Anthony J. Colozza

Qinetiq North America, Cleveland, Ohio

Radioisotope Stirling Engine Powered Airship 

for Low Altitude Operation on Venus

NASA/CR—2012-217665

August 2012
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Anthony J. Colozza

Qinetiq North America, Cleveland, Ohio

Radioisotope Stirling Engine Powered Airship 

for Low Altitude Operation on Venus

NASA/CR—2012-217665

August 2012

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared under Contract NNC07E252T-8
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NASA/CR—2012-217665 iii

Contents

Abstract.........................................................................................................................................................1

1.0 Introduction...........................................................................................................................................1

2.0 Atmospheric Environment of Venus ....................................................................................................3

3.0 Airship Configuration and Sizing.........................................................................................................7

3.1 Airship Mass................................................................................................................................9

3.1.1 Structure Mass.................................................................................................................9

3.1.2 Propulsion System Mass................................................................................................10

3.1.3 Power System Mass.......................................................................................................12

3.1.4 Pressure Vessel Mass.....................................................................................................15

3.1.5 Total Mass.....................................................................................................................19

3.2 Power Required .........................................................................................................................20

3.2.1 Propulsion Power...........................................................................................................20

3.2.2 Cooling Power...............................................................................................................22

3.3 Power Production ......................................................................................................................25

4.0 Analysis Results..................................................................................................................................27

4.1 Baseline Airship Design ............................................................................................................27

4.2 Variation in the Internal Operating Temperature of the Payload Enclosure .............................30

4.3 Variation in Flight Altitude .......................................................................................................35

5.0 Evaluation of Alternate Buoyancy Methods.......................................................................................37

6.0 Summary.............................................................................................................................................41

Appendix—List of Symbols.......................................................................................................................43

References...................................................................................................................................................48

NASA/CR—2012-217665 1

Radioisotope Stirling Engine Powered Airship for 

Low Altitude Operation on Venus

Anthony J. Colozza

Qinetiq North America

Cleveland, Ohio 44135

Abstract

The feasibility of a Stirling engine powered airship for the near surface exploration of Venus was 

evaluated. The heat source for the Stirling engine was limited to 10 general purpose heat source (GPHS) 

blocks. The baseline airship utilized hydrogen as the lifting gas and the electronics and payload were 

enclosed in a cooled insulated pressure vessel to maintain the internal temperature at 320 K and 1 Bar 

pressure. The propulsion system consisted of an electric motor driving a propeller. An analysis was set up 

to size the airship that could operate near the Venus surface based on the available thermal power. The 

atmospheric conditions on Venus were modeled and used in the analysis. The analysis was an iterative 

process between sizing the airship to carry a specified payload and the power required to operate the 

electronics, payload and cooling system as well as provide power to the propulsion system to overcome 

the drag on the airship. A baseline configuration was determined that could meet the power requirements 

and operate near the Venus surface. From this baseline design additional trades were made to see how 

other factors affected the design such as the internal temperature of the payload chamber and the flight 

altitude. In addition other lifting methods were evaluated such as an evacuated chamber, heated 

atmospheric gas and augmented heated lifting gas. However none of these methods proved viable. 

1.0 Introduction

Venus, shown in Figure 1.1, is the second planet from the Sun and is similar to Earth in size and 

density, but that is where the similarities end. Its atmospheric pressure near the surface is 90 times that of 

Earth’s and the surface temperature is around 455 °C. The high surface temperature and pressure pose an 

inhospitable environment for materials, mechanisms and electronics. Because of this the exploration of 

the surface and lower atmosphere of Venus has been fairly limited. The Russian Venera series of landers 

are the only probes to successfully send data back to Earth from the Venus surface, as shown in Figure 

1.1. These landers, however only survived for a short period of time, from approximately 20 minutes to a 

few hours, on the surface. To return the maximum amount of scientific data a vehicle that can survive for 

extended periods of time and is mobile enabling it to move about the surface or atmosphere in a 

controlled manner would be ideal. By being able to explore different surface features and locations, 

similar to the Mars rovers (Spirit and Opportunity) this type of vehicle can provide significant insight into 

the geology and surface/atmospheric conditions of Venus. 

Venus however is much different than Mars and an exploration vehicle designed for operation on 

Venus will have significantly different characteristics and requirements than one utilized on Mars. The 

first difference is related to the power source for the vehicle. On Mars photovoltaic arrays can be utilized 

as a power source, whereas on Venus, even though it is closer to the Sun, the thick cloud cover 

encompassing the planet, as well as the high surface temperature, makes utilizing solar power difficult. 

Therefore a different power source is required, one based on the conversion of heat generated through 

radioactive decay of Plutonium to electricity. These radioisotope heat sources are commonly utilized for 

deep space missions, where insufficient solar energy is available, and similarly can be utilized for a Venus 

surface mission. The one downside to a radioisotope based power system is that they tend to be heavier 

than an equivalent PV based system. This is critical since for a mobile vehicle the lower its mass the less 

power will be required to move. Therefore, maximizing the thermal to electrical conversion efficiency is a 

critical factor in the power system design. Of the available thermal to electrical conversion systems, a 

Stirling engine provides the highest efficiency and therefore the greatest benefit to the vehicle. 
NASA/CR—2012-217665 2

Figure 1.1.—True color image of Venus from Mariner 10 (Ref. 1) and surface image from the 

Soviet Venera-14 (Ref. 2).

The difference between the atmosphere of Venus and Mars also factor into the type of vehicle which 

can be used for exploration. Both planet’s atmospheres are comprised mainly of CO2. However, as 

mentioned previously, Venus’s atmosphere is thick and dense whereas the atmosphere of Mars is rarified, 

with a density near the surface similar to that of Earth’s atmosphere at 30 km altitude. The thick, dense 

atmosphere of Venus provides both benefits and obstacles in the design of a surface vehicle. One 

advantage is that the high surface density enables the possibility of utilizing a low speed fight vehicle 

such as an airship. Whereas on Mars this option is not feasible (Ref. 3). An airship provides a number of 

benefits to scientific exploration. The main advantages include:

• The ability to cover large amounts of surface terrain.

• To capability to descend to the surface and perform scientific investigation at various locations.

• The ability to go over or around obstacles and explore terrain features that would not be 

accessible to surface vehicles. 

• The ability to sample the atmosphere over a range of altitudes. 

Although the high surface density is an advantage for an airship in generating lift, the pressure and 

temperature poses problems for operating equipment and electronics. Because of this the electronics and 

payload must be contained in a cooled pressure vessel in order to survive for an extended period of time 

on the surface. The need for a pressure vessel and cooling system adds significant mass and power 

requirements to any vehicle design. 

Overall an airship could provide a unique capability for exploring the surface of Venus. Although 

technically challenging, as the design and development of any surface vehicle would be, the airship 

platform could provide significant terrain coverage as well as the means to explore and sample both the 

surface and lower atmosphere. This capability would provide unequaled science data return and therefore 
NASA/CR—2012-217665 3

should be thoroughly examined as an option for Venus exploration. The analysis and results discussed in 

this report are a first step in evaluating the feasibility and capabilities of the Stirling engine powered 

Venus airship concept. 

2.0 Atmospheric Environment of Venus

The environmental conditions on Venus are very unique and unlike those on any other known planet or 

moon. Venus is a place of environmental extremes. Near the surface, the atmospheric temperature is very 

hot (over 700°K) and the sunlight is dim due to the extensive cloud cover that shrouds the whole planet. The 

cloud cover extends from approximately 45 km above the surface to approximately 64 km above the 

surface. At the top of the cloud layer, the atmospheric pressure is around 0.1 bar. Within this altitude range, 

the atmospheric temperatures are between 80 to –35 °C respectively. The top of the cloud layer corresponds 

to a pressure altitude of 16 km (52,500 ft) on Earth. A diagram of the Venus atmosphere is shown in 

Figure 2.1 and the physical and orbital properties of the Venus are shown in Table 2.1. 

Another unique aspect of Venus is that the day length is longer than the year. Due to this slow rotational 

rate, the speed to remain at the same solar time is very low, approximately 13.4 km/hr. This slow rotation 

rate will enable the airship to operate in daylight for an extended period of time (~120 Earth days). 

Because of the thick atmosphere, the pressure and density throughout most of the atmosphere is much 

greater than that on Earth. The atmospheric pressure and density we experience near the surface of Earth 

occurs at an altitude of just over 50 km on Venus. 

Figure 2.1.—Venus atmospheric structure.
NASA/CR—2012-217665 4

TABLE 2.1.—PHYSICAL AND ORBITAL

PROPERTIES OF VENUS (REFS. 1 AND 4)

Property Value

Maximum Inclination of Equator to Orbit (δmax).................................................. 3.39°

Orbital Eccentricity (ε) .......................................................................................0.0068

Mean Radius of Orbit (rm)............................................................................... 108×106

Day Period......................................................................................... 243 (Earth Days)

Solar Radiation Intensity ...............................................................Mean: 2613.9 W/m2

.................................................................................................. Parihelion: 2649 W/m2

.................................................................................................. Apehelion: 2579 W/m2

Albedo ....................................................................................................................0.67

Gravitational Constant (gv).............................................................................8.87 m/s2

Sidereal Year ......................................................................................224 (Earth Days) 

Surface Temperature ......................................................................................... 737 °K

Diameter.......................................................................................................12,104 km

Above the cloud layer there is an abundant amount of solar energy. The solar flux at the orbit of 

Venus is 2600 W/m2

, which is much greater than the 1360 W/m2 available at Earth orbit. At the bottom of 

the cloud layer (45 km altitude), the solar intensity is between 520 W/m2 and 1300 W/m2 depending on 

the wavelength of the radiation being collected. This is comparable to the solar intensity at Mars or Earth,

respectively. 

The winds within the atmosphere blow fairly consistently in the same direction as the planetary 

rotation (East to West) over all latitudes and altitudes up to 100 km. Above 100 km, the winds shift to 

blow from the dayside of the planet to the night side. The wind speeds decrease as a function of altitude 

from ~100 m/s at the cloud tops (60 km) to ~0.5 m/s at the surface. These high wind speeds and the slow 

rotation of the planet produce a super rotation of the atmosphere (nearly 60 times faster than the surface). 

The gravitational acceleration on Venus (8.87 m/s2

) is slightly less than that on Earth. The 

atmospheric composition on Venus is mostly CO2 but there are also trace amounts of corrosive 

compounds such as hydrochloric, hydrofluoric and sulfuric acids (Refs. 1 and 4). The atmospheric 

composition is given in Table 2.2. Because of this composition, the speed of sound within the atmosphere 

is generally less than it is within Earth’s atmosphere. 

TABLE 2.2.—VENUS ATMOSPHERIC COMPOSITION (REFS. 1 AND 4)

Gas Percent volume

Carbon Dioxide (CO2) ....................................................................96.5

Nitrogen (N2) ....................................................................................3.5

Sulfur Dioxide (SO2)................................................................150 ppm

Carbon Monoxide (CO).............................................................17 ppm

Water Vapor (H2O)....................................................................20 ppm

Neon (Ne) ................................................................................... 7 ppm

Argon (Ar) .................................................................................70 ppm

Helium (He)...............................................................................17 ppm

The main characteristics of the atmosphere (density, temperature, viscosity, and wind velocity) are 

critical in determining the feasibility of flight within the Venus atmosphere. These quantities are provided 

as functions of altitude (z) in kilometers by Equations (2.1) through (2.7) (Ref. 5).

The temperature on Venus (Ta) decreases fairly linearly from the surface up to approximately 60 km in 

altitude, as seen in Figure 2.2. The temperature as a function of altitude is approximated by Equations (2.1). 

6 5 9 6

2 3 4

1.2336 10 3.7325 10

738.26 9.1909 0.17429 0.007965 0.0001518

z z

T z z z z a

− − − × + ×

= − + − + (2.1)

Because of the thick atmosphere, the pressure and density throughout most of the atmosphere is much 

greater than that on Earth. The atmospheric pressure and density we experience near the surface of Earth 
NASA/CR—2012-217665 5

Figure 2.2.—Temperature profile of Venus’s atmosphere (Ref. 6).

occurs at an altitude of just over 50 km on Venus. For a flight vehicle, this means that flying at 50 km on 

Venus is similar aerodynamically to flying near the surface on Earth. The atmospheric density (ρa) within 

the Venus atmosphere can be represented by Equation (2.2) as a function of altitude in kilometers and the 

viscosity (μa) is given by Equation (2.3). This density as a function of altitude is plotted in Figure 2.3. 

