Anthony J. Colozza

Vantage Partners, LLC, Brook Park, Ohio 

Robert L. Cataldo

Glenn Research Center, Cleveland, Ohio

Radioisotope Stirling Engine Powered Airship for

Atmospheric and Surface Exploration of Titan

NASA/TM—2014-218321

July 2014
	
	
	








	



	

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Anthony J. Colozza

Vantage Partners, LLC, Brook Park, Ohio 

Robert L. Cataldo

Glenn Research Center, Cleveland, Ohio

Radioisotope Stirling Engine Powered Airship for

Atmospheric and Surface Exploration of Titan

NASA/TM—2014-218321

July 2014


	



	


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NASA/TM—2014-218321 iii 

Contents 

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

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

2.0 Environment on Titan ........................................................................................................................... 3

3.0 Airship Configuration and Sizing ......................................................................................................... 6

3.1 Airship Mass ................................................................................................................................. 8

3.1.1 Structure Mass ................................................................................................................... 8

3.1.2 Propulsion System Mass ................................................................................................... 8

3.1.3 Power System Mass .......................................................................................................... 9

3.1.4 Payload Enclosure Mass.................................................................................................. 10

3.1.5 Lifting Gas Mass ............................................................................................................. 13

3.1.6 Total Mass ....................................................................................................................... 14

3.2 Lift Generation ........................................................................................................................... 14

3.3 Power Required .......................................................................................................................... 15

3.3.1 Propulsion Power ............................................................................................................ 15

3.3.2 Heating Power ................................................................................................................. 16

3.4 Power Production ....................................................................................................................... 20

4.0 Analysis Results .................................................................................................................................. 22

4.1 Baseline Airship Design ............................................................................................................. 22

4.2 Variation from the Baseline Design ........................................................................................... 26

4.2.1 Variation of Electronics Section Operating Temperature ............................................... 26

4.2.2 Variation in Flight Altitude ............................................................................................. 28

4.2.3 Variation in Payload Mass and Volume .......................................................................... 29

5.0 Summary ............................................................................................................................................. 31

Appendix—Symbols List ............................................................................................................................ 33

References ................................................................................................................................................... 37

NASA/TM—2014-218321 1 

Radioisotope Stirling Engine Powered Airship for 

Atmospheric and Surface Exploration of Titan 

Anthony J. Colozza 

Vantage Partners, LLC 

Brook Park, Ohio 44142 

Robert L. Cataldo 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Abstract 

The feasibility of an advanced Stirling radioisotope generator (ASRG) powered airship for the near 

surface exploration of Titan was evaluated. The analysis did not consider the complete mission only the 

operation of the airship within the atmosphere of Titan. The baseline airship utilized two ASRG systems 

with a total of four general-purpose heat source (GPHS) blocks. Hydrogen gas was used to provide lift. 

The ASRG systems, airship electronics and controls and the science payload were contained in a payload 

enclosure. This enclosure was separated into two sections, one for the ASRG systems and the other for 

the electronics and payload. Each section operated at atmospheric pressure but at different temperatures. 

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 surface of Titan based on the available power from the ASRGs. The 

atmospheric conditions on Titan 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 Titan surface. From this baseline design additional trades were made to see how 

other factors affected the design such as the flight altitude and payload mass and volume. 

1.0 Introduction 

Titan, shown in Figure 1, is the largest moon of Saturn. It is approximately 50 percent larger than 

Earth’s moon and is the only known moon in the solar system to have a significant atmosphere. Its 

atmospheric pressure near the surface is approximately 1.45 times that of Earth’s and the surface 

temperature is around 94 K (–180 °C). The atmosphere is comprised mainly of nitrogen and is completely 

covered with clouds and haze. Wind speeds near the surface based on the Huygens probe are low less 

than 1 m/s. Other than accommodating the low atmospheric temperature, operation on Titan is ideal for an 

airship. The dense atmosphere can provide significant lift and the low wind speed near the surface 

minimizes the required propulsion power for controlled flight. The nitrogen atmosphere is non-corrosive 

and would be compatible with most materials. 

To date the exploration of Titan has consisted mainly of images and data taken from flyby probes 

such as the Voyager series and the Cassini Saturn orbiter. The Huygens probe was the only vehicle to 

enter the atmosphere and provide data from beneath the cloud cover, as shown in Figure 1. The data and 

images from the Huygens probe showed a dynamic surface environment with interesting geologic 

features not that dissimilar to Earth. The Huygens probe however supplied data only for a few hours and 

most of this was during the descent phase of its mission. 

To perform a more detailed evaluation of Titan a long duration vehicle is needed, one that can move 

around on or near the surface in a controlled manner and over the unpredictable surface terrain of Titan 

that includes steep inclines, liquid methane lakes, mountain ranges and rocks. An airship is the ideal 

platform to accomplish this type of mission. 
NASA/TM—2014-218321 2 

 

Figure 1.—True color image of Titan from Cassini (Ref. 1) and surface image from the 

Huygens Probe (Ref. 1). 

Wheeled rovers have previously been the only type of mobile vehicles used for planetary exploration 

and these have only been utilized on the Moon (Russian Lunokhod series, U.S. Apollo Rover) and Mars 

(Pathfinder: Sojourner, MER: Spirit and Opportunity, MSL: Curiosity) On Mars photovoltaic arrays were 

utilized as the main power source for all of the rovers except Curiosity which utilized a multi-mission 

radioisotope thermoelectric generator (MMRTG). However on Titan, due to its distance from the Sun and 

the thick cloud and haze cover encompassing the moon, utilizing solar power is not feasible. Therefore a 

different power source is required, one similar to the MMRTG that can convert the 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 Titan 

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

that of a typical 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 based ASRG provides the highest efficiency and therefore the greatest benefit to the airship. 

The thick, dense atmosphere of Titan provides both benefits and obstacles in the design of a surface 

or near surface vehicle. One advantage is that the high surface density enables the possibility of utilizing a 

low speed flight vehicle such as an airship, whereas on Mars this option is not feasible (Ref. 2). For Titan 

an airship provides a number of benefits to scientific exploration. The main advantages include: 

The ability to cover large amounts of surface terrain. 

The capability to descend to the surface and perform scientific investigation at various locations. 
NASA/TM—2014-218321 3 

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 higher pressure 

and cold temperature may pose problems for operating equipment and electronics. Therefore the 

electronics and payload must be contained in a heated payload enclosure in order to survive for an 

extended period of time near the surface. The need for heating adds significantly to the power 

requirements of the vehicle, increasing its mass and size. 

Overall an airship could provide a unique capability for exploring the surface of Titan. 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 should be 

thoroughly examined as an option for Titan exploration. The analysis and results discussed in this report are 

a first step in evaluating the feasibility and capabilities of an ASRG powered Titan airship concept. 

2.0 Environment on Titan 

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

moon. In ways it is very Earth like. It has a mostly nitrogen atmosphere, clouds, lakes, rivers and rain. 

However, with a surface temperature of under 100 K the free liquid is not water but methane. The low 

atmospheric temperature also lowers the speed of sound through the atmosphere. Near the surface the 

speed of sound is approximately half that on Earth. Due to the distance from the Sun, cloud cover and 

haze, little sunlight reaches the surface. The atmospheric density at the surface is 5 times that of Earth and 

the pressure is 1.5 times greater than that at Earth’s surface. A diagram of the atmosphere is shown in 

Figure 2 and select properties of Titan are given in Table 1. 

Figure 2.—Illustration of Titan Atmosphere (Refs. 3 and 4). 
NASA/TM—2014-218321 4 

TABLE 1.—PHYSICAL AND ORBITAL PROPERTIES OF TITAN (REFS. 4, 5, AND 6) 

Property Value 

Maximum inclination of equator to orbit to Saturn (max) ..................................................... 0.35° 

Orbital eccentricity () ....................................................................................................... 0.0288 

Mean radius of orbit (rm) around Saturn .................................................................... 1.22106 km 

Day period (synchronous to the orbital period around Saturn) ......................... 15.95 (Earth days) 

Surface pressure ............................................................................................................ 146.7 kPa 

Albedo .................................................................................................................................... 0.22 

Gravitational constant (gv) .............................................................................................. 1.35 m/s2

Orbital period around Saturn ............................................................................ 15.95 (Earth days) 

Surface temperature ........................................................................................................... 93.7 K 

Diameter .......................................................................................................................... 5152 km 

Solar flux outside Titan’s atmosphere ........................................................................ 14.87 W/m2

Speed of sound at the surface ......................................................................................... 196.5 m/s 

Atmosphere gas constant (Ra) ................................................................................... 296.8 J/kg-K 

Atmosphere ratio of specific heats (a) ..................................................................................... 1.4 

Atmosphere specific heat (cpa) ................................................................................... 1039 J/kg-K 

TABLE 2.—TITAN ATMOSPHERIC COMPOSITION (REF. 7)

Gas Percent Volume 

Nitrogen (N2) ................................................................. 94.2% 

Methane (CH4).................................................................. 5.6% 

Hydrogen (H2) .................................................................. 0.1% 

Argon (Ar) .................................................................... 34 ppm 

Because of the thick atmosphere, the pressure and density at the surface is greater than that on Earth. 

