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Research Papers

# Prospects for Implementing Variable Emittance Thermal Control of Space Suits on the Martian SurfaceOPEN ACCESS

[+] Author and Article Information
Christopher J. Massina

Aerospace Engineering Sciences,
429 UCB,
Boulder, CO 80309

David M. Klaus

Aerospace Engineering Sciences,
429 UCB,
Boulder, CO 80309

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF THERMAL SCIENCE AND ENGINEERING APPLICATIONS. Manuscript received December 11, 2015; final manuscript received May 5, 2016; published online June 14, 2016. Assoc. Editor: Steve Cai.

J. Thermal Sci. Eng. Appl 8(4), 041002 (Jun 14, 2016) (8 pages) Paper No: TSEA-15-1350; doi: 10.1115/1.4033618 History: Received December 11, 2015; Revised May 05, 2016

## Abstract

Extravehicular activity (EVA) will play an important role as humans begin exploring Mars, which, in turn, will drive the need for new enabling technologies. For example, space suit heat rejection is currently achieved through the sublimation of ice water to the vacuum of space, a mechanism widely regarded as not feasible for use in Martian environment pressure ranges. As such, new, more robust thermal control mechanisms are needed for use under these conditions. Here, we evaluate the potential of utilizing a full suit, variable emittance radiator as the primary heat rejection mechanism during Martian surface EVAs. Diurnal and seasonal environment variations are considered for a latitude 27.5°S Martian surface exploration site. Surface environmental parameters were generated using the same methods used in the initial selection of the Mars Science Laboratory's initial landing site. This evaluation provides theoretical emittance setting requirements to evaluate the potential of the system's performance in a Mars environment. Parametric variations include metabolic rate, wind speed, radiator solar absorption, and total radiator area. The results showed that this thermal control architecture is capable of dissipating a standard nominal EVA metabolic load of 300 W in all the conditions with the exception of summer noon hours, where a supplemental heat rejection mechanism with a 250 W capacity must be included. These results can be used to identify when conditions are most favorable for conducting EVAs. The full suit, variable emittance radiator architecture provides a viable means of EVA thermal control on the Martian surface.

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## Introduction

When humans take their first steps on the Martian surface, a space suit will be required to support human life and enable functionality of the explorers [1,2]. In the history of human spaceflight, EVA has played a key role in the success of many missions. From the time astronauts were first untethered from their spacecraft during the Apollo program, EVA thermal control has been achieved through the sublimation of water [3,4]. However, the continued use of a sublimator for exploration has several drawbacks. Sublimated water is the single largest mass consumable expended during an 8-h EVA, and that water also has the potential to contaminate both scientific instruments and the environment being explored [57]. The cumulative loss of water associated with sublimator-type systems, over several EVAs, is largely considered too costly for Mars exploration [8,9]. Additionally, Martian surface pressures are generally between 4.8 and 10 Torr, which is just above the general operational limit of 3.5 Torr for a sublimator system, making even their potential use unrealistic [3,10,11].

While several EVA thermal control architectures have been suggested throughout the years; here, we focus on those most relevant to the architecture we are evaluating for use on Mars. As early as 1965, the full suit radiator was identified as one potential means of reducing the mass burden of EVA [14]. The Richardson investigation evaluated the full suit radiator in a low earth orbit environment. Under the conditions of that investigation, it was concluded that purely passive radiative thermal control would not provide adequate thermal control through the selection of static absorptivity and emissivity surface properties. However, this study showed that by incorporating variable conductance suit wall, which was not available at that time, the operational heat dissipation capacity could be increased.

In the early 2000s, a team from then Hamilton Sundstrand elaborated on several of the original Richardson ideas to develop the Chameleon Suit concept [15]. The Chameleon Suit concept was intended to couple the suit material to the working environment for as many functions as possible. The suit's core thermal control scheme utilized variable loft insulation layers to provide variable conductance from the skin to outer surface, a scheme suggested by Richardson. Variable emittance electrochromic devices were included within each variable loft layer to provide further suit wall heat exchange control. Finally, microelectromechanical system louvers are included over the suit's static property surface radiator. The louver system then provided an intelligent infrared (IR) shielding mechanism that ensured the radiator was exposed to an optimal environment.

In recent years, a derivative of the Chameleon Suit concept for thermal control has been under investigation in our lab [16]. The concept utilizes variable IR emittance electrochromics on the outside of the full suit radiator to actively modulate heat exchange with the environment. Initial feasibility studies showed that the architecture provided a viable means of reducing the water mass losses in a lunar environment [17]. Additional investigations elaborated upon this work to include more complex environmental interactions, defined initial pixel sizing considerations, and evaluated the impact on the human's thermal condition [1820]. To date, however, these feasibility assessments have focused on lunar surface applications.

Here, we provide a first-order feasibility assessment of using an electrochromic radiator based control architecture for EVA thermal control on the Martian surface. Theoretically required steady-state emittance settings are calculated over the Martian day for several metabolic rates. The thermal environment of Mars at latitude 27.5°S was used as the basis for this investigation. Seasonal variations in the external environment, based on the work of Vasavada et al. [21], are included for completeness.

## Background

###### Full Suit, Variable Emittance Radiator Extension.

Integration of the proposed full suit radiator architecture has been envisioned to occur via one of the two fundamental schemes. The human would be coupled to the radiator either directly via conductive heat transfer from the skin through the suit wall, or indirectly, via some dual-loop convective architecture that collects and distributes the heat for dissipation [20,22]. While some suit integration architectures could accommodate either coupling method, direct coupling is generally associated with use in a mechanical counter pressure (MCP) suit, while indirect coupling is generally associated with use in a traditional gas pressure suit [23].

