The measure of shields, hull armor, and the structural durability of starships, armored vehicles, etc., is difficult in most cases. A shield (or armor plate) resists different types of weapons differently, depending on what kind of armor, shield, and the type of weapon. It may be highly vulnerable to a particular kind of attack - and sometimes, there are holes or weak spots in shields or armor, making it particularly difficult to quantify how much of a beating shields can take. Will a small fast projectile with the same energy hurt more than a large slow projectile? Would you be better off trying to melt the hull, or smash it? We have many methods of examining shield and hull toughness: Examining the temperature the hull may be heated to. When a ship flies near or in a star, estimating the radiation it is subject to. Estimating the relationship between weapon energies and damage to the shielding of a ship, or the hull of an unshielded ship. Examining the relationship between weapon power over time. Analysis of impacts of physical objects on starship hulls. Endurance against weapons is our most frequent form of measurement. Methodology is relatively simple; the power or energy seen overwhelming shields or penetrating the hull, or vaporizing/destroying some volume of starship, or that a ship can survive, is calculated as an upper limit, approximate estimate, or lower limit. All the problems about the consistency of weapon power are multiplied by the uncertainty in the angle of impact, number of attacks employed, and open questions about what type of attack the shields or armor are best suited to block. The last item on the list, though, happens to be a matter of considerable study. The study of ballistic impacts on armor has been a matter of pressing concern since the invention of tanks and warships with enough armor to resist modern guns. Although the penetration of shaped charges on armor is fairly complex, simple ballistic impacts by well-designed shells has been exhaustively formulated. The depth of armor that a projectile can penetrate depends on its mass, radius, and speed. All things being equal, a narrower and denser projectile penetrates better. In most cases, penetration is directly proportional to kinetic energy, but in others, penetration may be proportional to the square root. The original penetration formulae generalize over all shells of a certain shape by measuring penetration in calibers. On these pages, we somewhat abuse the empirical armor penetration formulae, pretending that ships, asteroids, logs, etc., are as well shaped for hull penetration - and as solidly constructed - as bullets. This may tend to produce overestimates. However, the formulae available give us very good estimations for the equivalent thickness of steel armor needed to match the resistance to physical impact displayed in Star Wars and Star Trek.	An article on empirical armor penetration formulae by noted expert Nathan Okun.