Kenneth A. Burke

Glenn Research Center, Cleveland, Ohio

Small Portable PEM Fuel Cell Systems for

NASA Exploration Missions

NASA/TM—2005-213994

December 2005

AIAA–2005–5680
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Kenneth A. Burke

Glenn Research Center, Cleveland, Ohio

Small Portable PEM Fuel Cell Systems for

NASA Exploration Missions

NASA/TM—2005-213994

December 2005

National Aeronautics and

Space Administration

Glenn Research Center

Prepared for the

Third International Energy Conversion Engineering Conference

sponsored by the American Institute of Aeronautics and Astronautics

San Francisco, California, August 15–18, 2005

AIAA–2005–5680
Acknowledgments

The author wishes to thank Thomas Tomsik, Glenn Research Center, for his analysis of cryogenic and supercritical

reactant storage.

Available from

NASA Center for Aerospace Information

7121 Standard Drive

Hanover, MD 21076

National Technical Information Service

5285 Port Royal Road

Springfield, VA 22100

Available electronically at http://gltrs.grc.nasa.gov
NASA/TM—2005-213994 1 

Small Portable PEM Fuel Cell Systems 

for NASA Exploration Missions 

Kenneth A. Burke 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Abstract

The exploration of the Moon and Mars, whether by manned or unmanned spacecraft, will need portable power 

sources. Diverse manned and unmanned exploration will be done at greater distances from the initial landing sites 

and require greater amounts of power for spacesuits, portable tools, manned and unmanned rovers, as well as 

equipment used for construction and remote in-situ resource utilization. The energy-rich environment envisioned for 

these new missions will push the limits of state of the art battery technology because greater amounts of power for 

longer periods of operation are required while the mass and volume allotted for power sources will need to remain 

the same or be decreased. 

Oxygen-Hydrogen PEM-based fuel cell systems are being examined as a portable power source in addition to 

advanced battery technology. Fuel cell power systems have been used by the Gemini, Apollo, and Space Shuttle 

programs. These systems have not been portable, but have been integral parts of their spacecraft, and have used 

reactants from a separate cryogenic supply. These systems typically have been higher in power. They also have had 

significant ancillary equipment sections that perform the pumping of reactants and coolant through the fuel cell 

stack and the separation of the product water from the unused reactant streams. The design of small portable fuel 

cell systems will be a significant departure from these previous designs. These smaller designs will have very 

limited ancillary equipment, relying on passive techniques for reactant and thermal management, and the reactant 

storage could be an integral part of the fuel cell system. 

This paper is an analysis of the mass and volume of oxygen-hydrogen PEM fuel cell systems that was performed 

to evaluate fuel cell technology as an alternative to batteries for small portable power applications, and to quantify 

areas of technological improvement. An assessment of current fuel cell technology and reactant storage and 

management technology was completed to validate the analysis and to identify technology challenges. 

This preliminary study indicates that fuel cell systems have the potential for energy densities of >400 W-hr/kg 

and >150 W-hr/liter. This level of performance makes fuel cells attractive as portable high-power density, highenergy density sources for exploration missions. 

I. Introduction

The purpose of this study was to expand on previous analyses of the mass and volume characteristics of fuel cell 

systems,1,2 and in particular look specifically at smaller power fuel cell systems that could potentially be used for 

Lunar and Mars portable power exploration applications. Part of this study is an initial assessment of storage 

techniques for the hydrogen and oxygen used by the fuel cell system. 

II. Background

The heart of a fuel cell is an electrochemical "cell" that combines a fuel and an oxidizing agent, and converts the 

chemical energy directly into electrical power. A "stack" of cells is usually employed in applications. For this paper, 

only primary fuel cells are considered. Primary fuel cells like primary batteries are not electrically rechargeable; 

however unlike primary batteries, primary fuel cells are capable of being “recharged” by simply refilling the reactant 

storage tanks. This allows the primary fuel cell to continue to produce power. Secondary fuel cells (also referred to 

as regenerative fuel cells) use hydrogen and oxygen and produce water and electrical power. Secondary fuel cells 

like secondary batteries are rechargeable. To recharge a secondary fuel cell an external power source is used to 

electrolyze the water to replenish the hydrogen and oxygen. Figure 1 shows a conceptual diagram of primary and 

secondary fuel cells. 
NASA/TM—2005-213994 2 

The amount of energy stored in the fuel and oxidant 

per unit mass is large compared to the energy stored in a 

typical battery. Unlike batteries, fuel cells generally do 

not store their fuel and oxidizer within the cell stack, but 

instead fuel and oxidizing agent are stored externally to 

the stack. Because of this characteristic, the energy 

capacity of a fuel cell power system is determined by the 

size of the fuel tanks, whereas the size of the fuel cell 

stack determines the power level. This situation is 

analogous to an automobile where the size of the fuel tank 

dictates how far you can drive, whereas the size of the 

automobile engine determines how fast you can drive. For 

space applications with long discharge times, the mass of 

the fuel cell and other process units is small compared to 

the mass of stored fuel, oxidant and tankage. This is the 

realm where fuel cells are most competitive on an energy 

per unit mass basis. 

III. Analysis of Small Portable Fuel Cells for Exploration Missions

Fuel cells have been used for manned space vehicle power generation. These fuel cells have had power 

generation rates of 2 to 12 kilowatts and have used hydrogen and oxygen from cryogenic storage tanks. This 

analysis, while applicable to high power fuel cells, was done to address fuel cell systems within a power generation 

range of 0.1 to 1 kilowatt and discharge times of 24 hours or less. These types of primary fuel cell systems are 

envisioned to potentially play a role in portable power generation for exploration. The kinds of portable power 

applications are for use on small unmanned rovers, light construction equipment, small re-locatable power systems, 

and power for astronaut suits. Unlike previously used fuel cell systems where the fuel tanks were not refilled, the 

hydrogen and oxygen tanks of these small fuel cell systems will be refilled multiple times. For the purpose of this 

study only Proton Exchange Membrane (PEM) fuel cell systems were analyzed. 

Fuel cell systems were analyzed to determine key metrics. A previous analysis of fuel cells for space science 

applications2

 took into account the reactants, the reactant containment and the fuel cell stack, but not any ancillary 

equipment. The method of reactant containment that was previously analyzed was limited to pressurized gas storage. 

This study expands on the previous study by including the mass and volume of ancillary equipment, and also by 

expanding the reactant storage methods to include options other than pressurized gases. The water produced during 

power generation was assumed to be collected and recycled by other exploration systems rather than vented to 

space. 

A. Fuel Cell System Mass Power Density and Energy Density 

One of the key comparison metrics for fuel cells is power density, measured in watts per kilogram. This is the 

power delivered by the fuel cell divided by the mass of the fuel cell. 

F S T A I

P M M M M M

P

+ + + +

ρ = (1) 

Where 

ρP = Power Density, watts/kg 

P = Output Power, watts 

MF = Mass of Fuel (O2, H2, and H2O), kg 

MS = Mass of the PEMFC Stack, kg 

MT = Mass of the Reactant Storage, kg 

MA = Mass of the Ancillary Equipment, kg 

MI = Mass of the Insulation & Packaging, kg 

Primary Fuel Cells

Hydrogen

Oxygen

Fuel Cell Stack

Secondary Fuel Cells

Hydrogen

Oxygen

Fuel Cell/Electrolysis 

Stack(s)

Water 

Storage

Reactant Tanks

Reactant Tanks

Figure 1. Primary and Secondary Fuel Cells
NASA/TM—2005-213994 3 

Rewriting the right-hand side of Eq. (1), 

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

ρ

+⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

ρ

+⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

ρ

+⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

ρ

+⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

ρ

ρ =

F S T A I

P

1 1 1 1 1

1 (2) 

Where 

ρF = Fuel Power Density, watts/kg 

ρS = Stack Power Density, watt/kg 

ρT = Tankage Power Density, watt/kg 

ρA = Ancillary Equipment Power Density, watt/kg 

ρI = Insulation/Packaging Power Density, watt/kg 

The appendix of this paper contains a detailed derivation of the mathematical expressions for the each of these 

power densities. The substitution of these mathematical expressions into Eq. (2) provides an overall expression of 

the power density of primary fuel cell systems using high pressure gaseous storage (which is Eq.(3)), or primary fuel 

cell systems using supercritical or cryogenic storage (which is Eq.(5)). The energy density of primary fuel cell 

systems is the fuel cell power density multiplied by the discharge time (Eq. (4) for high pressure gaseous storage or 

Eq.(6) for supercritical or cryogenic storage). 