The atmospheric pressure on Titan at approximately 8 km altitude is similar to the atmospheric pressure at 

Earth’s surface. 

The solar intensity outside the atmosphere is only approximately 15 W/m2

. The low solar intensity 

coupled with the haze and clouds within the atmosphere make the surface light very dim. This can be a 

concern for imaging cameras especially on a moving platform where exposure time will be limited. 

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

rotation (Ref. 5). At altitudes that can be considered for airship operation, below 20 km, the wind speed 

decreases from approximately 5 m/s to near 0 at the surface. 

The gravitational acceleration on Titan (1.35 m/s2

) is less than that of Earth’s moon. The atmospheric 

composition on Titan is mostly nitrogen with a small amount of methane (Ref. 6). The atmospheric 

composition is given in Table 2. Although, like Earth, the atmosphere is composed mostly of nitrogen, the 

speed of sound within the atmosphere is about half that on Earth. This is mainly due to the low 

temperature of the atmosphere compared to Earth’s. 

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

determining the feasibility of airship flight on Titan. These parameters, shown in Figure 3 for an altitude 

up to 20 km, are provided as functions of altitude (Z) in kilometers by Equations (2.1) to (2.3).

The atmospheric temperature on Titan (Ta in K) decreases fairly linearly from the surface up to 

approximately 60 km in altitude, as seen in Figure 3. The temperature as a function of altitude in 

kilometers is approximated by Equation (2.1). 

2 3 6 4 Ta 93.005 1.2204Z 0.024754Z 0.0003082Z 2.5861 10 Z  	      (2.1) 
NASA/TM—2014-218321 5 

Figure 3.—Temperature, Density and Wind Velocity on Titan (Refs. 4, 5, and 8). 

The atmospheric density (
a in kg/m3

) on near the surface on Titan is much greater than that on Earth. 

It is given by Equation (2.2) as a function of altitude in kilometers. 

2 5 3 7 4 a 5.4444 0.20758Z 0.0018503Z 2.3217 10 Z 3.5849 10 Z   
 	       (2.2) 

The average wind speed (va in m/s) below 20 km is given by Equation (2.3) as a function of altitude 

in kilometers. 

2 va 	 0.0023761 0.12585Z  0.0061063Z (2.3) 

The atmospheric viscosity and thermal conductivity are two additional properties that are critical in 

evaluating the airship operation. Since the atmosphere is composed mainly of nitrogen, the viscosity and 

thermal conductivity of nitrogen was used (Ref. 9). The atmospheric viscosity (a in kg/m-s) as a function 

of the atmosphere temperature and density is given by Equations (2.4) to (2.10) (Ref. 7). 

6

2 3 4 5 6

1

10 1057 


















 	 C C C C C

C

. Ta a (2.4) 





















 



 




 



  



 



 




 



  



 



 




 



 




 



 

	

2 3 4

98 94

0 00331 ln

98 94

0 005341 ln

98 94

0 0846 ln

98 94

0 431 0 4623ln

1

.

T . .T . .T . .T . . a a a a

C e (2.5) 

0.1

2

4

2 17728 10 a

a

T

C . 
 	   (2.6) 
NASA/TM—2014-218321 6 

31319

0 25

10

26

3 1472 10 . . a

a a

e

T

C .


   
 	  (2.7) 

313 19

3.2

12

27

4 7.1726 10 .

a

a a

e

T

C


   
 	  (2.8) 

2

31319

0.09

2

27

5 0 00587






 



 
   
 	  .

a

a a

e

T

C . (2.9) 

3

31319

0.3 6 0 062971






 



 
 
 

	 .

a

a a

e

T

C . (2.10) 

The atmospheric thermal conductivity (ka in W/mK) as a function of the atmosphere temperature and 

density is given by Equations (2.11) to (2.16) (Ref. 9). 

3

7 8 9 10 11

0 07

1

0 0168 2 375 10

1597 


















	  . T  . T  C  C  C  C  C

C

. T k . a a

a

a (2.11) 

0.3

2

4

7 0 028 3 6671 10 a

a a T

C . . 
 	 
    (2.12) 

31319

0.2

3

6

8 6 264 10 .

a

a a

e

T

C .




 
 	   (2.13) 

2

31319

0.8

4

9

9 99 833 10






 



 


 
 	  .

a

a a

e

T

C . (2.14) 

2

31319

0.6

8

19

10 1.3969 10






 



 


 
 	  .

a

a a

e

T

C (2.15) 

2

313 19

1.9

10

22

11 2.888 10






 



 


 
 	  .

a

a a

e

T

C (2.16) 

The last atmospheric property that will be needed to evaluate the airship is the speed of sound within 

the atmosphere (a in m/s). This is given by Equation (2.17). 

a 	  aRaTa (2.17) 

3.0 Airship Configuration and Sizing 

For flight on Titan 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 

an elliptical shaped insulated enclosure. An electric motor and propeller are used for propulsion and a 

radioisotope power Stirling engine is used to provide electrical power to operate the onboard equipment, run 

internal heaters and provide power to the propulsion system. This general layout is shown in Figure 4. 
NASA/TM—2014-218321 7 

Figure 4.—Titan Airship Main Component layout. 

Figure 5.—Logic diagram for airship sizing analysis.

Sizing the airship for flight on Titan 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 

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 5. 
NASA/TM—2014-218321 8 

TABLE 3.—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: (ASRG) Number of ASRG systems, flight speed, altitude Power availability, mass 

Payload and Electronics: Flight control computer, 

communications equipment, payload, sensors Variables, constants Power consumption, mass 

Payload/Electronics Enclosure: Insulation, view 

port, sensor feed through Interior volume and temperature Mass and cooling power 

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, altitude, etc. The 

components and their associated scaling factors are listed in Table 3. 

3.1.1 Structure Mass 

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

and the diameter being the maximum thickness in the center of the airship. The fineness ratio of the 

airship is the ratio of length to diameter. The length and fineness ratio are used as the input variables to 

vary the airship size and geometry. 

The airship structure mass (ms) is based on the aerial density (assumed to be 0.25 kg/m2

) of the 

covering, the number of control fins and ratio of fin area to airship volume along with a fin structure 

factor (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 (Ref. 10) (mtot). This component is added to account for the fixed structure needed to attach 

components to the envelope. 

Details on the calculation of the airship structure mass are given in Reference 11. 

3.1.2 Propulsion System Mass 

The propulsion system mass consists of the mass of the electric motor, motor controller, gearbox, 

propulsion power conditioning electronics and propeller. 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 6. The total efficiency of the propulsion system drive train is composed of 

the motor controller efficiency electric motor efficiency gearbox efficiency power conditioning efficiency 

and propeller efficiency. They are combined to get the driveline 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. Details on the drive train efficiencies 

are given in Reference 11. 

The electric motor mass, motor controller mass, gearbox mass, and mass of the power conditioning 

systemis based on a linear scaling with power output (Pdt) (Refs. 11, 12, and 13). The propeller mass is 

based on the propeller diameter and the number of blades. The diameter is dependent on the amount of 

thrust generated by the propeller. This thrust will be equal to the airship drag (Dtot) 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, and the void fraction within the blade. For a given airfoil 

cross-sectional area and the chord length distribution the volume of the propeller blade can be calculated. 

An initial trade off was performed on the number of propeller blades to utilize. For the environmental 

conditions on Titan a four bladed propeller was chosen. The propeller blades would be constructed of 

carbon composite, with a density of 1380 kg/m3

, and with no void space within the blade. Also a 

10 percent increase in the total propeller blade mass was added to account for the hub and attachment to 
NASA/TM—2014-218321 9 

the drive shaft. The total propulsion system drive train mass (mdt) is the sum of the masses of all the 

components shown in Figure 4. Additional details on the mass calculation for the drive train components 

are given in Reference 11. 

3.1.3 Power System Mass 

The baseline power generation system consists of two advanced Stirling radioisotope generators 

(ASRG). They provide electrical power to the drive motor as well as to the electronics, payload and 

heaters. The ASRG, illustrated in Figure 7, generates electrical power through a Stirling engine operating 

off of two plutonium-238, general purpose heat source (GPHS) blocks. The system shown in Figure 7 is a 

typical arrangement for a space mission. Two of the systems shown in Figure 7 will be used for powering 

the baseline Titan airship. The mass of each ASRG power system (masrg) is estimated at 25 kg (Ref. 14). 

