Small Satellite Capability Analysis: A Systems Approach for Defining Translational Performance in Small Satellites

Transcription

1 SSC10-VII-10 Small Satellite Capability Analysis: A Systems Approach for Defining Translational Performance in Small Satellites Mathew Zwack Air Force Research Labs (AFRL/RVSS) Ph zwack005@umn.edu Brian Engberg Air Force Research Labs (AFRL/RVSS) 3550 Aberdeen Ave SE Kirtland AFB, NM Ph brian.engberg@kirtland.af.mil Jeff Ganley Air Force Research Labs (AFRL/RVSS) 3550 Aberdeen Ave SE Kirtland AFB, NM Ph jeff.ganley@kirtland.af.mil ABSTRACT With recent technological advances, small satellite systems have evoked great interest from both commercial and military sectors. These systems offer reductions in both development time and mission cost, which make them attractive alternatives to the large systems in use today, especially for developing space nations. Small satellites are inherently less capable due to their resource constraints, yet as technology advances, a widening array of supportable missions may be enabled. Due to this, it is important for future Space Situational Awareness (SSA) applications to understand and analyze the capabilities and limitations of these small systems. In order to achieve this, a subsystem-by-subsystem analysis approach may be employed to define the capabilities of each sub-system that may be found in a small satellite. This study is intended to analyze the propulsion sub-system and define an upper bound for translational performance in micro-satellites. During the study, each element of the propulsion subsystem was characterized in terms of the satellite size to define the metrics that have the greatest effect on the overall performance. Both monopropellant and cold gas propulsion, which are proven and viable options for small satellites, were chosen for the analysis. From this study, conclusions can be drawn for both systems that identify the upper bounds of available Delta-V in terms of the sub-system and overall satellite size. APPROACH & ASSUMPTIONS Before beginning the analysis, assumptions were made to place boundaries on the satellite and system size parameters. First, the satellite size range will be constrained in order to focus the study on the smallsat regime. The starting point for the satellite size spectrum to be analyzed will be defined as a 10 cubic centimeter, 1 kilogram, CubeSat. Currently, CubeSat development can be found in the commercial and government sectors alike due to their promise of reduced cost and development time. Therefore, these satellites are a logical lower bound for this study due to an increased interest to use them as test-beds for new technology development and demonstration. The upper bound for satellite size has been defined as a 100- centimeter cube with an estimated weight of between 100 and 150 kilograms. This will allow for analysis in the classifications of pico, nano, and microsatellites. For the entire range, the satellites will be assumed to be cube shaped as alternative geometries present more complicated considerations that may be the topic of future studies. Zwack 1 24 th Annual AIAA/USU

2 The total satellite mass used in the study is defined as a structural mass estimate plus the propulsion component masses of the plumbing, thruster valves, and propellant tank. This creates a minimal satellite mass estimate due to the exclusion of other satellite sub-systems. Based upon the Delta-V equation, an absolute upper bound for the results will be found, as any addition of other subsystem mass will decrease the value of Delta-V. Satellite mass, in this case, is only relevant for the final Delta-V calculations because satellite volume is the controlling parameter for determining the fuel mass. For this study the propulsion system size was then set as a percentage of the total volume as opposed to a percentage of total mass. This effectively defines the maximum tank size for a given satellite because the available volume is fixed while the total mass budget can vary. In addition, most small satellites will be launched as secondary payloads where a predefined volume can often become a greater design driver than mass [2]. Structural mass was taken into account because it is an essential element in satellite bus design. However, an in depth analysis of the satellite structure was beyond the scope of this study. Instead, a model based upon real cataloged data was used. A full structural analysis could be added in the future to create an even more accurate mass model. Next, assumptions for system parameters must be made to provide an accurate but not too specific representation of real propulsion systems. First, the propulsion types selected for the study were Cold Gas and Monopropellant Hydrazine due to their current widespread applications in the satellite industry. Other systems such as electric and bipropellant were thought to be less viable for the selected size range due to their added complexity. Electric propulsion may be feasible for some satellites in the study range, but would require many more considerations including an in depth power sub-system analysis. Bipropellant is not practical for this size range due to the required addition of a second propellant tank as well as a much more