9 5 12 6

2 3 6 4

5.6694 10 1.8971 10

64.85 3.3257 0.067373 0.00066981 3.224 10

z z

z z z z a

− −

−

− × − ×

ρ = − + − + ×

(2.2)

17 7 20 9

9 4 11 5 13 6 15 6

5 9 7 2 8 3

2.5199 10 4.9099 10

2.1929 10 4.8611 10 6.6513 10 5.5001 10

3.5827 10 5.906 10 8.8642 10 5.9485 10

z z

z z z z

z z z a

− −

− − − −

− − − −

+ × − ×

+ × − × + × − ×

μ = × − × + × − ×

(2.3)

The average wind speed on Venus varies considerably from the surface to upper part of the 

atmosphere. The wind speed near the surface is very low and increases to a maximum of just under 

100 m/s at approximately 65 km altitude, as shown in Figure 2.4. A curve fit of mean wind speed (va) in 

meters per second versus altitude in kilometers is given by Equations (2.4) through (2.6). Each of these 

equations represents a different region of the atmosphere. 

Mean wind speed from the surface to 58 km altitude:

5 5 6 6 8 7 10 8

2 3 4

9.96 10 3.28 10 4.7 10 2.495 10

0.89941 0.11201 0.017082 0.0040604 0.0010345

z z z z

v z z z z a

− − − − − × + × − × + ×

= − − + + (2.4)

Mean wind speed from 58 to 66 km altitude:

2 3 v 21498 1087.9z 18.31z 0.10214z a = − + − (2.5)
NASA/CR—2012-217665 6

Mean wind speed from 66 to 100 km altitude:

2 3 4 5 5 7 6 v 3860.1 637.42z 32.206z 0.76199z 0.009357z 5.783 10 z 1.42 10 z a

− − = − + − + − + × − × (2.6)

Figure 2.3.—Atmospheric density as a function of altitude (Ref. 7).

Figure 2.4.—Average wind speed versus altitude within the Venus atmosphere (Ref. 7).
NASA/CR—2012-217665 7

Figure 2.5.—Speed of sound as a function of altitude within the Venus atmosphere (Ref. 7).

The speed of sound (a) in meters per second as a function of altitude above the surface in kilometers 

can be represented by Equation (2.7) and is shown in Figure 2.5 as a function of altitude. This is based on 

the speed of sound in CO2 at the atmospheric pressure at a given altitude. As can be seen in this figure, 

the speed of sound increases fairly linearly with decreasing altitude from the upper atmosphere to the 

surface.

2 3 5 4 8 5 a 410.15 2.1102z 0.008751z 0.00072086z 1.0136 10 z 3.6825 10 z − − = − + − + × − × (2.7)

The last properties of the atmosphere that are of interest are the thermal conductivity (ka) and the specific 

heat (cpa). For carbon dioxide near the surface the conductivity is 0.588 W/mK and the specific heat is 

1181 J/kg K. 

3.0 Airship Configuration and Sizing

For flight on Venus the airship is configured similarly to a standard airship that would operate on 

Earth. The envelope is ellipsoidal with rear fins for stability and control. The equipment and payload are 

housed in a spherical, insulated pressure vessel. An electric motor and propeller are used for propulsion 

and a radioisotope power Stirling engine is used to provide electrical power as well as run the cooler for 

maintaining the interior of the pressure vessel at a temperature in which the electronics and payload can 

operate. This general layout is shown in Figure 3.1. 

Sizing the airship for flight on Venus is an iterative process based on the desired flight altitude and 

speed. The component masses and sizes are calculated from an initial guess at the required lift and power 

needed for the airship to operate. From these the actual lift and power requirements are determined. These 

are compared against the estimated values. If different, then the vehicle size is adjusted and the mass, lift 

and power is recalculated. This iterative process is continued until the initial and calculated lift and power 
NASA/CR—2012-217665 8

values converge. A converged solution represents a design point for the vehicle that meets the selected 

flight environment and payload requirements. This airship sizing method is illustrated in Figure 3.2. 

Figure 3.1.—Venus airship main component layout.

Figure 3.2.—Logic diagram for airship sizing analysis.
NASA/CR—2012-217665 9

3.1 Airship Mass 

The total airship mass is the sum of all the components and systems that make up the airship. These 

components are scaled based on various factors such as power level, size, velocity etc. The components 

and their associated scaling factors are listed in Table 3.1.

TABLE 3.1.—SCALING AND EFFECT DEPENDENCE OF AIRSHIP COMPONENTS

Component Scaling Factor Effect on Airship

Airship Structure: Envelope, Tail, Structural Supports, 

Lifting Gas

Airship Geometry and Size, 

Flight Speed, Altitude

Lifting Capability, Drag, 

Mass

Propulsion Drive Train: Electric Motor, Motor Controller, 

Gearbox, Power Conditioning, Propeller

Propulsion Power and Thrust, 

Flight Speed, Altitude

Power Consumption, Flight 

Velocity, Mass

Stirling Engine System: Stirling Engine, Cooler and

Alternator, Pneumatic Coupling, Cooling Fins, GPHS Blocks

Number of GPHS Blocks, 

Flight Speed, Altitude

Power Availability, 

Cooling Capability, Mass

Payload and Electronics: Flight Control Computer, 

Communications Equipment, Payload, Sensors Inputted Values, Constants Power Consumption, Mass

Payload/Electronics Enclosure: Pressure Vessel, Insulation, 

View Port

Interior Volume and 

Temperature Mass, Cooling Power

3.1.1 Structure Mass

The airship shape is assumed to be an ellipsoid with its length (l) going from the front tip to the rear 

tip and the diameter (d) being the maximum thickness in the center of the airship. The fineness ratio (f) of 

the airship is the ratio of length to diameter as given by Equation (3.1). The length and fineness ratio are 

used as the input variables to vary the airship size and geometry. The airship volume (Va) and surface area 

(Sa) are given by Equations (3.2) and (3.3). 

f = l

d (3.1)

f

l Va 34 3 π = (3.2)

















































































 



 + 













 = π

−

−

f

l f

f

l Sa 1

tan cos

1

cos

2 2

2

1

1

2 2

(3.3)

The airship structure mass (ms), given in Equation (3.4), is based on the aerial density (ρe, assumed to 

be 0.25 kg/m2

) of the covering, the number of control fins (nf) and ratio of fin area to airship volume (Rf) 

along with a fin structure factor (Sf,, assumed to be 1.2) to account to the internal structural support and 

controls for the fins. In addition a structure factor assumes that the internal structure of the airship 

envelope scales as 1/4 of the total mass of the airship (mtot) (Ref. 4). This component is added to account 

for the fixed structure needed to attach components to the envelope. 

a a tot s f f a e f S m

m = n R V ρ S + + ρ 4 (3.4)
NASA/CR—2012-217665 10

Figure 3.3.—Propulsion system component layout.

3.1.2 Propulsion System Mass

The propulsion system mass consists of the mass of the electric motor (mem), motor controller (mmc), 

gearbox (mg), propulsion power conditioning electronics (mpc) and propeller (mprop). The operational 

efficiency of each of the components of the power system must also be taken into account when sizing the 

airship. The airship power train is shown in Figure 3.3. The total efficiency of the propulsion system drive 

train (ηp) , given by Equation (3.5), is composed of the motor controller efficiency (ηmc), electric motor 

efficiency (ηem), gearbox efficiency (ηg), power conditioning (ηpc)and propeller efficiency (ηprop). 

ηp = ηmcηemηgηprop (3.5)

The operational efficiency associated with each of these components is given in Table 3.2. They are 

combined to get the drive-line efficiency which consists of all components up to the propeller. The 

propeller efficiency has to be calculated based on a propeller sizing for the operational altitude and thrust 

requirement. These efficiencies are representative approximations for each of the components under 

optimized operating conditions. 

TABLE 3.2.—DRIVE LINE COMPONENT EFFICIENCIES 

Component Efficiency

Control Electronics..........................................ηmc 0.98

Motor ..............................................................ηem 0.90

Gearbox.............................................................ηg 0.90

Power Conditioning ........................................ηpc 0.98

Drive Line Efficiency........................................ηp 0.78

Sizing the propeller is an iterative process that is dependent on the airship flight speed and thrust 

requirement. To achieve the desired thrust at the needed airspeed, the propeller diameter, rpm, and pitch 

angle are iterated upon. The goal is to provide a combination of these that maximizes efficiency for a 
NASA/CR—2012-217665 11

given propeller geometry (airfoil section, blade twist and chord distribution). For this analysis it was 

assumed that a variable pitch two bladed propeller was utilized. An approximation for the thrust (ct) and 

power (cp) coefficients were derived as a function of advance ratio (J) (Refs. 8 and 9). The thrust and 

power coefficient equations, (3.6) and (3.7), respectively, are valid for advance ratios within the range of 

0.18 to 3.0. 

2 3 4

c 0.012122 0.14577J 0.1408J 0.05374J 0.0068444J t = − + − + − (3.6)

2 3 4

c 0.012752 0.094954J 0.053694J 0.017534J 0.0007872J p = − + − + − (3.7)

The advance ratio, given in Equation (3.8), can be expressed in terms of the flight velocity (U) the speed 

of sound within the atmosphere (a) and the desired tip Mach number (M). 

( )

2 2 aM U

U J

−

π = (3.8)

By selecting a tip Mach number, the propeller efficiency can be calculated from the above equations. 

p

t prop c

c J

η = (3.9)

The electric motor mass (Refs. 9 and 10), motor controller mass (Refs. 9 and 10), gearbox mass

(Refs. 9 and 10), and mass of the power conditioning system (Refs. 9 and 10) are based on a linear scaling 

with power output (P). The lower-limit at which the equations are valid are listed after each equation. If 

the required power was sufficiently small so that the calculated mass of any component was below this 

minimum then the minimum value was used.

p1291

mc em

P

m

η

η = (minimum of 0.5 kg) (3.10)

p 6233 mc

P

m

η = (minimum of 0.1 kg) (3.11)

p 3278

em mc g

P

m

η

η η = (minimum of 0.5 kg) (3.12)

1000 pc

p

pc

P

m

η

η = (minimum of 0.2 kg) (3.13)

The propeller mass is based on the propeller diameter (dprop), given in Equation (3.14), and the number of 

blades (nb). The diameter is dependent on the amount of thrust generated by the propeller. This thrust will 

be equal to the airship drag (D) at the desired flight speed. With the diameter and number of blades 

known, the mass of the propeller will depend on the volume of each blade, its material density (ρprop), and 

the void fraction within the blade (vb). Using the airfoil cross-sectional area and the chord length 

distribution given in Reference 8, the volume of the propeller blade (Vprop) can be calculated. This volume 

is given by Equation (3.15) and the total propeller mass is given by Equation (3.16). For this analysis it 

was assumed that the propeller had two blades and was constructed of carbon composite, with a density of
NASA/CR—2012-217665 12

1380 kg/m3, and with no void within the blade. Also a 10 percent increase in the total propeller blade 

mass was added to account for the hub and attachment to the drive shaft.

(( ) ) 2 2

2

c aM U

D d

t

prop

−

π = (3.14)

5 3 9.25739 10 prop prop V d − = × (3.15)

( ) prop prop b b Vprop m =1.1ρ n 1− v (3.16)

The total propulsion system drive train mass (mps), given by Equation (3.17), is the sum of the masses 

from Equations (3.10) through (3.16). 

mdt = mem + mmc + mg + mpc + mprop (3.17)

3.1.3 Power System Mass

The power generation system provides electrical power to the drive motor as well as to the electronics 

and payload. It also provides mechanical power for operating the cooler for maintaining the electronics/ 

payload enclosure at its operating temperature. Electrical power is generated by an isotope powered 

Stirling engine. The mass breakdown for the power system includes the mass of the Stirling engine (mse, 

given in Eq. (3.18)), mass of the cooler and alternator (mca given in Eq. (3.19)), mass of the engine 

pneumatic coupling (msepc given in Eq. (3.20)), mass of the radioisotope blocks including their support 

structure (mr given in Eq. (3.21)) and mass of the cooling fins (mf given in Eq. (3.30)). The baseline for 

this design study used 10 GPHS blocks. Since the number of GPHS blocks (nr) was predetermined and 

any variation examined would be near this number of blocks, a linear scaling of the power system 

components was use. This mass scaling of the components is based on the number of GPHS blocks used. 