Figure 6.—Propulsion System component layout. 

Figure 7.—ASRG typical arrangement and components (Ref. 15). 
NASA/TM—2014-218321 10 

3.1.4 Payload Enclosure Mass 

The payload enclosure is used to house the ASRG power sources, avionics, electronics and science 

payload. It is composed of an inner and outer wall constructed of carbon composite with aerogel 

insulation between the walls. The enclosure operates at the ambient pressure and with ambient 

atmospheric gas within the chamber. The layout of the payload enclosure is shown in Figure 8. The 

enclosure is separated into two sections, the upper section houses the ASRGs and the lower section 

houses the remaining equipment. This was done due to the different ambient temperature operating 

requirements between the ASRG and the other equipment. 

Because the atmosphere is composed mainly of nitrogen without any corrosive trace gasses it is fairly 

inert and capable of being utilized within the enclosure. This along with operating at atmospheric pressure 

provides a number of benefits to the system design which include: 

The chamber can be vented so that it would not be required to maintain a pressure differential 

through the different phases of the mission (Earth ground operations, launch, spaceflight and 

operation on Titan). 

The structure mass is minimized by eliminating the need for pressurization during the mission. 

Lightweight aerogel can be utilized as the interior insulation. 

Internal convection can be used to evenly distribute the internal heating. 

Enables easier atmospheric sampling and testing. 

Figure 8.—Payload enclosure layout. 
NASA/TM—2014-218321 11 

Figure 9.—Pressure vessel structure and insulation layout. 

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

density. These are illustrated in Figure 9. The outer shell wall (thickness taow and teow) is mainly structural 

and is used to maintain the aerodynamic shape of the enclosure and resist aerodynamic loads. The inner wall 

is the main structural element of the payload enclosure. It is used to support the payload components. 

Between the inner and outer wall is the insulation. Its thickness determines the separation distance between 

the two structural walls. Because of the different temperature requirements the insulation thickness will vary 

between the portion of the enclosure containing the ASRG power systems and the lower section containing 

the electronics and other systems. However the outside dimensions of both sections are the same to provide 

a smooth continuous surface on the exterior of the enclosure in order to reduce aerodynamic drag. 

Therefore, mass of each layer of the enclosure is based on the electronics portion interior dimensions 

(length Le, width We and height he) and the thickness of the wall for each layer. To determine the mass of 

each layer, the perimeter for each layer is calculated at the center of the layer or half its thickness. The 

layer perimeter (pi) is given in general form by Equations (3.1) and (3.2). The layer thickness variables 

used to determine the perimeter for a specific layer and section of the enclosure is given in Table 4. 

    
















    


 



 

 	 

4 64 256

1

2

2 3

i i i

i e e i

c c c d L W

p (3.1) 

2

2

2 2

2 2






 



 










 



   

	

e i e i

e i e i

i

L d W d

L d W d

c (3.2) 
NASA/TM—2014-218321 12 

TABLE 4—MASS VARIABLES FOR THE DIFFERENT LAYERS FOR EACH 

PERIMETER WALL SECTION OF THE PAYLOAD ENCLOSURE 

Location 

Section 

height 

(hi) 

Perimeter 

variable 

(pi) 

Layer 

thickness 

(tpwi) 

Incremental thickness 

(di) 

Layer material 

density 

(
pwi) 

Layer mass 

variable 

(mpwi) 

ASRG 

section 

Inner wall 

ha

paiw taiw teiw + tie + teow – taow – tai 
aiw maiw

Insulation pai tai teiw + tie + teow – taow 
ai mai

Outer paow taow teiw + tie + teow 
aow maow

Electronic/ 

payload 

section 

Inner wall 

he

peiw teiw teiw 
eiw meiw

Insulation pei tei teiw + tei 
ei mei

Outer peow teow teiw + tei + teow 
eow meow

The mass for each layer of the perimeter walls (mpwi) can then be calculated based on the 

corresponding perimeter (pi) value given by Equations (3.1) and (3.2). The mass is also dependent on the 

height of each section (hi) of the enclosure and the density of the material utilized (
pwi). The general mass 

equation for each of the layers is given by Equation (3.3). By inserting the variables listed in Table 4, the 

corresponding mass of each layer of both sections can be determined. 

pwi i i pwi pwi m 	 p h t 
 (3.3) 

The total mass of the outer elliptical walls of the payload enclosure (mpw) is the sum of the individual 

layer masses given in Table 4, as given by Equation (3.4). 

mpw 	 maiw  mai  maow  meiw  mei  meow (3.4) 

The payload enclosure also has an insulated lower and upper end cap and an insulated deck separating 

the ASRG compartment from the electronics and payload compartment. 

These end layers are constructed in the same fashion as the outer elliptical walls. There is an upper 

wall, insulation and lower wall. The mass of the horizontal wall layers (mhwi) is given by Equation (3.5) 

and the variables for each layer of the three walls are given in Table 5. 

4

e e hwi hwi

hwi

W L t

m 
 	  (3.5) 

As with the outer perimeter walls, the total mass of the horizontal walls (mhw) is the sum of the 

individual layers of each wall, as given by Equation (3.6). 

mhw 	 muiw  mui  muow  mmuw  mmi  mmlw  mliw  mli  mlow (3.6) 

The total mass of the payload enclosure (mpe), given by Equation (3.7), is the sum of the masses of the 

perimeter walls and horizontal walls represented by Equations (3.5) and (3.6), respectively. An additional 

10 percent margin is added to the total mass to account for items such as internal structure and 

miscellaneous hardware. 

mpe 	   mpw  mhw 1.1 (3.7) 
NASA/TM—2014-218321 13 

Figure 10.—Insulated structural layers within the payload enclosure.

TABLE 5.—MASS VARIABLES FOR THE DIFFERENT LAYERS FOR

EACH HORIZONTAL WALL SECTION OF THE PAYLOAD ENCLOSURE 

Location Layer thickness 

(thwi) 

Layer material density 

(
hwi) 

Layer mass variable 

(mhwi) 

Upper end 

Inner wall tuiw 
uiw muiw

Insulation tui 
ui mui

Outer tuow 
uow muow

Middle deck 

Upper wall tmuw 
muw mmuw

Insulation tmi 
mi mmi

Lower wall tmlw 
mlw mmlw

Lower end 

Inner wall tliw 
liw mliw

Insulation tli 
li mli

Outer tlow 
low mlow

3.1.5 Lifting Gas Mass 

The airship shape determines the available internal volume for the lifting gas. It 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 (3.8). The length and fineness ratio are used as the input variables to vary the airship 

size and geometry. The corresponding lifting gas volume (Va) is given by Equation (3.9). 

d

l f 	 (3.8) 

f

l Va 34 3  	 (3.9) 
NASA/TM—2014-218321 14 

The lifting gas mass (mlg) also factors into the total airship mass. Its mass is dependent on the lifting 

gas molecular weight (MWg), atmospheric temperature and pressure (Pa) and the airship gas volume (Va), 

as given by Equations (3.10) and (3.11). Where the universal gas constant (R) has a value of 

0.0831 m3

Bar/kMol K and it is assumed the lifting gas is at atmospheric conditions. 

Pa 	 
aRaTa (3.10) 

T R

M V P

m a

Wg a a

1g 	 (3.11) 

3.1.6 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 6. 

The sum of these fixed mass items is given by Equation (3.12). 

mfi 	 mfc  mce  mfs  mpl (3.12) 

From the above equations the total airship mass (mtot), given by Equation (3.13), can be calculated. 

mtot 	 ms  mdt  masrg  mpe  mlg  mfi (3.13) 

3.2 Lift Generation 

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

airship envelope volume 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 (3.14), which is dependent on the gravitational force on Titan 

(g =1.35 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 = 296.8 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. 

g M T

M T

L V

Wa g

Wg a

a a
































 	 
 1 (3.14) 

TABLE 6.—AIRSHIP FIXED COMPONENT MASSES 

Component Mass 

(kg) 

Power 

(W) 

Flight control computer (mfc, Pfc) 3.8 25 

Communications equipment (mce, Pce) 4.6 50 

Flight control sensors (mfs, Pfs) 3.5 25 

Payload (mpl, Ppl) 25.0 50 
NASA/TM—2014-218321 15 

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

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

the airship weight. 

Wtot 	 gmtot (3.15) 

3.3 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 propulsion system power needed to overcome drag due to its size and shape along 

with the power needed to provide heating to the payload enclosure and operate the airship systems and 

payload. As with the total mass, the total required power (Pr) will be a summation of the power required 

by the various systems of the airship given by Equation (3.16). The power consuming items, on the 

airship include the propulsion system (Pdt), payload enclosure heating (Ph) and sensors/payload, 

communications and control. These items are listed in Table 6. 