There are two key differences between those architectures: the radiator's surface area and the nature of the heat path between the astronaut and the radiator. The total surface area of a tight fitting suit is approximately that of a nude astronaut and using the standard average of the expected crew population gives an expected total area of 1.91 m2 [24]. The total surface area of a traditional gas pressure suit is roughly double that of a nude astronaut at approximately 3.90 m2 [25]. An additional radiating area factor can be included to restrict the total available area to that which is actively participating in radiation exchange with the external environment (e.g., omitting arm pits, inner thighs, etc.). The actual radiating factor is dynamic, however, and will generally vary with body posture [26].

By including variable IR electrochromic devices on the exterior of the space suit, the system can actively modulate its surface properties and thereby alter the radiation interaction between the suit and the local environment. The feasibility of utilizing electrochromics in this type of application has been made possible by advancements in the robustness of the devices over multiple flexion cycles [27]. Broadband emissive property variations of as much as 0.50 have been demonstrated in some devices and can currently be tailored to a minimum low state of 0.19 or a high state of 0.90 [28]. Additional work is needed to fully characterize required thermal properties of an integrated garment.

If a purely radiative system cannot sustain the thermal balance, some additional mechanism may be warranted. Depending on the nature of the thermal control deficiency, mechanisms could include heaters, a phase change material (venting or nonventing), additional insulation, etc. Ideally, these alternative mechanisms would be relatively simple and not introduce unnecessary system complexity or mass. Note that we consider the term emittance $(ϵ)$ to be synonymous with broadband IR emissivity and IR absorptivity (emittance and absorptance). This is done with the understanding that the fraction of energy emitted or absorbed over the IR spectrum will be the same over those common wavelengths [29].

A constant nonzero suit surface solar absorptance $(α)$ is included to provide a more realistic approximation of a physical device. Including a nonzero solar absorptance also dictates that, in the presence of solar spectrum energy, the effective radiative sink temperature will vary as the electrochromic's emittance properties are changed. This approximation was not explicitly considered in early evaluations of the architecture on the lunar surface [16,17]. Baseline evaluations throughout this work considered a solar absorptance of 0.2, near the current space suit's value of 0.18 [3,4]. A parametric evaluation of different solar absorptivities is also included to illustrate the impact of other values on the overall potential system performance.

###### Internal and External Environments.

The internal environment, regarded as heat loads generated within the suit, consists primarily of human metabolic loads and avionics loads [30]. The avionics load will largely be a function of the suit's final design, which we cannot explicitly consider in this evaluation. During the Apollo lunar landings, metabolic rates ranged from minimums of ∼150 W to 15 min peak maximums of ∼725 W, and the nominal metabolic rate was ∼290 W [24]. These values are largely consistent with the expected metabolic expenditure during Martian EVAs [8,31,32]. However, additional investigations are required to refine metabolic expenditure estimates of Martian surface EVAs and include actual suit heat loads as the design matures.

The Martian environment has notable differences that must be included in the analysis when compared to lunar or low earth orbit environments. Key differences include the solar day length, seasonal flux variations, soil property values, and the low-pressure CO2 atmosphere [33]. The lunar sidereal day is approximately 27.3 earth days long, so bulk heat flux variations associated to changes in the solar elevation angle over the duration of an EVA can largely be disregarded [34]. The Martian day, on the other hand, is approximately 24.65 Earth hours long, so the resulting change in incident heat flux conditions over the duration of an EVA should be explicitly included [21]. Diurnal results are presented in terms of a local solar time (LST) whereby the Martian day is split into an equivalent 24 h day (or sol), rather than using the Earth hour standard. The Mars orbital position for a given season is captured in the Solar Longitude (Ls).

The surface thermal environment data used in this evaluation were taken from investigations that were completed during the determination of the Mars Science Laboratory's landing site. These data were generated using the Jet Propulsion Laboratory 1D surface–atmosphere model and the New Mexico State University 1D Mars general circulation model [21]. Diurnal and seasonal variations in the surface temperature, 1 m elevation atmosphere temperature, effective sky temperature, direct solar flux, and diffuse solar flux were all provided by the Vasavada et al. [21] investigation. The atmosphere considered here consisted of pure carbon dioxide at a constant pressure of 7 Torr [1,3]. The atmosphere imposes some degree of additional convective cooling at sustained wind speeds between 0 m/s (free convection) and 15 m/s [21,35]. These wind speed limits are used to provide a relevant operational envelope for the expected conditions of each season. A parametric of wind speed's impact on the theoretically required emittance setting was also conducted to illustrate the impacts of intermediate wind speeds and high velocity gust conditions. These results provided an indication of emittance set point variability within expected wind variation limits.

The interaction of the suit with the external environment was modeled through a single thermal node. Fundamentally, the system's thermal balance is described by Eq. (1). A summation of IR and solar energies $(qIR and qsol)$ was included to represent the potential for these fluxes to originate from different sources. The participating suit area is assumed to be oriented vertically on an infinite surface plane. This configuration allowed a simple view factor of 0.5 to be assumed for radiative interactions between solar and IR sources [18,20].

The amount of energy radiated from the suit $(qrad)$ is a function of the current emittance setting, radiating area, and the radiator's temperature. As described earlier, the radiator area was set equal to the total nude body surface area of 1.91 m2. This configuration is consistent with the thermal architecture's integration into an MCP type space suit and allows desirable skin temperatures to drive the radiator temperature. Additionally, we assumed that the MCP garment had a thermal resistance of zero, such that skin temperature comfort guidelines could be used directly as a reasonable approximation of the radiator's temperature [20,36] Display Formula

(1)$Δqstored=∑(qIR+qsol)+qMR,k−qconv−qrad,k$

Metabolic rates $(qMR)$ were chosen to be representative of minimum, nominal, and peak rates that may be experienced throughout the space walk. Together, this approach provided a reasonable first-order approximation of the suit and environment interaction, from which the potential performance of the thermal system can be assessed.

