The sizing of a control moment gyro (CMG) cluster is covered sparsely in literature, but it is of considerable interest to a practicing engineer. In this paper, the sizing of a cluster of four control moment gyros is investigated based on the mission angular momentum requirement of a typical agile spacecraft. The CMG skew angle $\beta$ and individual CMG angular momentum $\mathit{h}$ are determined as part of the sizing. The work focuses on the sizing of a minimally redundant cluster of four CMGs in a pyramid and roof-type arrangement considering their external angular momentum surfaces. Two approaches are discussed: the first considers maximum angular momentum about individual axis separately, and the second considers the momentum requirement about two axes simultaneously. The internal momentum surfaces of the CMG clusters are analyzed. Gimbal angle desaturation and the fuel consumed for it by the roof-type and pyramid configurations are also examined. Both the four CMG clusters are able to meet the maximum nonspherical angular momentum demanded by a typical mission about each axes. However, using method 1, the cluster is able to generate only 88% of the two-axis mission demand. The clusters meet the mission demand completely with method 2 using 20% more angular momentum per CMG and an increase in skew angle by $8–11°$ compared to method 1. The 20% increase in momentum increases power consumption by 11%. For a typical gimbal angle desaturation, the roof-type cluster uses 8.5% more fuel than the pyramid arrangement. However, the former has only one major internal singular surface in contrast with seven for the latter. This makes the roof-type arrangement very desirable to keep the singularity avoidance algorithm simple and amenable with the CMGs operating within the momentum capability, and achieve the required spacecraft agility.

控制力矩陀螺仪 (CMG) 集群的尺寸在文献中很少涉及，但对于执业工程师来说却相当有趣。本文根据典型敏捷航天器的任务角动量需求，研究了由四个控制力矩陀螺组成的集群的尺寸。CMG 倾斜角$\beta$和单个 CMG 角动量$\mathit{H}$被确定为尺寸的一部分。考虑到它们的外部角动量表面，这项工作的重点是在金字塔和屋顶型排列的四个 CMG 中确定最小冗余集群的大小。讨论了两种方法：第一种方法分别考虑关于单个轴的最大角动量，第二种方法同时考虑关于两个轴的动量要求。分析了 CMG 星团的内部动量面。还检查了万向节角度去饱和度以及屋顶型和金字塔型配置所消耗的燃料。四个 CMG 集群都能够满足围绕每个轴的典型任务所需的最大非球形角动量。但是，使用方法一，集群只能产生88%的双轴任务需求。$8–11°$与方法 1 相比。动量增加 20% 会使功耗增加 11%。对于典型的万向节角度去饱和，屋顶型集群使用的燃料比金字塔型配置多 8.5%。然而，前者只有一个主要的内部奇异面，而后者则有七个。这使得屋顶型布置非常可取，以保持奇点避免算法简单，并在 CMG 在动量能力范围内运行，并实现所需的航天器敏捷性。