It should be noted that this scaling is only valid for a system using approximately 10 GPHS blocks (±5). 

The accuracy of the power system mass estimates will diminish as the power level varies from the 

baseline 10 GPHS blocks. 

se r m = 1.25n (3.18)

ca r m =1.138n (3.19)

sepc r m = 0.0625n (3.20)

r r r m = 1.44n +1.2n (3.21)

The GPHS blocks are housed in an insulated pressure vessel designed to minimize the heat loss from the 

blocks to the surrounding atmosphere. This pressure vessel is illustrated in Figure 3.4 and Figure 3.6 for a 

configuration with 10 GPHS blocks in two stacked groups of five blocks. The mass of the radioisotope 

heat source pressure vessel (mhv), given by Equation (3.22), is the sum of the masses of the insulation 

(mhi), inner wall (mhwi) and the outer pressure vessel (mhwo), as illustrated in Figure 3.4 and given by 

Equations (3.23) through (3.26). The inner wall mass is dependent on its material density (ρhwi), the inner 

radius (rhi) of the radioisotope heat source enclosure and its wall thickness (thwi). The inner wall radius is 

based on the arrangement of the GPHS blocks. In the configuration illustrated it is set by the height of the 

two-stacked blocks and their distance from the center of the pressure vessel sphere.

mhv = mhi + mhwi + mhwo (3.22)
NASA/CR—2012-217665 13

Figure 3.4.—Radioisotope heat source pressure vessel layout.















 = πρ + +

3 2

8 2

2 hwi

hwi hwi hwi hi hi hwi

t

m t r r t (3.23)

[( ) ( ) ] 3 3

3

4

hi i hi hwi hi hi hwi m = πρ r + t + t − r + t (3.24)

The outer wall provides the structural barrier between the interior pressure (Pi) and the atmospheric 

pressure (Pa). The pressure vessel external wall thickness (thwo) necessary to maintain this pressure 

difference is given by Equation (3.25) and is dependent on the outer wall material yield strength (σypo). 

The subsequent mass for the heat source outer pressure vessel wall is given by Equation (3.26). 

( )( )

( ) yho i a

S hwi hwi hi a i

hwo FS P P

F r t t P P

t

σ + −

+ + − = 42 (3.25)















 = πρ − − 3

4

2

2 hwo

hwo hwo hwo ho hwo ho

t

m t r t r (3.26)

Where the outer radius (rho) is given by Equation (3.27).

ho hwi hwi hi hwo r = r + t + t + t (3.27)

Cooling fins are sized to remove the waste heat from the Stirling engine and transfer it to the atmosphere. 

Sizing the cooling fins is an iterative process based on the temperature difference between the engine heat 

rejection temperature (Tr) and the atmosphere temperature (Ta), the engine heat rejection housing height 

(le) and diameter (de), the cooling fin diameter (df), the cooling fin thickness (tf), the number of cooling 

fins (ncf) and the convective heat transfer coefficient to the surroundings (hf). These variables are 

illustrated in Figure 3.5. 
NASA/CR—2012-217665 14

Figure 3.5.—Engine cooling fin geometry.

The heat transfer from each cooling fin (Qf) is given by Equation (3.28). 

( )( ) f e r a

f

f d d T T

h

Q − − π = 2 2

2 (3.28)

The convective heat transfer coefficient for the fins is dependent on the Reynolds number of the flow 

through the fins Ref and the corresponding Prandtl (Pr) and Nusselt numbers (Nuf) given by Equations

(3.29), (3.31), and (3.32), respectively (Ref. 12).

a

a h

f

Ud

μ

ρ Re = (3.29)

Where the hydraulic diameter (dh) of the spacing between the fins is given by Equation (3.30). 

( ) 1

2 −

− = − +

cf

e cf f

h f e n

l n t

d d d (3.30)

k

c paμa Pr = (3.31)

(Pr 1) 8

1.07 12.7

Re Pr

8

Nu

0.667

0.5

− 















+

















=

f

f

f

f

f

f

(3.32)
NASA/CR—2012-217665 15

The fin friction factor (ff) used in the calculation of the Nusselt number is based on Reynolds number and 

given by Equation (3.33).

( ( ) ) 2

10 1.82log Re 1.64 − f f = f − (3.33)

Using Equations (3.29) through (3.33) the convective heat transfer coefficient for the cooling fins can be 

determined from Equation (3.34). 

h

a f f d

k h = Nu (3.34)

In addition to heat rejection from the fins, there is also some heat transferred to the atmosphere from the 

exterior of the engine heat exchanger housing (Qh) as given by Equation (3.35). 

( ) h e e f Tr Ta Q = πd l h − (3.35)

To size the cooling fins, the total heat rejection capability of the housing and fins has to be equal to 

the total waste heat generated (Qw) by the Stirling engine, as given by Equation (3.36). 

Qw = Qf + Qh (3.36)

By iterating on the fin size and number to satisfy the equality, given above, the size and corresponding 

mass of the cooling fins, given by Equation (3.37), can be determined, based on the density of the cooling 

fin material (ρf).

( ) f cf f e f f m = n π d − d t ρ 2 2 (3.37)

With the size and mass of the cooling fins determined, the total power system mass (mps), given by 

Equation (3.38) can be calculated. 

mps = mse + mca + msepc + mr + mf (3.38)

3.1.4 Pressure Vessel Mass

The pressure vessel is used to house the electronics and payload. It is composed of an outer wall 

capable of withstanding the pressure differential between the outside environment and the interior. The 

pressure vessel interior is designed to operate at 1 bar whereas the exterior surface pressure on Venus is 

approximately 90 bar. Inside the outer wall is a layer of aerogel insulation. A second structural shell is 

used as a means of removing heat through a two stage cooler if desired. On the inside of this second 

structural shell is another layer of aerogel insulation. The layout of the pressure vessel is shown in 

Figure 3.6. 
NASA/CR—2012-217665 16

Figure 3.6.—Pressure vessel structure and insulation layout.

The 1 bar internal pressure provides a number of benefits to the system design which include:

• The interior would not have to be evacuated prior to launch.

• Lightweight aerogel can be utilized as the interior insulation.

• Small leaks of atmospheric gas into the interior would not significantly degrade the insulation’s 

insulating ability over a system designed for vacuum operation. 

• Internal convection can be used to evenly distribute the internal cooling.

The mass of each layer of the pressure vessel is based on its thickness, surface area and material 

density. The thickness (tpo) of the outer shell wall has to be able to withstand the pressure difference 

between the atmospheric pressure and the interior pressure. The thickness can be calculated for a 

specified material based on its yield strength and the desired interior radius (rpi) plus the thickness of the 

inner and outer insulation layers (tii, tio) and interior wall structure, as illustrated in Figure 3.7. A factor of 

safety (FS) is also used so that the stress at the operational conditions is sufficiently below the yield stress 

of the material. The pressure vessel exterior wall thickness (tpo) is given by Equation (3.39). Using this 

thickness and the material density of the outer wall (ρpo), its mass is calculated by Equation (3.40).

( )( )

( ) ypo S i a

S pi ii io pi pm a i

po F P P

F r t t t t P P

t

σ + −

+ + + + − = 42

(3.39)















 = πρ − − 3

4

2

2 po

po po po po po po

t

m t r t r (3.40)

The outer radius of the pressure vessel (rpo) is given by Equation (3.41).

rpo = rpi + t pi + tii + t pm + tio + t po (3.41)
NASA/CR—2012-217665 17

Figure 3.7.—Interior layers of the pressure vessel.

The mass of the middle (mpm) and inner (mpi) structural layers are also calculated based on their thickness 

(tpm and tpi, respectively), material density (ρpm, ρpi, respectively) and surface area, as given by Equations

(3.42) and (3.43), respectively. However, since there is no structural load on the middle and inner walls, 

the thickness was provided as an input and not calculated. 

[( ) ( ) ] 3 3

3

4

pm pm pi pi ii pm pi pi ii m = πρ r + t + t + t − r + t + t (3.42)















 = πρ + +

3 2

8 2

2 pi

pi pi pi pi pi pi

t

m t r r t (3.43)

The last component mass of the pressure vessel is the inner (mii) and outer (mio) insulation layers. The 

orientation of these layers is shown in Figure 3.8. Both layers are inside the outer pressure vessel wall and 

are therefore at the interior pressure. The insulation layer thickness is a variable that can be adjusted 

during the design process to control the heat leak from the atmosphere into the pressure vessel and 

therefore control the required cooling power. The corresponding mass of the insulation layers is based on 

the insulation density (ρi) and thickness, given by Equations (3.44) and (3.45). 

[( ) ( ) ] 3 3

3

4

ii i pi pi ii pi pi m = πρ r + t + t − r + t (3.44)

[( ) ( ) ] 3 3

3

4

io i pi pi ii pm io pi pi ii pm m = πρ r + t + t + t + t − r + t + t + t (3.45)
NASA/CR—2012-217665 18

Figure 3.8.—Nusselt number as a function of Reynolds number for cross flow over cylinder 

and a sphere.

The total mass of the pressure vessel (mp), given by Equation (3.46), is the sum of the masses from 

Equations (3.40) through (3.45). An additional 10 percent margin is added to the total mass to account for 

items such as internal structure and miscellaneous hardware. 

( ) mp = 1 mpo + mpm + mpi + mii + mio 1. (3.46)

The last component is the structural supports that hold the pressure vessel to the airship envelope. The 

struts are composed of solid circular cylinders. The mass of the struts, given by Equation (3.47), is 

dependent on the strut material density (ρss), number of struts (nss), strut length (ls) and diameter (dss). It 

was assumed that the struts would connect to the centerline of the payload pressure vessel and would 

extend to the base of the envelope as shown in Figure 3.1. The length of the struts is based on the 

diameters of the payload and heat source pressure vessels, the height of the engine heat exchanger and its 

spacing from the bottom of the lifting gas envelope. As with the pressure vessel there is a 10 percent

margin added onto the struts to account for additional material at the attachment points. 

s s s s ss l n

d

m  ρ 

 



 = π

2

2

1.1 (3.47)
NASA/CR—2012-217665 19

The lifting gas mass (mlg), given by Equation (3.48), also factors into the total airship mass. Its mass 

is dependent on the lifting gas molecular weight (MWg), temperature and pressure and the airship gas 

volume. The universal gas constant (R) has a value of 0.0831 m3

Bar/kMol K and it is assumed the gas is 

at atmospheric conditions.

T R

M V P

m

a

W g a a

lg = (3.48)

3.1.5 Total Mass

The last series of components that have to be accounted for in determining the total mass of the 

airship are fixed and do not scale with the airship size. These fixed mass components are listed in 

Table 3.3. 

