Equivalent System Mass

The equivalent system mass (ESM) metric is commonly used in the ECLSS community. The analyzed parameters are mass, volume, required power, cooling, and crew time used to operate and maintain the LSS. For conversion into kg, mission specific mass equivalency factors must be determined and applied to the parameters.

The ESM is an indicator to give a rough understanding what type of loop closure is optimal and to develop a mass-based metric to compare between different technologies. For the use in this thesis it is of special interest, because the ITS is planned for reusability and therefore the launch costs are very important. While normally for an ESM analysis no technologies are selected out by parameters like safety or TRL, this is done in this thesis, since the overall system would otherwise not fulfill the constraints.

The advantages of ESM are:

• It is an easy to use, straightforward method that can even be automated when used in computer programs like Excel.

• Transportation costs for a technology are proportional to its mass and ESM can therefore be used to quantify these costs.

• ESM is an objective approach since the mass equivalency factors are based on verifiable numbers.

But there are some disadvantages as well:

• There is a focus on only 5 parameters. Other important parameters like TRL or complexity are not analyzed.

• Precise values for the ESM parameters must be known.

• Non-feasible technologies may perhaps be advised.

• Especially the crew factor is somewhat controversial [98] and not included in most of the trades in this thesis.

7.1.1 Calculation

The simplified formula for ESM calculation from [6] is outlined in Eq. ( 7-1 ) below.

𝐸𝑆𝑀 = 𝑀 + (𝑉 𝑉_𝑒𝑞) + (𝑃 𝑃_𝑒𝑞) + (𝐶 𝐶_𝑒𝑞) + (𝑡_{𝑐𝑟𝑒𝑤} 𝐷 𝑡_{𝑐𝑟𝑒𝑤,𝑒𝑞}) Eq. ( 7-1 ) with:

• 𝐸𝑆𝑀 [kg] - ESM value of the ECLSS

• 𝑀 [kg] - Total mass of the system

• 𝑉 [m³] - Total pressurized volume of the system

• 𝑉_𝑒𝑞 [kg m^-3] - Volume equivalency factor for pressurized infrastructure

• 𝑃 [kW] - Total power requirement of the system

• 𝑃_𝑒𝑞 [kg kW^-1] - Mass equivalency factor for power infrastructure

• 𝐶 [kW] - Total cooling requirement of the system

• 𝐶_𝑒𝑞 [kg kW^-1] - Mass equivalency factor for cooling infrastructure

• 𝑡_{𝑐𝑟𝑒𝑤} [CM-h y^-1] - Total crew time requirement of the system

• 𝐷 [y] - Duration of the mission segment

• 𝑡_{𝑐𝑟𝑒𝑤,𝑒𝑞} [kg CM-h^-1] - Mass equivalency factor for the crew time

The total mass of the system (𝑀) includes ECLSS hardware as well as connections, working masses and gases in the pressurized habitat. For the pressurized volume (𝑉) it is important not to include the free space for the crew, because this volume is not considered to be part of the ECLSS. The corresponding equivalency factor (𝑉_𝑒𝑞) is driven by the pressure loads, the radiation and micrometeroid protection shields, as well as the ablative thermal shielding. For the crew time (𝑡_{𝑐𝑟𝑒𝑤}), only scheduled maintaince should be included. Unscheduled maintenance, like repairs, are only included for off-nominal studies. The corresponding factor (𝑡_{𝑐𝑟𝑒𝑤,𝑒𝑞}) could be set to zero if only the equivalent mass is desired to be analyzed.

7.1.2 ESM Mass Equivalency Factors

As already stated above, mass equivalency factors are required to translate the non-mass parameters to non-mass equivalencies. These non-mass equivalency factors can be found in the BVAD ([10, p. 23]), [87, p. 57], and [5]. When not applicable, more suitable mass equivalency factors can be established.

The mass equivalency factor assumptions for a Mars transit mission from the sources above are outlined in Table 7-1.

Table 7-1: ESM mass equivalency factors for Mars transit mission [5, 10, p. 23, 10, p. 48, 10, p. 37, 87, p. 57]

Parameter Lower Nominal Upper Unit Shielded volume 215.50 219.70 [kg m^-3] Unshielded volume 9.16 13.40 [kg m^-3]

Power 12 (nuclear) 149 [kg kW^-1]

Thermal control 30 60 70 [kg kW^-1]

Crew time 0.526 0.802 [kg CM-h^-1]

Both mass equivalency factors for volume (shielded volume and unshielded volume) in Table 7-1 are for primary structures in pressurized and debris protected environments. Contrary to the unshielded volume, the upper value of shielded volume provides a sufficient radiation protection so that this environment is safe for the crew and radiation sensitive technology. For equipment outside the pressurized cabin, like pressure tanks, only minimal structures with micrometeoroid shields are needed and the value would be around 6 kg m^-³ (𝛾_𝑉). All volume values are assumed for an inflatable module like the TransHab. Because the SpaceHab consists of a composite structure, these values can´t be used. Furthermore, contrary to NASA designs the SpaceHab includes propellant structures and engines. For the calculation of a decent equivalent volume factor, the total mass of the pressure shell and the volume must be known. As stated in [11], the dry mass of the SpaceHab is 150,000 kg (𝑚_𝑑𝑟𝑦). For the pressurized volume, detailed calculations were made in chapter 2.3 Volume, which revealed that the pressurized volume (𝑉) of the SpaceHab is 1090.28 m³ and for the Evolved-SpaceHab design it is 1710.76 m³. Therefore, the volume equivalency factor can be calculated with Eq. ( 7-2 ) to 137.58 kg m^-3 for the SpaceHab design and 87.68 kg m^-3 for the Evolved-SpaceHab design.