complicated fuel management system, for arguably little added benefit in I sp. After the propulsion system types were selected, other assumptions about tank geometry and number of thrusters can be made. The number of thrusters was assumed to be six, which is the minimum for three translational degrees of freedom without attitude control. Although satellites frequently use more than six thrusters this minimum was chosen because it will give the upper bound on the satellite s translational performance. The propellant tanks were assumed to be spherical in shape because they are the most logical choice for high-pressure applications. Cylindrical and other alternative shapes could be considered for the very low-pressure ranges (100 s of Psi) where they would allow for a larger fuel volume, but at higher pressures are not nearly as efficient as spheres. These alternative geometries may give interesting results for the low-pressure ranges, which could be the focus of future studies. After these initial assumptions were made the analysis strategy for both propulsion systems was then to find and define a relationship between satellite size and component mass and volume. The satellite mass was defined by the following equation, which takes into account the masses of the components of structure, plumbing, thruster valves and fuel tank. m sat = mstr + mplumb + mthr + m tank (1) This total satellite mass along with the fuel mass was then used in the Delta-V equation to give the available Delta-V for each satellite size and propulsion system percentage of total volume. Each of these terms can be estimated from the size parameter. COMPONENT ANALYSES First, the structural mass will be estimated. As noted earlier, the structure is included because it is an essential component to satellite design (i.e. you can t have a satellite without a structure to hold it together) but for this study an in depth analysis is not necessarily required. First, a catalog of satellites and their respective total masses was put together in order to get an estimate for the total mass of satellites between 10 and 100 centimeters in side length. The estimate was obtained by finding a best-fit function of the cataloged data points, which can be seen in figure 1. The plotted points are satellites cataloged from the AMSAT database, while the line represents the function used to obtain a total mass estimate for the satellite at a given size. Figure 1: Satellite Total Mass Estimate vs. Satellite Side Length Zwack 2 24 th Annual AIAA/USU

3 After the mass estimate function was found, the structure mass was assumed to be 20 percent of the total. This value is an average value found from other cataloged real satellites based on the mass budget of each subsystem [1]. Although the point of reference for this percentage tends to discuss satellites larger than seen in this study, this estimate can still be deemed valid for small satellites. Upon comparison to data obtained from past entries to the University Nanosat Program, it can be seen that small satellites will tend to have between 20 and 30 percent of their mass allocated for structure. The 20 percent assumption is biased towards the conservative end of this range. A conservative assumption for the structural mass will further ensure that the Delta-V results are an absolute upper bound. After the structural mass is calculated the propulsion system components can then be evaluated. The first propulsion system components to be analyzed were the thruster valves. Beginning with the cold gas system, various available valves were cataloged in order to model the expected performance and specifications of these thrusters. Table 1 gives the specifications for the thruster valves considered. It includes both cold gas and Hydrazine thrusters along with their mass, volume, max thrust, operating pressure, and length specifications. consideration for this study, a one size fits all type approach to the use of these thruster valves is not an accurate representation of real life systems. Another important observation that can be made is related to valve length at the smallest satellite size. For a CubeSat, or any satellite up to 14 centimeters, the valve length becomes the limiting factor when choosing the proper valves. The valves cannot be longer than half the satellite side length in order to avoid problems with placement in the desired locations about the structure. If the valves are too long, for example, it will be much more difficult to place them opposite each other or centered on each face of the satellite. These considerations are needed only for the very small satellite sizes though, as all larger satellites will have ample volume to support any of the valves, which can be seen in figure 2, which shows the percentage of the total satellite mass and volume taken by the cold gas valves over the range of satellite sizes. The spikes on the plot at side lengths of 18, 30, and 70 cm are due to the implementation of different thrusters over the range of satellite sizes. Table 1: Cold Gas (Shaded) and Monopropellant Hydrazine Thruster Valves Model Moog 58X125A Moog 58E142 Mass (kg) Vol. (cm 3 ) Max Thrust (N) P-Op (psig) Length (cm) Marotta Vacco V1E1 Astrium CHT-1 Orion OPI Northrop MRE To relate the valve