Richelieu-class battleship and more broadly the proximity between the two main artillery magazines (one for each turret), was the greatest risk: one hit could potentially neutralize the entire main battery, or even cause the ship's loss from an ammunition explosion. On "Dunkerque", to avoid this risk the forward turrets had been positioned apart from each other, further apart than on the "Nelson"-class battleships. The French also studied three-turret designs, such as one quadruple and two double, two triple and one double, or three triple. In every case, three turrets would have increased weight vs two quadruple turrets, reduced propulsion to and speed
Quadruple product Quadruple product In mathematics, the quadruple product is a product of four vectors in three-dimensional Euclidean space. The name "quadruple product" is used for two different products, the scalar-valued scalar quadruple product and the vector-valued vector quadruple product or vector product of four vectors . The scalar quadruple product is defined as the dot product of two cross products: where a, b, c, d are vectors in three-dimensional Euclidean space. It can be evaluated using the identity: or using the determinant: The vector quadruple product is defined as the cross product of two cross products: where a, b, c, d