Pr 	 Pdt  Ph  Pfc  Pce  Pfs  Ppl (3.16) 

3.3.1 Propulsion Power 

The propulsion power required by the airship to fly at a specified velocity (U) is dependent on the 

total airship drag (Dtot) and the propulsion system efficiency (dt) as given by Equation (3.17). 

dt

tot dt

D U P

 	 (3.17) 

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 (3.18) is based on the airship’s velocity, the volume of the lifting gas and its drag 

coefficient (cde). 

3

2

2

2

1 De 	 
aU cdeVa (3.18) 

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

Equation (3.19). This equation represents a curve fit to drag coefficient data for various airship fineness 

ratios (Ref. 10). 

2 3 4 4 5 5 c 0.2318 0.1576 f 0.04744 f 0.007041f 5.135 10 f 1.48 10 f de 	        (3.19) 

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

(3.20) (Ref. 10). 

Dt 167De 	 0. (3.20) 

The next main drag is for the payload enclosure. The payload enclosure is mounted on the bottom of 

the elliptical lifting gas envelope. The enclosure is symmetrical with an elliptical cross-section, as shown 

in Figure 10. 
NASA/TM—2014-218321 16 

The main payload enclosure drag (Dp) is given by Equation (3.21). The drag coefficient (cdp) for the 

payload enclosure is approximated from empirical data (Ref. 16) as a function of Reynolds number (Rep) 

by Equations (3.22) and (3.23). 

     p a dp e eow ei eiw ha he D 	 0.5
 c U W  2 t  t  t  2 (3.21) 

7 13 2 20 Re3 cdp 0.7 6.3 10 Re p 1.97 10 Re p 1.74 10 p    	       (3.22) 

   

a

a e eow ei eiw

p

U L t t t




    	 2 Re (3.23) 

From these components the total drag for the airship can be determined, as given by Equation (3.24). 

Dtot 	 De  Dt  Dp (3.24) 

3.3.2 Heating Power 

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

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

through the payload enclosure to the surroundings. The required heater power is based on the heat loss 

from the following sources. 

Through the insulation and enclosure walls to the atmosphere (Qi) 

Through the insulation to the ASRG portion of the enclosure (Qa) 

Wire and cable pass-through for the sensors through the insulation to the atmosphere (Qpt) 

Through the view port windows to the atmosphere (Qvp) 

The power consumed by the internal electronics and payload is eventually turned into heat therefore it 

is subtracted from the total required heater power. 

Ph 	 Qi  Qa  Qpt  Qvp  Pfc  Ppl (3.25) 

The heat loss through the insulation to the atmosphere is based on the temperature difference between 

the interior (Tie) and exterior, the thermal resistance of the materials that make up the walls and the 

thermal resistances associated with the natural convection within the payload enclosure and the 

convection from its exterior. The equations for heat loss through the insulation in the electronics and 

payload portion of the payload enclosure to the atmosphere is given by Equations (3.26) to (3.30). 

eiw ei eow eic oc

a ie

i R R R R R

T T Q

   

 	 (3.26) 

The thermal resistance (Rt) terms for the different material layers that comprise the payload enclosure 

are all similar and are based on the surface area (Alp) of the layers as well as the thickness (tpwi) of the 

layer and its thermal conductivity (kp), as given by Equation (3.27). 

p lp

pwi

t k A

t

R 	 (3.27) 

For the elliptical shape of the payload enclosure, the surface area is dependent on the outer perimeter 

for that layer, the height of the payload section and the bottom surface area of the enclosure as given by 

Equation (3.28). 
NASA/TM—2014-218321 17 

4

e e lp i i

L W A 	 p h   (3.28) 

The perimeter for each layer is determined from Equations (3.1) and (3.2). 

Heat is also lost from the electronics and payload portion of the enclosure to the ASRG portion of the 

enclosure since it is held at a much lower temperature (Tia). This heat loss is given by Equation (3.29). 

muw mi mlw eic aic

ia ie a R R R R R

T T Q

   

 	 (3.29) 

The thermal resistances for the layers between the two sections of the payload enclosure are also given by 

Equation (3.28) where the first term is zero. 

For the separation between the two sections of the payload enclosure the surface area is the same for 

each layer. The variables, used for the corresponding thermal resistance variables for each of the layers 

within the payload enclosure, in Equations (3.26) to (3.29), are given in Table 7. 

The remaining three resistance terms from Equations (3.26) and (3.29) are due to the internal and 

external convection within the electronics section of the payload enclosure (Reic), within the ASRG 

section of the payload enclosure (Raic) and outside (Roc) to the atmosphere from the electronics portion of 

the payload enclosure. The convective resistance terms are given by Equations (3.30) to (3.32), 

respectively. These thermal resistances are dependent on the internal convection coefficients for the 

electronics (hei) and ASRG sections (hai) of the enclosure and the external convection coefficient (ho) 

outside the enclosure. 

ei eiw

eic h A

R 1 	 (3.30) 

ai la

aic h A

R 1 	 (3.31) 

o eow

oc h A

R 1 	 (3.32) 

TABLE 7.—THERMAL RESISTANCE VALUES AND THEIR CORRESPONDING VARIABLES 

Resistance term 

(Rt) 

Thermal 

conductivity 

(kp) 

Layer area 

(Alp) 

Perimeter 

(pi) 

Layer 

thickness 

(tpwi) 

Incremental 

thickness 

(di) 

Electronics section inner wall (Reiw) keiw Aeiw peiw teiw teiw

Electronics section insulation layer (Rei) kei Aei Pei tei teiw + tei

Electronics section outer wall (Reow) keow Aeow peow teow teiw + tei + teow

ASRG/payload separation inner wall (Rmuw) kmuw Ala 0 tmuw N/A 

ASRG/payload separation insulation layer (Rmi) kmi Ala 0 tmi N/A 

ASRG/payload separation outer wall (Rmlw) kmlw Ala 0 tmlw N/A 
NASA/TM—2014-218321 18 

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 payload enclosure. 

The interior convection coefficients for the electronics and ASRG sections of payload enclosure are given 

by Equations (3.33) and (3.34), respectively. The convection coefficient for the exterior surfaces is given 

by Equation (3.35). These coefficients are determined by utilizing the geometry and atmospheric gas 

properties calculated for the conditions at each location. The main factor in calculating the convective 

coefficients is in determining the Nusselt number (Nudi and Nudo) for each location. 

e

a di

ei h

k h Nu 	 (3.33) 

a

a di

ai h

k h Nu 	 (3.34) 

e eiw ei eow

a do o L t t t

k h

   	 Nu (3.35) 

For calculating the internal convective coefficient the interior is filled with atmospheric gas at 

atmospheric pressure. The thermal conductivity for this gas (ka) is given by Equation (2.11), calculated at 

the gas temperature for the section in which the coefficient is being determined as given in Table 8. The 

internal convective heat transfer is assumed to be free convection with no active mixing of the gas within 

the enclosure. 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. 

The Nusselt number (Nudi) for internal free convection within the payload enclosure is given by 

Equation (3.36) (Ref. 17). 

0.29

0.2 Pr

Pr Ra Nu 0.18 
















 	 i

i i

di (3.36) 

The payload enclosure internal gas Prandtl number (Pri) is based on the internal gas specific heat, 

thermal conductivity and dynamic viscosity (a), calculated for the temperature and gas density within 

each section of the payload enclosure, as defined by Equation (3.37). 

a

pa a

i k

c  Pr 	 (3.37) 

To calculate the Prandlt number for the internal gas the thermal conductivity is given by Equation 

(2.11), using the temperature listed in Table 8 for the appropriate section within the payload enclosure. 

The specific heat for the atmosphere is 1039 J/kg-K and the dynamic viscosity is given by Equation (2.4). 

TABLE 8—TEMPERATURE FOR CALCULATING THE GAS THERMAL CONDUCTIVITY 

AT DIFFERENT LOCATIONS ON THE PAYLOAD ENCLOSURE 

Location Temperature 

Internal walls of the electronics portion of the payload enclosure Tie – Twi/2 

Internal walls of the ASRG portion of the payload enclosure Tia – Twi/2 

External walls of the payload enclosure Ta
NASA/TM—2014-218321 19 

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

payload enclosure internal gas (Rai), defined in Equation (3.38). The Rayleigh number is based on the 

interior wall film temperature (Tif), the kinematic viscosity (a, given by Eq. (3.39)) and the thermal 

diffusivity (a, given by Eq. (3.40)) of the atmospheric gas at the internal conditions for each section of 

the payload enclosure. 

if a a

wi i

i T

g T h

 

 	 3

Ra (3.38) 

 a

a a 


  	 {m2

/s} (3.39) 

6 8 10 2 213 10 2 51 10 184 10 a if if . . T . T    	       {m2

/s} (3.40) 

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

Equation (3.35). 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 2 m/s the Reynolds number, as given by Equation (3.20), is 

on the order of 3 million. There were no available correlations found for the Nusselt number for flow over 

an elliptical cylinder at a Reynolds number in this range. Therefore a correlation for flow over a cylinder 

was used as an approximation. Equation (3.41) 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 (3.41)

With this expression for Nusselt number, the convective coefficient for the atmosphere flow around 

the payload enclosure, given by Equation (3.35), can be calculated and in turn the exterior convective 

resistance term, given by Equation (3.33). 