 

[ ]

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+

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η

+

ρ =

A

e

d

W

W M,W

O

O M,O

H

H M,H

e d d m

d

I

P

k

65.898

t

P V P V P V

V I A

1

3661

t 1 k

1

 (3) 

 

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μ

+

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+

μ

+⎟

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η

+

ρ =

A

e

d

W

W M,W

O

O M,O

H

H M,H

e d d m

d I

d E

k

65.898

t

P V P V P V

V I A

1

3661

t 1 k

t

 (4) 

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+⎟

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⎠

⎞

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η

+

ρ =

A

T,H T,O T,W

e d d m

d I

P

k

P

M

P

M

P

M

V I A

1

3661

t 1 k

1 (5) 

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+ + + ⎟

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+⎟

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η

+

ρ =

A

T,H T,O T,W

e d d m

d I

d E

k

P

M

P

M

P

M

V I A

1

3661

t 1 k

t (6) 

Where 

Am = Fuel cell active area per unit mass m2

/kg 

Id = Fuel cell discharge current density, A/m2

 of active area 

kA = Ancillary Equip. Factor, dimensionless 

kI = Packaging/Insulation Factor, dimensionless 

ηe = Energy Conversion Efficiency, dimensionless 

PH = Hydrogen Tank Burst Pressure, atm 

PO = Oxygen Tank Burst Pressure, atm 
NASA/TM—2005-213994 4 

PW = Water Tank Burst Pressure, atm 

td = Discharge Time, hr 

μH = Hydrogen Tank Figure-of-Merit, atm-liter/kg 

μO = Oxygen Tank Figure-of-Merit, atm-liter/kg 

μW = Water Tank Figure-of-Merit, atm-liter/kg 

VM,H = Hydrogen Molar Volume, liter/gmole 

VM,O = Oxygen Molar Volume, liter/gmole 

VM,W = Water Molar Volume, liter/gmole 

B. Fuel Cell System Volumetric Power Density and Energy Density 

Expressions similar to that developed for mass were developed for volumetric power density and volumetric 

energy density. The volumetric power density for fuel cells can be expressed as: 

T S A I V

P V V V V V

P

+ + + +

γ = (7) 

 

Where 

γP = Volumetric power density, watt/liter 

VT = Tankage volume, liter

VS = Fuel cell stack volume, liter 

VA = Ancillary Equipment volume, liter 

VI = Packaging/Insulation volume, liter 

VV = Void Space volume, liter 

Equation (7) can be rewritten as: 

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

γ

+⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

γ

+⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

γ

+⎟

⎟

⎠

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⎜

⎝

⎛

γ

+⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

γ

γ =

T S A I V

P

1 1 1 1 1

1 (8) 

Where 

γT = Tankage volumetric. power density, watt/liter 

γS = Stack volumetric. power density, watt/liter 

γA = Ancillary Equip volumetric. power density, watt/liter 

γI = Pack./Insulation volumetric. power density, watt/liter 

γV = Void Space volumetric. power density, watt/liter 

The appendix of this paper contains a detailed derivation of the mathematical expressions for the each of these 

volumetric power densities. The substitution of these mathematical expressions into Eq. (8) provides an overall 

expression of the volumetric power density of primary fuel cell systems using high pressure gaseous storage (which 

is Eq. (9)), or primary fuel cell systems using supercritical or cryogenic storage (which is Eq. (11)). The volumetric 

energy density of primary fuel cell systems is the fuel cell volumetric power density multiplied by the discharge 

time (Eq. (10) for high pressure gaseous storage or Eq. (12) for supercritical or cryogenic storage). 

[ ]

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ρ ρ

+⎟

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ρ ρ

+⎟

⎟

⎠

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+

η

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⎟

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⎠

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ρ μ

+ + ⎟

⎟

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⎛

ρ μ

+ + ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

ρ μ

+

+

γ =

e d d V A A I I

T,W W

W M,W

T,O O

O M,O

T,H H

H d M,H

V

P

~

1 ~1

V I A

1

65.898

~

P V 1 ~P 0.5V 1 ~

P

t V 1

1 k

1

 (9) 
NASA/TM—2005-213994 5 

[ ]

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ρ ρ

+⎟

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⎞

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⎛

ρ ρ

+⎟

⎟

⎠

⎞

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+

η

⎥

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⎟

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ρ μ

+ + ⎟

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⎞

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⎛

ρ μ

+ + ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

ρ μ

+

+

γ =

e d d V A A I I

T,W W

W M,W

T,O O

O M,O

T,H H

H d M,H

V

d E

~

1 ~1

V I A

1

65.898

~

P V 1 ~

P 0.5V 1 ~

P

t V 1

1 k

t

 (10) 

[ ] ⎥

⎦

⎤ ⎢

⎣

⎡

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⎟

⎠

⎞

⎜

⎜

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ρ ρ

+⎟

⎟

⎠

⎞

⎜

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⎝

⎛

ρ ρ

+⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+⎥

⎦

⎤ ⎢

⎣

⎡

+ + +

γ =

d d V A A I I

T,H T,O T,W

V

P

~

1 ~1

V I A

1

P

V

P

V

P

V

1 k

1 (11) 

[ ] ⎥

⎦

⎤ ⎢

⎣

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⎟

⎟

⎠

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⎜

⎝

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ρ ρ

+⎟

⎟

⎠

⎞

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⎜

⎝

⎛

ρ ρ

+⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+⎥

⎦

⎤ ⎢

⎣

⎡

+ + +

γ =

d d V A A I I

T,H T,O T,W

V

d E

~

1

~

1

V I A

1

P

V

P

V

P

V

1 k

t (12) 

Where 

Av = Fuel cell active area per unit volume, m2

/liter 

kV = Void Space Factor, dimensionless 

 Mean Material density of ancillary equipment, kg/liter ~ρA =

 Mean material density of packaging/insulation, kg/liter ~

ρI =

Hydrogen tank material mean density, kg/liter ~ρT,H =

Oxygen tank materialmean density,kg/liter ~ρT,O =

 Water tank materialmean density, kg/liter ~ρT,W =

γE = Volumetric fuel cell energy density, watt-hr/liter 

C. Performance Parameter Assessment 

Many of the variables in Eqs. (3) to (6) and (9) to (12) can generally be described as performance parameters which 

are measures of the status of technology development. Part of this analysis was an assessment of what numerical 

values for each of these performance parameters could be used to credibly assess the potential of primary fuel cell 

systems for portable power exploration applications. 

1. Fuel Cell Performance 

The fuel cell polarization performance that was used 

in the analysis is shown in Figure 2. The curve is 

generally reflective of high performance hydrogenoxygen PEM fuel cells, but is not intended to reflect 

the performance of any single fuel cell manufacturer. 

The energy efficiency of the fuel cell is the product of 

both the voltage efficiency and the current efficiency, 

but the current efficiency is generally very close to 

100 percent except when fuel cells are operated at 

high internal pressure or when the ion exchange 

membrane is compromised. For this analysis the 

current efficiency was assumed to be 100%. The 

voltage efficiency of the fuel cell was taken as the 

ratio of the discharge voltage to the theoretical 

Figure 2 Fuel Cell Polarization Performance reversible cell voltage of 1.229 volts. The 

For Current Density < 200mA/cm2

y = 4.037E-11x4

 - 2.789E-08x3 + 8.339E-06x2 - 1.692E-03x + 1.031E+00

For Current Density >200mA/cm2

y = 1.412E-13x4

 - 6.577E-10x3 + 9.155E-07x2 - 7.303E-04x + 9.830E-01

0

0.2

0.4

0.6

0.8

1

1.2

0 200 400 600 800 1000 1200 1400

Current Density, mA/cm2

Cell Voltage, Volts
NASA/TM—2005-213994 6 

performance curve shown in Figure 2 is based on an operating temperature of 80 °C and an operating internal 

pressure of 3.4 atm (50 psia). These conditions (or very similar conditions) are the conditions expected for portable 

fuel cell systems. Operating at lower temperatures and internal pressures will reduce the performance of fuel cells, 

but these variations were not addressed in this analysis. In section D of this paper plots were made of the fuel cell 

system power density and energy density where the energy efficiency of the fuel cell was varied to illustrate the 

sensitivity of the power and energy density to this parameter. In other cases where other parameters were varied a 

efficiency value of 0.65 was used as a representative efficiency. 

Besides the electrochemical performance, the fuel cell stack’s power density is strongly affected by the efficiency of 

its construction. Two performance parameters were defined to quantify this construction efficiency. These quantify 

the cell stack active area per kilogram of stack mass (Am) and the cell stack active area per liter of stack volume 

(Av). The greater the numerical value for these parameters, the greater the efficiency of construction. The best 

examples of low mass and low volume construction found by the author are listed in Table 1 (Refs. 3 to 7). Each of 

the examples are PEM hydrogen-air fuel cell stacks. While fuel cell systems for exploration will operate on 

hydrogen and pure oxygen, for the purposes of assessing stack construction, the assumption was made that the 

efficiency of construction of these hydrogen-air fuel cell stacks could be duplicated in a hydrogen-oxygen fuel cell 

stack. Most of the examples are for stacks producing 80kW or greater, yet one example is for a stack producing 

0.67kW which is more in the power regime of interest for small portable fuel cell systems. In section E of this paper 

plots of the sensitivity of fuel cell system power density and energy density to variations in these two fuel cell 

parameters were made. In other cases where other parameters were varied values of Am= 2000 cm2

/kg and 

Av=2400 cm2

/liter were used as conservative estimates of light weight fuel cell stacks based on the data in Table 1. 

