Hybrid rockets have several advantages with respect to current propulsion systems like simplicity, safety, reliability, environmental friendliness, and lower cost. To size the combustion chamber, it is fundamental to understand how the length, the external diameter, the volume loading, and the length-to-diameter ratio vary with the design parameters like scale, burning time, average mixture ratio, initial oxidizer flux, and propellant combination. The equations available in the literature are not in explicit form with respect to the aforementioned design parameters, and sometimes they can be misinterpreted by hybrid rocket engineers. Moreover, it is not possible to determine the instantaneous and average characteristic velocities during the burn without a numerical time integration. To show explicitly the real trends, a set of analytical equations has been developed. The key step is the definition of the relation between initial and average mixture ratio and the asymptotic treatment with respect to the ratio between the external and internal diameters. Moreover, an approximate explicit semi-analytical expression of the instantaneous and average characteristic velocities is provided. The explicit analytical equations are validated with the exact implicit solutions showing good agreement and exact asymptotic behavior.

混合动力火箭相对于当前的推进系统具有多个优势，例如简单性，安全性，可靠性，环境友好性和较低的成本。要确定燃烧室的大小，最基本的方法是了解长度，外径，体积载荷以及长度与直径之比如何随设计参数（例如氧化皮，燃烧时间，平均混合比，初始氧化剂流量，和推进剂的组合。关于上述设计参数，文献中可用的方程式不是明确的形式，有时它们可​​能会被混合火箭工程师误解。此外，在没有数值时间积分的情况下不可能确定燃烧期间的瞬时和平均特征速度。为了明确显示实际趋势，已经开发出一套解析方程。关键步骤是定义初始混合比与平均混合比之间的关系以及相对于内径与外径之比的渐近处理。此外，提供了瞬时和平均特征速度的近似显式半解析表达式。显式分析方程式使用精确的隐式解进行验证，这些隐式解显示出良好的一致性和精确的渐近行为。