Comparison of the Solar Sail with Electric Propulsion Systems

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NASA CONTRACTOR REPORT

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COMPARISON OF THE SOLAR SAIL WITH ELECTRIC PROPULSION SYSTEMS

Prepared by . -... THE MACNEAL-SCHWENDLER CORPORATION Los Angeles, Calif. 90041 for . ..

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION. WASHINGTON, D. c. ea FEBRUARY 1972 TECH LIBRARY KAFB, NM

1. Report No. 2. Government Accession No. NASA CR-1986 I 4. Title and Subtitle 5. Report Date COMPARISON OF THE SOLAR SAIL WITH ELECTRIC February 1972 PROPULSIONSYSTEMS 6. Performing Organization Code

7. Author(s) 8. Performing Organization Report No. Richard H. MacNeal 'EMSR 13A 10. Work Unit No. 9. Performing Organization Name and Address

The MacNeal-SchwendlerCorpmTtkCm ~-~ 74.42 NO. FigueroaStreet 11. Contract or Grant No. Los Angeles , California90041 NAS7-699

13. Type of Re rt and Period Covered 2. Sponsoring AgencyName and Address ContracGr NationalAeronautics and Space Administration FinalReport Washington, D. C. 20546 14. Sponsoring AgencyCade RWS

5. Supplementary Notes

6. Abstract A studyof the propulsive efficiencies of solar sails and electric propulsionsystems which shows increasing efficiency for solar sails for. launch mission durations.

7. Key- Words (Suggested by Author(s) 1 18. Distribution Statement Solar sails, electricpropulsion systems Unlimited advancedspace concepts. i

~~ "- .. 19. Security Classif. (of this report) 20. Security Classif. (of this page) 21. No. of Pages 22. Price'

Unclassified Unclassified 13 $3 .?70

For sale by the National Technical InformationService, Springfield, Virginia 22151

COMPARISON OF THE SOLAR SA1 L WITHELECTRIC PROPULSION SYSTEMS

By Richard H. MacNeal The MacNeal-SchwendlerCorporation

ABSTRACT

The propulsiveefficiencies of the solar sail and ofelectric propulsion systemsare compared on the basis of specificimpulse. It is shown thatthe solar sail is more efficientat onea.u. formission durations greaterthan about two months, that the advantage is increasedfor missions towardthe inner planets, and that the same conclusionsare reached when thecomparison is basedon maximizing the momentum transferred to thepay- load.Other factors that will influencethe choice of a propulsionsystem for a specificmission are mentioned.

iii

LI ST OF SYMBOLS

A surface area

C specific power (P/m ) at onea.u. P gravitationalforce of the sunon thesail at onea.u. FG

9 acce erationof gravity

g rav tationalattraction of thesun at one a.u. in Earth gls GS I spec fic impulse SP m mass flowrate mt tota I launch mass m fixed mass of the power plant P P power containedin the beam ofexpelled particles

solarradiation pressure at onea.u. PO T thrust t time

U distancefrom the sun inastronomical units

_I_

V " characteristicvelocity, see Eq. (14) wt totallaunch weight W totalweight of propulsion system PS a tankageweight parameter, see Eq. (9)

B m /it P Y li7 t /mt e incidenceangle of the sun's rays

lightness number ofthe sail

V "

COMPARISON OF THESOLAR SAIL WITHELECTRIC PROPULSION SYSTEMS

By Richard H. MacNeal TheMacNeal-Schwendler Corporation

Theidea ofusing solar radiation pressure for the propulsion of spacevehicles was exploredby several authors in the technical litera- ture of thelate 1950's (refs. l, 2, 3). The concept was notimmediately givenserious consideration because of theextremely large surface areas thatare required (5.3 x lo6 sq. ft. per pound of thrustat the Earth's distancefrom the sun). A morerecent investigation (refs. 4 and 5) has described a technicallyfeasible scheme fordeploying, rigidizing andcon- trollingthe large required areas and has therefore enhancedthe credibility of theconcept.

Performanceanalyses of the solar sail have, inthe past, beencon- cernedmainly with specific missions. It isdifficult to comparecompeting propulsionsystems for specific missions unless care is taken to equalize boundaryconditions (such as the characteristics of the launch vehicle) and tooptimize each competing system to the same degree.This has not fre- quently beendone, primarily because it is noteasy to do.There would appear to be a need, therefore,for a simplermeasure of comparison be- tweencompeting space propulsion systems that could be used forgross estimates.