mass and volume to satellite size, the valves were placed along the satellite size range to have increasing thrust coinciding with increasing size. It is important to note that, although the valves were selected in this way, the valves providing the lowest thrust could still be used on the largest satellite in the range. The small thrust may be sufficient for any size but could severely increase time needed for each maneuver. Though time is not an important 5 Figure 2: Percentage of total Mass and Volume vs. Satellite Side Length for Cold Gas valves The limitations for small satellites using cold gas propulsion are further amplified when considering the use of monopropellant hydrazine. The hydrazine thrusters are much larger in both mass and volume due to the addition of the catalyst beds and heat management surfaces. The smallest hydrazine thrusters are over ten times the volume and twice the mass of the largest cold gas valves, which will not allow them to fit into any satellite smaller than 13 centimeters in side length. However, at this satellite size the thrusters would occupy 90 percent of the total volume, leaving no space for a fuel tank. The minimum satellite size that would enable the useful application of hydrazine propulsion is approximately 21 centimeters. At this Zwack 3 24 th Annual AIAA/USU

4 size, the thrusters account for almost 25 percent of the total volume but allow for the use of the smallest possible radius for the fuel tank (i.e. ~8 cm). Past this minimum size constraint the monopropellant hydrazine thrusters can then be placed similar to the cold gas valves, in order of increasing thrust. Figure 3 displays the percent volume and percent mass of the monopropellant thrusters over the range of satellite sizes. The size limitations can be seen as the thruster valves account for a high percentage of mass and volume at small satellite sizes. The spikes on the plot at the side lengths of 50 and 70 cm are due to the implementation of different thrusters over the range of satellite sizes. It is significant to note that this portion of the analysis relies on the parameters of commercially-available components rather than the theoretical state-of-the-art. While engineering specialized, smaller thruster components might be possible, it would add significantly to development timelines and cost, likely pushing the design outside the normal bounds for practical solutions. In addition, since component size, weight and power is always of primary importance for space systems, it is a reasonable approximation to assume that components of this type have already been optimized for the application in question. However, it is understood that technology advances will continue to be made in this area and may (in the future) affect the study results. Figure 3: Percentage of total Mass and Volume vs. Satellite Side Length for Hydrazine thrusters After the thruster valves were selected the plumbing for the system could be considered. For the cold gas system, the most important factor for the plumbing is the operating pressure of the thruster valves, which determines whether a pressure regulator is needed. Without a regulator the mass of the plumbing is quite simple and is defined by the number of thrusters multiplied by the length of tubing needed per thruster and the linear density of the tube itself. If a pressure regulator is required, other considerations must be made because the regulators are very large, especially when placed in a small satellite. These pressure regulators are cylindrical in shape and would ideally be placed along one corner of the satellite. The following figure shows how, depending upon the radius of the required regulator, the maximum tank radius could be limited. Figure 4: Pressure Regulator Considerations By calculating the space needed for the pressure regulator the minimum satellite size to avoid tank radius limitation can be found. Three different regulators with maximum inlet pressures of 6, 10, and 15 thousand psi were considered for the study. The corresponding minimum satellite side lengths for each regulator can be seen in Table 3. For each pressure regulator the given minimum side length represents the satellite size at which the maximum fuel tank radius will no longer be limited by the pressure regulator. The ideal maximum tank radius would be very close to half of the satellite side length, but with the addition of a given regulator this maximum will be reduced for satellites on the lower end of the size range. Once the pressure regulator limitations are taken into account, the mass and volume specifications for the required regulator can be added to the mass and volume of the tubing to find the totals for the plumbing component. Table 2: Minimum Satellite Side Length to Avoid Max Tank Radius Limitations Maximum Regulator Inlet Pressure (psi) Minimum Sat Side Length (cm) 6, , , When considering a monopropellant hydrazine system, pressure regulators are not needed for the plumbing mass and volume calculations. Although pressure regulated systems are an alternative, the typical state of Zwack 4 24 th Annual AIAA/USU