TABLE 3.3.—AIRSHIP FIXED COMPONENT MASSES

Component Mass,

kg

Power,

W

Flight Control Computer (mfc, Pfcc) 3.8 10

Communications Equipment (mce , Pce) 4.6 19

Flight Control Sensors (mfs, Pfcs) 3.5 9

Payload (mpl, Ppl) 25.0 19

The sum of these fixed mass items is given by Equation (3.49).

mfi = mfc + mce + mfs + mpl (3.49)

From the above equations the total airship mass (mtot), given by Equation (3.50), can be calculated.

mtot = ms + mdt + mps + mp + mhv + mss + mlg + mfi (3.50)

Determining the total airship mass and subsequent gas envelope size is an iterative process. The 

airship envelope volume, given by Equation (3.2), determines the total weight that the airship can lift. The 

lifting force (L) of the airship is based on a centuries old principle discovered by Archimedes, “A body 

wholly or partly immersed in a fluid is buoyed up with a force equal to the weight of the fluid displaced 

by the body”. This principle is expressed by Equation (3.51), which is dependent on the gravitational 

force on Venus (g =8.93 m/s2

), the ratio of the molecular weights of the lifting gas and the atmosphere 

(MWa), the density of the atmosphere and the gas constant of the atmosphere (Ra=188.92 J/kg-K). This 

equation assumes that the pressure within the lifting gas envelope is the same as that of the atmosphere 

and unless the lifting gas is actively heated, its temperature (Tg) will also be the same as that of the 

atmosphere. This equation also takes into account the lift that would be generated by the payload and 

GPHS block enclosures due to their internal pressure being lower than the atmospheric pressure. 

g R T

P

r

R T

P

r

M T

M T

L V

a h

i

hwi a

a i

i

pi a

Wa g

Wg a

a a

















































+ ρ − 















+ π ρ − 













 = ρ − 3 3

3

4 1 (3.51)

The total lifting force is then compared to the total weight of the airship (Wtot), as given by Equation 

(3.52). In the analysis the envelope size is then iterated on until the lifting force is greater than or equal to 

the airship weight.

tot tot W = gm (3.52)
NASA/CR—2012-217665 20

3.2 Power Required

The next step in sizing the airship is determining the total power required to fly and operate the 

airship and payload systems. Determining this is an iterative process between the sizing of the airship to 

lift its mass and the power needed to overcome drag due to its size and shape along with the power 

needed to provide cooling to the pressure vessel. As with the total mass, the total power will be a 

summation of the power required by the various systems of the airship given by Equation (3.53). The 

main power consuming items on the airship is propulsion and cooling (Pc).

Pr = Pfc + Pce + Pfs + Ppl + P + Pc (3.53)

3.2.1 Propulsion Power

The propulsion power required by the airship to fly at a specified velocity is given by Equation (3.54).

p

DU P

η = (3.54)

The total airship drag is the summation of the drag of each component exposed to the atmosphere 

flow over the airship as it moves. The main airship structure containing the lifting gas can be broken into 

two segments, the gas envelope and the tail section with control fins. The lifting gas envelope drag (De), 

given by Equation (3.55) is based on the airship’s velocity, the volume of the lifting gas and its drag 

coefficient (cde). 

3

2

2

2

1 e a deVa D = ρ U c (3.55)

The gas envelope drag coefficient is based on the fineness ration for the airship and is given by 

Equation (3.56). This equation represents a curve fit to drag coefficient data for various airship fineness 

ratios (Ref. 13). 

2 3 4 4 5 5 c 0.2318 0.1576 f 0.04744 f 0.007041 f 5.135 10 f 1.48 10 f de = − + − + × − × (3.56)

The tail section drag (Dt) is scaled linearly from the lifting gas envelope drag as given by Equation (3.57)

(Ref. 13).

Dt De = 0.167 (3.57)

The next main drag components are for the pressure vessels. Since the pressure vessels for the 

electronics/payload is similar to that for the heat source the drag for each (Dp and Dh respectively) is 

calculated in a similar manner. The main electronics/payload pressure vessel drag is given by 

Equation (3.58), and that for the heat source enclosure is given by Equation (3.59).

2 2

2 p a dpv po D ρ U c r

π = (3.58)

2 2

2 h a dpv ho D ρ U c r

π = (3.59)

The drag coefficient for either pressure vessel (cdpv) is dependent on the flow Reynolds number. The 

drag coefficient for a sphere is given by Equation (3.60) and the coefficients are given in Table 3.4 for 
NASA/CR—2012-217665 21

different ranges of Reynolds number (Repv), given by Equation (3.61), for the pressure vessel based on its 

diameter (dpv). These are based on a curve fit from experimental data (Ref. 12).

2

0 1 Re 2 Re dpv s s do s do c = c + c + c (3.60)

a

a pv

do

Ud

μ

ρ Re = (3.61)

TABLE 3.4.—SPHERICAL PRESSURE VESSEL DRAG COEFFICIENT CONSTANTS 

Reynolds Number Range c0s c1s c2s

Repv <= 100 3.6279 –0.045484 1.9292×10–4

100 < Repv <= 1000 0.92 –7.08×10–4 2.40×10–7

1000 < Repv <= 1×104 0.4675 –7.80×10–6 4.00×10–10

1×104 < Repv <= 1×105 0.43 4.00×10–7 0.00

1×105 < Repv <= 1×106 0.19 1.80 ×10–6 –2.56×10–12

1×106 < Repv <= 1×107 0.10167 9.00×10–9 –6.67×10–16

The drag for the heat exchanger (Dhe), shown in Figure 3.5, is given by Equation (3.62). The first part 

of the equation provides the drag for the cooling fins and the second part is the drag of the main heat 

exchanger cylinder.

2 2

2 2 2

a e e dhe

h

a f e f

he

U l d c

d

f U l d

D ρ +

ρ = (3.62)

As with the pressure vessel, the drag coefficient for the heat exchanger (cdhe, given by Eq. (3.63)) is a 

function of the Reynolds number for the flow over its surface (given in Eq. (3.29)). The heat exchanger 

drag coefficient also includes an adjustment factor to account for the aspect ratio (length to diameter) for 

the cylinder (Refs. 12and 14). 

( ) 















+













 = + Re + Re 0.0787ln 0.5143 2

0 1 2

e

e dhe c c f c f d

l

c c c c (3.63)

As discussed previously there are four cylindrical struts used to hold the pressure vessels and the 

other components to the gas envelope. The drag for these struts (Ds) is given by Equation (3.64). Since the 

struts are cylindrical in shape the coefficients used in Table 3.5 can be used to calculate the drag 

coefficient (cds) for the struts based on the Reynolds number (Res) of the flow around them. 

s s a s s ds D n U l d c

2

2

1 = ρ (3.64)

( ) 















+













 = + Re + Re 0.0787ln 0.5143 2

0 1 2

s

s ds c c s c s d

l

c c c c (3.65)

a

a s s

Ud

μ

ρ Re = (3.66)
NASA/CR—2012-217665 22

TABLE 3.5.—INFINITE CYLINDER DRAG COEFFICIENT CONSTANTS 

Reynolds Number Range c0c c1c c2c

Repv <= 100 3.5645 –0.04215 2.088×10–4

100 < Repv <= 1000 1.4464 –7.241×10–4 2.92×10–7

1000 < Repv <= 1×104 1.0191 –2.21×10–5 3.18×10–9

1×104 < Repv <= 1×105 1.0897 5.34×10–6 –4.01×10–11

1×105 < Repv <= 1×106 1.4263 –1.18×10–6 1.00×10–14

1×106 < Repv <= 1×107 0.32731 2.76×10–8 –5.46×10–16

From these components the total drag (Dtot) for the airship can be determined, as given by Equation 

(3.67).

Dtot = De + Dt + Dp + Dh + Dhe + Ds (3.67)

3.2.2 Cooling Power

The cooling power for maintaining the desired operating temperature for the electronics/payload 

enclosure is the largest power-consuming item. The required cooling power is dependent on the heat loss 

through the electronics/payload pressure vessel to the surroundings. For a single stage cooling system the 

heat loss (Qp) through the insulation and pressure vessel walls is given by Equation (3.68). It is based on 

the temperature difference between the interior and exterior and the thermal resistance for each layer of 

material within the pressure vessel and the thermal resistances associated with the natural convection 

within the pressure vessel and the convection from its exterior.

ci wi ii wm io wo co

a i

p R R R R R R R

T T Q

+ + + + + +

− = (3.68)

The thermal resistance (Rt) terms for the different material layers that comprise the pressure vessel are 

all similar and are based on the inner (ri) and outer (ro) radius of the layers as well as the layer thermal 

conductivity (km) of the layer material, as given by Equation (3.69). 















 − π =

m i o k r r

R 1 1

4

1 (3.69)

The values, used for the corresponding thermal resistance variables in Equation (3.69), are given in 

Table 3.6. 

TABLE 3.6.—THERMAL RESISTANCE VALUES FOR EACH 

MATERIAL LAYER IN THE PAYLOAD PRESSURE VESSEL

Resistance Term,

Rt

Thermal Conductivity, 

km

Inner Radius,

ri

Outer Radius,

ro

Inner Wall (Rwi) kwi rpi rpi + tpi

Inner Layer of Insulation (Rii) kii rpi + tpi rpi+ tpi + tii

Middle Wall (Rwm) kwm rpi + tpi + tii rpi+ tpi + tii + tpm

Outer Layer of Insulation (Rio) kio rpi + tpi + tii + tpm rpi+ tpi+ tii+ tpm + tio

Outer Wall (Rwo) kwo rpi + tpi + tii + tpm + tio rpo

The remaining two resistance terms are due to the internal convection within the pressure vessel (Rci) 

and the external convection (Rco) to the atmosphere. These are given by Equations (3.70) and (3.71),

respectively. These thermal resistances are dependent on the internal (hi) and external (ho) convection 

coefficients.
NASA/CR—2012-217665 23

2 4

1

i pi

ci h r

R

π = (3.70)

2 4

1

o po

co h r

R

π = (3.71)

Determining the convection coefficients for each of the convection thermal resistance terms is a key 

aspect in accurately calculating the heat leak through the walls and insulation of the pressure vessel. The 

convection coefficients for both the interior and exterior convection are given by Equations (3.72) and 

(3.73), respectively. These coefficients are determined by utilizing the geometry and gas properties at 

each location. The main factor in calculating the convective coefficients is in determining the Nusselt 

number for each location. 

pi

i di

i

r

k h

2

Nu = (3.72)

po

a do o r

k h

2

Nu = (3.73)

For calculating the internal convective coefficient the interior gas was assumed to be CO2 at 1 atm. The 

thermal conductivity for this gas (ki) is given by Equation (3.74), which is based on the interior wall film 

temperature (Tif). The internal convective heat transfer is assumed to be natural convection with no active 

mixing of the gas within the pressure vessel. Therefore there will be a boundary layer with a temperature 

gradient between the interior wall and the internal gas. The film layer temperature is the average of the 

interior temperature and the wall temperature. The difference between the wall and the interior gas 

temperature (∆Twi) was assumed to be 10 °C with a baseline internal temperature of 320 K. 

5 9 2 0.0091 8.79 10 9.03 10 i Tif Tif k − − = − + × − × {W/m K} (3.74)

The internal gas Nusselt number (Nudi) for internal free convection within the pressure vessel is given by 

Equation (3.75) (Ref. 11).

0.29

0.2 Pr

Pr Nu 0.18 















+ =

i

i i

di

Ra (3.75)

The pressure vessel internal gas Prandtl number (Pri) is based on the internal gas specific heat (cpi), 

thermal conductivity and dynamic viscosity (μi) of the gas as defined by Equation (3.76). 

i

pi i

i k

c μ Pr = (3.76)

To calculate the Prandtl number for the internal gas the thermal conductivity is given by Equation (3.74)

and the specific heat and dynamic viscosity is given by Equations (3.77) and (3.78), respectively as a 

function of the wall film temperature. 

7 2 0.509 0.00134 6.46 10 pi Tif Tif c − = + − × {kJ/kg K} (3.77)
NASA/CR—2012-217665 24

7 8 11 2 4.69 10 5.13 10 1.21 10 i Tif Tif− − − μ = × + × − × {kg/m s} (3.78)

The last factor in calculating the Nusselt number is the determination of the Rayleigh number for the 

pressure vessel internal gas (Rai), defined in Equation (3.78). The Rayleigh number is based on the 

interior wall film temperature, the kinematic viscosity (νi, given by Eq. (3.80)) and the thermal diffusivity 

(αi, given by Eq. (3.81)) of the internal gas. 

if i i

wi pi

i T

g T r

Ra

ν α

∆ =

3 8

(3.79)

6 8 11 2 3.2 10 2.03 10 5.95 10 i Tif Tif− − − ν = − × + × + × {m2

/s} (3.80)

6 8 11 2 6.18 10 3.24 10 8.1 10 i Tif Tif

− − − α = − × + × + × {m2

/s} (3.81)

The convective coefficient for the flow over the exterior of the pressure vessel is given by Equation 

(3.73). Unlike the interior, the convective heat transfer for the flow over the exterior of the pressure vessel 

is forced convection. Therefore, the Nusselt number calculation will be different than that for the interior.

Calculating the Nusselt number for the exterior flow is somewhat difficult due to the very high Reynolds 

number of the flow over the exterior of the sphere. 