A standardmeasure of the efficiency of a propulsivedevice is its specificimpulse, i.e., the ratio of thetime integral of its thrustto its weight.Different propulsion systems can be comparedon thebasis of theirspecific impulse,although it isnot the only important factor to be considered,nor is it necessarilythe best measure of efficiency for any particularapplication. Specific impulse is, perhaps, a direct measure of efficiencyonly in those cases where the thrust is used tocounteract otherforces, as inthe case of station keeping. For cases in which the thrust is used to changethe velocity of the vehicle, the ratio of the momentum added tothe payload to the total mass is a betterperformance indicator.This ratio can,however, be directlyrelated to specific impulse as will be shown later.Other performance indicators, such as comparisons oftravel times for equal payloads, generally require detailed calculations.

The specificimpulse of thesolar sail is computedas follows. The thrustis directed normal to the surface of thesail andhas themagnitude

where

po = solarradiation pressure at theEarth's solar radius

8 = incidenceangle of the sun's rays

U = distancefrom the sun in astronomical units

A = areaofthe surface The product, p A, is relatedto the lightness number ofthe sail, 0 Xs' by

PoA = ASFG

where F is thegravitational attraction of the sunon thesail at one G a.u.Lightness number is theprimary performance parameter for solar sails.It is inverselyproportional to the mass perunit area. When 1- = 1.0 thegravitational attraction of the sun is exactlybalanced by theradiation pressure. The specificimpulse is t [T dt 0' SP W

where W is theweight of the sail and itssupporting structure. Sub- PS stitutingfrom Eqs. (1) and (2) into Eq. (3)

FG . where G = - IS thegravitational attraction of the sun at onea.u. sw PS expressed in Earth g's and where the quantity (':z2')- is averaged over themission. The valueof the dimensionless constant, is ,611 x IOm3. GS, Notethat the specific impulse is linearlyproportional to lightness number and alsoto time. Note also that specific impulse decreases with the square ofthe distance from the sun.

The specificimpulse of an electricpropulsion device including, for example, a solar power supply andan ionengine, is computed as follows. The thrust is relatedto the powerexpended and the mass flowrate by

1 T = (2 Ph)" (5 )

where is the mass flowrate and P is theuseful power that goes into thekinetic energy of the expelled particles. The useful power is relatedto the mass ofthe power plantby

2 P = Cm P inthe case of a nuclearpower plant or by

1 P=Cm- u2 inthe case of a solarelectric power plant. m isthe fixed mass ofthe P powerplant, U is thedistance from the sun in astronomical units and C is thespecific power. It includesthe conversion efficiency of the power plant as a factor.Substituting Eq. (7) into Eq. (5)

1 (2Cm T= U

The totallaunch weight of thepropulsive system is

W 9(mp + (1 +a)ht) PS where g is theacceleration of gravity,and a is a parameterthat accounts forthe weight of the tankage, assumed to be proportionalto the weight of expel lant.

The specific impulse of thepropulsive system is t

where, inthe second form, a constant mass flowrate is assumed. Rearrange Eq. (10) slightly to obtain

I= 5P

m The quantity, .-f , is a designparameter that can be variedby changingthe voltage in the ion engine. The maximum value of I is SP

3 obtained when

m = mt(1 + CI) P

i.e., when thefixed power plantweight is equal to the fuel weight. Thus the maximum valueof is IS

Notethat the specific impulse is proportionalto the square root of the product of thespecific power ofthe power plant andthe mission time.

Comparing Eqs. (4) and(13), it isevident that the solar sail has the advantageover electric propulsion for very long missions, t+m.

Equations (4) and(13) are plotted in Fig. 1 forthe conditions: 8 = 30" in Eq . (4); a = 0 in Eq. (13); and U = 1.0 in Eqs. (4) and (13). The lower 1 imit ofthe range of sail lightness number, X = 0.50,repre- S sentscurrent ly available 0.08 mil polycarbonate film with 1500 A" of aluminumcoat ing,Ref. 6. X = 1.0represents a modestincrease in per- S formanceover currentstate-of-the-art, and AS = 2.0 represents a sub- stantialincrease. The lower limit ofthe specific power ofsolar electric propulsion (C - 25 watts/Kg)represents the current state-of-the-art of solarelectric power plants(Refs. 7, 8). Theupper limit (200watts/Kg) representsprojected capabilities for nuclear-electric and other advanced systems(Refs. 9, 10). The specificimpulse ranges for chemical and non- electricnuclear propulsion systems (Ref. 11) arealso indicated in Fig. 1.

If thepresent state-of-the-art is assumed (X = 0.50, C = 25 watts/Kg), S thesolar sail is more efficientthan solar electric propulsion for mission durationsgreater than about 30 days.For a missionduration of 1000days thesolar sail is about 6 timesas efficient as solarelectric propulsion.

