There are seven types of different roof rafters that are used to build a roof. Gable is the simple one, it uses only one common rafter. Three other types are the common, hip and hip jack, all needed to frame the hip roof. All of these can be cut from common framing lumber, laminated veneer, glued laminated beams, timbers, steal or I beams from wood called TJI.
The common rafter is found in framed roofs that run from the exterior wall up to the ridge board. These set the height and center the ridge board of the span. The ridge board locations establishes the hip and valley rafters location. Hip rafters are 45 degree angles to the commons, they are from the outside corners of the building to the ridge board. Hip jacks on the outside walls, then run up to the hip rafter which is in line with common rafters. Valley rafters are then placed at the inside corners to the ridge, and then they are also at 45 degree angles to the commons. The valley jacks then run from the valley rafter up to the ridge board, and are in line with the commons. Then there are the cripple jacks, they are used if a valley and hip are located close together, and go from a valley to the hip rafter. A flying hip, is also known as the mystery hip, and go from a valley rafter meeting a ridge to the end of a higher ridge board.
Cutting a notch that allows a rafters underside to sit flat on the wall's top plate is called a "birds mouth" or a "birds beak". To properly cut one of these you must know the desired slope or pitch of your roof and the length of the individual rafter. Knowing this you can use a carpenter's rafter table with framing square to then layout the location in where all the rafter cuts will include a bird's mouth cut.
Know that rafters are sloped timbers that are supporting a building's roof from the gable peak to the overhang. The rafters ends are noses of those beams at the edge of the roof. Southwest architecture are long exposed rafters that extend from the end of a roof, and has decorative mill work which is called rafter tail. This gives the support beams visual appeal.
What is a bullnose rafter? These are ends that are popular southwest style that are simple to mill and easily added to existing roofs which already have exposed rafter ends. To make these, is to round off the lower end of a rafter. Then you have a double bullnose, these are popular also in the southwest style, a variation on the basic bullnose style. The end of these are composed of two curves on the same end. The upper portion is heart shaped carved out of the lower corner of a rafter. The crown and the scroll rafter ends are another southwestern rafter style, they both ornate more than the bullnose varieties, but are just as appealing. The ends of the crown rafters are inset bullnose with sharp edges at both of the ends of the curve. Ends are scrolled to resemble a S shape curve that is just below the upper corner of the rafter, and terminates a small notch at the bottom.
The typical roof is made of units called rafters, which we have gone over. The size and the spacing of these rafters are made according to the snow loads that are expected in a particular area. Dead loads and live loads is what is called the weight of the roofing materials. Live loads are loads from the external sources, which could be the workers standing on the roof, winds that are strong, and even snow. A snow load is the heaviest load a roof must support. So this makes them a dominate factor in rafter designing. The are measured in pounds per square foot. The snow load usually ranges from 5 to 10 psf in the southern US to 80 psf in the northern US. A complex formula then allows you to calculate rafter design for building dimensions and loading situation.