1
[10] utf8_1.2.2 R6_2.5.1 statsExpressions_1.2.0
[13] DBI_1.1.1 colorspace_2.0-2 withr_2.4.2
[16] tidyselect_1.1.1 bit_4.0.4 compiler_4.1.2
[19] git2r_0.28.0 performance_0.8.0 cli_3.1.0
[22] rvest_1.0.2 xml2_1.3.2 labeling_0.4.2
[25] bayestestR_0.11.5 BWStest_0.2.2 scales_1.1.1
[28] mvtnorm_1.1-3 mc2d_0.1-21 multcompView_0.1-8
[31] systemfonts_1.0.3 digest_0.6.28 rmarkdown_2.11
[34] svglite_2.0.0 WRS2_1.1-3 pkgconfig_2.0.3
[37] htmltools_0.5.2 highr_0.9 dbplyr_2.1.1
[40] fastmap_1.1.0 rlang_0.4.12 readxl_1.3.1
[43] rstudioapi_0.13 SuppDists_1.1-9.5 farver_2.1.0
[46] jquerylib_0.1.4 generics_0.1.0 jsonlite_1.7.2
[49] vroom_1.5.5 magrittr_2.0.1 patchwork_1.1.1
[52] parameters_0.15.0 Rcpp_1.0.7 munsell_0.5.0
[55] fansi_0.5.0 lifecycle_1.0.1 stringi_1.7.5
[58] whisker_0.4 yaml_2.2.1 MASS_7.3-54
[61] plyr_1.8.6 paletteer_1.4.0 grid_4.1.2
[64] parallel_4.1.2 promises_1.2.0.1 crayon_1.4.1
[67] PMCMRplus_1.9.3 haven_2.4.3 hms_1.1.1
[70] zeallot_0.1.0 pillar_1.6.4 kSamples_1.2-9
[73] reprex_2.0.1 glue_1.4.2 evaluate_0.14
[76] modelr_0.1.8 vctrs_0.3.8 tzdb_0.1.2
[79] httpuv_1.6.3 cellranger_1.1.0 gtable_0.3.0
[82] rematch2_2.1.2 reshape_0.8.8 assertthat_0.2.1
[85] datawizard_0.2.1 cachem_1.0.6 xfun_0.27
[88] correlation_0.7.1 broom_0.7.9 Rmpfr_0.8-7
[91] later_1.3.0 viridisLite_0.4.0 memoise_2.0.0
[94] gmp_0.6-2.1 ellipsis_0.3.2