or solved simultaneously. The results are exact dimensions for grain, nozzle, and case geometries: The grain burns at a predictable rate, given its surface area and chamber pressure. The chamber pressure is determined by the nozzle throat diameter and grain burn rate. Allowable chamber pressure is a function of casing design. The length of burn time is determined by the grain "web thickness". The grain may or may not be bonded to the casing. Case-bonded motors are more difficult to design, since the deformation of the case and the grain under flight must be compatible. Common modes of failure in solid rocket motors include fracture of the grain, failure of case bonding, and air pockets in the grain. All of these produce an instantaneous increase in burn surface area and a corresponding increase in exhaust gas production rate and pressure, which may rupture the casing. Another failure mode is casing seal failure. Seals are required in casings that have to be opened to load the grain. Once a seal fails, hot gas will erode the escape path and result in failure. This was the cause of the Space Shuttle Challenger disaster. Grain geometry Solid rocket fuel deflagrates from the surface of exposed propellant in the combustion chamber. In this fashion, the geometry of the propellant inside the rocket motor plays an important role in the overall motor performance. As the surface of the propellant burns, the shape evolves (a subject of study in internal ballistics), most often changing the propellant surface area exposed to the combustion gases. Since the propellant volume is equal to the cross sectional area times the fuel length, the volumetric propellant consumption rate is the cross section area times the linear burn rate , and the instantaneous mass flow rate of combustion gases generated is equal to the volumetric rate times the fuel density : Several geometric configurations are often used depending on the application and desired thrust curve: Circular bore: if in BATES configuration, produces progressive-regressive thrust curve. End burner: propellant burns from one axial end to other producing steady long burn, though has thermal difficulties, center of gravity (CG) shift. C-slot: propellant with large wedge cut out of side (along axial direction), producing fairly long regressive thrust, though has thermal difficulties and asymmetric CG characteristics. Moon burner: off-center circular bore produces progressive-regressive long burn, though has slight asymmetric CG characteristics Finocyl: usually a 5-