5 the art is a hydrazine blow-down system [2]. By using a blow-down set up the system architecture is kept simple, which helps to ensure its reliability. The plumbing mass and volume are then defined using the tubing length and linear density as well as the crosssectional area. Now that the thruster valves and plumbing have been considered, the remaining system volume is allocated for the fuel tank. The next component of the system to be analyzed is the propellant tank. With the other system components defined, the total tank volume can be found by subtracting the previous component volumes from the desired system volume, which is a fixed percentage of the total satellite volume. This ensures that all of the system components together will account for the selected volume percentage, which is incremented from 1 to 47 percent depending on the maximum allowable tank radius. From the total tank volume the outer radius of the tank can then be found. Next, the outer radius along with the properties of 6AL-4V Titanium alloy, commonly used for propellant tanks, are used to calculate the required tank thickness. The thickness is based upon the desired tank operating pressure and is estimated using the simple hoop stress equation, which relates the stress on the tank to the internal pressure, tank radius, and tank thickness. The thickness, however, only needs to be calculated in this manner for a cold gas system. If the monopropellant hydrazine tank is being analyzed, a uniform thickness can be used for all tank sizes based on a standard operating pressure of 400 pounds per square inch [3]. Once the tank thickness is known both the tank mass and the interior volume can be determined. For a cold gas propellant tank the mass and interior volume calculations are straight forward, only requiring tank thickness, radius, and material density. A hydrazine tank, however, will require some sort of propellant management device (PMD) to expel the liquid fuel. There are a handful of options for PMDs but a diaphragm was chosen for this study because of its more simple and efficient design, which provides the ability to attain fuel expulsion efficiencies of around 99.9 percent [3]. With the addition of a PMD the mass of a hydrazine tank is then defined by adding the mass of the diaphragm material to the mass as calculated for a spherical titanium tank. Besides the extra mass considerations, it is also important to note that, unlike a cold gas propellant tank, a hydrazine tank will not have 100 percent of its interior volume available for fuel storage. This consideration will be taken into account during the fuel mass and volume calculations. The final component to be evaluated is the fuel itself. Fuel mass is an essential part of the Delta-V calculations and can be found by using the fuel volume. For the cold gas propulsion system, the fuel volume is equal to the interior volume of the tank. With this volume the following gas law equation relating tank pressure, fuel volume, temperature, and the gas constant can be used to find the fuel mass: m fuel = PV RT (2) where, P is the tank operating pressure, V is the fuel volume, R is the gas constant for the fuel used (in this case, nitrogen), and T is the temperature. When finding the fuel mass for a hydrazine system a slightly different method must be used to find the fuel volume. Based upon currently available diaphragm tanks, an average of 15 percent of the interior tank volume will be taken by a pressurant gas, leaving 85 percent of the total volume for fuel storage. Therefore, during the study, the hydrazine tanks were assumed to contain fuel volumes equal to 85 percent of the tank interior. To find the hydrazine fuel mass, the fuel volume was then multiplied by the density of hydrazine. RESULTS After all of the propulsion system components were analyzed the final system and fuel masses were used in the following Delta-V equation to show the satellite s translational capability versus size and propulsion system volume: # "V = I sp gln 1+ m fuel % $ m satellite & ( (3) Here, I sp is the specific thrust of the fuel being used, g is the Earth s gravitational acceleration, m fuel is the total fuel mass, and m satellite is the total mass of the structure and propulsion system components including fuel. The cold gas propulsion system was run using three different tank pressures of 100, 1000, and 10,000 pounds per square inch and an estimate I sp of 68 seconds, which represents the use of nitrogen as propellant. These pressures are meant to represent (relative to known small satellite designs) a commonly used pressure, a near-state-of-the-art pressure, and a theoretical tank pressure, respectively. The total Delta- V given for each of these cases was then plotted versus the satellite size and the percentage of the total volume taken by the propulsion system. The results show that, even for extreme tank operating pressures, the cold gas ' Zwack 5 24 th Annual AIAA/USU

