The shape of the heads used can vary. The most common head shapes are:
A sphere is the ideal shape for a head, because the stresses are distributed evenly through the material of the head. The radius (r) of the head equals the radius of the cylindrical part of the vessel.
This is also called an elliptical head. The shape of this head is more economical, because the height of the head is just a fraction of the diameter. Its radius varies between the major and minor axis; usually the ratio is 2:1.
2:1 Semi-Ellipsoidal dished heads are deeper and stronger than the more popular torispherical dished heads. The greater depth results in the head being more difficult to form, and this makes them more expensive to manufacture. However, the cost is offset by a potential reduction in the specified thickness due to the dished head having greater overall strength and resistance to pressure.
These heads have a dish with a fixed radius (r1), the size of which depends on the type of torispherical head.The transition between the cylinder and the dish is called the knuckle. The knuckle has a toroidal shape.