## Methods

###### Overall Heat Balance.

The output of this investigation consists of theoretically required steady-state emittance value for the suit system to maintain thermal neutrality as shown in Eq. (2). This emittance value was derived from Eq. (3) at steady-state, where the net energy stored $(qstored)$ equaled zero. Astronaut metabolic rates $(qMR)$ of 100 W, 300 W, 500 W, and 700 W were considered throughout the evaluation. The radiating temperature of the suit $(Tsuit)$ was taken directly from the optimal skin temperature comfort guidelines provided by Chambers [36]. The temperatures used were: 305.8 K, 303.8 K, 302.0 K, and 300.6 K from the 100 W to 700 W cases, respectively. Note that this radiator temperature variation from 305.8 K to 300.6 K experienced between low and high metabolic rates reduces the blackbody flux capacity by 6.6%. Incident IR radiation was considered to originate from the provided ground and sky temperatures $(TIR,i)$. Incident solar radiation consisted of a direct solar flux and a diffuse solar flux $(qsol,i″)$. No additional shading or complex geometry interactions were explicitly considered. The 1 m elevation atmospheric temperature $(T1m)$ data were used as the baseline wind temperature for the convective heat transfer contribution Display Formula

(2)$ϵk=∑(αAFsuit,iqsol,i″)+qMR,k−h¯A(Tsuit−T1m)(σATsuit4−∑(σAFsuit,iTIR,i4))$
Display Formula
(3)$qstored=∑(ϵkσAFsuit,iTIR,i4+αAFsuit,iqsol,i″)+qMR,k−h¯A(Tsuit−T1m)−ϵkσATsuit4$

###### Determination of Convection Coefficients.

Average free- and forced-convection coefficients were calculated for each of the seasonal environments investigated. Each coefficient is based on an average film temperature in a pure CO2 atmosphere at a pressure of 7 Torr. Table 1 provides a list of the coefficients used throughout the evaluation and is included for posterity. These data were extracted from a National Institute of Standards and Technology [37] web resource and used to determine relevant Reynolds, Prandtl, and Rayleigh numbers per their standard definitions for heat transfer from a vertical cylinder [38].

Average convection coefficients were calculated for both the operational envelope limit case wind speeds of 0 m/s and 15 m/s. The free-convection coefficient was determined from the Nusselt number correlation for an isothermal cylinder as described by Popiel et al. [39], which is found in Eqs. (4)(6). The characteristic length in the free-convection case is the cylinder's height (H) considered to be 1.8 m; D is the cylinder's diameter considered to be 0.311 m. The ends of the cylinder (circular areas) are not considered as participating areas in the determination of the convection coefficients. The variables C and n are included as geometric configuration factors Display Formula

(4)$Nu¯H=h¯Hk=CRaHn$
Display Formula
(5)$C=0.519+0.03454(HD)+0.0008772(HD)2+8.855x10−6(HD)3$
Display Formula
(6)$n=0.25−0.00253(HD)+1.152x10−5(HD)2$

In the forced-convection case, wind velocity of 15 m/s, the atmospheric properties of each season provided in Table 1 result in Reynolds numbers on the order of 103 such that a laminar boundary conditions are experienced. The characteristic dimension in this forced case is the diameter of the cylinder. Here, we use the comprehensive equation for the Nusselt number described by the below equation to determine the average convection coefficient [38] Display Formula

(7)$Nu¯D=h¯Dk=0.3+0.62ReD12Pr13[1+(0.4/Pr)23]14[1+(ReD282,000)58]45$

Calculated convection coefficients ranged from 0.276 W/m2 K to 0.287 W/m2 K in the free-convection case and from 1.909 W/m2 K to 2.038 W/m2 K in the forced-convection case.

###### Determination of Excess Energy Requirements.

The total thermal control power that must be supplied by the life support system in order to maintain thermal neutrality is described in Eq. (8). Ideally, the electrochromic radiator architecture would be capable of regulating the overall thermal balance without including additional mechanisms. However, environmental conditions which exceed achievable emittance limits, 0.19–0.9, will require some supplemental thermal control mechanism. Values for the difference in theoretically required dissipation energy and the corresponding high or low limit can then be used to define supplemental heat regulation requirements. When the theoretical emittance setting is in violation of achievable limits, the supplemental heat regulation guidelines are described by Eq. (9). As presented, a positive excess energy requirement correlated to needing some additional heat dissipation mechanism, e.g., an evaporator. A negative excess energy indicated that the astronaut would require additional energy be added to the system or an improved insulation scheme Display Formula

(8)$q=ϵkσATsuit,k4$
Display Formula
(9)$qsup=(ϵk−ϵlim)σATsuit,k4$

## Results and Discussion

The theoretically required emittance values needed to maintain thermal neutrality at a 0 m/s wind speed, free-convection case, are provided in Fig. 1. The corresponding high and low diurnal limits for the required emittance are provided in Table 2. From these data, one can see that in the nominal 300 W metabolic load case, emittance limits are only violated around the summer noon hours. This tends to suggest that when there are very low winds on Mars, the electrochromic radiator architecture can support the astronaut's thermal condition with little or no contribution from other mechanisms. However, work rates varying significantly outside of the nominal 300 W range will tend to require some additional mechanism depending on the time of day the EVA is being conducted. For instance, peak metabolic loads, near 700 W, are not sustainable by the system in any season if they are incurred near the local noon hours. Nevertheless, peak rates can be accommodated during night time and low solar angle hours (early morning and late evening).