2. Reactant Storage Performance 

Three different methods of hydrogen and oxygen storage were included in the analysis; high pressure gaseous 

storage, supercritical fluid storage, and cryogenic storage. Table 2 lists the properties of hydrogen and oxygen for 

the high pressure, supercritical, and cryogenic conditions used in the analysis. For cryogenic storage the reactants 

are in a liquid phase with a gaseous phase above the liquid phase when in a gravitational field. This, not surprisingly, 

 

a

 For the cell stacks where the number of cells was not available, the number of cells was estimated based on the 

nominal output voltage provided by the manufacturer or a photograph of the cell stack 

b

 Cell active area estimated based on 80 percent of cross sectional area 

c

 Calculated based on the estimated total stack active area and the specified mass 

d

 Calculated based on the estimated total stack active area and the specified dimensions 

e

 Dimensions estimated from photograph 

Table 1 Examples of Low Mass and Low Volume Fuel Cell Stack Construction 

Manufacturer Type Power Mass Dimensions Cellsa

 Active Areab Am

c

 Av

d

 kW kg cm cm2/cell cm2/kg cm2/liter 

GM (HyWire) H2/Air 94 100 47.2x25.1x49.6 200 996(2) 1992 3390 

GM/Hydrogenics 

GM2001 

H2/Air 102 82 82x50x14 640 560(2) 4371 6244 

Nuvera (2005) H2/Air 80 115 90x55x21 380(1) 924(2) 3027 2666 

Nuvera (2006) H2/Air 80 80 90x50x21 380(1) 840(2) 3990 2666 

Ballard Power Systems H2/Air 85 96 80.5x37.5x25 350(1) 750(2) 2734 3478 

Manhattan Scientific H2/Air 0.67 0.78 10∅ x 13.5e 40(1) 63(2) 3231 2377 
NASA/TM—2005-213994 7 

is the lowest pressure and densest form of reactant storage which leads to the lowest volume and lightest weight fuel 

cell system. Cryogenic storage may not be well suited to portable fuel cell systems which are likely to experience 

accelerations that will cause sloshing of the stored reactant. This sloshing could make the control of this type of 

reactant system difficult. For other types of portable systems that would be set up and then remain stationary during 

their operation, cryogenic storage would likely be an optimal choice. Supercritical storage is the type of reactant 

storage used aboard the space shuttle.8

 Unlike cryogenic storage, the reactants are in a single phase, and so would 

not be susceptible to accelerations or the lack of a gravitational field. The storage pressure for supercritical 

hydrogen and oxygen is far less than the high pressure storage; so that the supercritical storage vessels are lower in 

mass compared to their high pressure counterparts. Even though the molar volumes are comparable between 

supercritical storage and 400 atm high pressure gaseous storage, the supercritical tanks are somewhat greater in 

volume due to the insulation jacketing required by the low temperature storage. Lastly, since the portable fuel cell 

systems are reliant upon the ability to refill the reactant storage tanks, the choice of reactant storage method is 

obviously dependent on the other exploration site infrastructure, and that infrastructure choice may be driven by 

factors other than the use of portable fuel cells. 

Table 2 Properties of Stored Hydrogen and Oxygen 

 High Pressure Storage Supercritical Storage(f) Cryogenic Storage 

Physical Property Hydrogen Oxygen Hydrogen Oxygen Hydrogen Oxygen 

Temperature, K 300 300 32.8 155 20.1 90 

Pressure, atm 400 400 12.76 49.76 1 1 

Molar Volume, liter/mole 0.0781 0.0662 0.0290 0.0287 0.0282 0.0280 

⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯

(f) Molar volumes calculated based on data on space shuttle supercritical hydrogen and oxygen tanks. 

Table 3 lists examples of low mass composite wrapped pressure vessels for storing high pressure gaseous hydrogen 

and oxygen (Refs. 9 and 10). This type of tank construction typically uses a non-permeable metal liner which is 

wrapped with high strength carbon composite fiber embedded within an epoxy matrix. The performance parameter 

defined in this analysis for high pressure tanks is a figure-of-merit, μ, which is the product of the tank capacity and 

burst pressure divided by the dry mass of the tank. Table 3 lists different quality pressure vessels. Commercial-offthe-shelf (COTS) pressure vessels differ from State-of-the-art (SOTA) pressure vessels primarily in the thickness of 

the metal liner used to construct the tanks. The thicker liners used for COTS hardware improves the cycle life of the 

tank at the expense of greater mass. The SOTA hardware reduces the thickness of this liner to reduce the mass at the 

expense of cycle life. The SOTA hardware is typically used in space applications which are very mass sensitive and 

Table 3 Examples of Low Mass Composite Wrapped Pressure Vessels 

Supplier Quality Capacity Burst Pressure Mass Liner μ

 Liter atm kg Atm-liter/kg 

Hypercomp COTS 3.2 1000 1.36 Al 2353 

Hypercomp COTS 1.3 1000 2.09 Inconel 622 

Hypercomp SOTA 3.2 1000 1.18 Al 2712 

Hypercomp SOTA 1.3 1000 0.95 Inconel 1368 

Hypercomp COTS 25 1000 8.48 Al 2948 

Hypercomp COTS 25 1000 16.65 Inconel 1502 

Hypercomp SOTA 25 1000 6.31 Al 3962 

Hypercomp SOTA 25 1000 9.48 Inconel 2637 

Carleton SOTA 43.4 640 10.66 Al 2605 

Carleton SOTA 22.6 970 9.89 Al 2217 
NASA/TM—2005-213994 8 

are not expected to experience many pressure cycles. Aluminum liners are most commonly used for composite 

wrapped tanks because aluminum is light and easily shaped into liners. Inconel, while considerably heavier than 

aluminum is much better suited for high pressure oxygen storage because of its resistance to combustion in a high 

pressure, pure oxygen environment. In section D of this paper plots of the sensitivity of fuel cell system power 

density and energy density to variations in these pressure vessel parameters were made. In other cases where other 

parameters were varied values of μH = 2500 atm-liter/kg and μO = 1300 atm-liter/kg were used as representative of 

light weight pressure vessels, based on the data in Table 3. The maximum storage pressure and the safety factors 

were used to calculate the burst pressure of each of the storage tanks. The safety factor used for the hydrogen and 

oxygen composite wrapped pressure vessels was 1.5. The density of the composite material used in the analysis was 

1.80 gm/cm3

 (Ref. 11) 

The tank mass and tank volume associated with the supercritical fluid storage and the cryogenic storage was data 

generated internally at the NASA Glenn Research Center. Insulation for the tanks was included as part of the mass 

and volume of the tanks. The plots of that data are shown in the Appendix. These tanks were sized assuming a safety 

factor of 2.0, a 1.3 cm (0.5 in.) thick vacuum jacket filled with multilayer insulation, a five percent tank ullage, and a 

tank accessory mass equal to 25 percent of the total tank mass. 

It was assumed that the water produced by the fuel cell system would be stored as a liquid. The molar volume for 

water is 0.018 liter/mole which is much lower than either hydrogen or oxygen. The fuel cell system was assumed to 

operate at relatively low pressure (3 atm or less), so the pressure of the stored water was also assumed to be 

similarly low pressure. Data for this type of water storage was obtained from beverage bottle manufacturers and is 

plotted in Table 4 (Ref. 12). The range of tank sizes goes up to 2 liters which represents about 4000 to 6000 watthours of fuel cell energy production. These types of bottles are often made of polyethylene terephthalate (PET) and 

have burst pressure of 10 atm. 

Table 4 Water Storage Pressure Vessels 

Supplier Quality Capacity Burst Pressure Mass Material Density μW

 Liter Atm Kg kg-liter-1 Atm-liter-kg-1

Westbridge COTS 0.5 10 .024 1.33 208 

Westbridge COTS 1 10 .036 1.33 278 

Westbridge COTS 1.5 10 .042 1.33 357 

Westbridge COTS 2 10 .053 1.33 377 

3. Fuel Cell System Ancillary, Insulation/Packaging Performance 

The mass of the ancillary equipment for a fuel cell system is very difficult to rigorously estimate. For the 

purposes of this study the fuel cell system ancillary equipment was assumed to include all fluidic, electrical, and 

electronic equipment necessary for the fuel cell system to deliver power. It was assumed that any equipment 

associated with the control and use of the power produced by the fuel cell system was to be considered part of an 

overall electrical power system, and not as fuel cell system ancillary equipment. 

There is little data to derive estimates for the constants kA (the ancillary equipment factor, kg/watt) and kI (the 

packaging/insulation factor, dimensionless). The data that was used comes from the space shuttle powerplant. The 

shuttle power plant produces a peak power of 12kW. It’s mass is 122 kg, of which, 73 kg is the combined mass of 

the three fuel cell substacks. The remaining 49 kg is the mass of the ancillary equipment, the insulation around the 

fuel cell substacks, and the supporting packaging structure. Since no further breakdown of the 49 kilograms was 

available, an estimate was made that the mass was evenly split between the ancillary equipment and the 

insulation/packaging (i.e., 24.5 kg of ancillary equipment and 24.5 kg of packaging/insulation). Based on this, kA

would be approximately 0.002 kg/watt (or 24.5kg/12kW). Also, based on space shuttle powerplant, the packaging 

and insulation are estimated to be about 24.5kg/(122-24.5) or about 25 percent of the combined fuel cell stack mass 

and ancillary equipment mass. It was assumed in the analysis that the 25 percent of the fuel cell stack, ancillary 

equipment, and reactant storage mass would comprise the total mass of insulation and packaging (i.e., kI = 0.25). For 

the supercritical and cryogenic tanks the insulation mass and volume were included as part of the tank mass and 

volume and not accounted for separately. The sensitivity of the fuel cell system power end energy density to these 

parameters was included as part of this analysis. 
NASA/TM—2005-213994 9 

Table 5 summarizes the values for the various constants that were assumed for this analysis. 