At flight speeds near the wind velocity of 1 to 2 m/s the Reynolds number, as given by Equation 

(3.66), is on the order of 3 million. There were no available correlations found for the Nusselt number for 

flow over a sphere at a Reynolds number in this range. The closest Nusselt number correlation found for 

flow over a sphere is valid only up to a Reynolds number of 78,000 (Ref. 15), this correlation is graphed 

in Figure 3.8. A curve fit of data (Ref. 16) on the Nusselt number for flow over a cylinder within a 

Reynolds number range of 3×104 < Rep < 4×106 is also graphed on Figure 3.9. In addition to the data, 

Equation (3.82) also represents the Nusselt number as a function of Reynolds number for a cylinder in a 

cross-flow (Ref. 17).This equation is valid for the product of Prandtl and Reynolds numbers greater than

0.2 (PrRed > 0.2).

0.8 0.625

0.25 2 / 3

0.5 1/ 3

282000

Re 1

Pr

0.4 1

0.62Re Pr Nu 0.3















 



 



 +















 



 



 +

= + do do

do (3.82)

The valid Reynolds number range for the cross-flow cylinder Nusselt number curves is within the values 

encountered for flow over the payload pressure vessel near the surface of Venus. Also the Nusselt number 

for a sphere within the Reynolds number range in which it is valid, is very close to that given by Equation 

(3.82) for a cylinder in cross-flow (as can be seen on Figure 3.8). Therefore Equation (3.82) was used to 

approximate the Nusselt number for flow over the spherical pressure vessel. With this expression for 

Nusselt number, the convective coefficient for the atmosphere flow around the pressure vessel, given by 

Equation (3.73), can be calculated and in turn the exterior convective resistance term, given by Equation 

(3.71). 
NASA/CR—2012-217665 25

Figure 3.9.—GPHS block assembly drawing (Ref. 18).

The Stirling cooler has to not only remove the heat leaking in through the insulation, but also the 

wires and view port as well as the heat internally generated by the computer control system and payload. 

The heat leak through the pass-through wires and view port windows (Qpw and Qvp respectively) is 

depending on the number of wires (nw) and view ports (nvp), their diameter (dw, dvp) and the thermal 

conductivity of the wire (kw) or viewport (kvp). The heat leak through the wires and view ports is given by 

Equations (3.83) and (3.84), respectively. 

( )

( ) po pi

w w w a i

pw r r

n d k T T Q −π − = 4

2

(3.83)

( )

( ) po pi

vp vp vp a i

vp r r

n d k T T

Q −

π − = 4

2

(3.84)

From Equations (3.68) through (3.84) the total required cooling power could be determined. This required 

power is the sum of the internal heat that must be removed divided by the efficiency of the Stirling cooler 

(ηc), as given by Equation (3.85). The cooler efficiency was assumed to be 44 percent. 

( )

c

fc fs pl p pw vp

c

P P P Q Q Q P

η

+ + + + + = (3.85)

3.3 Power Production

The last area to model in sizing the airship is the amount of power available from the Stirling 

radioisotope powered engine. The Stirling engine converts heat from the isotope blocks to provide 

electrical and mechanical power. Each radioisotope block, termed a GPHS, provides 250 W of thermal 

power at their beginning of life. The blocks are comprised of a number of plutonium-238 pellets, as 

illustrated in Figure 3.9. Each block measures 9.948- by 9.32- by 5.82-cm and has a mass of 1.44 kg. 
NASA/CR—2012-217665 26

The blocks are arranged in a circular fashion around the heater head of the engine as illustrated in 

Figure 3.4 and Figure 3.6. The GPHS blocks are enclosed in an insulated pressure vessel similar to that 

used for the electronics and payload. The insulated pressure vessel is necessary in order to limit heat loss 

from the blocks to the surroundings. The heat loss from the GPHS pressure vessel (Qhs) is given by 

Equation (3.86).

ci wi ii wo co

h a hs R R R R R

T T Q

+ + + +

− = (3.86)

The thermal resistance terms for the different material layers that comprise the heat source pressure vessel 

are all similar to those used for the payload pressure vessel, given by Equation (3.69). The corresponding 

values for the heat source pressure vessel to be used with Equation (3.69) are given in Table 3.7. Since the 

heat source pressure vessel has only one layer of insulation only the inner insulation resistance term is 

used in Equation (3.86).

TABLE 3.7.—THERMAL RESISTANCE VALUES FOR EACH 

MATERIAL LAYER IN THE HEAT SOURCE PRESSURE VESSEL

Resistance Term,

R

Thermal Conductivity 

k

Inner Radius,

ri

Outer Radius,

ro

Inner Wall (Rwi) khwi rhi rhi + thwi

Insulation Layer (Rii) khi rhi + thwi rhi+ thwi + thi

Outer Wall (Rwo) khwo rhi + thwi + thi rhi + thwi + thi + thwo

The interior and exterior convective thermal resistance terms for the heat source pressure vessel are 

calculated in the same manner as those for the payload pressure vessel, given by Equations (3.70) and 

(3.71), respectively. The inner (rhi) and outer (rho) radius for the heat source pressure vessel is substituted 

for those of the payload pressure vessel. The convective coefficients for the heat source pressure vessel 

are calculated in a similar manner as those for the payload pressure vessel. Since the heat source pressure 

vessel is operating with the same internal gas and pressure as that of the electronics enclosure, the inner 

and outer convective coefficients can be determined from Equations (3.72) through (3.82) by substituting 

in the appropriate dimensions for the heat source pressure vessel in place of those for the electronics 

pressure vessel and using a baseline internal operating temperature of 1473 K. 

To determine the heat available to the engine (Qe), the heat loss to the environment from the heat 

source pressure vessel is subtracted from the total heat available from the GPHS blocks, as given by 

Equation (3.87). With the heat loss through the heat source pressure vessel known, the heat available to 

the engine can be calculated from Equation (3.85). 

Qe = 250nr − Qhs (3.87)

The Stirling engine output power is then calculated from this available heat and the engine’s efficiency 

(ηe) as given in Equation (3.88). 

Pe = ηeQe (3.88)

The engine efficiency is based on the hot end engine temperature and the rejection temperature as given 

by Equation (3.89). This equation was derived from data on the operation of the Stirling engine over a 

range of hot end temperatures (Ref. 19).

( ) ( ) 4 7 2 0.223 5.933 10 3.10 10 ηe = − + × Th −Tr − × Th −Tr

− − (3.89)
NASA/CR—2012-217665 27

4.0 Analysis Results

The analysis described in Section 3.0 was used to evaluate the airship configuration and flight 

requirements to determine the size, mass and power to operate near the surface of Venus. An initial sizing 

was performed to provide a baseline design utilizing 10 GPHS blocks as the heat source that can fly faster 

than the wind speed near the surface and provide sufficient cooling and power to maintain and operate the 

payload and electronics. From this design various trades were performed to determine what effect they 

had on the airship sizing and overall feasibility. These tradeoffs included:

• The flight altitude

• The internal operating temperature of the payload enclosure

4.1 Baseline Airship Design

The goal of the baseline airship design was to provide an airship configuration that could operate near 

the surface of Venus utilizing 10 GPHS blocks as the power and cooling system heat source. The number 

of GPHS blocks set the available thermal power at 2500 W, which drove all aspects of the design. The 

baseline airship configuration is shown in Figure 4.1. This figure represents a proportionally to scale 

illustration of the airship. 

The lifting gas envelope for the airship has an ellipsoidal shape with four control surfaces, fins, 

symmetrically positioned at the rear of the envelope. Hydrogen is utilized as the lifting gas for the 

envelope. The two pressure vessels, one for the payload and electronics and the other for the heat source, 

are positioned one atop the other directly below the envelope. The heat exchanger for the engine sits atop 

the heat exchanger pressure vessel. The electric motor and propeller is mounted off of the heat source 

pressure vessel. The electric motor is positioned at the center of mass of the airship. The pressure vessels 

are attached to the envelope with four struts. 

Figure 4.1.—Baseline airship design dimensions.
NASA/CR—2012-217665 28

The main geometry, characteristics and flight specifications for the airship are listed in Table 4.1 and 

the mass and power breakdowns are given in Table 4.2 and Table 4.3, respectively. The airship was sized 

so that the available lift and power were equal to or slightly greater than the required lift and power. No 

additional margin was used in the sizing since power and mass margin was used for sizing of the 

individual components, as discussed in Section 3.0. The lifting force available for this design point is 

3349 N, which corresponds to 375 kg of mass. The total estimated mass of the airship is 374.4 kg, just 

under the available lift. Similarly the total available power generation capability is 582.5 W, 3.2 W above 

the required power of 579.3.

TABLE 4.1.—BASELINE AIRSHIP PHYSICAL CHARACTERISTICS

Item Value

Airship General Specifications

Airship Fineness Ratio (length to max diameter)...................................................... 4

Flight altitude ..................................................................................................... 50 m

Flight Velocity (0.5 m/s faster than the max wind speed)..............................1.39 m/s

Lifting Gas .................................................................... DiAtomic Hydrogen MW=2

Airship Envelope Length................................................................................. 5.57 m

Airship Envelope Maximum Diameter............................................................ 1.39 m

Airship Envelope Volume ..............................................................................5.66 m3

Total Lifting Force (mass)................................................................3349 N (375 kg)

Number of Control Fins............................................................................................ 4

Tail Fin Area (per fin) ..................................................................................0.198 m2

Envelope Material .............................................................Metalized Foil 0.25 kg/m2

Support Strut Material ......................................................Carbon-Carbon Composite

Propulsion System

Propeller Diameter........................................................................................... 0.81 m

Propeller Advance Ratio...................................................................................... 0.18

Thrust Coefficient................................................................................................ 0.01

Power Coefficient.............................................................................................. 0.003

Propeller Tip Mach Number................................................................................ 0.06

Propeller Efficiency............................................................................................. 0.66

Total Driveline Efficiency................................................................................... 0.51

GPHS Block Enclosure and Heat Exchanger

Heat Source Sphere Outside Diameter............................................................. 0.56 m

Heat Source Sphere Inside Diameter............................................................... 0.35 m

Structure:

Inner Wall ................................................................... Stainless Steel 1 mm thick 

Insulation ..............................................................................Aerogel 10 cm thick

Outer Wall.............................................Carbon/Carbon Composite 4.9 mm thick

Heat Exchanger:

Number of Cooling Fins...................................................................................... 8

Housing Diameter ....................................................................................... 10 cm

Fin Length.................................................................................................. 1.5 cm

Fin Thickness.................................................................................................. 2 m

Electronics/Payload Enclosure

Electronics Sphere Outside Diameter.............................................................. 1.33 m

Electronics Sphere Inside Diameter................................................................. 0.90 m

Structure:

Inner Wall ......................................................................... Aluminum 1 mm thick

Inner Insulation ..................................................................Aerogel 10.1 cm thick

Middle Wall .............................................Thermo Pyrolytic Graphite 1 mm thick

Outer Insulation..................................................................Aerogel 10.1 cm thick

Outer Wall.............................................. Carbon/Carbon Composite 1.2 cm thick

Number of wire passthroughs................................................................................. 10

Number of viewports................................................................................................ 1
NASA/CR—2012-217665 29

TABLE 4.2.—BASELINE AIRSHIP MASS BREAKDOWN

Item Mass,

kg

Structure (includes envelope, fins and structural support)............................................................. 98.8

Electric Motor................................................................................................................................. 0.5

Gearbox .......................................................................................................................................... 0.5

Motor Controller............................................................................................................................. 0.1

Motor Power Conditioning.............................................................................................................. 0.2

Propeller.......................................................................................................................................... 0.3

Stirling Engine .............................................................................................................................. 12.5

Coupling ..................................................................................................................................... 0.625

Cooler and Alternator.................................................................................................................. 11.38

Flight Control Computer and Electronics........................................................................................ 3.8

Communications Equipment........................................................................................................... 4.6

Sensors and Data Acquisition ......................................................................................................... 3.5

Payload ............................................................................................................................................25

Electronics Pressure Vessel (Includes pressure vessel inner 

and outer walls, insulation and internal structure)................................................................... 154.5

GPHS Blocks................................................................................................................................ 14.4

GPHS Block Enclosure (includes inner and outer wall and insulation)......................................... 12.6

GPHS Block internal support structure and attachment ................................................................... 12

Cooling Fin ................................................................................................................................... 0.19

Struts............................................................................................................................................... 2.4

Lifting Gas.................................................................................................................................... 16.6

Total Mass .................................................................................................................................. 374.4

The drag of the airship is a factor in determining the required airship propulsion power. The drag 

breakdown for the airship is given in Table 4.3.