6 propulsion will not provide more than 900 m/s of Delta- V. For operating pressures of 100 and 1000 pounds per square inch this Delta-V is decreased drastically to 100 and 500 m/s respectively. It is important to note that these maximums occur at the largest satellite side length of 100 cm and the highest propulsion system percentage of the total volume, which means that for smaller satellites the available Delta-V will be even lower. At both of these pressures, however, the total satellite mass will be at 25 kilograms for a 100 psi tank and 70 kg for a 1000 psi tank, which is well below the estimated mass budget for a 100 cubic centimeter satellite. Figures 5 and 6 display the available Delta-V versus satellite side length for the tank pressures of 100 and 1000 psi. The various lines represent the point at which the propulsion system accounts for 10, 20, 30, and 40 percent of the total satellite volume. be far too large at nearly 400 kilograms. However the large increase in pressure does cause the Delta-V plots to flatten, which will give much higher Delta-V for smaller satellite sizes while maintaining a reasonable satellite mass. This change in shape that can be seen in the plots for the various tank pressures is due to the mass of the tank itself. At the lower pressures only very thin tank walls are required, which causes the plots to increase exponentially because the ratio of fuel mass to tank mass is relatively high. In the case of the high pressure at 10,000 psi, the tank needs to be excessively thick causing the ratio of fuel mass to tank mass to be much smaller. Due to this, the plot begins to approach a limit in Delta-V based on the tank mass becoming as large as the fuel mass itself. A restraint can then be added to the plot to limit the satellite mass in order to view a more realistic representation of the Delta-V. Figure 7 displays the plot of Delta-V versus satellite side length for a tank pressure of 10,000 psi, which shows the change in Delta-V at smaller satellite sizes. Figure 5: Delta-V vs. Satellite Side Length at a tank operating pressure of 100 psi Figure 6: Delta-V vs. Satellite Side Length for state-of-the-art tank operating pressure of 1000 psi At the highest pressure of 10,000 psi the available Delta-V will approach 1 km/s but the satellite mass will Figure 7: Delta-V vs. Satellite Side Length for a theoretical tank operating pressure of 10,000 psi Due to the liquid nature of the hydrazine fuel, only one case was run for the monopropellant thrusters using a tank operating pressure of 400 psi without a pressure regulator as discussed above. Although the liquid hydrazine will weigh much more than the cold gas, there is a large increase in the available Delta-V due to the increased I sp of 230 seconds. Unrestricted, the hydrazine can provide a maximum of 4.6 km/s of Delta- V at a satellite side length of 100 cm. The maximum is almost ten times higher than that of the cold gas system but the satellite mass would be far too large for a functional satellite at 450 kg. It is then necessary to add constraints to the system in order to get a more accurate illustration of the possible translational performance. As noted in the results of both the cold gas and hydrazine systems, constraints are needed in order to Zwack 6 24 th Annual AIAA/USU

7 observe a more realistic representation of the available Delta-V. Now that the method for finding Delta-V has been defined, it is possible to look at a more specific example representing a more feasible satellite. For this example, the propulsion system mass percentage will be limited using the total satellite mass budget model as shown in Figure 1. The propulsion system total mass, including fuel, will be limited to 30 percent of the total mass budget. This limit means that 50 percent of the total mass will be allocated to the structure and propulsion system. By constraining the structure and propulsion system in this way it can then be assumed that the remaining 50 percent of the total mass budget is available for other systems (power, thermal, payload, etc.). For the nitrogen cold gas a tank pressure of 1000 psi, representing a state-of-the-art system will be used, while the hydrazine system will remain unchanged. The maximum propulsion system volume percentage has been left at 40 percent for both systems because the mass will now be the limiting factor. However, this value can be changed at any time to further model a feasible satellite. Figure 8 displays the available Delta- V plot for the example cold gas system. Figure 8: Delta-V vs. Satellite Side Length and Propulsion System Percentage of total volume for limited cold gas example It can be seen in the figure that the Delta-V plot has been cut down due to the mass constraint, which has reduced the maximum Delta-V from 475 m/s to 397 m/s. The maximum has also been shifted from a satellite size of 100 cm to a size of 90 cm. This shift is due to the relationship between the fuel mass and total mass budget. In this case the ratio of fuel mass to total mass is larger for the 90 cm satellite and thus, based on the Delta-V equation, gives a larger Delta-V. An alternate view of the plot is provided in Figure 9, which shows the various contours added to the surface due to the constraints. Figure 9: Alternate view of Figure 8 Delta- V Plot In figure 9 contours A and C represent the points where the propulsion system mass was limited to 30 percent of the total mass budget. Along these lines the propulsion system mass plus the structure mass accounts for half of the overall satellite mass as defined in figure 1. The line labeled B is the propulsion system percentage of total volume limit. On this line the propulsion system accounts for 40 percent