T,O ~ ρ

T,W ~ ρ

T ,H ~ ρ

V Volt 0.799 d kg/liter 2.0

μ atm-liter/kg 300 W P atm 400 MOP,W

μ atm-liter/kg 1300 O P atm 400 MOP,O

μ atm-liter/kg 2500 H P atm 400 MOP,H

P watt 200 T K 300

η − 0.65 SFW − 1.5 e

SF − 1.5 O k − 0.25 V

SF − 1.5 H k − 0.3 I

k kg/watt .002 kg/liter 1.33 A

Id Amp/cm2 0.398 kg/liter 1.80

Av cm2/liter 2400 kg/liter 1.80

A cm2/kg 2000 kg/liter 0.60 m

Variable Symbol Units Value Variable Symbol Units Value

Table 5 Assumed Variable Values

I

~ ρ

A

~ ρ

D. Fuel Cell System Power Density and Energy Density Analysis Results 

The power density of a 200W nominal power fuel cell system is plotted in Figure 5 using Eqs. (3) and (5) and 

the performance parameters listed in Table 5. Curves are plotted for gaseous storage using different values for the 

fuel cell stack energy efficiency. Curves at 65 percent 

efficiency are also plotted using supercritical and 

cryogenic storage. The horizontal asymptote in each curve 

represents a situation where the fuel cell stack is the 

predominant mass component. This is because as the 

discharge time gets shorter and shorter the fuel cell stack 

mass stays the same while the reactant storage tanks get 

smaller and smaller. As the discharge time gets longer the 

power from the fuel cell stack stays the same while the 

mass of the reactant storage tanks gets larger so the 

overall power density eventually approaches zero. The 

effect of the different fuel cell energy efficiencies is most 

prominent at short discharge times where the stack mass 

is the predominant mass. The effect of the efficiency is 

best seen by looking at the family of curves for high 

pressure gaseous storage. As the efficiency increases the 

power density decreases. The reason for this is that in 

order to achieve greater efficiency the fuel cell stack must 

operate at lower current density, thus to achieve the same 

power level the active area must be increased which 

results in a bigger stack. The same power out of a larger 

and larger cell stack results in a lower and lower power 

density. It should also be noticed that as the discharge 

time gets longer the effect of fuel cell energy efficiency 

becomes smaller. 

The energy density of a 200W nominal power fuel cell 

system is plotted in Figure 6 using Eqs. (4) and (6) and 

the performance parameters listed in Table 5. Curves are 

plotted for gaseous storage using different values for the 

fuel cell stack energy efficiency. Curves at 65 percent 

efficiency are also plotted using supercritical and 

cryogenic storage. Each of the curves starts to plateau as Figure 6 Energy Density of Fuel Cell Systems

0

200

400

600

800

1000

1200

1400

1600

0.01 0.1 1 10 100

Discharge Time, hr

Energy Density, watt-hr/kg

ne=70% Hi Pressure

ne= 68% Hi Pressure

ne= 66% Hi Pressure

ne= 64% Hi Pressure

ne= 62% Hi Pressure

ne= 60% Hi Pressure

ne=65% supercritical

ne= 65% cryogenic

Lithium Ion

Figure 5 Power Density of Fuel Cell Systems

0

50

100

150

200

250

300

0.01 0.1 1 10 100

Discharge Time, hr

Power Density, watt/kg

ne= 70% Hi Pressure

ne= 68% Hi Pressure

ne= 66% Hi Pressure

ne= 64% Hi Pressure

ne= 62% Hi Pressure

ne= 60% Hi Pressure

ne= 65% supercritical

ne= 65% cryogenic
NASA/TM—2005-213994 10 

the discharge time gets longer and the reactant storage tanks are the predominant mass components. The differences 

between the three methods of reactant storage on energy density become prominent when the discharge times 

exceed a few hours with cryogenic storage being the most energy dense followed by supercritical storage and then 

high pressure gaseous storage. For the small portable fuel cell application where the discharge time exceeds a few 

hours the choice of fuel storage is of much greater consequence than the fuel cell stack efficiency. For discharge 

times between 2 and 24 hours a fuel cell system using cryogenic storage is between 60 and 120 percent more energy 

dense than one using high pressure gaseous storage. Similarly, supercritical storage is between 30 and 60 percent 

more energy dense than high pressure gaseous storage. The effect of the efficiency on energy density is best seen by 

looking at the family of curves for high pressure gaseous storage in Figure 6. At discharge times of less than 10 

hours, as the efficiency increases, the energy density decreases. This effect is a reflection of the difference in fuel 

cell stack mass, with more efficient cell stacks being bigger. Beyond 10 hours, the effect of efficiency is reversed. 

Beyond 10 hours, the energy density increases as the 

efficiency increases for a given discharge time. This 

effect is a reflection of the difference in fuel mass out 

weighing the difference in fuel cell stack mass. The 

more efficient the fuel cell system, the less mass in fuel 

and storage tanks that is required which results in a more 

energy dense system. Figure 6 also shows that for 

discharge times exceeding two hours fuel cells appear 

capable of higher energy densities than state-of-the-art 

secondary lithium batteries which are < 150 watt-hr/kg 

( Ref. 13 ). 

Figure 7 plots energy density on the horizontal axis 

and power density on the vertical axis for a 200W 

nominal power fuel cell system. This plot clearly shows 

the effect of discharge time on the energy and power 

density of fuel cells. As the discharge time gets longer 

and longer, the fuel cell stack mass has a negligible 

effect, the reactant storage tanks predominate and the 

energy density reaches a limit dictated by the 

performance of the reactant tanks. As the discharge time 

gets shorter and shorter, the reactant storage tankage 

mass becomes negligible, the fuel cell stack mass 

predominates, and the power density reaches a limit 

dictated by the performance of the fuel cell stack. 

Figure 8 plots the volumetric power density of a 

200W nominal power fuel cell system as a function of 

discharge time using Eq. (7). Curves are plotted for 

gaseous storage using different values for the fuel cell 

stack energy efficiency. Curves at 65 percent efficiency 

are also plotted using supercritical and cryogenic 

storage. As was the case with the mass analysis, the 

greatest volumetric power density occurs when the fuel 

cell stack, the power-producing component, occupies 

most of the volume. The volumetric power density is 

greatest when the fuel cell stack operates at the lowest 

efficiency (the highest current density) which makes the 

cell stack the smallest. As the discharge time gets 

longer, more and more of the volume is occupied by the 

reactant storage tankage, and the volumetric power 

density falls off. 

Figure 9 plots the volumetric energy density of a 

200W nominal power fuel cell system as a function of 

discharge time. Curves are plotted for gaseous storage 

using different values for the fuel cell stack energy 

efficiency. Curves at 65 percent efficiency are also 

0

50

100

150

200

250

300

0.01 0.1 1 10 100

Discharge Time, hr

Volumetric Power Density, watt/liter

ne=70%

ne= 68%

ne= 66%

ne= 64%

ne= 62%

ne= 60%

ne= 65% supercritical

ne= 65% cryogenic

Figure 8 Fuel Cell System Volumetric Power Density

0

50

100

150

200

250

300

350

0.01 0.1 1 10 100

Discharge Time, hr

Volumetric Energy Density, watt-hr/liter

ne=70%

ne= 68%

ne= 66%

ne= 64%

ne= 62%

ne= 60%

ne= 60% supercritical

ne= 60% cryogenic

Figure 9 Fuel Cell System Volumetric Energy Density

Figure 7 Energy Density versus Power Density

10

100

1000

1 10 100 1000 10000

Energy Density,watt- hr/kg

Power Density, watt/kg

ne=70%

ne= 68%

ne= 66%

ne= 64%

ne= 62%

ne= 60%

ne= 65% supercritical

ne= 65% cryogenic

1 hr 2 hr 5 hr 10 hr

20 hr

discharge time =

Lithium Ion
NASA/TM—2005-213994 11 

plotted using supercritical and cryogenic storage. As was the case with the mass analysis, as the discharge time gets 

longer and longer, the reactant tanks occupy more and more of the overall volume of the fuel cell. Since the reactant 

storage is the energy storage component, the volumetric energy density continues to increase. Figure 9 illustrate that 

at discharge times greater than 2 hours cryogenic storage has substantially better volumetric energy density than 

either of the other reactant storage methods. The supercritical storage, which clearly has mass energy density 

advantage over high pressure gaseous storage, does not have a similar advantage when comparing volumetric energy 

density. To the contrary, supercritical storage has a lower volumetric energy density (i.e., it will occupy more 

volume) than the high pressure gaseous storage option for discharge times less than 30 hours. This difference 

decreases as the discharge time gets longer (i.e., the storage tanks get larger) because supercritical storage has an 

advantage over high pressure gaseous storage when the molar volumes are compared (see Table 2). The effect of 

energy efficiency can be seen by looking at the family of curves for high pressure gaseous storage. At discharge 

times less than 3 hours the fuel cell system with the lowest efficiency (i.e., the smallest cell stack) has the greatest 

volumetric energy density, but beyond 5 hours the fuel 

cell system with the highest efficiency (i.e., the smallest 

reactant tanks) has the greatest volumetric energy density. 

Figure 10 plots volumetric energy density on the 

horizontal axis and volumetric power density on the 

vertical axis for a 200W nominal power fuel cell system. 

This plot shows that high pressure gaseous storage is 

generally more volume efficient than supercritical 

storage, but generally not as volume efficient as cryogenic 

storage when the discharge times exceed about 2 hours. 

The volumetric energy density of fuel cells using high 

pressure gaseous storage or supercritical storage is lower 

than state-of-the-art lithium batteries which have battery 

volumetric energy densities exceeding 200 watt-hr/liter 

(Reference 13). The volumetric energy density of fuel 

cells with discharge times greater than 5 hours, and that 

use cryogenic storage is about equivalent to lithium ion 

batteries. 