The theoretically required emittance values needed to maintain thermal neutrality at the sustained 15 m/s wind speed condition are provided in Fig. 2. Again, corresponding high and low diurnal limits are provided in Table 2. Here, the sustained wind speeds have the uniform effect of lowering the required emittance setting to maintain the astronaut's thermal condition. Note that in this case, the 100 W and 300 W overnight theoretical emittance values are near or below zero, which indicates that additional heat input is required by the system. Alternatively, if EVA was to be conducted in these conditions, additional insulation, layers of thermal clothing (a coat, etc.), could be worn in lieu of including a full suit heater system. Again, we see that even with the increase in convective cooling, peak metabolic rates near the noon hour cannot be accommodated by the proposed architecture alone. In these conditions, the additional heat rejection capacity provided by the atmosphere reduces the theoretical high limit for daytime EVAs. However, while the summer case still violates the achievable maximum limit, the supplemental heat rejection requirement is reduced.

To further elaborate on the physical and operational limitations which can be extracted from this data set, Fig. 3 provides a heavily annotated version of summer conditions with 15 m/s wind speeds. Theoretical emittance limits of 0 to 1 are included to bound the absolute operational envelope in which a variable emittance system could function. Additionally, the practical limits of a variable emittance electrochromic system are included to illustrate the current performance limitations. The space within these limits defines the operational capacity of the proposed system for the given conditions of that time of day. Any metabolic excursion outside of those limits implies an additional supplemental cooling (energy excess) or heating/insulating mechanism (energy deficit) would need to be included to reduce the risk of potential astronaut performance degradation.

These data could also be used to define operational requirements for the time of day in which an EVA can be conducted. For instance, assuming the astronaut will maintain a constant metabolic load near the nominal 300 W case, an EVA can be conducted safely between the Martian LSTs of approximately 7:45–12:00 and 14:30–18:15 without additional thermal control mechanisms.

As described in Eq. (9), the difference of the theoretical emittance required from Table 2 and the corresponding limit describes the power deficiency for a given case. Table 3 provides the supplemental thermal control powers required to maintain thermal neutrality under the given conditions. Minimum values come from the worst case cold condition which occurs overnight at the 15 m/s wind speed. Maximum values come from worst case hot condition which occurs just after the local noon hour at the 0 m/s wind speed. Again, negative table values represent a heat input requirement to accommodate an energy deficit and positive values represent an additional heat rejection requirement to accommodate the energy excess in the system. As described earlier, these excursion ranges either dictate operational limits or will require some sort of supplemental thermal control scheme.

In either case, even the supplemental energy limits may be prohibitively large, although these limits are over an entire day so shorter EVAs may still be acceptable. As was done in the discussion of Fig. 3, daily profiles can be used to define notional EVA excursion limits for the hours in which a spacewalk could be conducted. The addition of some supplemental heat rejection and/or heat supply mechanism would serve to increase the allowable EVA window. While both the heat rejection and supply mechanisms may represent the use of a consumable, heat rejection is typically associated with the loss of a mass consumable (e.g., water) and heat supply with the use of power (or offset by incorporating additional insulating garments to reduce heat loss in this case).

Note that the 300 W metabolic rate case only requires additional cooling in summer conditions. If the supplemental cooling system was sized for summer conditions, it could be designed to offer a modest 250 W of cooling capacity, which is less than half of what the current sublimator system is capable of supplying [4].

In addition to the conditions investigated above, here we provide illustrations of the impact of additional variations in solar absorptance and wind speed. Each of the parametrics is based on a 300 W metabolic rate in the spring environment. The impact of changes to the suit's solar absorptance on the theoretically required emittance setting is found in Fig. 4. As the evaluated absorptance of the suit is increased, the fraction of solar energy retained by the suit system is likewise increased; this results in the observed increase in the suit's required emittance setting. The different solar absorptance profiles overlap during night time hours when there are no solar fluxes to influence the thermal balance.

The absorptance degradation profiles were created to span the theoretical range of achievable absorptance surface properties, 0–1, to illustrate the impact of radiator fouling in this regard. The high practical emittance limit was not near violation in our nominal α = 0.2 case, however, an additional increase in the absorptance of 0.2, to α = 0.4, would dictate that additional cooling mechanisms be included. Furthermore, an increase in solar absorptance to the theoretical limit of 1 would more than double the heat rejection required to maintain the astronaut's thermal condition. This nuance is worth consideration due to the potential impacts of the inevitable accumulation of Martian dust on the suit's radiator. Dust accumulation was an issue well documented during the Apollo program [40] and will have a significant impact on potential performance of a variable emittance space suit radiator based thermal control architecture. Further investigations are required to determine the extent to which surface contamination would affect the potential use of this architecture for surface EVA.

The impact of variations in wind speed on the theoretical emittance requirements is found in Fig. 5. A uniform reduction in required emittance was observed as wind speed is increased due to the added convective cooling component. These data can be used for a given EVA time to determine the system's capability for coping with wind gusts of different magnitudes or bulk variations in sustained wind speeds. While the required minimum to maximum emittance range increases in order to accommodate the full spectrum of wind speeds, the high limit for achievable emittance would not be encountered. With atmospheric temperatures always being lower than the radiator temperature at this location, any relative velocity between the astronaut and atmosphere would increase the dissipation capacity of the architecture. Additionally, if the radiator's solar absorptance properties begin to degrade as demonstrated in Fig. 4, EVAs on windy days will tend to have a positive impact on the amount of heat rejection the suit's thermal control mechanisms will need to supply. That is, less supplemental cooling capacity is needed because the increase in convective cooling can partially compensate for the additional solar energy absorbed.

(10)$ϵ2=ϵ1A1A2$

These results indicate that the use of the full suit variable emittance radiator architecture would provide a viable means of significant thermal control throughout much of the Martian year. Additionally, thermal control power limits were identified for the stated metabolic rates in each season. These limits could be used to define requirements for any necessary additional thermal control mechanisms that would enable EVA operations with higher metabolic loads and/or over larger portions of the Martian Day.