The heaters will not only need to provide heat to make up for the heat leaking in through the 

insulation, but also the wires and view port as well. The heat leak through the pass-through wires and 

view port windows (Qpt 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 (3.42) and (3.43), respectively. 

 

  wip ip wop

w w w a ie

pt

t t t

n d k T T Q

 

  	 4

2

 (3.42) 

 

  wip ip wop

vp vp vp a ie

vp

t t t

n d k T T

Q

 

  	 4

2

 (3.43) 

From Equations (3.22) to (3.43) the total required heater power could be determined. 
NASA/TM—2014-218321 20 

Figure 11.—GPHS block assembly drawing (Ref. 19). 

3.4 Power Production 

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

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

electrical power for all of the airship’s systems. Each radioisotope block, termed a general-purpose heat 

source (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 11. Each block measures 9.95- by 9.32- by 

5.82-cm and has a mass of 1.44 kg. 

Two blocks are utilized in each ASRG power system as illustrated in Figure 7. The ASRG power 

systems are enclosed in the upper portion of the payload enclosure as shown in Figure 8 and Figure 10. 

The output power from each ASRG system (Pao) is dependent on temperature within the ASRG portion of 

the enclosure as given by Equation (3.44), which is derived from data from Reference 18. 

Pao 294Tia 	194.5  0. (3.44) 

Determining the available power from the ASRG systems is an iterative process between the power 

produced and the heat loss to the surroundings. The total heat (Qt) available is the sum of the thermal 

output of the GPHS blocks within the ASRG systems as given by Equation (3.45). Which is based on the 

number of ASRG systems (na) used considering each ASRG has two GPHS blocks. 

Qt 	 500na (3.45) 

The total heat generated by the GPHS blocks also must be equivalent to the heat lost and power 

generated through the following mechanisms, which is represented by Equation (3.46). 

Heat gained from the electronics portion of the payload enclosure 

Heat lost to the atmosphere through the exterior walls of the payload enclosure (Qae) 

Heat gained from the pass-through wires from the Electronics section of the payload enclosure to 

the ASRG section (Qapw) 

The electrical power generated by the ASRGs 
NASA/TM—2014-218321 21 

Qt 	 Qae  Pa  Qa  Qaw (3.46) 

The heat loss to the atmosphere through the ASRG portion of the enclosure is calculated in a similar 

fashion as that for electronics section and is given by Equation (3.47). 

aiw ai aow aic oc

a ia ae R R R R R

T T Q

   

 	 (3.47) 

The thermal resistance terms for the different material layers that comprise the ASRG section of the 

payload enclosure are all similar to those used for the electronics portion, given by Equation (3.29). 

The corresponding values for the ASRG section to be used with Equations (3.24) to (3.29) are given in 

Table 9. It should be noted that since the external dimensions of both the ASRG and payload sections of 

the enclosure are the same, the total thickness variable is calculated from the outer wall inwards by 

subtracting off the wall and insulation layers. 

The interior and exterior convective thermal resistance terms for the ASRG section of the payload 

enclosure are calculated in the same manner as those for the electronics section, given by Equations (3.32) 

and (3.33), respectively. The area term for determining the convective resistance terms is given by 

Equation (3.25) and the variables used are listed in Table 9 for each convective resistance term. The 

convective coefficients for the ASRG section of the payload enclosure are calculated in a similar manner 

as those for the electronics section given by Equations (3.34) to (3.35). Since the interior dimensions are 

different between the two sections the internal height of the ASRG section (ha) is substituted for the 

height of the electronics section shown in Equation (3.34). 

The heat leak through the pass-through wires from the electronics section to the ASRG section of the 

payload enclosure is dependent on the number of wires (naw), their diameter (daw) and the thermal 

conductivity of the wire (kaw). Since these are the wires for conducting power they will be larger than the 

sensor wires used in the electronics section. The heat leak through the wires is given by Equation (3.48). 

 

  mlt mi mut

aw aw aw i ia

apw

t t t

n d k T T Q

 

  		 4

2

 (3.48) 

Since the ASRG section temperature is not known Equations (3.45) to (3.48) are solved iteratively to 

determine the engine output power. 

TABLE 9.—THERMAL RESISTANCE VALUES FOR EACH MATERIAL 

LAYER IN THE HEAT SOURCE PRESSURE VESSEL 

Resistance term 

(Rt) 

Thermal 

conductivity 

(kp) 

Layer 

area 

(Alp) 

Perimeter 

(pi) 

Layer 

thickness 

(tpwi) 

Incremental 

thickness 

(di) 

ASRG section inner wall (Raiw) kaiw Aaiw paiw taiw teiw + tie +teow – taow – tai

ASRG section insulation layer (Rai) kai Aai pai tai teiw + tie + teow – taow

ASRG section outer wall (Raow) kaow Aaow paow taow teiw + tie + teow

ASRG Section inner wall convection (Raic) N/A Aaiw paiw taiw teiw + tie + teow – taow – tai – taiw

ASRG section outer wall convection (Roc) N/A Aaow paow taow teiw + tie +teow
NASA/TM—2014-218321 22 

4.0 Analysis Results 

The analysis described in Section 3 was used to evaluate the airship configuration and flight 

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

was performed to provide a baseline design utilizing two ASRG power systems that can fly faster than the 

wind speed near the surface and provide sufficient heating and power to maintain and operate the payload 

and electronics. From this design the flight altitude was varied to determine what affect it had on the 

aircraft sizing. 

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 Titan utilizing two ASRG power system modules for providing all the power and heating 

requirements for the airship. The number of GPHS blocks utilized in the two ASRGs set the available 

thermal power at 1000 W, which drove all aspects of the design. The baseline airship configuration is 

shown in Figure 12. 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 payload enclosure is separated into two sections one for the electronics and the other for 

the ASRG power systems. The payload enclosure is mounted directly to the bottom side of the gas 

envelope. The electric motor and gearbox are mounted within the payload enclosure to increase their 

operating temperature and avoid issues with materials and lubrication operating at the ambient Titan 

conditions. The propeller is connected to the gearbox through a driveshaft. The propeller is located behind 

the payload enclosure and operates in a pusher configuration. 

The payload enclosure specification and the main geometry, characteristics and flight specifications 

for the airship are listed in Table 10 and Table 11. The mass and power breakdowns are given in Table 12 

and Table 13, 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. For the 

baseline design the lifting force available for this design point is 344 N, which corresponds to 254.8 kg of 

mass. The total estimated mass of the airship is 252.7.4 kg, just under the available lift. Similarly the total 

available power generation capability is 286.8 W, 7.6 W above the required power of 279.2 W. 

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 13. 

Figure 12.—Baseline airship design dimensions. 
NASA/TM—2014-218321 23 

TABLE 10.—PAYLOAD ENCLOSURE MATERIAL 

AND GEOMETRY VARIABLES 

Item Value 

Payload enclosure 

ASRG section variables 

Height (ha) ................................................................................................................ 0.35 m 

Inner wall thickness (taiw) ........................................................................................... 1 mm 

Insulation thickness (tai) ............................................................................................. 1 mm 

Outer wall thickness (taow).......................................................................................... 1 mm 

Upper bulkhead inner wall thickness (tuiw) ................................................................. 1 mm 

Upper bulkhead insulation thickness (tui) ................................................................... 1 mm 

Upper bulkhead outer wall thickness (tuow) ................................................................ 1 mm 

Inner wall thermal conductivity (kaiw) .................................................................. 10 W/mK 

Insulation thermal conductivity (kai) ............................................................... 0.017 W/mK 

Outer wall thermal conductivity (kaow) ................................................................. 10 W/mK 

Inner wall density (
aiw) .................................................................................... 1700 kg/m3 

Insulation density (
ai) .......................................................................................... 20 kg/m3

Outer wall density (
aow) ................................................................................... 1700 kg/m3

Upper bulkhead inner wall density (
uiw) .......................................................... 1700 kg/m3

Upper bulkhead insulation density (
ui) ................................................................ 20 kg/m3

Upper bulkhead outer wall density (
uow) ......................................................... 1700 kg/m3

Structural wall material................................................................. Carbon Fiber Composite 

Insulation material .................................................................................................. Aerogel 