E. Analysis Sensitivity Results 

In addition to obtaining the results using the assumed values for the performance parameters, plots were made 

using values of the performance parameters both higher and lower than those assumed in Table 5. The purpose of 

this was to examine the sensitivity of the energy density to changes in performance parameters. Figures 11 and 12 

plot the fuel cell power and energy density while varying the fuel cell stack performance parameters, Am and Av . In 

both figures the middle yellow curve used the value of the performance parameter listed in Table 5. Figure 11 shows 

that for a variation of Am of 3 to 1, and for a discharge time of 5 hours, the energy density varies from about 300 to 

500 watt-hr/kg (a variation of about 66 percent). Figure 12 shows that for a variation of Av of 3 to 1, and for a 

10

100

1000

0.1 1 10 100 1000

Volumetric Energy Density,watt- hr/liter

Volumetric Power Density, watt/liter

ne=70%

ne= 68%

ne= 66%

ne= 64%

ne= 62%

ne= 60%

ne= 65% supercritical

ne= 65% cryogenic

Figure 10 Volumetric Energy Density vs. Power Density

1 hr

2 hr

5 hr

10 hr

20 hr

discharge time = 

Lithium ion

Figure 11 Energy Density versus Power Density

10

100

1000

1 10 100 1000

Energy Density,watt- hr/kg

Power Density, watt/kg

ne=66%, Am = 1000

ne= 66%, Am = 2000

ne= 66%, Am = 3000

discharge time = 1 hr 2 hr 5 hr 10 hr 20 hr

10

100

1000

1 10 100 1000

Volumetric Energy Density,watt- hr/liter

Volumetric Power Density, watt/liter

ne=66%, Av = 1200

ne= 66%, Av = 2400

ne= 66%, Av = 3600

Figure 12 Volumetric Energy Density vs. Power Density

1 hr

2 hr

5 hr

10 hr

20 hr

discharge time = 
NASA/TM—2005-213994 12 

discharge of 5 hours, the volumetric energy density varies from about 160 to 180 watt-hr/liter (a variation of about 

10 percent). The reason that the volumetric energy density does not vary significantly is that the fuel cell stack does 

not occupy a significant overall percentage of the fuel cell system volume. The variation in Am has a greater effect 

because the fuel cell stack is a substantial portion of the overall percentage of the fuel cell system mass. 

 Figure 13 plots the fuel cell system power and energy density while varying the values used for the figure-ofmerit, μ, for the high pressure hydrogen and oxygen tanks. The values for μ were varied ± 25 percent from the 

nominal values listed in Table 2. As might be expected, the effects of variations in μ are most noticeable at 

discharge times exceeding 5 hours. For discharge times 

exceeding 5 hours each curve is “below the knee” and is 

on the more vertical asymptotic portion where the 

tankage mass is the predominant mass of the fuel cell 

system. For these longer discharge times it will be very 

important to have very efficient tank construction. 

 Figure 14 plots the fuel cell system power and energy 

density while varying the storage pressure of the high 

pressure reactant storage. The purpose of this plot was to 

examine the effect of the storage pressure on the 

volumetric power and energy density, and to relate these 

effects to the other reactant storage options. For 

discharge times exceeding 5 hours, cryogenic storage 

offers the lowest volume solution. For those very mobile 

portable power applications where cryogenic storage 

may not be workable, high pressure gaseous storage of 

400 atmospheres or greater offers the next lowest volume 

solution. Supercritical storage offers the lowest volume 

solution for those applications unsuitable for cryogenic 

storage, the discharge time exceeds 5 hours, and where 

the reactant pressure is limited to 200 atmospheres or 

less. In general, cryogenic or high pressure gaseous 

storage offers the lowest volume solutions. For small 

portable power applications where cryogenic storage is 

not suitable, the choice between high pressure gaseous 

storage and supercritical storage appears to come down 

to a trade between mass and volume. If mass is more 

constrained, supercritical storage is favored. If volume is 

more constrained, high pressure gaseous storage is 

favored. 

Figure 15 plots the power and energy density while 

varying the ancillary equipment performance parameter. 

Since there was little data available to address this 

portion of the fuel cell system, the purpose of this plot 

was to assess the effect that a substantial difference in the 

value of ka (the ancillary equipment factor) might have 

on the overall energy density of the fuel cell system. The 

value of ka is varied from 0.001 to 0.004 kg/watt. The 

impact of this 4:1 variation is most prominent at 

discharge times of less than 2 hours where the effect is a 

30 percent or greater change. For discharge times of 

5 hours or greater the effect on energy density is a 

25 percent change or less. Until more data is available, 

this portion of the fuel cell system will continue to have 

the greatest uncertainty. Many of the portable power 

applications will have operational durations exceeding 5 

hours so the impact of this uncertainty is less than if the 

operational time were 2 hours or less. Figure 15 Energy Density versus Power Density

10

100

1000

1 10 100 1000

Energy Density,watt- hr/kg

Power Density, watt/kg

ne=66%, ka = .001

ne= 66%, ka = .002

ne= 66%, ka = .004

discharge time = 1 hr 2 hr 5 hr 10 hr 20 hr

Figure 13 Energy Density versus Power Density

10

100

1000

1 10 100 1000

Energy Density,watt- hr/kg

Power Density, watt/kg

ne=66%, Uh/Uo= 1875/975

ne= 66%, Uh/Uo= 2500/1300

ne= 66%, Uh/Uo= 3125/1625

discharge time = 1 hr 2 hr 5 hr 10 hr 20 hr

10

100

1000

1 10 100 1000

Volumetric Energy Density,watt- hr/liter

Volumetric Power Density, watt/liter

ne=66%, 200 atm

ne= 66%, 400 atm

ne= 66%, 600 atm

ne= 66%, supercritical

ne=66%, cryogenic

Figure 14 Volumetric Energy Density vs. Power Density

1 hr

2 hr

5 hr

10 hr

20 hr

discharge time = 
NASA/TM—2005-213994 13 

IV. Conclusions 

The analysis of power density and energy density of fuel cells, lead to the following conclusions: 

1) Hydrogen-oxygen PEM fuel cells appear to offer a lower mass approach than state-of-the-art batteries for 

portable power applications where the discharge time exceeds 2 to 3 hours. The mass savings will vary depending 

on the discharge time and the method of fuel cell reactant storage. This preliminary study indicates that fuel cell 

systems have the potential for energy densities of >400 W-hr/kg when the discharge times exceed 3 to 5 hours. This 

level of performance makes fuel cells attractive as portable high-power density, high-energy density sources for 

exploration missions. 

2) Hydrogen-oxygen PEM fuel cells using high pressure gaseous storage or supercritical storage occupy more 

volume than state-of-the-art batteries. A volumetric energy density of >150 W-hr/liter is possible for fuel cell 

systems using high pressure gaseous storage if the discharge time exceeds 3 hours. For fuel cell systems using 

cryogenic storage, if the discharge time exceeds 5 hours, the volumetric energy density is comparable to lithium ion 

batteries. The volumetric energy density will vary depending on the discharge time and the method of fuel cell 

reactant storage. 

3) Cryogenic hydrogen and oxygen storage appears to be the most mass and volume efficient of the methods 

analyzed. Supercritical storage is more mass efficient than high pressure gaseous storage, but occupies more space 

than high pressure gaseous storage. The choice of reactant storage method will also depend on other factors such as 

cooling (supercritical and cryogenic storage could potentially offer some cooling whereas gaseous storage would 

not). Also cryogenic storage may not be compatible with systems anticipated to have accelerations that could cause 

“sloshing” of the liquid cryogens. Availability of the type of reactant on the lunar or Martian surface will also be a 

deciding factor. 