𝑉_𝑒𝑞 =^{𝑚𝑑𝑟𝑦}

𝑉 Eq. ( 7-2 )

The lower mass equivalency factor for power is based on a Rankine cycle nuclear power plant that produces 572 kW. The nominal value is based on a 28 % efficient solar photovoltaic array without any storage [10, p. 37]. Solar photovoltaic will be the main power source for the SpaceHab. To get to an actual equivalent power value for the SpaceHab, a UltraFlex™ solar array from Orbital ATK [99] is assumed in combination with battery storage. The UltraFlex™ solar array is a state-of-the-art lightweight solar array with 30 % efficient triple-junction cells and scalability up-to 350 kW. Eq. ( 7-3 ) shows, that the power equivalency factor (𝑃_𝑒𝑞) is a combination of the equivalency factors for the solar array (𝛾_{𝑃,𝑠𝑜𝑙𝑎𝑟}) and the power storage (𝛾_{𝑃,𝑏𝑎𝑡𝑡𝑒𝑟𝑦}).

The equivalency factor of the solar array is the sum of the specific mass (𝛾_{𝑃,𝑀,𝑠𝑜𝑙𝑎𝑟}) with the product of the specific stowage volume (𝛾_{𝑃,𝑉,𝑠𝑜𝑙𝑎𝑟}) and the volume infrastructure cost factor (𝛾_𝑉). The specific mass and stowage volume given in [99], are 6.67 kg kW^-1 and 0.025 m³ kW^-1, respectively. The equivalency factor for the battery can be estimated using table 3.14 in [63] and by subtracting the specific power of “Solar Photovoltaic Cells w/o Energy Storage” (101 kg kW^-1) from “Solar Photovoltaic Cells w/ Battery Storage” (133 kg kW^-1), which gives a equivalency factor for the batteries (𝛾_{𝑃,𝑏𝑎𝑡𝑡𝑒𝑟𝑦}) of 32 kg kW^-1. Adding the solar photovoltaic and the battery equivalency factors gives 38.82 kg kW^-1 for the power equivalency factor.

𝑃_𝑒𝑞 = 𝛾_{𝑃,𝑠𝑜𝑙𝑎𝑟}+ 𝛾_{𝑃,𝑏𝑎𝑡𝑡𝑒𝑟𝑦} Eq. ( 7-3 ) 𝛾_{𝑃,𝑠𝑜𝑙𝑎𝑟} = 𝛾_{𝑃,𝑀,𝑠𝑜𝑙𝑎𝑟}+ 𝛾_{𝑃,𝑉,𝑠𝑜𝑙𝑎𝑟} 𝛾_𝑉 Eq. ( 7-4 ) The lower thermal control equivalency factor is for a lightweight, flow-through radiator with a supplemental expendable cooling subsystem [10, p. 39]. Because the ITS is optimized on low weight, this value is used for the further analysis.

The values for the crew time equivalency factor in Table 7-1 are for a Mars transit vehicle. But because the Concept of Operations in this thesis is assuming that at least one engineer is included in the crew for maintenance, the crew time equivalency factor is only 0.1 kg CM-h^-1, which is on the lower end of typical values for the crew time stated in [10].

Depicted in Table 7-2 is a breakdown of the equivalency factors used in this thesis.

Table 7-2: ESM equivalency factors for SpaceHab and Evolved-SpaceHab

Parameter Value Unit nonobservance of important parameters like TRL. The Multi-criteria decision making (MCDM) is a very common branch of decision making which is independent of the type of criteria. It is used to solve problems within a discrete decision space. In multi-attribute decision making, the set of alternatives (like O2 storage technologies) is established at the beginning of the process.

Selected technical terms associated with MCDM are defined below [100, pp. 1-2]:

• Alternatives: This describes the different choices that can be made. These are the assemblies and components to be compared.

• Multiple Attributes or decision criteria: MCDM problems are related to multiple criteria. These criteria represent the characteristics by which the different alternatives shall be compared.

• Decision Matrix: An MCDM problem can simply be summarized in a matrix.

The resulting m x n matrix is called decision matrix and consists of the elements aij that represent the performance of alternative Ai with respect to a certain criterion Cj, where i = 1, 2, 3, …, m and j = 1, 2, 3, …, n.

In contrast to most MCDM methods, no criteria weights are used, because these are mostly subjective. Depending on the choice the decision maker has made for the weight, the outcome can differ greatly. Therefore, no weights between the different criteria are used. But it should be noted that the ESM is part of the final decision (7.3) and this has inherently a weight on the different parameters.