Number of wire pass-through (nwa) .................................................................................... 4 

Wire material and thermal conductivity (kwa) ...................................... Copper: 401 W/mK 

Wire diameter (dwa) ................................................................................ 2.6 mm (10 gauge) 

Electronics section variable 

Height (he) ............................................................................................................... 0.65 m 

Interior length (Le) ........................................................................................................ 2 m 

Interior max width (We) ................................................................................................ 1 m 

Inner wall thickness (teiw) ........................................................................................... 1 mm 

Insulation thickness (tei) .......................................................................................... 11.7 cm 

Outer wall thickness (teow) .......................................................................................... 1 mm 

Lower bulkhead inner wall thickness (tliw) ................................................................. 1 mm 

Lower bulkhead insulation thickness (tli) ................................................................ 11.7 cm 

Lower bulkhead outer wall thickness (tlow) ................................................................ 1 mm 

Middle bulkhead upper wall thickness (tmuw) ............................................................. 1 mm 

Middle bulkhead insulation thickness (tmi) ................................................................. 12 cm 

Middle bulkhead lower wall thickness (tmlw) .............................................................. 1 mm 

Inner wall thermal conductivity (keiw) .................................................................. 10 W/mK 

Insulation thermal conductivity (kei) ............................................................... 0.017 W/mK 

Outer wall thermal conductivity (keow) ................................................................. 10 W/mK 

Middle bulkhead upper wall thermal conductivity (kmuw) ..................................... 10 W/mK 

Middle bulkhead insulation thermal conductivity (kmi) ................................... 0.017 W/mK 

Middle bulkhead lower wall thermal conductivity (kmlw) ..................................... 10 W/mK 

Inner wall density (
eiw) .................................................................................... 1700 kg/m3

Insulation density (
ei) .......................................................................................... 20 kg/m3

Outer wall density (
eow) ................................................................................... 1700 kg/m3

Lower bulkhead inner wall density (
liw) .......................................................... 1700 kg/m3

lower bulkhead insulation density (
li) ................................................................. 20 kg/m3

Lower bulkhead outer wall density (
low) .......................................................... 1700 kg/m3

Middle bulkhead inner wall density (
miw) ........................................................ 1700 kg/m3

Lower bulkhead insulation density (
mi) ............................................................... 20 kg/m3

Lower bulkhead outer wall density (
mow) ........................................................ 1700 kg/m3

Structural wall material................................................................... carbon fiber composite 

Insulation material .................................................................................................. Aerogel 

Number of wire pass-through (nw) .................................................................................. 30 

Wire material and thermal conductivity (kw) ........................................ Copper: 401 W/mK 

Wire diameter (dw) ................................................................................... 1 mm (18 gauge) 

Number of view ports (nvp) ............................................................................................... 2 

View port material and thermal conductivity (kvp) ......................... Pyrex Glass: 1.4 W/mK 

View port diameter (dvp) ............................................................................................ 10 cm 
NASA/TM—2014-218321 24 

TABLE 11.—BASELINE AIRSHIP 

PHYSICAL CHARACTERISTICS 

Item Value 

Airship general specifications 

Airship fineness ratio (length to max diameter) ............................................... 4 

Flight altitude ............................................................................................ 1 km 

Flight velocity (2.25 m/s faster than 

the estimated average wind speed) .................................................... 2.38 m/s 

Lifting gas ............................................................. Hydrogen (diatomic)MW=2 

Airship envelope length ........................................................................ 11.66 m 

Airship envelope maximum diameter ..................................................... 2.92 m 

Airship envelope volume ....................................................................... 51.7 m3

Total lifting force (mass) ..................................................... 340.7 N (251.9 kg) 

Number of control fins .................................................................................... 4 

Tail fin area (per fin) ............................................................................. 1.83 m2

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

Propulsion/Power System 

Propeller diameter .................................................................................. 1.69 m 

Propeller advance ratio ............................................................................... 0.56 

Thrust coefficient ..................................................................................... 0.034 

Power coefficient...................................................................................... 0.026 

Propeller tip Mach number ......................................................................... 0.07 

Propeller efficiency .................................................................................... 0.71 

Total driveline efficiency ........................................................................... 0.56 

Number of ASRG power systems (nasrg) .......................................................... 2 

TABLE 12.—BASELINE AIRSHIP MASS BREAKDOWN 

Item Mass (kg) 

Structure (includes envelope, fins and structural support)........................... 87.0 

Electric motor ............................................................................................... 0.5 

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

Motor controller ............................................................................................ 0.1 

Motor power conditioning ............................................................................ 0.2 

Propeller ....................................................................................................... 2.7 

ASRG Engine Systems .................................................................................. 50 

Flight control computer and electronics ........................................................ 3.8 

Communications equipment ......................................................................... 4.6 

Sensors and data acquisition ......................................................................... 3.5 

Payload/science equipment ............................................................................ 25 

Payload enclosure (ASRG and electronics sections) ................................... 54.2 

Lifting gas ................................................................................................... 20.6 

Total mass................................................................................................ 252.7 

TABLE 13.—AIRSHIP DRAG BREAKDOWN 

Item Drag (N) 

Electronics and payload enclosure ............................................................... 2.89 

Airship lifting gas envelope ......................................................................... 5.50 

Airship tail ................................................................................................... 0.92 

Total drag ................................................................................................... 9.39 

The heat flow from the electronics and ASRG sections of the payload enclosure is illustrated in 

Figure 13. 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 payload enclosure are 

given in Table 15. 
NASA/TM—2014-218321 25 

TABLE 14.—BASELINE AIRSHIP POWER PRODUCTION AND CONSUMPTION 

Variable Value 

Power production related variables 

Total thermal power ................................................................................................................ 1000 W 

ASRG section internal temperature (Tia) ................................................................................. 184.3 K 

Total ASRG power produced ................................................................................................. 280.6 W 

Power consumption related variables 

Electronics section internal temperature ..................................................................................... 265 K 

ASRG section heat loss through the walls and insulation to exterior ..................................... 740.5 W 

ASRG section pass-through wire heat leak in from electronics section ...................................... 5.6 W 

Electronics section heat loss to exterior .................................................................................. 113.8 W 

Electronics section pass-through wires heat leak ...................................................................... 13.4 W 

Electronics section view port heat leak..................................................................................... 31.2 W 

Electronics section heat loss to ASRG section ......................................................................... 15.6 W 

Communications, control and payload power........................................................................... 85.0 W 

Propulsion system power.......................................................................................................... 71.6 W 

Total power required ........................................................................................................... 280.6 W 

TABLE 15.—CHARACTERISTIC FLOW AND HEAT TRANSFER 

VALUES FOR THE PAYLOAD ENCLOSURE 

Variable Electronics enclosure 

section

ASRG enclosure 

section 

Nusselt number 4356 exterior 

47.57 interior 

4356 exterior 

40.64 interior 

Reynolds number 3.88106

 exterior 3.88106 exterior 

Prandlt number 0.83 exterior 

0.66 interior 

0.83 exterior 

0.70 interior 

Raleigh number 2.93108

 interior 1.68108 interior

Convective heat transfer coefficient (W/m2K) 17.5 exterior 

1.84 interior 

17.5 exterior 

2.09 interior 

Figure 13.—Heat flow into and out of the payload enclosure. 
NASA/TM—2014-218321 26 

The results are based on an estimated power level for the science, internal vehicle operations and 

communications. However the distribution of that total power can be adjusted between those systems as 

needed to meet the demands of the mission. The only constraint on this is that the power for the 

communications system was not included in the waste heat utilized to help maintain the internal 

temperature at the desired level. 

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 heating power. Or the airship could reduce its airspeed to provide additional power for 

communication or other activities. It is assumed that the power consumed by the propulsion system does 

not provide any internal heating of the payload enclosure. Therefore reducing the propulsion system 

power consumption and increasing the communications system output does not affect the internal 

temperature of the enclosure. 

4.2 Variation from the Baseline Design

Changing the input variables of the baseline design can have a significant effect on the airship sizing. 

The two main parameters that will be affected by changes in the input variables are the gas envelope size 

and the insulation thickness of the electronics section of the payload enclosure. Changes in envelope size 

produce changes to the airship lift whereas changes to the insulation thickness produce changes in the 

power consumption by the heaters. Because the output power of the ASRG systems is mostly fixed the 

only means to accommodate changes in power demand is to reduce that demand from one of the loads on 

the airship. For the baseline case these power system loads are shown in Figure 14. The heater power is 

the only item that can be adjusted without changing the mission or operation of the airship. It can be 

adjusted by changing the insulation thickness on the electronics section of the payload enclosure. 

Adjusting these two items, airship length and insulation thickness, enables variations from the 

baseline case to be evaluated. 