Nomenclature 

Am = Fuel cell active area per unit mass m2/kg 

Av = Fuel cell active area per unit volume, m2

/liter 

E = Actual Energy Output, watt-hr 

ξ = Theoretical Energy Output, watt-hr 

Id = Fuel cell discharge current density, A/m2

 of active area 

kA = Ancillary Equip. Factor, kg/watt 

kI = Packaging/Insulation Factor, dimensionless 

kV = Void Space Factor, dimensionless 

MA = Mass of the Ancillary Equipment, kg 

MF = Mass of Fuel (O2, H2, and H2O),kg 

MH = Hydrogen Mass, kg 

MI = Mass of the Insulation & Packaging, kg 

MO = Oxygen Mass, kg 

MS = Mass of the PEMFC stack, kg 

MT = Mass of the reactant storage, kg 

MT,H = Hydrogen Tank Dry Mass, kg 

MT,O = Oxygen Tank Dry Mass, kg 

MT,W = Water Tank Dry Mass, kg 

nH = Moles of hydrogen, gmole 

nW = Moles of water, gmole 

nO = Moles of oxygen, gmole 

ηe = Energy Conversion Efficiency, % 

P = Output Power, watts 

PH = Hydrogen Tank Burst Pressure, atm 

PMOP,H = Maximum Hydrogen Operating Pressure, atm 

PMOP,O = Maximum Oxygen Operating Pressure, atm 

PMOP,W = Maximum Water Operating Pressure, atm 

PO = Oxygen Tank Burst Pressure, atm 
NASA/TM—2005-213994 14 

PW = Water Tank Burst Pressure, atm 

ρA = Ancillary Equipment Power Density, watt/kg 

ρE = Energy density, watt-hr/kg 

ρF = Fuel Power Density, watts/kg of fuel 

ρI = Insulation/Packaging Power Density, watt/kg 

ρP = Power Density, watts/kg 

ρS = PEMFC stack power density, watt/kg of stack mass 

ρT = Reactant storage power density, watt/kg 

ρ =  A Mean Material density of ancillary equipment, kg/liter

I ρ =  Mean material density of packaging/insulation, kg/liter

ρ = T,H Hydrogen tank material mean density, kg/liter

ρ = T,O Oxygen tank material mean density, kg/liter

ρ = T,W Water tank material mean density, kg/liter

SFH = Hydrogen Tank Safety Factor, dimensionless 

SFO = Oxygen Tank Safety Factor, dimensionless 

SFW = Water Tank Safety Factor, dimensionless 

T = Gas temperature, K 

td = Discharge Time, hr 

μH = Hydrogen Tank Figure-of-Merit, atm-liter/kg 

μO = Oxygen Tank Figure-of-Merit, atm-liter/kg 

μW = Water Tank Figure-of-Merit, atm-liter/kg 

VA = Ancillary Equipment volume, liter 

Vd = Fuel cell discharge voltage, volts 

VH = Hydrogen Tank Volumetric Capacity, liter 

VI = Packaging/Insulation volume, liter 

VM,H = Hydrogen Molar Volume, liter/gmole 

VM,O = Oxygen Molar Volume, liter/gmole 

VM,W = Water Molar Volume, liter/gmole 

VO = Oxygen Tank Volumetric Capacity, liter 

VS = Fuel cell stack volume, liter 

VT = Tankage volume, liter 

VT,H = Hydrogen Tank Overall Volume, liter 

VT,O = Oxygen Tank Overall Volume, liter 

VV = Void Space volume, liter 

VW = Water Tank Volumetric Capacity, liter 

γA = Ancillary Equip volumetric. power density, watt/liter 

γE = Volumetric fuel cell energy density, watt-hr/liter 

γI = Pack./Insulation volumetric. power density, watt/liter 

γP = Fuel cell volumetric power density, watt/liter 

γS = Stack volumetric power density, watt/liter 

γT = Tankage volumetric power density, watt/liter 

γV = Void Space volumetric. power density, watt/liter 
NASA/TM—2005-213994 15 

Appendix 

This appendix contains the detailed derivation of the expressions for the fuel cell system power and energy 

density used in the analysis. 

A. Fuel Cell System Power and Energy Density Based on Mass 

Fuel cell system power density that is based on mass is measured in watts per kilogram. This is the power 

delivered by the fuel cell system divided by the mass of the fuel cell system. The mass of the fuel cell system can be 

split between the fuel (O2, H2, and H2O), the PEMFC stack, the reactant storage, the ancillary equipment, and the 

insulation/packaging. The power density is expressed mathematically as: 

F S T A I

P M M M M M

P

+ + + +

ρ = (1) 

Where 

ρP = Power Density, watts/kg 

P = Output Power, watts 

MF = Mass of Fuel (O2, H2, and H2O), kg 

MS = Mass of the PEMFC Stack, kg 

MT = Mass of the Reactant Storage, kg 

MA = Mass of the Ancillary Equipment, kg 

MI = Mass of the Insulation & Packaging, kg 

Rewriting the right-hand side of Eq. (1), 

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

ρ

+⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

ρ

+⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

ρ

+⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

ρ

+⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

ρ

ρ =

F S T A I

P

1 1 1 1 1

1 (2) 

Where 

ρF = Fuel Power Density, watts/kg 

ρS = Stack Power Density, watt/kg 

ρT = Tankage Power Density, watt/kg 

ρA = Ancillary Equipment Power Density, watt/kg 

ρI = Insulation/Packaging Power Density, watt/kg 

The reason for writing Eq. (2) is that it is instructive to keep track of the individual contributions to the overall 

power density of each part of the fuel cell system. 

1. Fuel Power Density 

Using the quantity E/td as the output power, the fuel power density can itself be rewritten as: 

d F

F t M

E

ρ = (3) 

Where 

E = Actual Energy Output, watt-hr 

td = Discharge Time, hr 
NASA/TM—2005-213994 16 

The actual energy output can be thought of as the product of the theoretical maximum energy output multiplied by 

the energy conversion efficiency. 

= η ξ E e (4) 

Where 

ξ = Theoretical Energy Output, watt-hr 

ηe = Energy Conversion Efficiency, dimensionless 

The symbol, ηe combines both voltage and current efficiency into a single energy conversion efficiency. Substituting 

Eq. (4) into equation (3) : 

d F

e

F t M

η ξ ρ = (5) 

The quantity ξ/MF is the theoretical energy output per unit mass of fuel. For the H2/O2 fuel cell reaction the 

theoretical energy output per unit mass is 3661 watt-hr per kg of water formed (assuming 1.23 volts as the 

100 percent voltage efficiency of the fuel cell). Substituting 3661 watt-hr per kg for the ratio ξ/MF: 

d

e

F t

3661η ρ = (6) 

2. Fuel Cell Stack Power Density 

The PEMFC stack power density can be expressed as: 

S d dAm ρ = V I (7) 

Where 

Vd = Discharge Voltage, volts 

Id = Discharge Current Density, amp/m2

Am = Active Area per Unit Mass, m2

/kg 

3. Fuel Cell System Reactant Storage Power Density 

The reactant storage power density can be written as: 

d T

e

d T

T t M t M

E η ξ ρ = = (8) 

For most primary fuel cell systems the mass of the reactant storage is the mass of the hydrogen and oxygen 

tanks. Since the water is envisioned to be stored and ultimately recycled, the mass of the water tank is also then 

included in the mass of the reactant storage tank mass. The mass of reactant storage can be expressed as: 

MT = MT,H + MT,O + MT,W (9) 

Where 

MT,H = Hydrogen Tank Dry Mass, kg 

MT,O = Oxygen Tank Dry Mass, kg 

MT,W = Water Tank Dry Mass, kg 
NASA/TM—2005-213994 17 

The mass of these tanks can be estimated based on a figure of merit that relates the pressure, volume and dry 

mass of a state-of-the-art light-weight pressure vessel. For the hydrogen and oxygen tanks the figure of merit for 

each tank is: 

T,H

H H

H M

P V

μ = (10) 

T,O

O O

O M

P V

μ = (11) 

T,W

W W

W M

P V

μ = (12) 

Where 

μH = Hydrogen Tank Figure-of-Merit, atm-liter/kg 

PH = Hydrogen Tank Burst Pressure, atm 

VH = Hydrogen Tank Volumetric Capacity, liter 

μO = Oxygen Tank Figure-of-Merit, atm-liter/kg 

PO = Oxygen Tank Burst Pressure, atm 

VO = Oxygen Tank Volumetric Capacity, liter 

μW = Water Tank Figure-of-Merit, atm-liter/kg 

PW = Water Tank Burst Pressure, atm 

VW = Water Tank Volumetric Capacity, liter 

The mass of the hydrogen, oxygen, and water tanks are expressed as: 

H

H H

T,H

P V M

μ = (13) 

O

O O

T,O

P V M

μ = (14) 

W

W W

T,W

P V M

μ = (15) 

The storage tank burst pressure is related to the maximum operating pressure by a safety factor, expressed as: 

 ( ) PH = SFH PMOP,H (16) 

( ) PO = SFO PMOP,O (17) 

( W ) PW = SFW PMOP, (18) 

Where 

SFH = Hydrogen Tank Safety Factor, dimensionless 

SFO = Oxygen Tank Safety Factor, dimensionless 

SFW = Water Tank Safety Factor, dimensionless 

PMOP,H = Maximum Hydrogen Operating Pressure, atm 

PMOP,O = Maximum Oxygen Operating Pressure, atm 

PMOP,W = Maximum Water Operating Pressure, atm 

The volumetric capacity of the hydrogen, oxygen and water tanks are expressed as: 

VH = VM,Hn H (19) 

VO = VM,OnO (20) 
NASA/TM—2005-213994 18 

VW = VM,WnW (21) 

Where 

VM,H = Hydrogen Molar Volume, liter/gmole 

nH = Moles of Hydrogen, gmole 

VM,O = Oxygen Molar Volume, liter/gmole 

nO = Moles of Oxygen, gmole 

VM,W = Water Molar Volume, liter/gmole 

nW = Moles of Water, gmole 

The molar volumes of hydrogen and oxygen are used because above 70 atmospheres of pressure the ideal gas 

law is not sufficiently accurate to model the pressure, volume, and temperature relationship. 

The tanks are sized based upon the maximum required capacity. It was also assumed that the maximum number 

of moles of hydrogen to be stored is equal to the maximum moles of water to be stored. Similarly, the maximum 

moles of oxygen to be stored are equal to one-half the maximum moles of water to be stored. Expressing this 

mathematically, 

H W O n = n = 2n (22) 

Substituting Eqs. (13),(14),(15),(19),(20),(21), and (22) into Eq. (9), 

W

W

W M,W

O

O M,O

H

H M,H

T n

P V

2

P V P V

M ⎥

⎦

⎤ ⎢

⎣

⎡

μ

+

μ

+

μ = (23) 

The number of moles of water can be expressed as: 

0.018 kg/gmole

M

n F

W = (24) 

When Eqs. (23) and (24) are substituted into Eq. (8) and the ratio of ξ/ MF is set equal to 3661 watt-hr/kg, the 

simplified result is: 

d

W

W M,W

O

O M,O

H

H M,H

e

T

t

P V

2

P V P V

65.898

⎥

⎦

⎤ ⎢

⎣

⎡

μ

+

μ

+

μ

η ρ = (25) 

The tank mass associated with the supercritical fluid 

storage and the cryogenic storage was data generated 

internally at the NASA Glenn Research Center. 

Insulation for the tanks was included as part of the 

mass and volume of the tanks. The plots of that data are 

shown in Figures A1. These tanks were sized assuming 

a safety factor of 2.0, a 1.3cm (0.5 in) thick vacuum 

jacket filled with multilayer insulation, a five percent 

tank ullage, and a tank accessory mass equal to 25 

percent of the total tank mass. 