of the total satellite volume. Finally, contour D represents a very small regime where the use of a pressure regulator will reduce the maximum tank radius as shown in figure 4. On this contour however, the available Delta-V is very small, amounting to less than 25 m/s, which may be impractical for satellites of such small size. Although the new mass constraints do not drastically change the Delta-V plots, these small changes are important when considering more specific satellite design cases. With further alteration of the constraints any combination of propulsion system mass or volume percentage can be simulated to find an estimate for translational performance. Next, the propulsion system mass constraint was added to the monopropellant hydrazine system in order to cut the Delta-V plot to a more feasible regime. In comparison to the cold gas system discussed in figures 8 and 9, the hydrazine system shows very drastic changes when constrained. Figure 10 displays the available Delta-V for the monopropellant system after the mass constraint was added. Zwack 7 24 th Annual AIAA/USU

8 further reduce the upper bounds for each system to give more practical results. By limiting the propulsion system mass to 30 percent of the total satellite mass budget, the new maximums were found to be 397 m/s for cold gas and 1.5 km/s for hydrazine. With these results a possible extension to this study would be to connect the Delta-V found to the reachability of other orbits. This extension could give the ability to identify threats based upon whether or not an object is able to reach a high value asset in orbit. Figure 10: Delta-V vs. Satellite Side Length and Propulsion System percentage of total volume for the limited hydrazine system example The maximum Delta-V was reduced to 1.5 km/s for a satellite of 65 cm, which is less than a third of the previous unconstrained maximum. In the new plot there is also a drastic decrease in the Delta-V for satellites larger than 70 cm. Above this satellite size the maximum Delta-V will not exceed 1.3 km/s. The jagged points that can be seen along the upper contour of the plot are due to the relation between the change in tank radius and the addition of fuel mass. Due to the fact that the tank radius is increased in 1 cm increments, each time a larger tank is employed there is a more drastic spike in the plot. Overall the given example demonstrates how the Delta-V plots can be constrained in order to model realistic systems. By changing the parameters of the study, specific satellite designs can be focused on. CONCLUSIONS From the results of the study many conclusions about the upper bounds of translational performance in small satellites can be made. First, it can be seen that for satellites smaller than 1 m 3 and any reasonable tank operating pressure, the maximum Delta-V given by a cold gas system will never exceed 900 m/s. Even when satellite mass is ignored and the tank is set at extremely high operating pressures this limit will not be broken. The upper bound for the monopropellant hydrazine system was found to be 4.75 km/s. Utilizing alternative tank geometries could increase the maximum Delta-V, however, the satellite mass at the maximum point is well beyond a realistic system. For both the cold gas and hydrazine systems the satellite mass becomes a limiting factor as these maximum Delta-V values are approached. Therefore, constraints were placed to Other interesting conclusions that can be drawn are related to the feasibility of each of the propulsion systems. From the results it can be seen that the cold gas system could be implemented for any satellite on the size spectrum, including CubeSats. These systems could be used in very small satellites but the Delta-V results show that the use of cold gas in a satellite smaller than 15 cubic centimeters would allow for station-keeping maneuvers only. At these sizes, however, cold gas would be the only viable option, as a hydrazine system cannot be implemented in satellites below 21 cubic centimeters. However, future alternative system configurations and tank geometries could potentially improve these performance results in the smallest satellites. With the upper bounds on translational performance defined by this study other sub-system analyses can be added to give a full representation of the performance of small satellites. Special focus should be given to these systems because of their increased usage today. The ability to quantify and understand the capabilities of these small satellites will be of utmost importance for the future. REFERENCES 1. Larson, W.J. and Wertz, J.R. (eds.), Space Mission Analysis and Design, 3 rd Ed., Microcosm, El Segundo, CA, Burkhardt, H., Sippel, M., Krülle, G., Janovsky, R., Kassebom, M., Lübberstedt, H., Romberg, O., Fritsche, B., Evaluation of Propulsion Systems for Satellite End-of-Life De-Orbiting, In Proceedings of the 38 th AIAA Joint Propulsion Conference and Exhibit, Indianapolis, IN, July 8-10, Ballinger, I.A., Lacy, W.D., Tam, W.H., Review and History of PSI Elastomeric Diaphragm Tanks, In Proceedings of the 31 st AIAA Joint Propulsion Conference and Exhibit, San Diego, CA, July 10-12, SELECTED WEBSITES Amsat.org, cubesat.org, moog.com, swagelok.com Zwack 8 24 th Annual AIAA/USU