## Conclusions

Implementing a full suit, variable emittance radiator for EVA thermal control on the Martian surface was evaluated under environmental conditions at a latitude of 27.5°S using a simplified thermal model where the heat transfer interactions with the suit occurred through a single node. Martian LSTs are identified where the electrochromic radiator architecture can theoretically provide adequate thermal control over a range of metabolic rates. At the evaluated location, the nominal average dissipation case of a 300 W metabolic load could be accommodated in nearly all daytime hours during any season without the addition of a supplemental thermal control mechanism. Additional heat dissipation for this case was only required near local noon hours in summer conditions, where a supplemental heat rejection mechanism with a capacity of around 250 W would provide sufficient buffer to enable continuous EVA operations throughout the day. The duration of a transient thermal excursion is also a factor, as the human comfort range may tolerate short periods of thermal imbalance [19].

The impact of variable wind speeds and solar absorptance variations was also considered. With the local Martian atmosphere always being at a lower temperature than the space suit, any increase in wind velocity will reduce the net heat dissipation demands on the thermal control system. Alternatively, degradation of the suit's radiator surface properties can result in an increase in the supplemental heat dissipation requirements of the system. These considerations should be included in future investigations aimed at incorporating a full suit radiator architecture for use in the Martian environment.

In summary, the results show that a full suit, variable emittance radiator thermal control architecture is theoretically capable of providing considerable heat dissipation capacity in the Martian environment, thereby reducing or eliminating consumable mass losses associated with traditional venting systems. Additional investigations are required to determine best practices for incorporating this approach into a space suit design as well as for adding supplemental cooling and/or heating/insulating mechanisms to further expand the operational envelope.

## Acknowledgements

This work was supported by a NASA Office of the Chief Technologist's Space Technology Fellowship (Grant No. NNX12AN17H). Special thanks to Keith Novak of the NASA Jet Propulsion Laboratory and Kevin Anderson of the California State Polytechnic University at Pomona for providing guidance in regards to expected Martian surface environments.

## Nomenclature

• A =

area, m2

• C =

geometric configuration factor (convection)

• D =

diameter, m

• F =

view factor

• h =

convection heat transfer coefficient, W/m2 K

• H =

height, m

• k =

thermal conductivity, W/m K

• n =

geometric configuration factor (convection)