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

0 0.5 1 1.5 2 2.5 3 3.5

Reactant Mass,gm

Reactant Tank Volume,cm3

Supercritical Hydrogen

Supercritical Oxygen

Cryogenic Oxygen

Cryogenic Hydrogen
NASA/TM—2005-213994 19 

The parametric equations for the supercritical and cryogenic tank mass shown in Figure A1 are: 

for supercritical tanks, 

MT,H = 2.1463 MH + .0761 (26) 

MT,O = 0.3908 MO + .0701 (27) 

for cryogenic tanks, 

MT,H = (-4.96E-01 MH

2

 + 9.56E-01 MH + 2.74E-02) (28) 

MT,O = (-4.72E-03 MO

2

 + 6.97E-02 MO + 2.17E-02) (29) 

Where 

MH = Hydrogen Mass, kg 

MO = Oxygen Mass, kg 

The reciprocal of the tankage power density that uses supercritical and cryogenic storage can be expressed as: 

P

M

P

M

P

1 MT,H T,O T,W

T

= + +

ρ

 (30) 

Taking the reciprocal of Eq. (30) yields the tankage power density for supercritical and cryogenic storage. 

⎥

⎦

⎤ ⎢

⎣

⎡

+ +

ρ =

P

M

P

M

P

M

1

T,H T,O T,W

T (31) 

4. Fuel Cell System Ancillary Equipment Power Density 

The ancillary equipment of a fuel cell system is used to accommodate the requirements of the fuel cell stack. 

Higher power stacks require higher reactant flows, which, in turn, require larger fluidic components and plumbing to 

accommodate increased flows and heat rejection requirements. Higher power fuel cell stacks require higher power 

(larger) electronics and wiring. On the other hand, the mass of the ancillary equipment does not seem particularly 

influenced by the amount of reactant used, but rather it seems more influenced by the rate at which that reactant is 

used. Based on these general observations, it appears reasonable to conclude that the greater the fuel cell system 

power the more massive the collection of ancillary equipment, and that the mass of ancillary equipment is relatively 

independent of the size of the reactant storage. Since the true relationship between the power of the fuel cell system 

and the mass of its attendant ancillary equipment is unknown, a linear approximation was assumed to be adequate 

for the range of fuel cell systems being considered in this study. This relationship can be expressed as: 

 

MA = kAP (32) 

Where 

kA = Ancillary Equip. Factor, kg/watt 

Rewriting Eq. (30) 

A

A MA

P

k

1 = = ρ (33) 
NASA/TM—2005-213994 20 

5. Fuel Cell System Packaging/Insulation Power Density 

The mass associated with the packaging and insulation for the fuel cell system is similarly difficult to estimate. It 

was assumed that items such as insulation and structural mass used to insulate and mount the fuel cell system were 

included. It was assumed that the mass of this portion of the fuel cell system could be estimated as a constant portion 

of the mass of all other fuel cell system components. That is, as the sum of the mass of the reactants, reactant tanks, 

fuel cell stack, or ancillary equipment increases, the mass of the insulation and packaging would proportionally 

increase. This is expressed as: 

t M t k (M M M M ) d I F S T A

e

d I

e

I + + +

η ξ = η ξ ρ = (34) 

Where 

kI = Packaging/Insulation Factor, dimensionless 

Equation (34) can be rewritten as: 

⎥

⎦

⎤ ⎢

⎣

⎡

+

ρ

+

ρ

+

ρ ⎥ =

⎦

⎤ ⎢

⎣

⎡

ρ

+

ρ

+

ρ

+

ρ = ρ

A

F S T

I

F S T A

I

I

k 1 1 1 k 1 1 1 1 k 1 (35) 

6. Detailed Expression for Fuel Cell System Mass-Based Power and Energy Density 

Substituting Eqs. (6), (7), (25), (33), and (35) into Eq. (2) and developing expressions for the fuel cell system power 

density, 

[ ]

P

H M,H O M,O W M,W

d

d HOW

I A

e dd m e

1

PV PV P V

t

t 1 1k k

3661 V I A 65.898

ρ = ⎡ ⎤ ⎛ ⎞ ⎡ ⎤ ⎢ ⎥ ⎜ ⎟ ⎢ ⎥ + + ⎛ ⎞⎛ ⎞ ⎣ ⎦ μμμ ⎜ ⎟ + ++ + ⎜ ⎟⎜ ⎟ ⎝ ⎠⎝ ⎠ η η

⎣ ⎦ ⎝ ⎠

 (36) 

The fuel cell system power density equation when using supercritical or cryogenic storage is similar to Eq.(36) 

except that Eq. (31) is substituted for the tankage power density, and the Eqs. (26) to (29) are used for MT,H and 

MT,O. This results in, 

[ ]

P

d T,H T,O T,W

I A

e dd m

1

t 1 MMM

1k k

3661 V I A P P P

ρ = ⎡ ⎤ ⎛ ⎞⎛ ⎞ ⎛ ⎞

+ + + ++ + ⎢ ⎥ ⎜ ⎟⎜ ⎟ ⎜ ⎟ ⎣ ⎦ ⎝ ⎠⎝ ⎠ η ⎝ ⎠

 (37) 

The energy density of an energy storage device is also a key metric. The energy density is simply the power 

density multiplied by the discharge time. For primary fuel cells with high pressure gaseous storage the energy 

density is, 

 

[ ]

d

E

H M,H O M,O W M,W

d

d HO W

I A

e dd m e

t

PV PV P V

t

t 1 1k k

3661 V I A 65.898

ρ = ⎡ ⎤ ⎛ ⎞ ⎡ ⎤ ⎢ ⎥ ⎜ ⎟ ⎢ ⎥ + + ⎛ ⎞⎛ ⎞ ⎣ ⎦ μμμ ⎜ ⎟ + ++ + ⎜ ⎟⎜ ⎟ ⎝ ⎠⎝ ⎠ η η

⎣ ⎦ ⎝ ⎠

 

 (38) 
NASA/TM—2005-213994 21 

and for supercritical or cryogenic storage the energy density is 

[ ] ⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

+⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+ + + ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

η

+

ρ =

A

T,H T,O T,W

e d d m

d I

d E

k

P

M

P

M

P

M

V I A

1

3661

t k1

t (39) 

Where 

ρE = Energy density, watt-hr/kg 

B. Fuel Cell System Power and Energy Density Based on Volume 

Expressions similar to that developed for mass were developed for volumetric power density and volumetric 

energy density. The volumetric power density for fuel cells can be expressed as: 

T S A I V

P V V V V V

P

+ + + +

γ = (40) 

 

Where 

γP = Volumetric power density, watt/liter 

VT = Tankage volume, liter

VS = Fuel cell stack volume, liter 

VA = Ancillary Equipment volume, liter 

VI = Packaging/Insulation volume, liter 

VV = Void Space volume, liter 

Equation (40) can be rewritten as: 

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

γ

+⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

γ

+⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

γ

+⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

γ

+⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

γ

γ =

T S A I V

P

1 1 1 1 1

1 (41) 

Where 

γT = Tankage volumetric. power density, watt/liter 

γS = Stack volumetric. power density, watt/liter 

γA = Ancillary Equip volumetric. power density, watt/liter 

γI = Pack./Insulation volumetric. power density, watt/liter 

γV = Void Space volumetric. power density, watt/liter 

1. Tankage Power Density 

The tankage volumetric power density can be expressed as: 

d T

e

T t V

η ξ γ = (42) 

The volume of the tankage can be expressed as: 

T,W

T,W

T,O

T,O

T,H

T,H

T H O W ~

M

~

M

~

M

V V V V

ρ

+

ρ

+

ρ = + + + (43) 

Where 

Hydrogen tank materialmean density,kg/liter ~ρT,H =

Oxygen tank material mean density, kg/liter ~ρT,O =

 Water tank materialmean density,kg/liter ~ρT,W =
NASA/TM—2005-213994 22 

Substituting Eqs. (13) to (15) and (19) to (21) into Eq. (43), 

W

T,W W

W

O M,W

T,O O

O

H M,O

T,H H

H

T M,H n ~

P

n V 1 ~

P

n V 1 ~

P V V 1 ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

ρ μ

+ + ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

ρ μ

+ + ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

ρ μ = + (44) 

Substituting Eq. (22) into Eq. (44), 

W

T,W W

W

M,W

T,O O

O

M,O

T,H H

H

T M,H n ~

P V 1 ~

P 0.5V 1 ~

P V V 1

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

ρ μ

+ + ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

ρ μ

+ + ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

ρ μ = + (45) 

Substituting Eq. (24) into Eq. (45), 

⎥

⎦

⎤ ⎢

⎣

⎡

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

ρ μ

+ + ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

ρ μ

+ + ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

ρ μ = +018.0

M

~

P V 1 ~

P 0.5V 1 ~

P V V 1 F

T,W W

W

M,W

T,O O

O

M,O

T,H H

H

T M,H (46) 

Substituting Eq. (46) into Eq. (42), and replacing the ratio, ξ/MF with 3661 watt-hr per kg, and simplifying the 

expression, 

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

ρ μ

+ + ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

ρ μ

+ + ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

ρ μ

+

η γ =

T,W W

W M,W

T,O O

O M,O

T,H H

H d M,H

e T

~

P

V 1 ~

P 0.5V 1 ~

P

t V 1

65.898 (47) 

The tank volume associated with the supercritical 

fluid storage and the cryogenic storage was data 

generated internally at the NASA Glenn Research 

Center. Insulation for the tanks was included as part of 

the mass and volume of the tanks. The plots of that data 

are shown in Figures A2. These tanks were sized 

assuming a safety factor of 2.0, a 1.3cm (0.5 in) thick 

vacuum jacket filled with multilayer insulation, a five 

percent tank ullage, and a tank accessory mass equal to 

25 percent of the total tank mass. 

