Limitations of scaling momentum control strategies to small spacecraft

As a spacecraft becomes smaller, a number of physical effects scale both favorably and unfavorably for passive stabilization of the craft. Unfortunately, two separate quantities both scale unfavorably for the use of traditional spinning rotor actuators (e.g. reaction wheels, momentum wheels, control moment gyros) for momentum and attitude control. First, the dominant disturbance torques on small spacecraft in low earth orbit, aerodynamic drag and solar radiation pressure, both become relatively larger as spacecraft size decreases. Second, the effectiveness of spinning rotors reduces as the rotor inertia decreases with the square or the wheel radius. These two factors conspire to greatly reduce the effectiveness of rotor-based momentum control systems at small scales. This reduction requires small spacecraft designers to either devote a significantly larger mass fraction to momentum control or adopt alternative momentum control systems. In this study we examine this problem from two viewpoints. First, empirical data is used to find a relationship between spacecraft size and mass fraction devoted to attitude control. While the International Space Station can devote less than 1% of its mass fraction to momentum control effectors, GEO telecom spacecraft tend to need around 1-2% of available mass, and some CubeSats must devote greater than 50% of their mass fraction. Second, we derive an expression for the smallest spacecraft that can use a reaction wheel for effective momentum management. For reasonable assumptions, this lower limit is on the order of 1 cm length scale, which is in good agreement with the empirical trend. Finally, we list some alternative momentum management strategies and discuss how they apply to spacecraft at the smallest size: the centimeter scale ChipSat.