## 4 Experimental Methods
### Natural Soil/Synthetic Soil Models and Prototypes  
Large-scale field experiments in which full-scale projectiles penetrate natural soil deposits are performed to deduce the extent of terminal penetration, time history of deceleration, and resistant forces, but these cannot be used to derive the empirical models due to soil profile variability [127]. The small-scale laboratory tests investigating the penetration process allow to attain more controlled soil conditions. However, the extrapolation to field behavior of relatively small laboratory tests requires consideration of several experimental design parameters such as relative density and over-consolidation, soil ageing, diameter ratio (ratio of diameter of projectile and diameter of test container), particle size, and gravity stress [12; 128]. In order to achieve complete similitude between the model and the prototype of a large geo-medium event, the model must be constructed and tested in such a way as to satisfy the conditions of geometric similarity (constant ratio of all corresponding lengths in the model and prototype), kinematic similarity (proportionality of the two systems in regards to all corresponding time and time intervals), mechanical similarity (proportionality of the weight and density between the two systems), and dynamic similarity (proportionality of all the forces in the system) [129]. It is reasonable to start a study with the simplest system after considering such limitations for the model tests. Once a satisfactory model design method has been developed, a more complex and physically realistic system may be investigated with a slight modification. [PERSON] and [PERSON] [130] use similitude or dimensional analysis to simulate a space capsule landing on soils using a model design. A series of cone model tests on \"Ottawa Sand and Colorado River Sand\" and with modified models on clay soils are conducted to examine the validity of the model design for cohesionless and cohesive soils. [PERSON] et al. [131] found that in typical 1-g laboratory model research, there is a major scaling discrepancy due to the self-weight dependence of stress and the resulting strength distribution in granular soil. [PERSON] et al. [132] describes a combined 1-g and centrifuge penetration model test of projectile penetration into granular soils of a full-scale projectile penetration process that overcomes both scaling difficulties and the problem of quantification of sample properties. Test results are compared with [PERSON]'s equation-based predictions and penetration depth modification. [PERSON] et al. [125] and \"[PERSON] et al. [126] present 1:200 model centrifuge experiments in kaolin clay and compare the results (particularly penetration features) with [PERSON] [133] and [PERSON] [134] approaches\". [PERSON] et al. [135] uses centrifugal experiments and numerical modelling to present a study on the performance of anchor penetration in clay and calcareous silt and discusses the difference in the output of the penetration event in clay targets. Figure 8 shows the variation of terminal penetration depth found from the large-scale prototype experiment-based empirical methods at various impact velocities of a rod-like projectile on different soil target media. The penetration depth varies as square of impact velocity, except in the case of [PERSON] [136] and [PERSON] [137] in which penetration depth predicts logarithmic variation with impact velocity [138]. The projectile geometry has a significant effect on peak resistance force on projectiles penetrating soil media. Figure 9, depicting penetration resistance forces on projectiles using model tests at various impact velocities, infers that blunt-shape projectiles experience higher peak resistance force than ogive-shaped projectiles, and decreasing nose sharpness decreases the resistance force on projectile. Recent work uses transparent soils to determine in detail the particle-structure interactions during impact penetration in cohesion-less soil [139] and cohssive soil [140]. [PERSON] et al.