• Nu =

Nusselt number

• Pr =

Prandtl number

• $q$ =

heat rate, W

• $q″$ =

heat flux, W/m2

• Ra =

Rayleigh number

• Re =

Reynolds number

• T =

temperature, K

Greek Symbols
• $α$ =

absorptivity, fraction solar spectrum energy absorbed

• $ϵ$ =

emissivity/emittance, fraction IR spectrum energy absorbed or emitted

• $σ$ =

Stefan–Boltzmann constant, 5.67 × 10−8 W/m2 K4

Subscripts
• i =

heat source designator

• IR =

infrared

• k =

parametric iteration designator

• lim =

limit

• sol =

solar

• suit =

space suit surface

• sup =

• 1 m =

atmosphere at 1 m

## References

Waligora, J. M. , and Sedej, M. M. , 1987, “ Physiological and Technological Considerations for Mars Mission Extravehicular Activity,” Johnson Space Center, NASA Technical Report No. N87-17798.
Klaus, D. , Bamsey, M. , Schuller, M. , Godard, O. , Little, F. , and Askew, R. , 2006, “ Defining Space Suit Operational Requirements for Lunar and Mars Missions and Assessing Alternative Architectures,” SAE Technical Paper No. 2006-01-2290.
Harris, G. L. , 2001, The Origins and Technology of the Advanced Extravehicular Space Suit (AAS History Series, Vol. 24), Univelt, San Diego, CA.
Larson, W. J. , and Pranke, L. K. , 1999, Human Spaceflight: Mission Analysis and Design, McGraw-Hill, New York.
Nabity, J. , Mason, G. , Copeland, R. , and Trevino, L. , 2008, “ A Freezable Heat Exchanger for Space Suit Radiator Systems,” SAE Int. J. Aerosp., 1(1), pp. 355–363.
Hedgeland, R. J. , Hansen, P. A. , and Hughes, D. W. , 1994, “ Integrated Approach for Contamination Control and Verification for the Hubble Space Telescope First Servicing Mission,” Proc. SPIE, 2261, pp. 10–21.
Race, M. S. , Criswell, M. E. , and Rummel, J. D. , 2003, “ Planetary Protection Issues in the Human Exploration of Mars,” SAE Technical Paper No. 2003-01-2523.
Jones, H. , 2009, “ Spacesuit Cooling on the Moon and Mars,” SAE Technical Paper No. 2009-01-2418.
Bue, G. C. , Hodgson, E. , Izenson, M. , and Chen, W. , 2013, “ Multifunctional Space Evaporator-Absorber-Radiator,” AIAA Paper No. 2013-3306.
Kuznetz, L. H. , 1990, “ Space Suits and Life Support Systems for the Exploration of Mars,” AIAA Paper No. 90-3732.
Pater, I. , and Lissauer, J. J. , 2010, Planetary Sciences, 2nd ed., Cambridge University Press, Cambridge, UK.
Hodgson, E. , Izenson, M. , Chen, W. , and Bue, G. C. , 2012, “ Spacesuit Evaporator-Absorber-Radiator (SEAR),” AIAA Paper No. 2012-3484.
Izenson, M. G. , Chen, W. , Chepko, A. , Bue, G. , and Quinn, G. , 2014, “ Performance of a Multifunctional Space Evaporator-Absorber-Radiator (SEAR),” 44th International Conference on Environmental Systems, Tucson, AZ, Paper No. ICES-2014-51.
Richardson, D. L. , 1965, “ Study and Development of Materials and Techniques for Passive Thermal Control of Flexible Extravehicular Space Garments,” Aerospace Medical Research Laboratories, Aerospace Medical Division, Report No. AMRL-TR-65-156.
Hodgson, E. W. , Bender, A. , Goldfarb, J. , Hansen, H. , Quinn, G. , Sribnik, F. , and Thibaud-Erkey, C. , 2004, “ A Chameleon Suit to Liberate Human Exploration of Space Environments,” NASA Institute for Advanced Concepts, Phase II Final Report, Contract No. 07600-082.
Metts, J. G. , Nabity, J. A. , and Klaus, D. M. , 2011, “ Theoretical Performance Analysis of Electrochromic Radiators for Space Suit Thermal Control,” Adv. Space Res., 47(7), pp. 1256–1264.
Metts, J. G. , and Klaus, D. M. , 2012, “ First-Order Feasibility Analysis of a Space Suit Radiator Concept Based on Estimation of Water Mass Sublimation Using Apollo Mission Data,” Adv. Space Res., 49(1), pp. 204–212
Massina, C. J. , Klaus, D. M. , and Sheth, R. B. , 2014, “ Evaluation of Heat Transfer Strategies to Incorporate a Full Suit Flexible Radiator for Thermal Control in Space Suits,” 44th International Conference on Environmental Systems, Tucson, AZ, Paper No. ICES-2014-89.
Massina, C. J. , Nabity, J. A. , and Klaus, D. M. , 2015, “ Modeling the Human Thermal Balance in a Space Suit Using a Full Surface, Variable Emissivity Radiator,” 45th International Conference on Environmental Systems, Bellevue, WA, Paper No. ICES-2015-26.
Massina, C. J. , and Klaus, D. M. , 2015, “ Defining a Discretized Space Suit Surface Radiator With Variable Emissivity Properties,” ASME J. Therm. Sci. Eng. Appl., 7(4), p. 041014.
Vasavada, A. R. , Chen, A. , Barnes, J. R. , Burkhart, P. D. , Cantor, B. A. , Dwyer-Cianciolo, A. M. , Fergason, R. L. , Hinson, D. P. , Justh, H. L. , Kass, D. M. , Lewis, S. R. , Mischna, M. A. , Murphy, J. R. , Rafkin, S. C. R. , Tyler, D. , and Withers, P. G. , 2012, “ Assessment of Environments for Mars Science Laboratory Entry, Descent, and Surface Operations,” Space Sci. Rev., 179(1–4), pp. 793–835.
Metts, J. G. , and Klaus, D. M. , 2009, “ Conceptual Analysis of Electrochromic Radiators for Space Suits,” SAE Technical Paper No. 2009-01-2570.
Pitts, B. , Brensinger, C. , Saleh, J. , Carr, C. , Schmidt, P. , and Newman, D. , 2001, “ Astronaut Bio-Suit for Exploration Class Missions,” NIAC Phase I Report, Cambridge, MA, Institute of Technology.
NASA, 2010, “ Human Integration Design Handbook (HIDH),” National Aeronautics and Space Administration, NASA Technical Report No. NASA/SP-2010-3407.
Tepper, E. H. , Trevino, L. A. , and Anderson, J. E. , 1991, “ Results of Shuttle EMU Thermal Vacuum Tests Incorporating an Infrared Imaging Camera Data Acquisition System,” SAE Technical Paper No. 911388.
Guibert, A. , and Taylor, C. L. , 1952, “ Radiation Area of the Human Body,” J. Appl. Physiol., 5(1), pp. 24–37. [PubMed]
Kislov, N. , Groger, H. , and Ponnappan, R. , 2003, “ All-Solid-State Electrochromic Variable Emittance Coatings for Thermal Management in Space,” AIP Conference Proceedings on Space Technology and Applications International Forum, Albuquerque, NM, Feb., 2–5, 654, pp. 172–179.
Chandrasekhar, P. , Zay, B. J. , Lawrence, D. , Caldwell, E. , Sheth, R. , Stephan, R. , and Cornwell, J. , 2014, “ Variable-Emittance Infrared Electrochromic Skins Combining Unique Conducting Polymers, Ionic Liquid Electrolytes, Microporous Polymer Membranes, and Semiconductor/Polymer Coatings, for Spacecraft Thermal Control,” J. App. Polym. Sci., 131(19), p. 40850.
Gilmore, D. G. , ed., 2002, Spacecraft Thermal Control Handbook (Fundamental Technologies), 2nd ed., Vol. 1, The Aerospace Press, El Segundo, CA, Chap. 2.
Sompayrac, R. , Conger, B. , and Trevino, L. , 2009, “ Lunar Portable Life Support System Heat Rejection Study,” SAE Technical Paper No. 2009-01-2408.
Pu, Z. , Kapat, J. , Chow, L. , Recio, J. , Rini, D. , and Trevino, L. , 2004, “ Personal Cooling for Extra-Vehicular Activities on Mars,” AIAA Paper No. 2004-5970.
Wilde, R. , Hodgson, E. , and Mumford, R. , 2004, “ What Does it Take to Work on Mars? A New Direction in Spacesuit Systems,” AIAA Paper No. 2004-5967.
Kaplan, D. , 1988, “ Environment of Mars,” National Aeronautics and Space Administration, NASA Technical Memorandum No. 100470.
Heiken, G. H. , Vaniman, D. T. , and French, B. M. , eds., 1991, Lunar Sourcebook: A User's Guide to the Moon, Cambridge University Press, New York.
Campbell, A. B. , French, J. D. , Nair, S. S. , Miles, J. B. , and Lin, C. H. , 2000, “ Thermal Analysis and Design of an Advanced Space Suit,” J. Thermophys. Heat Transfer, 14(2), pp. 151–160.
Chambers, A. B. , 1970, “ Controlling Thermal Comfort in the EVA Space Suit,” ASHRAE J. 12, pp. 33–38.
NIST, 2011, “ Isobaric Properties for Carbon dioxide,” National Institute of Standards and Technology, Material Measurement Laboratory, Last accessed Apr. 8, 2015,
Incropera, F. P. , Dewitt, D. P. , Bergman, T. L. , and Lavine, A. S. , 2007, Fundamentals of Heat and Mass Transfer, 6th ed., Wiley, Hoboken, NJ, pp. 348–572.
Popiel, C. O. , Wojtkowiak, J. , and Bober, K. , 2007, “ Laminar Free Convective Heat Transfer From Isothermal Vertical Slender Cylinder,” Exp. Therm. Fluid Sci., 32(2), pp. 607–613.
Gaier, J. R. , 2005, “ The Effects of Lunar Dust on EVA Systems During the Apollo Missions,” Glenn Research Center, Cleveland, OH, NASA Technical Report No. NASA TM-2005-213610.
View article in PDF format.

