## 2 Modular Multifunctional Approach Advantages
### The Volumetric Efficiency  
The necessity of increased CubeSat volume has recently emerged in the most advanced CubeSat space missions. For example, for the Optical Communication and Sensor Demonstration (OCSD) mission, two 1.5U CubeSats were employed, and the authors explicitly admitted that \"This is a dense spacecraft\" [17] (p. 4). The need for an additional spacecraft volume for the payload could explain the success of the 3U and other multiple form factors [1]. One possibility to save volume is to exploit the CubeSat external volume. The CubeSat form factor mechanical requirements impose a maximum protrusion thickness of 6.5 mm from the plane of the rails (CubeSat mechanical requirement 3.2.3 [2] (p. 9), Figure 1a). The rails are employed during the CubeSat deployment from the launch vehicle into space [2] (p. 7) and are usually part of the CubeSat skeleton (Figure 1b). The smart tiles approach aims to save the internal volume by moving spacecraft bus components to the outer volume. The saved internal volume could be used for the payload, as is shown in the present section. The payload volume gain can be described by the bus volumetric efficiency \(\gamma\). The total internal volume of a 1U CubeSat can be schematized with a cube whose side length is 100 mm and is called \(V_{int}\). This internal volume can be exploited to host either:  
* The payload, whose subscript is \"payl\";
* The spacecraft bus subsystems, whose subscripts are 1, 2,..., s.  
In traditional CubeSat configurations, the subsystems occupy part of the internal volume. The volumetric efficiency \(\gamma_{i}\) of the i-th bus system is defined as the volume gain obtainable through the proposed smart tile solution, with respect to traditional configurations:  
\[\gamma_{i}=\frac{V_{int}}{V_{int}-V_{sys,i}} \tag{1}\]  
where \(V_{int}\) is the remaining internal volume with the smart tiles approach and \(V_{sys,i}\) is the volume of the i-th subsystem moved from the internal volume \(V_{int}\) to the tiles external volume. As a consequence, \(V_{int}-V_{sys,i}\) is the remaining internal volume in the case of the traditional approach. In general, the volume moved to the tiles can be just a portion of the total volume of the subsystem. For simplicity, in the remainder of the section, it is assumed that one single tile hosts one single bus subsystem. The tiles are mounted on the six sides of the CubeSat skeleton on the external side of the spacecraft (Figure 1). A volumetric efficiency \(\gamma_{CS}\) for the entire set of \(s\) bus subsystems can also be defined. It is the volumetric efficiency of the whole CubeSat:  
\[\gamma_{CS}=\frac{V_{int}}{V_{int}-\sum_{i=1}^{s}V_{sys,i}} \tag{2}\]  
The maximum number of tiles for a 1U CubeSat is clearly \(s=6\), although an inferior number of tiles could be adopted to allow openings in the structure, for example, to expose the payload to the space environment or to host optical sensors. The volumetric efficiency is always greater than 1, as given in its definition at Equation (1). If the efficiency is only slightly greater than 1:  
\[\gamma_{i}=1+\delta_{i},\quad\delta_{i}<<1 \tag{3}\]  
Figure 1: (**a**) Maximum protrusion allowed from the plane of the rails; and (**b**) commercial CubeSat skeleton. where \(\delta_{i}\) is called volumetric increment. The same hypothesis can be made for the CubeSat volumetric efficiency:  
\[\gamma_{CS}=1+\delta_{CS},\quad\delta_{CS}<<1 \tag{4}\]  
where \(\delta_{CS}\) is the CubeSat volumetric increment.