TABLE 4.3.—AIRSHIP DRAG BREAKDOWN

Item Drag,

N

GPHS Block Pressure Vessel ............................................................ 1.76

Electronics and Payload Enclosure.................................................. 10.89

Airship Lifting Gas Envelope............................................................ 5.30

Heat Exchanger ................................................................................. 0.72

Airship Tail ....................................................................................... 0.89

Support Struts.................................................................................... 5.20

Total Drag ....................................................................................... 24.76

TABLE 4.4.—BASELINE AIRSHIP POWER

PRODUCTION AND CONSUMPTION 

Variable Value

Power Production Related Variables

Total Thermal Power ........................................................................ 2500 W

Stirling Engine Hot End Temperature................................................1473 K

Stirling Engine Cold End Temperature .............................................787.8 K

Stirling Engine Conversion Efficiency............................................... 23.9 %

Stirling Engine Output Power .......................................................... 582.5 W

Power Consumption Related Variables

Electronics Pressure Vessel Internal Temperature ...............................320 K

Heat Loss Through the GPHS Block Enclosure Insulation ...................62 W

Stirling Cooler Efficiency ...................................................................... 44%

Heat Leak Through the Electronics Enclosure Insulation................. 120.7 W

Heat Leak Through the Passthroughs and View Port ....................... 12.85 W

Total Cooling Power Required............................................................390 W

Propulsion System Power Required .................................................67.57 W

Communications, Control and Payload Power......................................57 W

Total Power Required .................................................................... 579.26 W
NASA/CR—2012-217665 30

Figure 4.2.—Heat flow into and out of the pressure vessels.

The heat flow from the electronics and heat source pressure vessels is illustrated in Figure 4.2. The 

values of the parameters, such as the convective heat transfer coefficient, Reynolds number and Nusselt 

Number, used to determine the heat transfer to and from the pressure vessels and cooling fins is given in 

Table 4.5. 

TABLE 4.5.—CHARACTERISTIC FLOW AND HEAT TRANSFER 

VALUES FOR THE ENCLOSURES AND HEAT EXCHANGER

Value Payload/Electronics 

Enclosure

GPHS Block 

Enclosure

Engine Waste Heat 

Cooling Radiator

Nusselt Number 3610 Exterior

78.5 Interior

1674 Exterior

4.1 Interior 113

Reynolds Number 3.4×106 Exterior 1.4×106 Exterior 5.9×104 Fins

2.5×105 Housing

Prandtl Number 0.71 Exterior

0.75 Interior

0.71 Exterior

0.53 Interior 0.71

Raleigh Number 1.6×109 Interior 1.49×105 Interior N/A

Convective Heat Transfer Coefficient, W/m2K 159.5 Exterior

1.61 Interior

175.2 Exterior

1.19 Interior 284.7

Insulation thickness 10 cm 2 Layers 10.1 cm each N/A

Insulation Thermal Conductivity, W/mK 1.7×10–2 1.7×10–2 N/A

4.2 Variation in the Internal Operating Temperature of the Payload Enclosure

One of the main requirements that drive the airship design is the temperature within the electronics 

and payload enclosure. For the base case this temperature was set at 320 K. To achieve this temperature a 

Stirling cooler is used, driven by the Stirling engine. This temperature difference, between the interior and 

the surrounding, plays a large role in the power required as well as the size of the enclosure. The cooling 

power is dependent on this temperature difference and the subsequent heat leak in from the surroundings. 

The heat leak is directly related to the amount of insulation within the pressure vessel. For a given interior 

diameter, the amount of insulation determines the exterior diameter, which in turn affects its mass and 

drag, the larger the enclosure outside diameter the greater, its mass and drag.
NASA/CR—2012-217665 31

One means of reducing the airship size and power consumption is to increase the temperature within 

the electronics/payload enclosure. To determine what effect changing the internal temperature has on the 

total airship cases were run varying the internal temperature. For the first case the baseline geometry 

(interior diameter and insulation thickness) was maintained and the interior temperature of the enclosure 

was increased from 320 K to the ambient temperature of 737 K. The required cooling power was 

determined over this interior temperature range, as shown in Figure 4.3. This figure shows that the 

cooling power decreases linearly from just above 400 to 91 W at ambient temperature. The 91 W of 

cooling power was still required at ambient temperature because the waste heat from the electronics and 

payload must still be removed from within the enclosure. 

For the next case the effect of internal temperature on the available internal volume was examined. 

Instead of reducing cooling power, increasing the interior temperature could be used as a way of 

providing more interior volume by reducing the insulation thickness while maintaining a constant cooling 

power. Figure 4.4 show the increase in interior diameter and the corresponding interior volume with 

increasing internal temperature. Holding the cooling power constant at the baseline level and reducing the 

insulation thickness achieved this while maintaining the pressure vessel baseline exterior diameter of 

1.33 m. As would be expected the internal volume increases from just under 0.4 m3 at an internal 

temperature of 320 K to 1.1 m3 at the atmospheric temperature of 737 K providing a 275 percent increase 

in volume. 

Figure 4.3.—Required cooling power for increasing interior temperature.
NASA/CR—2012-217665 32

Figure 4.4.—Change in payload enclosure interior diameter and volume with increasing internal temperature.

Another way to evaluate the effect of reducing the required insulation thickness is to maintain a fixed 

interior volume and decrease the outside diameter of the enclosure. Although with this approach there is 

no increase in interior volume there is a decrease in the enclosure mass as well as its drag which both 

factor into the required airship size. This change in exterior diameter as well as the available excess power 

is shown in Figure 4.5. As the interior temperature was increased, the insulation thickness was reduced so 

that the cooling power remained the same. Therefore, as shown in the figure, over most of the interior 

temperature range there is no excess power available. However once the interior temperature gets near 

700 K excess power becomes available because there is no more insulation on the interior of the 

enclosure. Therefore, at this temperature and above the exterior diameter is constant. The wall material 

does provide some thermal resistance and structurally it must remain at its initial thickness due to the 

pressure difference between the interior and exterior of the enclosure, 1 and 90 atm, respectively. So with 

the fixed exterior diameter and an increase in the internal temperature (beyond 700 K), the cooling power 

therefore decreases providing excess power at this internal temperature and above.

Reducing the payload enclosure diameter has an effect on the overall airship sizing by decreasing its 

drag and mass. This affect is shown Figure 4.6 where the airship mass decreases from 373 to 243 kg, a 

reduction of 35 percent, and the length decreases from 5.70 to 4.94 m a reduction of 13 percent for a 

corresponding temperature increase from 320 K to the atmospheric temperature of 737K. 
NASA/CR—2012-217665 33

Figure 4.5.—Change in payload enclosure exterior diameter and available excess power with increasing internal 

temperature.

Figure 4.6.—Change in airship total mass and length with increasing enclosure internal temperature.
NASA/CR—2012-217665 34

The temperature evaluation to this point has involved an enclosure designed as a pressure vessel 

designed to maintain 1 bar of internal pressure. However, if the interior is at atmospheric temperature 

there is no need for internal insulation and therefore no need to maintain the 1 bar internal pressure. 

Therefore, operating the enclosure interior at atmosphere temperature and pressure would have the 

greatest effect on reducing the airship’s size, mass and power requirement as shown in Table 4.6. These 

results show that there is a significant drop in the airship’s mass (52.7 percent), required power 

(60.2 percent) and length (20.1 percent) between the baseline case and operating at atmospheric 

conditions. This difference is also illustrated in Figure 4.7 and Figure 4.8 for the total vehicle and payload 

enclosure respectively.

TABLE 4.6.—COMPARISON BETWEEN THE BASELINE AIRSHIP CHARACTERISTICS 

AND THOSE WITH THE PAYLOAD ENCLOSURE OPERATING AT ATMOSPHERIC CONDITIONS

Variable Base Case Payload Enclosure at 

Atmospheric Temperature and

Pressure

Internal Temperature/Pressure 320 K/1 Bar 737 K/90 Bar

Airship Length 5.57 m 4.45 m

Airship Mass 374.4 kg 177 kg

Number of GPHS Blocks 10 4

GPHS Block Interior Enclosure Diameter 0.35 m 0.245 m

Propulsion Power 67.6 W 45 W

Total Power 579.2 W 230.4 W

Enclosure Outside Diameter 1.33 m 0.904 m

Figure 4.7.—Comparison of the airship size between operating the payload 

enclosure at the baseline or atmospheric conditions
NASA/CR—2012-217665 35

Figure 4.8.—Comparison of the payload and GPHS enclosure geometry 

between the baseline case and atmospheric conditions.

It should be noted that for the case in which the payload enclosure is operating at atmospheric 

conditions the GPHS block enclosure must still be kept at 1 atm for the internal insulation to function. 

The insulation within the heat source enclosure is required to limit the heat loss from the blocks to the 

surroundings. In this case the payload enclosure utilizes a thin walled vessel. Excess heat generated 

internal to the vessel is transferred to the exterior through a conductive path to a small radiator on its 

surface. No active cooling is required. Because there is no cooling requirement the amount of power 

needed for operating the airship is significantly reduced. Therefore the number of GPHS blocks was 

reduced from 10 to 4. 

As shown in these figures increasing the operating temperature of the interior of the payload 

enclosure can provide significant benefits in reducing the airship size and mass, with the greatest 

advantage being when operating at atmospheric conditions. However, being able to construct electronics 

and other equipment that can survive and function at the temperature and pressure on the surface of 

Venus will take a considerable development effort over today’s capabilities. 

4.3 Variation in Flight Altitude

The last evaluation examined the operation of the airship at different altitudes. The airship was sized 

for flight at altitudes above the baseline case. The airship length was varied from the baseline length in 

order to provide sufficient lift at the higher altitudes. By changing altitude the environmental conditions, 

such as the ambient temperature, atmospheric density and wind velocity, changed. The required airship 

length and corresponding total mass is shown in Figure 4.9 for an altitude range of 50 m (the baseline 

flight altitude) up to 5.5 km. All aspects of the airship, except the length, remained at the baseline design 

values. 

Figure 4.9 shows that there is a fairly linear increase in airship length and mass with increasing flight 

altitude. This result would be expected since as the altitude increases the atmospheric density decreases 

fairly linearly at the lower altitudes, as shown in Figure 2.3. Therefore the lifting force decreases 

requiring increased lifting gas volume. 

Because the baseline airship configuration was used over the altitude range instead of optimizing the 

configuration, excess power was available over most of the altitude range. The airship’s required power 

and corresponding excess power is shown in Figure 4.10. The reduction in required power, as seen in this 

figure, as the altitude increased from the baseline altitude was due to the lower drag on the airship as well 

as the reduction in required cooling power due to the decrease in atmospheric temperature. The minimum 

required power, of around 420 W, occurs from approximately 2 to 4 km in altitude. 
NASA/CR—2012-217665 36

Figure 4.9.—Baseline airship length and mass over a range of flight altitudes.

Figure 4.10.—Baseline airship required and excess power over a range of flight altitudes.
NASA/CR—2012-217665 37

This flight altitude range is optimal for minimizing the airship power requirements. Above this range, 

as can be seen on Figure 4.10, the required power begins to increase sharply to a flight altitude of 5.5 km. 

Beyond 5.5 km altitude there were no solutions for the baseline airship configuration. The 6.36 m long 

airship capable of flight at 5.5 km would also be capable of flight down to the baseline airship altitude of 

50 m. To achieve this its velocity beyond the wind speed would need to be reduced slightly to 0.49 m/s 

faster than the winds as it gets closer to the surface. 

This altitude analysis shows that an airship 12.4 percent longer (6.36 m versus the baseline airship 

length of 5.57 m) and 4 percent heaver (387 kg versus the baseline mass of 374.4 kg) can provide a large 

increase in operational altitude range. Also these results indicate a means of providing additional power to 

other systems during mission operations. For example if additional power is needed for short periods of 

time for communications or data processing then, based on these results, the airship could move to an 

altitude that requires less propulsion and cooling power freeing up power for these other systems.

