# 3D Modelling for Solar Erythermal UV Protection Provided by Human Hair
## 4 Discussion  
The study quantifies the eryt UV protection through human hair for different orientations and SZAs using SimUVEx, a 3D modelling tool predicting solar UV exposure. Simulations were run in a clear-sky day to eliminate cloudy situations that can affect significantly UV exposure. The hairs were considered opaque objects, providing full shielding against UV radiation. Different scenarios have been conceived according to the fact that UV protection provided by hair may be influenced by the density, the thickness, the colour, the alignment and the tilt of the head with respect to the sun. In this research, the density and thickness were fixed, and we focused on the geometric influence of hair protection over the head, studying specifically the effects of the alignment and the tilt of the hair. We depicted an average scenario, taking into consideration a medium-low hair density and a medium hair  
Figure 6: Daily PPFs using a moving average smoothed curve with 1 hour window for all the hair orientations and alignments. The marked hours in the plots (6, 9, 12, 15, 18) correspond to the following SZA: \(71.1^{\circ}\), \(40.9^{\circ}\), \(26^{\circ}\), \(47.9^{\circ}\), \(78.2^{\circ}\). diameter (50-80 \(\upmu\)m) [49] for hairs approximately 3 cm in length. We chose to investigate short hair effects to better understand the link between orientation of the hair and position of the sun. Indeed, the case of long hair would have been more protective, since it would have covered almost the entire scalp surface. We did not consider the dynamic motion of hair because the movements of the head and the body do not lead to big change in the short hair, so that the model can consider the hair as a static object. Low-medium hair density was chosen to investigate the most endangered cases among men. We did not treat the influence of colour in this analysis since it can be considered as an extra protection factor, as well as the skin phototype. Indeed, hair colour results from the biosynthesis of melanin within hair follicles. Melanin molecules in the skin constitute a built-in defence system to protect the skin against UV radiation, and when a follicle stops producing melanin, the hair turns colourless [51]. A dark-skinned person has more melanin molecules in the upper layers of the skin than a light-skinned person [52]. According to [24], approximately 300 hairs cm\({}^{-3}\) would be needed to achieve an SPF of 0-10 in the case of brown, blond and red hair, and about 400 hairs cm\({}^{-3}\) of white hair. Moreover, it is noteworthy that SPF ratings are calculated for an application thickness of 2 mg cm\({}^{-2}\), which is unrealistic, as most people apply significantly thinner layers. Additionally, results for bald situations can be measured in the usual routine of SimUVEx. Protection was estimated in terms of PPF that represents a sort of mean bias that is the difference between the values with and without hair protection. It does not indicate the amount of UV reaching the skin, but just the effectiveness of the protection. As the SZA increases, the PPF also increases for all hair types. PPFs provided by hair with a certain degree of order (parallel alignment) were generally higher by a range of about 10%-30% than the ones provided by random arrangements. This is due to the fact that tidy arrangements may confer higher cover than random alignments because of the loss of effectiveness by overlap of hair [25]. On the contrary, upright orientation provided more exposure because a greater surface area of the scalp is prone to solar radiation intrusion, especially at around noon (minimum SZA). Considerable progresses have been made in the understanding of artificial sun protections such as hats [20; 37; 53], sunglasses [36] or shade structures [35; 54; 55; 56], but little is still known about the photo-protective function of human hair. The effects of UV radiation on hair have only lately attracted the attention of the medical community.