As the particle radius increases the volume (and, therefore, mass and heat capacity) increases as the cube of the radius. However, the surface area increases as the square of the radius, which is roughly proportional to the heat flux into the particle. Therefore, a particle's rate of temperature rise is maximized when the particle size is minimized. Common APCP formulations call for 30–400 µm AP particles (often spherical), as well as 2–50 µm Al particles (often spherical). Because of the size discrepancy between the AP and Al, Al will often take an interstitial position in a pseudo-lattice of AP particles. Characteristics Geometric APCP 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. The mass flux (kg/s) [and therefore pressure] of combustion gases generated is a function of the instantaneous surface area (m2), propellant density (kg/m3), and linear burn rate (m/s): 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 another producing steady long burn, though has thermal difficulties, CG shift. C-slot: propellant with large wedge cut out of the 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 or 6 legged star-like shape that can produce very level thrust, with a bit quicker burn than circular bore due to increased surface area. Burn rate While the surface area can be easily tailored by careful geometric design of the propellant, the burn rate is dependent on several subtle factors: Propellant chemical composition. AP, Al, additive particle sizes. Combustion pressure. Heat transfer characteristics. Erosive burning (high-velocity flow moving past the propellant). Initial temperature of propellant. In summary, however, most formulations have a burn rate between 1–3 mm/s at STP and 6–12 mm/s at 68 atm. The burn characteristics (such as linear burn rate) are often determined prior to rocket motor firing using a strand burner test. This test allows