Another approach, based on these results, would be to design and operate the airship within the 

minimum power altitude range (2 to 4 km). With the baseline case configuration, an airship designed to 

operate within this altitude range would require eight GPHS blocks instead of 10.

5.0 Evaluation of Alternate Buoyancy Methods

The analysis, described in Section 3.0, utilizes a lifting gas, at atmospheric conditions, as the means 

of producing lift for the airship. There are however, other options that can be considered as a means of 

producing or enhancing lift. These options include:

• A low pressure or vacuum enclosure (similar to a submarine)

• Heated atmospheric gas

• Heated lifting gas

The first of these options would produce lift because the gas density within the lifting gas chamber or 

envelope would be at a lower density than the atmosphere. The difference in density between the gas 

within the envelope and the atmosphere would produce lift (Lpe), as given by Equation (5.1). 

g R T

P

L V

a a

i a a 













 = ρ − (5.1)

To minimize the mass of the chamber used to hold the lower pressure gas, a spherical chamber is 

needed. This chamber design is similar to that of the payload pressure vessel used in the baseline airship 

design. The wall thickness of the envelope will need to be strong enough to resist the pressure difference 

between the interior and exterior pressure. Equation (3.39) can be used to determine the wall thickness 

needed for the envelope based on this pressure difference. From this wall thickness the mass of the 

envelope can be determined. This mass along with the corresponding lift generation (in kg) for a 1.25 m 

diameter sphere is plotted in Figure 5.1. With the atmospheric pressure at 90 bar, internal pressures (Pi) 

from 60 to 1 bar were examined. From this figure it can be seen that the lift generated is less than the 

mass of the enclosure itself over this range of internal pressures. 

The analysis was also performed with evacuated spheres with diameters between 0.5 and 2.5 m. The 

results from this analysis are shown in Figure 5.2. From this figure it can be seen that the lift (in kg) was 

less than the pressure vessel mass over the range of sphere diameters examined (0.5 to 2.5 m). Based on 

the results shown in these figures it is evident that an evacuated envelope cannot be utilized as the sole 

means of generating lift on Venus. The weight of the pressure vessel needed to withstand the pressure 

difference will be larger than the lift generated by the low-pressure volume within it. 

The next alternate lift generating approach is to utilize the buoyancy generated by heating the 

atmospheric gas to a specified temperature. This buoyancy is due to the difference in density between the
NASA/CR—2012-217665 38

Figure 5.1.—Comparison of mass and lift generation from an evacuated 1.25 m diameter sphere.

Figure 5.2.—Comparison of mass and lift generation from an evacuated sphere over a range 

of pressure vessel diameters.
NASA/CR—2012-217665 39

heated atmospheric gas and the atmosphere. Since the atmosphere is comprised mainly of carbon dioxide 

it was assumed that it would follow the ideal gas equation. Based on this the density of the heated gas 

within the envelope (ρg) is given by Equation (5.2). 

a g

a g R T

P

ρ = (5.2)

The waste heat from the Stirling engine will be utilized to heat the atmospheric gas within the 

envelope. This will cause the engine heat rejection temperature to increase and correspondingly reduce 

the efficiency of the engine. As an initial evaluation the baseline airship size was used and heated 

atmospheric gas was used with the baseline envelope volume to generate lift. The temperature of the gas 

within the envelope was raised from atmospheric to just under the hot end temperature of the engine 

(1473 K). The lift generated over this temperature range is shown in Figure 5.3. From this figure it can be 

seen that the lift generated is not sufficient to meet the required lift for the airship. Also, as the 

temperature difference increases the engine efficiency drops off significantly to a few percent at the 

largest temperature difference between the lifting gas and the environment. 

This analysis indicates that atmospheric heating alone is not sufficient to provide enough lift to meet 

the mission requirements. Beyond this initial analysis a number of additional factors would also have to 

be incorporated to fully evaluate this concept. These include:

• The addition of insulation on the gas envelope and the corresponding heat loss from the lifting 

gas to the environment.

• The effect of the reduction in the engine efficiency on the available power.

• The increase in vehicle drag and propulsion power requirement due to increasing the envelope 

volume. 

Figure 5.3.—Heated atmosphere gas lift, baseline airship required lift and the corresponding Stirling engine 

efficiency.
NASA/CR—2012-217665 40

All of these factors would provide a negative impact on the airship sizing. Further analysis could be 

performed to look at airships with larger envelope sizes or smaller payload capacity, however, based on 

these results and the additional factors that would have to be included to accurately evaluate this method 

for generating lift, it was considered to not be feasible within this environment. 

Augmenting the lifting gas by heating it was the last alternative method considered for generating lift. 

In this case the waste heat from the engine was used to heat the hydrogen lifting gas and decrease its 

density thereby providing additional lift. As with the heated atmosphere case using the waste heat from 

the engine to heat the lifting gas will increase the engine waste heat rejection temperature and will 

therefore decrease the efficiency of the engine. This analysis is based on a 50 K temperature difference 

between the engine rejection temperature and the lifting gas (sink) temperature. This is the same 

temperature difference that was used with the baseline design. The engine efficiency and corresponding 

output power for a system with 10 GPHS blocks as the heat source is shown in Figure 5.4. The engine 

efficiency decreases from 23.9 percent at the baseline case conditions, to 21.9 percent with a 100 K 

difference between the lifting gas temperature and the atmosphere. This decrease is fairly liner. It should 

be noted that the fluctuation in the efficiency curve shown in Figure 5.4 is due to round-off error. The 

corresponding output power drops off proportionally from 583 to 534 W. 

Figure 5.4.—Stirling engine efficiency and output power as a function of the temperature difference between the lifting 

gas (sink temperature) and the atmosphere temperature.
NASA/CR—2012-217665 41

Figure 5.5.—Required airship mass and length as a function of the temperature difference between the lifting 

gas (sink temperature) and the atmosphere temperature.

Although heating the lifting gas generates additional lift, the reduction in engine efficiency and 

subsequent available output power has a significant effect on the baseline airship design. Reducing the 

available power requires additional insulation to be utilized within the payload enclosure to reduce the 

required cooling power to compensate. This increases the overall diameter of the payload enclosure 

increasing its mass and drag. The resultant required airship length and corresponding mass for an increase 

in the lifting gas temperature from atmospheric to 100 K above atmospheric is shown in Figure 5.5. 

From this figure it can be seen that the airship size and mass increased exponentially as the 

temperature of the lifting gas is increased. Therefore there is no benefit gained in the airship sizing by 

utilizing the waste heat from the engine to heat the lifting gas. The effect of the reduction in engine 

efficiency overshadows any benefit in additional lift generated by the heated lifting gas. 

6.0 Summary

The goal of this analysis was to determine if an airship mission near the surface of Venus is feasible 

and if that type of mission could be carried out utilizing no more than 10 GPHS blocks as the heat source. 

Based on the airship analysis and design process outlined in Section 3.0 a baseline airship configuration 

and size was determined that could meet the mission goals and operate near the Venus surface. This initial 

analysis indicates that an airship utilizing Hydrogen as the lifting gas is feasible near the surface of 

Venus. For the baseline design there was sufficient power generated from the 10 GPHS blocks to provide 

cooling and operate the electronics and propulsion system for the airship. 

Off design analysis also provided some insight into some benefits that can be gained by altering the 

vehicle design and operation. Increasing the interior operating temperature of the electronics/payload 

enclosure has direct benefits on reducing the airship’s size and the overall power requirements. One of the 

more significant determinations came from evaluating the flight altitude for the airship. From this off-design 

analysis it was determined that the total required power for the airship is minimized by flying at an altitude 
NASA/CR—2012-217665 42

range of between 2 and 4 km and that an airship sized to fly at 5.5 km altitude would be capable of operating 

over the complete altitude range from near the surface to its design altitude of 5.5 km. This would provide a 

significant increase in capability over the smaller airship designed specifically for flight near the surface. 

The flight altitude limit for this airship configuration utilizing 10 GPHS blocks as the main heat source was 

5.5 km. For an airship sized to operate above this altitude there was not sufficient power available. 

The last evaluation performed examined an alternate means of producing lift for the airship. Of the 

two alternate methods examined, using a low pressure or evacuated chamber (similar to how a submarine 

works) and utilizing heated atmospheric gas (similar to a hot-air balloon) neither was capable of 

providing sufficient lift to raise the airship above the surface. An augmentation of the lifting gas by 

heating it with waste heat from the engine was also considered. Surprisingly this approach also provided 

no benefit and in fact increased the airship size over that of the baseline design. The reason this approach 

failed was that by using the waste heat of the engine to heat the lifting gas the rejection temperature for 

the engine increased thereby reducing its efficiency. Since engine output power is so critical to the design 

the reduction in power caused additional insulation to be utilized to maintain the desired internal 

temperature of the electronics/payload enclosure. This in turn increased its size and mass. Because of this 

the benefits of increased lift due to the heated lifting gas were overshadowed by the effect of reduced 

output power from the engine. Thereby providing a net negative benefit. 

Since this analysis was setup to determine the initial feasibility of the concept there are a number of 

areas of the design that warrant further more detailed analysis. These would include the following:

• A detailed analysis of the fluid flow over the pressure vessels and airship envelope. The heat 

transfer from the insulated pressure vessels is a critical factor in the airship sizing. Any change in 

this value can have a significant effect on the airship design. The total power required is also 

affected by the total vehicle drag. Therefore, this analysis would provide a more accurate 

determination of the heat transfer from the spheres as well as the drag of the airship itself. 

• An optimization of the propeller design for operation within the Venus environment. The 

propeller was a generic design that was not optimized for the Venus environment. Increasing the 

propeller efficiency could reduce the propulsion system power requirement. 

• The operation of the propulsion system drive train (electric motor, gearbox, propeller) within the 

Venus environment should be evaluated. Because of the harsh environment that they will be 

exposed to, the physical and material operation of these components could be examined to 

determine what effect this would have on their performance and operational lifetime. 

• A detailed analysis of the internal convection and corresponding heat transfer within the 

electronics/payload enclosure and the GPHS block enclosure. The heat transfer from the interior 

gas to the wall of these enclosures has a significant effect on the total heat transfer to and from 

the surroundings and therefore overall vehicle sizing. Providing a higher fidelity analysis of this 

heat transfer will correspondingly provide a more accurate determination of the airship sizing. 

This analysis will also provide a means of evaluating methods for reducing these convective heat 

transfer coefficients such as putting natural convection barriers along the internal walls. 

• The evaluation of a dual stage Stirling cooler. The baseline airship design utilized a single stage 

Stirling cooler to maintain the internal temperature of the electronics/payload enclosure. A dual 

stage cooler could also be utilized which could provide increased operational efficiency for the 

cooler. This increased efficiency would be traded off against removing heat from the first stage 

over a larger surface area than the single stage cooler. 

