## 1 Introduction  
About 4000 people died in 2019 in the European Union as a direct result of moped and motorcycle crashes, accounting for 18% of the total motor vehicle fatalities [1]. Motorcyclists have an increased risk of injury in case of collision, which is particularly relevant in the case of head injuries [2]. The use of helmets is the most effective way of preventing motorcyclists' head injuries [3], and improving the impact performance of helmets leads to reduce the risk of head injury and fatalities. Most helmets are developed and designed according to the requirements prescribed in the relevant helmet standards. There are numerous motorcycle helmet safety standards around the world: ECE-22.05/06 in Europe [4, 5], DOT and Snell in USA [6, 7], and JIS-T in Japan [8] are among some of them. The objective of a motorcycle helmet standard is to ensure a minimum level of head protection under some specific test conditions. However, methods and requirements vary from one standard to another and, therefore, the performance against impact of motorcyclist helmets is influenced by the requirements included in each standard [9, 10].  
One of these requirements, which has been controversial over the last decades, is the need of a penetration test. The penetration test measures the resistance of the helmet shell to impacts against sharp objects. In these tests, the helmet is positioned on a headform or a spherical device support. Then, a conical striker is dropped to hit the outer surface of the static helmet shell. The required performance criterion consists of ensuring that there is no contact between the striker tip and the headform or spherical support.  
Over the years, some research has pointed out that the penetration test was either not necessary or that it could negatively influence helmet performance in more common real-life crash scenarios. In a statistical study, [PERSON] et al. found that the frequency of motorcycle accidents involving penetrating objects was extremely small [11]. [PERSON] et al. stated that the penetration test is the main parameter that would determine the thickness of the helmet shell, leading to a thicker shell that would account for about 50% of the weight of the helmet [12]. Furthermore, some researchers stated that the penetration test causes helmets to be designed with a stiffer shell that could result in an increased risk of head injury in impacts against rigid flat surfaces [13; 14]. These concerns resulted in the elimination of the penetration tests from some standards, while others continue demanding this requirement. In Europe, a penetration test is not required in the current regulation ECE-22.05/06 [4; 5], while several other standards and regulations do require this procedure as part of the helmet assessment program [6; 7; 8; 15].  
However, the link between increased helmet shell stiffness and a higher acceleration headform response in case of impact has been addressed on the basis of simplified models of the helmet behavior that, for instance, do not take into account the effects on the helmet behavior of different impact velocities [16] and other contributing factors to impact energy management such as the role of the shell in producing a proper load distribution over a greater liner area [17] and the variation of protective padding density at different helmet locations [18; 19]. The aim of this study was to empirically demonstrate if the inclusion of a penetration test in motorcyclist helmet testing standards results in an increased risk of head injury for the motorcyclists in a set of commercially available helmets. More specifically, the goal of this paper was to assess the influence of the shell resistance to the penetration test on the impact performance of helmets at two different impact velocities.