The parametric equations for the supercritical and 

cryogenic tank volume shown in Figure A2 are: 

for supercritical tanks, 

VT,H = 4.284 MH + 0.6543 (48) 

VT,O = 3.3689 MO + 0.5341 (49) 

for cryogenic tanks, 

VT,H = 19.842 MH + 0.4019 (50) 

VT,O = 1.311 MO + 0.2898 (51) 

Where 

VT,H = Hydrogen Tank Overall Volume, liter 

VT,O = Oxygen Tank Overall Volume, liter 

Figure A2 Supercritical & Cryogenic Tank Volume

0

2

4

6

8

10

12

14

16

18

20

01234

Reactant Mass,kg

Reactant Tank Volume,liter

Supercritical H2

Supercritical O2

Cryogenic H2

Cryogenic O2
NASA/TM—2005-213994 23 

The reciprocal of the tankage volumetric power density that uses supercritical and cryogenic storage can be 

expressed as: 

P

V

P

V

P

1 VT,H T,O T,W

T

= + +

γ

 (52) 

Taking the reciprocal of Eq. (50) yields the tankage volumetric power density for supercritical and cryogenic 

storage. 

⎥

⎦

⎤ ⎢

⎣

⎡

+ +

γ =

P

V

P

V

P

V

1

T,H T,O T,W

T (53) 

2. Fuel Cell Stack Power Density 

The fuel cell stack volumetric power density can be expressed as: 

S d dAv γ = V I (54) 

Where 

Av = Active area per unit volume, m2

/liter 

3. Ancillary Equipment Power Density 

The ancillary equipment volumetric power density can be expressed as: 

A A A

~ γ = ρ ρ (55) 

Where 

Mean Material density of ancillary equipment, kg/liter ~ρA =

4. Packaging/Insulation Power Density 

Similarly, the volumetric power density for the packaging and insulation can be expressed as: 

I I I

~ γ = ρ ρ (56) 

Where 

Mean material density of packaging/insulation, kg/liter ~ρI =

5. Void Space Power Density 

The volumetric power density of the void space can be expressed as: 

d V

e

V t V

η ξ γ = (57) 

The void space was assumed to be a percentage of the combined volume of all other fuel cell system components. 

( ) V V VT VS VA VI V = k + + + (58) 
NASA/TM—2005-213994 24 

Where 

kV = Void Space Factor, dimensionless 

Substituting Eq. (58) into Eq. (57), and re-writing Eq. (57), 

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

γ

+

γ

+

γ

+

γ = γ T S A I

V

V

1 1 1 1 k 1 (59) 

6. Detailed Expression for Fuel Cell System Volumetric Power and Energy Density 

Substituting Eq. (59) into Eq. (41) and simplifying the expression for primary fuel cell volumetric power density 

yields: 

[ ] ⎥

⎦

⎤ ⎢

⎣

⎡

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

γ

+⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

γ

+⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

γ

+⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

γ

+

γ =

T S A I

V

P

1 1 1 1 k1

1 (60) 

Substituting Eqs. (47) and (54) to (56) into Eq. (60) provides the expression for primary fuel cell volumetric power 

density when using high pressure gaseous storage: 

[ ]

⎥

⎥

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎢

⎢

⎣

⎡

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

ρ ρ

+⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

ρ ρ

+⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+

η

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

ρ μ

+ + ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

ρ μ

+ + ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

ρ μ

+

+

γ =

e d d V A A I I

T,W W

W M,W

T,O O

O M,O

T,H H

H d M,H

V

P

~

1 ~1

V I A

1

65.898

~

P V 1 ~P 0.5V 1 ~

P

t V 1

k1

1

 (61) 

The fuel cell system volumetric power density equation when using supercritical or cryogenic storage is similar 

to Eq. (61) except that Eq. (52) is substituted for the tankage volumetric power density, and the Eqs. (48 to (51) are 

used for VT,H and VT,O. This results in, 

[ ] ⎥

⎦

⎤ ⎢

⎣

⎡

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

ρ ρ

+⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

ρ ρ

+⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+⎥

⎦

⎤ ⎢

⎣

⎡

+ + +

γ =

d d V A A I I

T,H T,O T,W

V

P

~

1 ~1

V I A

1

P

V

P

V

P

V

k1

1 (62) 

The volumetric energy density is obtained by multiplying the power density by discharge time. For primary fuel 

cells which use high pressure gaseous storage, 
NASA/TM—2005-213994 25 

[ ]

⎥

⎥

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎢

⎢

⎣

⎡

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

ρ ρ

+⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

ρ ρ

+⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+

η

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

ρ μ

+ + ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

ρ μ

+ + ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

ρ μ

+

+

γ =

e d d V A A I I

T,W W

W M,W

T,O O

O M,O

T,H H

H d M,H

V

d E

~

1 ~1

V I A

1

65.898

~

P V 1 ~

P 0.5V 1 ~

P

t V 1

k1

t

 (63) 

and for supercritical or cryogenic storage the volumetric energy density is 

[ ] ⎥

⎦

⎤ ⎢

⎣

⎡

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

ρ ρ

+⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

ρ ρ

+⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+⎥

⎦

⎤ ⎢

⎣

⎡

+ + +

γ =

d d V A A I I

T,H T,O T,W

V

d E

~

1 ~1

V I A

1

P

V

P

V

P

V

k1

t (64) 

Where 

γE = Volumetric energy density, watt-hr/liter 

References 

1

Kenneth A. Burke, “High Energy density Regenerative Fuel Cell Systems for Terrestrial Applications,” 

NASA/TM—1999-209429, SAE 00-01-2600, July 1999. 

 2

Kenneth A. Burke, “Fuel Cells for Space Science Applications,” NASA/TM—2003-212730, AIAA–2003–5938 

July 2003. 3

 Detailed specifications of General Motors Hy-wireTM advanced technology vehicle available at 

http://www.gm.com/company/gmability/adv_tech/images/fact_sheets/hywire_specs.html 4

 Detailed of specifications Nuvera Fuel Cells AdromedaTM HCS-575 Fuel Cell Satck Series available at 

http://www.nuvera.com/markets/androm.php 5

 WWW.Fuel Cells.org, Fuel Cells 2000 Online Fuel Cell Information Resource, available at 

http://www.fuelcells.org/info/charts/TransTechnical.pdf 6

 Specifications of Manhatten Scientifics, Inc. midrange fuel cell technology, available at 

http://www.mhtx.com/novars/index.htm 7

 Specifications of Ballard Power Systems Mark 902 Fuel Cell Module, available at 

http://www.ballard.com/be_a_customer/transportation/fuel_cell_modules/mark_902# 8

 Data obtained from NSTS 1988 News Reference Manual, available at 

http://science.ksc.nasa.gov/shuttle/technology/sts-newsref/stsref-toc.html 9

 Data obtained from Carleton Technologies Inc. 504 McCormick Drive, Glen Burnie, MD. 21061. 

10 Data obtained from HyPerComp Engineering, Inc, 1080 N. Main St. Suite 2, Brigham City, Utah, 84302. 11“Mechanical Engineers’ Handbook”, Chapter 9 Composite Materials and Mechanical Design, 2nd Edition, Myer 

Kutz, Editor, 1998 Wiley and Sons, Inc. ISBN 0-471-13007-9. 12 Data obtained from Westbridge PET Containers#10 31031 4th Ave. N.E.Calgary, Alberta, Canada T2A 7N6l, 

available at http://www.westbridge.ca/products/car_1.html 13“Energy Storage Technology for Future Space Science Missions,” JPL D-30268 Jet Propulsion Laboratory, 

Issued November 2004. 
This publication is available from the NASA Center for AeroSpace Information, 301–621–0390.

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NASA TM—2005–213994

AIAA–2005–5680

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WBS–22–612–50–06–14

31

Small Portable PEM Fuel Cell Systems for NASA Exploration Missions

Kenneth A. Burke

Fuel cells

Unclassified -Unlimited

Subject Categories: 20 and 44

Prepared for the Third International Energy Conversion Engineering Conference sponsored by the American Institute of

Aeronautics and Astronautics, San Francisco, California, August 15–18, 2005. Responsible person, Kenneth A. Burke,

organization code RPC, 216–433–8308.

Oxygen-Hydrogen PEM-based fuel cell systems are being examined as a portable power source alternative in addition

to advanced battery technology. Fuel cell power systems have been used by the Gemini, Apollo, and Space Shuttle

programs. These systems have not been portable, but have been integral parts of their spacecraft, and have used

reactants from a separate cryogenic supply. These systems typically have been higher in power. They also have had

significant ancillary equipment sections that perform the pumping of reactants and coolant through the fuel cell stack

and the separation of the product water from the unused reactant streams. The design of small portable fuel cell

systems will be a significant departure from these previous designs. These smaller designs will have very limited

ancillary equipment, relying on passive techniques for reactant and thermal management, and the reactant storage will

be an integral part of the fuel cell system. An analysis of the mass and volume for small portable fuel cell systems was

done to evaluate and quantify areas of technological improvement. A review of current fuel cell technology as well as

reactant storage and management technology was completed to validate the analysis and to identify technology

challenges.