# Numerical Analysis of Bicycle Helmet under Blunt Behavior
## 1 Introduction  
The burden of cyclist fatalities is of global scale. Only in 2016, over 2000 cyclists died in the EU [1], 840 in the US [2], and more than 2500 in India [3]. Hospital data recorded in the European Union show that the most common cycling injuries are related to the head (25% of injuries), upper extremities, and lower extremities [1]. Head-related injuries were found to be important on all major forms of transportation. Helmets are the safety equipment most frequently worn by cyclists. Helmet use is experiencing a growth [4] due to new legislative regulations [5] and an increased awareness on their effectiveness. [PERSON] et al. [6] performed a meta-analysis suggesting that helmet use is linked to a reduction in head, serious head, and fatal head injuries. [PERSON] et al. [5] found that helmet legislation leads to a decrease in head injuries while increasing helmet use, as do other studies, which suggest a positive effect of the helmet linked to a reduction in head injuries [7, 8]. Nevertheless, the use of bicycle helmets fluctuates depending on countries and regions, and it was statistically found that use is frequently less than 50% worldwide [9, 10]. There are research studies that disagree with the protective capacity of helmets and link their use to injuries, such as the research carried out by [PERSON] [11], which suggests an increased risk of neck injury. These contradictory results may lead to an opposition of the general population toward mandatory helmet regulation. For instance, [PERSON] et al. [12] showed that 57.1% of children in India violated traffic rules by not wearing a helmet, while even countries with extensive and long-standing mandatory helmet laws have the same issue, as shown by [PERSON] et al. [13] in Queensland where 12% of cyclists involved in police-reported crashes did not wear helmets. Bicycle helmets comply with standards as an assurance of their protection capabilities. Different standards are used in each country; nevertheless, all are closely related, certifying that the helmet stays attached to the head during impacts with various head forms, ensuring that helmets can adapt to all head dimensions. Minimum requirements on eye vision are imposed, preventing its obstruction. Material conditionings are made to replicate the effect of weather conditions and helmet storage on material properties. Additionally, they have similar impact testing methods, differing on the maximum g acceleration that the head can sustain, shown in Table 1.  
Impact velocity imposes the minimum kinetic energy that must absorbed by the helmet to remain below the acceleration threshold. An analysis of this relationship is presented in Equations (1) and (2), assuming that head forms and helmet weight are the same for all tests. \[\text{Ec (J)}=\frac{1}{2}\,\text{M(kg)}\
u^{2}\Big{(}\frac{\text{m}}{\text{s}} \Big{)}^{2} \tag{1}\]  
\[\text{Eag}\Bigg{(}\frac{\text{J}}{\Big{(}\frac{\text{m}}{\text{s}^{2}}\Big{)} \text{kg}}\Bigg{)}=\frac{\text{Ec(J)}}{\text{gt}\Big{(}\frac{\text{m}}{\text{s }^{2}}\Big{)}\,\text{M(kg)}} \tag{2}\]  
where: Ec is the kinetic energy (J); M is the sum of helmet mass and head form (kg); v is the initial velocity during impact (m/s); Eag is the energy absorbed per g acceleration and common weight (J/(kgm/s\({}^{2}\))); gt is the maximum g acceleration of each standard (m/s\({}^{2}\)). The minimum energy absorbed on each standard, for the same head form and helmet weight, based on Equation (2), is shown in Table 2.  
Table 2 suggests that all standards are comparable in terms of energy per maximum g acceleration. For flat anvils, the most thorough standards are the American and Chinese; in contrast, Europe has the most thorough standard for curbstone anvils. All standards remain within an 8.5% difference on the energy absorbed per maximum g acceleration. Thus, we can conclude that, despite different testing methods, all standards share a common grade of safety.