4.2.1 Variation of Electronics Section Operating Temperature 

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

and payload enclosure. For the baseline case this temperature was set at 265 K. To achieve this 

temperature both waste heat from the electronics and electrically powered heaters were utilized. The 

temperature difference, between the interior and the surrounding, plays a large role in the power required 

as well as the size of the enclosure, due to the required insulation thickness. The heating power is 

dependent on this temperature difference and the subsequent heat leak out to the surroundings from the 

insulation, wires, view ports and the ASRG section of the payload enclosure. The breakdown of heat loss 

from the electronics section is broken down in Figure 15. 

Figure 14.—Power breakdown in Watts for the baseline case operation. 
NASA/TM—2014-218321 27 

Figure 15.—Baseline case heat loss from the electronics section of 

the payload enclosure. 

The heat loss to the environment is directly related to the amount of insulation within the payload 

enclosure. For the interior dimensions specified in the baseline case, the amount of insulation determines 

the exterior dimensions, which in turn affects the mass and drag, the larger the enclosure outside 

dimensions the greater, its mass and drag. 

The waste heat and heater power needed to make up the heat losses shown in Figure 15 are the main 

power consuming items of the airship operation, as shown in Figure 14. This figure shows the power 

breakdown for the baseline case. From this figure it can be seen that the heater power consumes 

approximately 73 W, 26 percent of the total power required. This is in addition to the 100 W of waste heat 

that is also utilized to make up for the heat loss to the environment. 

The ASRG heat sources provide the total amount of available heat. Ultimately all of this heat is 

released to the environment or converted to electrical power and transmitted through the communications 

system. The resistance of the heat flow to the environment will set the steady state interior temperature of 

the payload enclosure. Therefore, to adjust this temperature the resistance to heat flow has to be adjusted 

up or down. Since, as shown in Figure 15, the greatest mechanism for heat loss is through the insulation, 

changing the insulation thickness will adjust the internal temperature of the payload enclosure. By 

changing the insulation thickness the mass and drag of the payload enclosure will also change. This will 

affect the overall required size of the airship, as shown in Figure 16. 

From Figure 16 it can be seen that increasing the internal temperature of the enclosure does increase 

the airship size but not significantly. The insulation thickness does increase significantly but since it is on 

the outside of the enclosure there is no reduction in the internal volume. This indicates that operating the 

electronics section at a higher temperature than that of the baseline case of 265 K would not have a 

significant effect on the airship or its performance. Changing the operating temperature by 25 K increased 

the airship length by only 0.8 percent. Therefore, electronics operating temperatures of around 290 K, 

which are more consistent with conventional spacecraft designs can be considered. 
NASA/TM—2014-218321 28 

Figure 16.—Required airship length and insulation thickness for a range of electronic section internal 

temperatures. 

4.2.2 Variation in Flight Altitude 

The baseline case was sized for operating at an altitude of 1 km. To examine the operation at other 

altitudes the airship was sized for flight at altitudes above and below the baseline case. The airship length 

was varied from the baseline length in order to provide sufficient lift at the different 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 17 

for an altitude range of 100 m up to 7.64 km, 1 km flight altitude was used in the baseline case. All 

aspects of the airship, except the dimensions of the gas envelope, remained at the baseline design values. 

Varying its length changed the volume of the lifting gas envelope. The lifting gas envelope proportions 

used for the baseline case remained the same. 

Figure 17 shows that there is a fairly linear increase in airship length and corresponding 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 3. Therefore the lifting force 

decreases requiring increased lifting gas volume. 

As the flight altitude is increased the insulation thickness also needed to increase to maintain the 

desired temperature within the electronics section of the payload enclosure. This was due to two factors; 

the increasing wind speed and the decreasing atmospheric temperature with altitude as shown in Figure 3. 

The higher flight speed and lower atmospheric temperature caused an increase in the convective heat 

transfer from the outside of the enclosure to the atmosphere. Due to this increased heat transfer the 

insulation thickness increases significantly with altitude as can be seen in Figure 17. 

The maximum altitude achievable by the airship was 7.64 km. Beyond this altitude there was no 

converged solution to the required airship size for the available power from two ASRG power systems. 
NASA/TM—2014-218321 29 

Figure 17.—Required electronics section insulation thickness and airship length for a range 

of flight altitudes. 

Since the insulation thickness and required airship length decrease as altitude decreases, an airship 

sized for a particular altitude should be able to descent to near the surface. Therefore increasing the 

airship size and insulation expands the flight envelope of the airship. 

This altitude analysis shows that small increases in the airship size can provide large benefits in 

increasing altitude range. For example an airship 7.2 percent longer (12.5 m versus the baseline airship 

length of 11.66 m) can provide an increase in maximum altitude from 1 km up to 4 km. 

4.2.3 Variation in Payload Mass and Volume 

The payload mass for the baseline case was set at 25 kg. Changing this mass will affect the size of the 

airship and the corresponding insulation thickness of the electronics enclosure. It may not seem obvious 

that increasing the payload mass should have an effect on the insulation but this is due to a second-order 

effect of the sizing analysis. By increasing the airship size to accommodate the increase in payload mass, 

the propulsion power also increases due to the increased drag. Therefore the power consumption has to be 

decreased in order to accommodate the increase in required propulsion power. To achieve this, the 

insulation thickness is increased to reduce the required heater power. This change in airship length and 

insulation thickness for a range of payload masses from 10 to 100 kg is shown in Figure 18. 
NASA/TM—2014-218321 30 

Figure 18.—The change in airship length and insulation thickness with payload mass. 

The increase in airship length and insulation thickness is fairly linear with increasing payload mass. 

There is approximately a 0.6 m increase in airship length for every 25 kg increase in payload mass. The 

slight step function appearance of the insulation thickness curve is due to the tolerance limits set on the 

iterative sizing of the airship and insulation. 

Either varying the height or length of the payload enclosure or both will change its internal volume. 

To evaluate how this affects the airship length and required insulation thickness. The payload enclosure 

length was varied from 2.0 m (the baseline case value) to 4.0 m and the payload height enclosure height 

was varied from 1.0 m (the baseline case value) to 2.0 m. This changed the internal volume of the payload 

enclosure from 1.57 to 3.14 m3

. These changes were done separately and the airship length and insulation 

thickness curves as a function of internal volume are shown in Figure 19 for both cases. 

Increasing the internal volume of the payload enclosure caused the airship length and increase as 

would be expected. The volume change by either an increase in payload enclosure length or height 

produced a similar rise in airship length through most of the range examined. For a payload enclosure 

volume greater than 2.8 m3

 there was a slight reduction in airship size by changing the length of the 

enclosure as compared to changing its height. The insulation thickness also had a benefit of reduced 

thickness by adjusting the payload enclosure length instead of its height. However this benefit was more 

pronounced and began at a smaller enclosure volume, approximately 1.9 m3

. These results indicate that if 

additional internal volume is needed it would be beneficial to increase the payload enclosure length 

instead of its height. This will minimize the impact of increased payload enclosure volume to the airship 

sizing. 
NASA/TM—2014-218321 31 

Figure 19.—Change in airship length and insulation thickness for changes in internal volume of the payload 

enclosure. 

5.0 Summary 

The goal of this analysis was to determine if an airship, powered by two ASRG power systems, is 

feasible near the surface of Titan. Based on the airship analysis and design process outlined in Section 3 a 

baseline airship configuration and size was determined that could meet the mission goals and operate near 

the Titan surface. This initial analysis indicates that an ASRG powered airship, utilizing hydrogen as the 

lifting gas, is feasible on Titan. For the baseline design there was sufficient power generated from the two 

ASRG systems to provide heating and operate the electronics and propulsion system for the airship. 

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

vehicle design and operation. It was determined that the airship can be sized to operate up to an altitude of 

7.64 km. Beyond this altitude there was no designed solution for an airship with two ASRG power 

sources. Also since the size of the airship decreased with flight altitude, an airship sized for flight at a 

specific altitude would be capable of descent to near the surface. 

Increasing the interior operating temperature of the electronics section of the payload enclosure did 

not have a significant effect on the airship size. Therefore if needed, operating the science equipment and 

electronics at temperatures above the 265 K specified in the baseline case would be feasible. 

Other factors, such as changing the payload mass or the internal volume of the payload enclosure, had 

a much more significant effect on the airship size. Therefore minimizing these would provide benefits to 

reducing the airship size. 

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: 

Evaluating the possibility of using the waste heat from the ASRGs to heat the envelope gas to 

augment the lift produced. This evaluation would have to take into account the affect this would 

have on the operating temperature of the ASRGs and their corresponding output power. Also 
NASA/TM—2014-218321 32 

looking at the tradeoff of insulating the gas envelope to increase the gas temperature versus the 

increased mass and higher operating temperature of the ASRG would provide a net benefit. 