## References

Waligora, J. M. , and Sedej, M. M. , 1987, “ Physiological and Technological Considerations for Mars Mission Extravehicular Activity,” Johnson Space Center, NASA Technical Report No. N87-17798.
Klaus, D. , Bamsey, M. , Schuller, M. , Godard, O. , Little, F. , and Askew, R. , 2006, “ Defining Space Suit Operational Requirements for Lunar and Mars Missions and Assessing Alternative Architectures,” SAE Technical Paper No. 2006-01-2290.
Harris, G. L. , 2001, The Origins and Technology of the Advanced Extravehicular Space Suit (AAS History Series, Vol. 24), Univelt, San Diego, CA.
Larson, W. J. , and Pranke, L. K. , 1999, Human Spaceflight: Mission Analysis and Design, McGraw-Hill, New York.
Nabity, J. , Mason, G. , Copeland, R. , and Trevino, L. , 2008, “ A Freezable Heat Exchanger for Space Suit Radiator Systems,” SAE Int. J. Aerosp., 1(1), pp. 355–363.
Hedgeland, R. J. , Hansen, P. A. , and Hughes, D. W. , 1994, “ Integrated Approach for Contamination Control and Verification for the Hubble Space Telescope First Servicing Mission,” Proc. SPIE, 2261, pp. 10–21.
Race, M. S. , Criswell, M. E. , and Rummel, J. D. , 2003, “ Planetary Protection Issues in the Human Exploration of Mars,” SAE Technical Paper No. 2003-01-2523.
Jones, H. , 2009, “ Spacesuit Cooling on the Moon and Mars,” SAE Technical Paper No. 2009-01-2418.
Bue, G. C. , Hodgson, E. , Izenson, M. , and Chen, W. , 2013, “ Multifunctional Space Evaporator-Absorber-Radiator,” AIAA Paper No. 2013-3306.
Kuznetz, L. H. , 1990, “ Space Suits and Life Support Systems for the Exploration of Mars,” AIAA Paper No. 90-3732.
Pater, I. , and Lissauer, J. J. , 2010, Planetary Sciences, 2nd ed., Cambridge University Press, Cambridge, UK.
Hodgson, E. , Izenson, M. , Chen, W. , and Bue, G. C. , 2012, “ Spacesuit Evaporator-Absorber-Radiator (SEAR),” AIAA Paper No. 2012-3484.
Izenson, M. G. , Chen, W. , Chepko, A. , Bue, G. , and Quinn, G. , 2014, “ Performance of a Multifunctional Space Evaporator-Absorber-Radiator (SEAR),” 44th International Conference on Environmental Systems, Tucson, AZ, Paper No. ICES-2014-51.
Richardson, D. L. , 1965, “ Study and Development of Materials and Techniques for Passive Thermal Control of Flexible Extravehicular Space Garments,” Aerospace Medical Research Laboratories, Aerospace Medical Division, Report No. AMRL-TR-65-156.
Hodgson, E. W. , Bender, A. , Goldfarb, J. , Hansen, H. , Quinn, G. , Sribnik, F. , and Thibaud-Erkey, C. , 2004, “ A Chameleon Suit to Liberate Human Exploration of Space Environments,” NASA Institute for Advanced Concepts, Phase II Final Report, Contract No. 07600-082.
Metts, J. G. , Nabity, J. A. , and Klaus, D. M. , 2011, “ Theoretical Performance Analysis of Electrochromic Radiators for Space Suit Thermal Control,” Adv. Space Res., 47(7), pp. 1256–1264.
Metts, J. G. , and Klaus, D. M. , 2012, “ First-Order Feasibility Analysis of a Space Suit Radiator Concept Based on Estimation of Water Mass Sublimation Using Apollo Mission Data,” Adv. Space Res., 49(1), pp. 204–212
Massina, C. J. , Klaus, D. M. , and Sheth, R. B. , 2014, “ Evaluation of Heat Transfer Strategies to Incorporate a Full Suit Flexible Radiator for Thermal Control in Space Suits,” 44th International Conference on Environmental Systems, Tucson, AZ, Paper No. ICES-2014-89.
Massina, C. J. , Nabity, J. A. , and Klaus, D. M. , 2015, “ Modeling the Human Thermal Balance in a Space Suit Using a Full Surface, Variable Emissivity Radiator,” 45th International Conference on Environmental Systems, Bellevue, WA, Paper No. ICES-2015-26.
Massina, C. J. , and Klaus, D. M. , 2015, “ Defining a Discretized Space Suit Surface Radiator With Variable Emissivity Properties,” ASME J. Therm. Sci. Eng. Appl., 7(4), p. 041014.
Vasavada, A. R. , Chen, A. , Barnes, J. R. , Burkhart, P. D. , Cantor, B. A. , Dwyer-Cianciolo, A. M. , Fergason, R. L. , Hinson, D. P. , Justh, H. L. , Kass, D. M. , Lewis, S. R. , Mischna, M. A. , Murphy, J. R. , Rafkin, S. C. R. , Tyler, D. , and Withers, P. G. , 2012, “ Assessment of Environments for Mars Science Laboratory Entry, Descent, and Surface Operations,” Space Sci. Rev., 179(1–4), pp. 793–835.
Metts, J. G. , and Klaus, D. M. , 2009, “ Conceptual Analysis of Electrochromic Radiators for Space Suits,” SAE Technical Paper No. 2009-01-2570.