• A detailed mechanical design for the airship envelope, gas handling and flight control. If it is 

desired to have the airship change altitude during flight, a ballast system will have to be 

incorporated so that the airship can change its buoyancy during operation. This ballast system 

will require mechanical pumps that would have to operate within the Venus environment. Overall 

a control scheme for the airship could be developed that would include changing altitude as well 

as direction. Either utilizing the control fins or directing the propeller thrust or both could perform 

directional changes. 
NASA/CR—2012-217665 43

Appendix—List of Symbols

D Airship Drag

De Gas Envelope Drag

Dh Heat Source Pressure Vessel Drag

Dhe Heat Exchanger Drag

Dp Payload Pressure Vessel Drag

Ds Support Strut Drag

Dt Tail Section Drag

Dtot Total Airship Drag

FS Material Yield Factor of Safety

J Propeller Advance Ratio

L Airship Lift

M Mach Number

MWa Atmosphere Molecular Weight

MWg Lifting Gas Molecular Weight

Nudi Pressure Vessel Internal Gas Nusselt Number

Nudo Pressure Vessel External Gas Nusselt Number

Nuf Heat Exchanger Nusselt Number

P Drive Train System Power 

Pa Venus Atmospheric Pressure

Pc Cooling Power 

Pce Communications Equipment Power 

Pe Stirling Engine Output Power

Pfc Flight Control Computer Power 

Pfs Flight Sensor Power

Pi Pressure Vessel Internal Pressure

Ppl Payload Power

Pr Prandtl Number

Pr Total Required Power

Pri Payload Pressure Vessel Internal Prandtl Number

Qe Stirling Engine Heat Input

Qf Heat Exchanger Fin Heat Transfer

Qh Heat Exchanger Housing Heat Transfer

Qhs Heat Source Pressure Vessel Heat Leak Out

Qp Payload Pressure Vessel Heat Leak In

Qpw Passthrough Wire Heat Leak

Qvp View Port Heat Leak

Qw Stirling Engine Waste Heat

R Universal Gas Constant

Ra Atmospheric Gas Constant

Rai Pressure Vessel Internal Gas Rayleigh Number

Rci Internal Convection Thermal Resistance

Rco External Convection Thermal Resistance
NASA/CR—2012-217665 44

Redo Exterior Pressure Vessel Reynolds Number

Ref Heat Exchanger Reynolds Number

Res Support Strut Reynolds Number

Rf Ratio of Fin Area to Envelope Volume

Rii Inner Insulation Thermal Resistance

Rio Outer Insulation Thermal Resistance

Rt Thermal Resistance Term

Rwi Inner Wall Thermal Resistance

Rwm Middle Wall Thermal Resistance

Rwo Outer Wall Thermal Resistance

Sa Airship Envelope Surface Area

Sf Tail Fin Structure Factor

Ta Venus Atmospheric Temperature

Tg Lifting Gas Temperature

Th Stirling Engine Hot End Temperature

Ti Pressure Vessel Internal Temperature

Tif Pressure Vessel Internal Wall Film Temperature

Tr Stirling Engine Heat Rejection Temperature

U Airship Velocity

Vprop Propeller Blade Volume

Wtot Airship Total Weight

Va Airship Envelope Volume

a Speed of Sound in the Atmosphere

c1c Cylinder Drag Coefficient Constant 1

c1s Sphere Drag Coefficient Constant 1

c2c Cylinder Drag Coefficient Constant 2

c2s Sphere Drag Coefficient Constant 2

cde Airship Gas Envelope Drag Coefficient

cdhe Heat Exchanger Drag Coefficient

cdpv Pressure Vessel Drag Coefficient

cds Support Strut Drag Coefficient

coc Cylinder Drag Coefficient Constant 0

cos Sphere Drag Coefficient Constant 0

cp Propeller Power Coefficient

cpa Atmosphere Specific Heat

cpi Pressure Vessel Internal Gas Specific Heat

ct Propeller Thrust Coefficient

d Airship Envelope Maximum Diameter

de Heat Rejection Housing Diameter

df Heat Rejection Outer Fin Diameter

dh Heat Exchanger Hydraulic Diameter

dprop Propeller Diameter

dpv Pressure Vessel Diameter

ds Support Strut Diameter
NASA/CR—2012-217665 45

dvp View Port Diameter

dw Pass Through Wire Diameter

f Airship Envelope fineness ratio

ff Cooling Fin Friction Factor

g Venus Gravitational Acceleration

hf Waste Heat Exchanger Convective Coefficient

hi Pressure Vessel Internal Convection Coefficient

ho Pressure Vessel External Convection coefficient

ka Atmosphere Thermal Conductivity 

khi Heat Source Pressure Vessel Insulation Conductivity

khwi Heat Source Pressure Vessel Inner Wall Conductivity

khwo Heat Source Pressure Vessel Outer Wall Conductivity

ki Pressure Vessel Internal Gas Thermal Conductivity 

kii Inner Insulation Thermal Conductivity

kio Outer Insulation Thermal Conductivity

km Material Layer Thermal Conductivity

kvp View Port Material Thermal Conductivity

kw Pass Through Wire Thermal Conductivity

kwi Inner Wall Thermal Conductivity

kwm Middle Wall Thermal Conductivity

kwo Outer Wall Thermal Conductivity

l Airship Envelope Length

le Heat Rejection Housing Length

ls Support Strut Length

mca Stirling Engine Cooler and Alternator Mass

mce Communication Equipment Mass

mdt Drive Train Total Mass

mem Electric Motor Mass

mf Heat Exchanger Cooling Fin Mass

mfc Flight Control Computer Mass

mfi Fixed Item Mass

mfs Flight Control Computer Mass

mg Gearbox Mass

mhi Heat Source Pressure Vessel Insulation Mass

mhv Heat Source Pressure Vessel Mass

mhwi Heat Source Pressure Vessel Inner Wall Mass

mhwo Heat Source Pressure Vessel Outer Wall Mass

mii Payload Pressure Vessel Inner Insulation Mass

mio Payload Pressure Vessel Outer Insulation Mass

mlg Lifting Gas Mass

mmc Motor Controller Mass

mp Payload Pressure Vessel Mass

mpc Power Conditioning Mass

mpi Payload Pressure Vessel Inner Wall Mass
NASA/CR—2012-217665 46

mpl Payload Mass

mpm Payload Pressure Vessel Middle Wall Mass

mpo Payload Pressure Vessel Outer Wall Mass

mprop Propeller Mass

mps Power System Mass

mr Total Radioisotope Bock Mass

ms Airship Structure Mass

mse Stirling Engine Mass

msepc Stirling Engine Pneumatic Coupling Mass

mss Support Strut Mass

mtot Total Airship Mass

nb Number of Propeller Blades

ncf Number of Heat Rejection Cooling Fins

nf Number of Tail Fins

nr Number of Radioisotope Blocks

ns Number of Support Struts

nvp Number of View Ports

nw Number of Pass-through Wires

rhi Heat Source Pressure Vessel Inner Radius

rho Heat Source Pressure Vessel Outer Radius

ri Material Layer Internal Radius

ro Material Layer Outer Radius

rpi Payload Pressure Vessel Inner Radius

rpo Payload Pressure Vessel Outer Radius

tf Heat Rejection Fin Thickness

thi Heat Source Pressure Vessel Insulation Thickness

thwi Heat Source Pressure Vessel Inner Wall Thickness

thwo Heat Source Pressure Vessel Outer Wall Thickness

tii Payload Pressure Vessel Inner Insulation Thickness 

tio Payload Pressure Vessel Outer Insulation Thickness

tpi Payload Pressure Vessel Inner Wall Thickness

tpm Payload Pressure Vessel Middle Wall Thickness

tpo Payload Pressure Vessel Outer Wall Thickness

va Venus Atmospheric Wind Velocity

vb Propeller Blade Internal Void Fraction

z Altitude above the Surface

αi Pressure Vessel Internal Gas Thermal Diffusivity

∆Twi Difference Between the Pressure Vessel Wall and Interior Temperature

ηc Cooler Efficiency

ηe Stirling Engine Operating Efficiency

ηem Electric Motor Efficiency

ηg Gearbox Efficiency

ηmc Motor Controller Efficiency
NASA/CR—2012-217665 47

ηp Propulsion System Efficiency

ηprop Propeller Efficiency

μa Venus Atmospheric Dynamic Viscosity

μi Pressure Vessel Internal Gas Dynamic Viscosity

νi Pressure Vessel Internal Gas Kinematic Viscosity

ρa Venus Atmospheric Density

ρe Envelope Material Aerial Density

ρf Cooling Fin Material Density

ρg Lifting Gas Density

ρi Pressure Vessel Insulation Density

ρhwo Heat Source Pressure Vessel Outer Wall Material Density

ρhwi Heat Source Pressure Vessel Inner Wall Material Density

ρprop Propeller Material Density

ρpi Payload Pressure Vessel Inner Wall Material Density

ρpm Payload Pressure Vessel Middle Wall Material Density

ρpo Payload Pressure Vessel Outer Wall Material Density

ρs Support Strut Material Density

σypo Pressure Vessel Outer Wall Yield Strength
NASA/CR—2012-217665 48

References

1. Loders, K., and Fegley, G. Jr., “Venus,” The Planetary Scientist’s Handbook, pp. 109-124, Oxford 

University Press 1998.

2. Mitchell, D.P., Venera 13 Perspective Image Mosaics, 

http://mentallandscape.com/C_CatalogVenus.htm, June 2011. 

3. Colozza, A., “Airships for Planetary Exploration,” NASA/CR—2004-213345, November 2004.

4. Saunders, R. S., “Venus,” in The New Solar System, 4th Edition, (Beatty, J.K., Petersen, C.C., and 

Chaikin, A., eds.), Cambridge University Press, 2000.

5. Ekonomov, A., Golovin, Yu., Moroz, V., and Moshkin, B., “19: Solar Scattered Radiation 

Measurements by Venus Probes,” Venus, University of Arizona Press 1983. 

6. Jenkins, J.M., Steffes, P.G., Hinson, D.P., Twicken, J.D., and Tyler, G.L., in “Radio Occultation 

Studies of the Venus Atmosphere with the Magellan Spacecraft,” Icarus, Vol. 110, pp. 79-94, 1994.

7. Colozza, A.J., “Solar Powered Flight on Venus,” NASA/CR—2004-213052, April 2004. 

8. Colozza, A.J., “High Altitude Propeller Design and Analysis Overview,” NASA/CR—1998-208520, 

October 1998.

9. Colozza, A.J., “Initial Feasibility Assessment of a High Altitude Long Endurance Airship,” 

NASA/CR—2003-212724, December 2003. 

10. Colozza, A.J., “Comparison of Mars Aircraft Propulsion Systems,” NASA CR-2003-212350, May 

2003.

11. Incropera, F.P., and DeWitt, D.P., Fundamentals of Heat and Mass Transfer, Third Edition, John 

Wiley & Sons Publisher, 1990.

12. White, F. M., Fluid Mechanics, McGraw-Hill Publisher, 1979.

13. Khoury, G.A. and Gillett, J.D., editors, Airship Technology, Cambridge Aerospace Series 10, 

Cambridge University Press, 1999.

14. Achenbach, E., “Experiments of the Flow Past Spheres at Very High Reynolds Numbers,” Journal of 

Fluid Mechanics, Vol. 54, part 3, pp. 565-575, 1972.

15. Wang,Y.Q., Jackson, P.L., and Ackerman, J.D., “Numerical Investigation of Flow over a Sphere 

using LES and the Spalart-Allmaras Turbulence Model,” Journal of Computational Fluid Dynamics, 

Vol. 15, No. 1, pp. 198-205, April 2006.

16. Achenbach, E., “Total and Local Heat Transfer from a Smooth Circular Cylinder in Cross-Flow at 

High Reynolds Number,” Journal of Heat and Mass Transfer, Vol. 18, pp. 1387-1396, 1975.

17. Churchill, S.W., and Bernstein, M., “A Correlation Equation for Forced Convection from Gases and 

Liquids to a Circular Cylinder in Cross Flow,” Journal of Heat and Mass Transfer, ASME 94, 

pp. 300-306, 1977.

18. “Space and Defense Power Systems,” U.S. Department of Energy, www.ne.doe.gov, October 2011. 

19. Dyson, R.W., “Advanced Stirling Duplex: Technology Advancement Project Review,” March 2011.

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Radioisotope Stirling Engine Powered Airship for Low Altitude Operation on Venus 

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14. ABSTRACT

The feasibility of a Stirling engine powered airship for the near surface exploration of Venus was evaluated. The heat source for the Stirling 

engine was limited to 10 general purpose heat source (GPHS) blocks. The baseline airship utilized hydrogen as the lifting gas and the 

electronics and payload were enclosed in a cooled insulated pressure vessel to maintain the internal temperature at 320 K and 1 Bar 

pressure. The propulsion system consisted of an electric motor driving a propeller. An analysis was set up to size the airship that could 

operate near the Venus surface based on the available thermal power. The atmospheric conditions on Venus were modeled and used in the 

analysis. The analysis was an iterative process between sizing the airship to carry a specified payload and the power required to operate the 

electronics, payload and cooling system as well as provide power to the propulsion system to overcome the drag on the airship. A baseline 

configuration was determined that could meet the power requirements and operate near the Venus surface. From this baseline design 

additional trades were made to see how other factors affected the design such as the internal temperature of the payload chamber and the 

flight altitude. In addition other lifting methods were evaluated such as an evacuated chamber, heated atmospheric gas and augmented 

heated lifting gas. However none of these methods proved viable. 

15. SUBJECT TERMS

Airships; Radioisotope heat sources; Stirling engines; Venus probes; Planetary aerial vehicles 

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