# 3D Modelling for Solar Erythermal UV Protection Provided by Human Hair
## 3 Results  
The PPFs (%) to the head through the hair for upright, random and parallel hairs are provided in Table 3 for different SZAs during a full clear-sky day. For each case, the surface was placed in four orientations (on the top, the front, the back, the right and the left). All the PPFs range from about 35% to 80%, with a general increase with the SZA. Indeed, the UV exposure through the hair decreases with the SZA, since UV radiation is stronger for lower SZAs (sun at its highest) compared with higher SZAs (lower sun), as the light travels through a shorter path of the atmosphere.  
Figure 5: Upright/Straight/Random orientations of the hair (top view).  
Comparing all the alignments, higher PPFs were found in parallel-aligned hairs, which usually cover homogeneously a larger part of the scalp. While the PPFs for parallel alignment range from 55% to 80%, upright alignment provides the lowest values (PPFs between 44% and 52%) and consequently more exposure, as a greater surface area of the scalp is prone to UV irradiance intrusion. The random arrangement shows results halfway between the two alignments for the top, the front and the back orientations. On the contrary, it is less protective (from 30% to 42%) for the right and left orientations of the head, even if the random alignment is less frequent in these parts.  
The front shows a good protection (higher than 50%) when the sun is at its highest (25\({}^{\circ}\)-30\({}^{\circ}\)), since the hairs are perpendicular to the incoming light, offering more shadow. Values of the back are quite constant for all situations, except for higher SZAs, when the protection is stronger.  
PPFs for each situation throughout the day are shown in Figure 6.  
PPF is generally higher for the parallel alignment and smaller for upright arrangement, which lets more radiation pass through. Except for the back, each situation reveals a peak where the dose exposure increases and the sun is at its highest elevation, around 12:00, corresponding to a minimum SZA value. Upright alignment shows a constant behaviour for all situations throughout the day, with values between 40% and 50%. The parallel and random alignments have a similar behaviour, with specular curves in the left and right cases. For the left and right side, the evaluation of the model is not trivial, as the results depend more significantly on the position of the sun, at both the zenithal and azimuthal levels. Therefore, it is not always easy to find a general explanation. In our case, we can observe that for the right and left sides, the random PPFs are once again smaller than that of upright alignment, in agreement with common sense, but in some cases, they are smaller than that of parallel alignment as well. This is probably due to the fact that upright alignment, in lateral zones, can provide more protection, since the hair strand is often perpendicular to UV rays, providing then more shade on the anatomical zone considered. However, upright alignment for right and left areas is more realistic for beard than for hair. On the contrary, a random behaviour, which is not in an upright position by definition, would protect less areas in terms of shade.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Top** & **Front** & **Back** & **Right** & **Left** \\ \hline SZA & & & Upright & & \\ \hline
25\({}^{\circ}\)–30\({}^{\circ}\) & 44.4 & 52.4 & 47.1 & 45.8 & 45.9 \\
30\({}^{\circ}\)–35\({}^{\circ}\) & 47.0 & 51.7 & 47.1 & 45.8 & 47.4