Pitts, B. , Brensinger, C. , Saleh, J. , Carr, C. , Schmidt, P. , and Newman, D. , 2001, “ Astronaut Bio-Suit for Exploration Class Missions,” NIAC Phase I Report, Cambridge, MA, Institute of Technology.
NASA, 2010, “ Human Integration Design Handbook (HIDH),” National Aeronautics and Space Administration, NASA Technical Report No. NASA/SP-2010-3407.
Tepper, E. H. , Trevino, L. A. , and Anderson, J. E. , 1991, “ Results of Shuttle EMU Thermal Vacuum Tests Incorporating an Infrared Imaging Camera Data Acquisition System,” SAE Technical Paper No. 911388.
Guibert, A. , and Taylor, C. L. , 1952, “ Radiation Area of the Human Body,” J. Appl. Physiol., 5(1), pp. 24–37. [PubMed]
Kislov, N. , Groger, H. , and Ponnappan, R. , 2003, “ All-Solid-State Electrochromic Variable Emittance Coatings for Thermal Management in Space,” AIP Conference Proceedings on Space Technology and Applications International Forum, Albuquerque, NM, Feb., 2–5, 654, pp. 172–179.
Chandrasekhar, P. , Zay, B. J. , Lawrence, D. , Caldwell, E. , Sheth, R. , Stephan, R. , and Cornwell, J. , 2014, “ Variable-Emittance Infrared Electrochromic Skins Combining Unique Conducting Polymers, Ionic Liquid Electrolytes, Microporous Polymer Membranes, and Semiconductor/Polymer Coatings, for Spacecraft Thermal Control,” J. App. Polym. Sci., 131(19), p. 40850.
Gilmore, D. G. , ed., 2002, Spacecraft Thermal Control Handbook (Fundamental Technologies), 2nd ed., Vol. 1, The Aerospace Press, El Segundo, CA, Chap. 2.
Sompayrac, R. , Conger, B. , and Trevino, L. , 2009, “ Lunar Portable Life Support System Heat Rejection Study,” SAE Technical Paper No. 2009-01-2408.
Pu, Z. , Kapat, J. , Chow, L. , Recio, J. , Rini, D. , and Trevino, L. , 2004, “ Personal Cooling for Extra-Vehicular Activities on Mars,” AIAA Paper No. 2004-5970.
Wilde, R. , Hodgson, E. , and Mumford, R. , 2004, “ What Does it Take to Work on Mars? A New Direction in Spacesuit Systems,” AIAA Paper No. 2004-5967.
Kaplan, D. , 1988, “ Environment of Mars,” National Aeronautics and Space Administration, NASA Technical Memorandum No. 100470.
Heiken, G. H. , Vaniman, D. T. , and French, B. M. , eds., 1991, Lunar Sourcebook: A User's Guide to the Moon, Cambridge University Press, New York.
Campbell, A. B. , French, J. D. , Nair, S. S. , Miles, J. B. , and Lin, C. H. , 2000, “ Thermal Analysis and Design of an Advanced Space Suit,” J. Thermophys. Heat Transfer, 14(2), pp. 151–160.
Chambers, A. B. , 1970, “ Controlling Thermal Comfort in the EVA Space Suit,” ASHRAE J. 12, pp. 33–38.
NIST, 2011, “ Isobaric Properties for Carbon dioxide,” National Institute of Standards and Technology, Material Measurement Laboratory, Last accessed Apr. 8, 2015,
Incropera, F. P. , Dewitt, D. P. , Bergman, T. L. , and Lavine, A. S. , 2007, Fundamentals of Heat and Mass Transfer, 6th ed., Wiley, Hoboken, NJ, pp. 348–572.
Popiel, C. O. , Wojtkowiak, J. , and Bober, K. , 2007, “ Laminar Free Convective Heat Transfer From Isothermal Vertical Slender Cylinder,” Exp. Therm. Fluid Sci., 32(2), pp. 607–613.
Gaier, J. R. , 2005, “ The Effects of Lunar Dust on EVA Systems During the Apollo Missions,” Glenn Research Center, Cleveland, OH, NASA Technical Report No. NASA TM-2005-213610.

## Figures

Fig. 1

Diurnal theoretical emittance requirements for 0 m/s wind speed for the given season

Fig. 2

Diurnal theoretical emittance requirements for 15 m/s wind speed in the given season

Fig. 3

Diurnal theoretical emittance values for summer conditions and sustained wind speed of 15 m/s

Fig. 4

Impact of variations in solar absorptance on the theoretical emittance required to maintain thermal neutrality. The 300 W metabolic rate case, with free convection, was used to illustrate the relative impact in a spring environment.

Fig. 5

Impact of variations in wind speed on the theoretical emittance required to maintain thermal neutrality. The 300 W metabolic rate case was used to illustrate the relative impact in a spring environment.

## Tables

Table 1 Thermophysical properties of CO2 at 7 Torr and various film temperatures, from NIST [37]
Table 2 Theoretical diurnal emittance limits for given metabolic rate and convection conditions
Table 3 Supplemental thermal control power requirements for given season and metabolic rate. Negative values represent a heat input requirement, while positive values represent an additional heat rejection requirement. Limit cases are highlighted.

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