A detailed analysis of the fluid flow over the payload enclosure and airship envelope. The heat 

transfer from the insulated payload enclosure is a critical factor in the airship sizing. Any change 

in this value can have a significant effect on the airship design by changing the required heater 

power. 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 payload enclosure as 

well as the drag of the airship itself. 

An optimization of the propeller design for operation within the Titan environment. The propeller 

was a generic design that was not optimized for Titan. Increasing the propeller efficiency could 

reduce the propulsion system power requirement. 

A detailed analysis of the internal convection and corresponding heat transfer within the 

electronics and ASRG sections of the payload enclosure. The heat transfer from the interior gas to 

the wall of these enclosure sections 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 the convective heat 

transfer coefficients. For example by putting natural convection barriers along the internal walls. 

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 Titan 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. 

The modeling and analysis performed for this report was based on basic physics and 

thermodynamics. Using this approach the modeling provided a simplified means to evaluate the 

airship concept. Since the analysis is based on well-established principles the validation of the 

equations utilized is not necessary. However, there are inherent assumptions incorporated by 

utilizing this approach that may affect the results. These items, such as incorporating threedimensional effects into the analysis, can be further evaluated to determine how increased detail 

and complexity of the analysis would affect the results. 

 
NASA/TM—2014-218321 33 

Appendix—Symbols List

Aai ASRG section insulation surface area

Aaiw ASRG section inner wall surface area 

Aaow ASRG section outer wall surface area 

Aei electronics section insulation surface area

Aeiw electronics section inner wall surface area 

Aeow electronics section outer wall surface area 

Ala middle horizontal surface area 

Alp payload enclosure layer area variable 

C1 viscosity term 1 

C2 viscosity term 2 

C3 viscosity term 3 

C4 viscosity term 4 

C5 viscosity term 5 

C6 viscosity term 6 

C7 thermal conductivity term 1 

C8 thermal conductivity term 2 

C9 thermal conductivity term 3 

C10 thermal conductivity term 4 

C11 thermal conductivity term 5 

De gas envelope drag 

Dp payload enclosure drag 

Dt tail section drag 

Dtot total airship drag 

L airship lift 

Le electronics section interior length 

MWa atmosphere molecular weight 

MWg lifting gas molecular weight 

Nudi Payload enclosure internal Nusselt number 

Nudo Payload enclosure external Nusselt number 

Pa atmosphere pressure 

Pao ASRG system output power 

Pce communications equipment power 

Pdt drive train system power 

Pfc flight control computer power 

Pfs flight sensor power 

Ph heating power 

Ppl payload power 

Pr atmosphere Prandtl number 

Pr total required power 

Pri payload enclosure internal Prandtl number 

Qa electronics section heat loss to the ASRG section 

Qae ASRG section atmosphere heat loss 

Qapw ASRG section pass-through wire heat leak 

Qi electronics section heat loss through the exterior walls 

Qpt electronics section pass through wire heat loss 

Qt ASRG System GPHS block total heat output 

Qvp view port window heat loss 

R universal gas constant 

Ra atmosphere gas constant 
NASA/TM—2014-218321 34 

Rai ASRG section insulation thermal resistance 

Rai payload enclosure internal Rayleigh number 

Raic ASRG section internal convection thermal resistance 

Raiw ASRG section inner wall thermal resistance 

Raow electronics section outer wall thermal resistance 

Redo payload enclosure external Reynolds number 

Rei electronics section insulation thermal resistance 

Reic electronics section internal convection thermal resistance 

Reiw electronics section inner wall thermal resistance 

Reow electronics section outer wall thermal resistance 

Rep payload enclosure external Reynolds number 

Rmi middle horizontal insulation thermal resistance 

Rmlw middle horizontal upper wall thermal resistance 

Rmuw middle horizontal lower wall thermal resistance 

Roc external convection thermal resistance 

Rt payload enclosure thermal resistance variable 

Ta Venus atmospheric temperature 

Tg lifting gas temperature 

Tia ASRG section internal temperature 

Tie electronics section internal temperature 

Tif payload enclosure internal wall film temperature 

U airship velocity 

Va airship envelope volume 

We electronics section interior width 

Wtot airship total weight 

Z altitude above the surface 

a atmosphere speed of sound 

cde airship gas envelope drag coefficient 

cdp payload enclosure drag coefficient 

ci parameter equation term 

cpa atmosphere specific heat

d airship envelope maximum diameter 

daw ASRG section pass through wire diameter 

di payload enclosure incremental layer thickness variable 

dvp view port diameter 

dw pass through wire diameter 

f airship envelope fineness ratio 

g Titan gravitational acceleration 

ha ASRG section height 

hai ASRG section internal convection coefficient 

he electronics section height 

hei electronics section internal convection coefficient 

hi payload enclosure section height variable 

ho payload enclosure external convection coefficient 

ka atmosphere thermal conductivity 

kai ASRG section insulation thermal conductivity 

kaiw ASRG section inner wall thermal conductivity 

kaow ASRG section outer wall thermal conductivity 

kaw ASRG section pass through wire thermal conductivity 

kei electronics section insulation thermal conductivity

keiw electronics section inner wall thermal conductivity 
NASA/TM—2014-218321 35 

keow electronics section outer wall thermal conductivity 

kmi middle horizontal insulation thermal conductivity 

kmlw middle horizontal upper wall thermal conductivity 

kmuw middle horizontal lower wall thermal conductivity 

kp payload enclosure thermal conductivity variable 

kvp view port material thermal conductivity 

kw pass through wire thermal conductivity 

l airship envelope length 

mai ASRG Section Insulation Mass 

maiw ASRG Section Inner Wall Mass 

maow ASRG Section Outer Wall Mass 

masrg ASRG Unit System Mass 

mce communication equipment mass 

mdt drive train total mass 

mei electronics section insulation mass 

meiw electronics section inner wall mass 

meow electronics section outer wall mass 

mfc flight control computer mass 

mfi fixed item mass 

mfs flight control sensor mass 

mhw payload enclosure horizontal wall mass 

mhwi payload enclosure horizontal wall mass variable 

mlg lifting gas mass 

mli lower horizontal insulation mass 

mliw lower horizontal inner wall mass 

mlow lower horizontal outer wall mass 

mmi middle horizontal insulation mass 

mmlw middle horizontal upper wall mass 

mmuw middle horizontal lower wall mass 

mpe payload enclosure mass 

mpl payload mass 

mpw payload enclosure elliptical wall mass 

mpwi payload enclosure layer mass variable 

ms airship structure mass 

mtot total airship mass 

mui upper horizontal insulation mass 

muiw upper horizontal inner wall mass 

muow upper horizontal outer wall mass 

na number of ASRG systems 

naw number of ASRG section wire pass-throughs 

nvp number of view ports 

nw number of pass-through wires 

pai ASRG section insulation parameter 

paiw ASRG section inner wall parameter 

paow ASRG section outer wall parameter 

pei electronics section insulation parameter 

peiw electronics section inner wall parameter 

peow electronics section outer wall parameter 

pi payload enclosure layer parameter variable 

tai ASRG section insulation thickness

taiw ASRG section inner wall thickness 
NASA/TM—2014-218321 36 

taow ASRG section outer wall thickness 

tei electronics section insulation thickness

teiw electronics section inner wall thickness 

teow electronics section outer wall thickness 

thwi payload enclosure horizontal wall thickness variable 

tli lower horizontal insulation thickness 

tliw lower horizontal inner wall thickness 

tlow lower horizontal outer wall thickness 

tmi middle horizontal insulation thickness 

tmlw middle horizontal lower wall thickness 

tmuw middle horizontal upper wall thickness 

tpwi payload enclosure layer thickness variable 

tui upper horizontal insulation thickness 

tuiw upper horizontal inner wall thickness 

tuow upper horizontal outer wall thickness 

va atmosphere wind velocity 

 wi payload enclosure inner wall and internal gas temperature difference 

a atmosphere thermal diffusivity 

a atmosphere ratio of specific heats

dt propulsion system efficiency 

a atmosphere dynamic viscosity 

a atmosphere kinematic viscosity 


a atmosphere density 


ai ASRG section insulation material density 


aiw ASRG section inner wall material density


aow ASRG section outer wall material density


ei electronics section insulation material density 


eiw electronics section inner wall material density


eow electronics section outer wall material density


hwi payload enclosure horizontal wall density variable 


li lower horizontal insulation density 


liw lower horizontal inner wall density 


low lower horizontal outer wall density 


mi middle horizontal insulation density 


mlw middle horizontal upper wall density 


muw middle horizontal lower wall density 


pwi payload enclosure layer material density variable 


ui upper horizontal insulation density 


uiw upper horizontal inner wall density 


uow upper horizontal outer wall density 
NASA/TM—2014-218321 37 

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