It is seenby comparing Eqs. (4) and(13) that the advantage of the solarsail is increasedfor missions toward the inner planets, U < 1, and is decreased foroutward bound missions, U > 1. Foroutward bound mis- sionsan indirect trajectory with an initialinward loop (similar to those describedin Ref. 12 forsolar electric systems) may improvethe relative efficiency of the solar sail.

Forall applications except orientation control and stationkeeping, thethrust of the propulsion system acts to changethe translational velocity ofthe vehicle. In these applications a more direct measure ofefficiency thanspecific impulse is the ratio of the momentum added tothe payload dividedby the total launched mass of thevehicle. Thus we definethe "characteristicvelocity" of the propulsion system to be where Wt isthe launch weight and W isthe weight of thepropulsion PS system.

The characteristicvelocity can be directlyrelated to the specific impulse.In the case of thesolar sail, the mass isconstant with time so that

and

." The maximum value of V", obtained when W = 1/2 We is: PS

-L

V " max = - 25 ISP

In thecase of electricpropulsion, the mass of the sys.tem changes withtime. Assume thatthe mass flowrate andthe thrust are constant withtime so that

The assumptionthat the thrust is constantwith time particularizes Eq. (18)

'5 to a nuclear power plant or to a solar power plantin Earth orbit. Equation (18) canbe simplifiedby means of theparameters

and

whichcan be selected by the designer of the spacecraft.

In terms ofthese parameters

Forthe special case of a = 0, the optimumvalues of the design parameters are y = 1/3 and B = 2/3.The corresponding maximum valueof the characteristicvelocity is

1 -I- V"ma x = .2944 (y)' = .2944g(Isp)max

where Eq. (13) hasbeen used inobtaining the second form.

Comparing Eq. (20)and (17), it is seen thatthe ratio of charac- teristic velocities for the .optimized solarsail andthe optimized electricpropulsion system is approximate ly equal tothe ratio of the optimized specificimpulses, with a smalladvan tage (18%) accorded tothe electric propulsionsystem.

Efficiency is, of course,not the only factor to be considered. Factorsthat favor electric propulsion over the solar sail are:

1. Abilityto vary the direction of the thrust without changing its magnitude,and vice-versa.

2. Morecompact configuration, and perhaps, therefore, greater reliability of deployment.

3. Angular momentum ofthe vehicle may be small,or zero.

Factorsthat favor the solar sail over electric propulsion are:

1. Lesscompl icatedhardware, and, therefore,greater re1 iabi 1 i ty duringoperation.

2. Additional uses of thelarge surface area (micrometeroid flux measurement, cmmun icat ions., etc. ).

6 3. Ability to exploit unexpected increases in mission duration, i.e., to continue to produce thrust for an indefinite time.

4. Lower cost. In this connection it is worth noting that .08 mil polycarbonate film canbe obtained commercially fora price of 2 cents per sq. ft.

It has been shown that,other factors being equal, the solar sail is superior to electric propulsion for mission durations greater than about two months. In spite of its evident advantages very little effort has been expended to date on the development of the solar sail concept into a practical propulsion system.

The MacNeal-Schwendler Corporation Los Angeles, California, May 1, 1970 REFERENCES

1. Cotter, T., "SolarSail ing," Sandia Corporation Research Coloquim SCR-78, April, 1959, Officeof Technical Services, Dept. of Commerce, Washington, D. C.

2.Garwin, "Solar Sailing, A Practical Method of PropulsionWithin the SolarSystem,'' Jet Propulsion, March, 1958.

3. Tsu, T., "InterplanetaryTravel by Solar Sails," ARS Journal,June, 1959.

4. MacNeal, R. H., "The Heliogyro, An InterplanetaryFlying Machine," NASA Contractor'sReport CR 84460,June, 1967.

5. MacNeal, R. H., Hedgepeth,J., and Schuerch, H.U., "HeliogyroSolar Sailer Summary Report," NASA Contractor'sReport CR 1329,June, 1969.

6. Schuerch, H. U., "Materials and FabricationMethods for Deployable Thin Film Structures Used in Space Operations,"Astro Research Corp. Report ARC-R-374, February, 1970.

7. Mullin,J. P., Barber, T., and Zolen, C., "Solar-Cell-Powered,Electric Propulsionfor Automated Space Missions,"Journal of Spacecraft and Rockets,Vol. 6, p.1217-1225, November, 1969.

8. Flandt-0, G. A., "SolarElectric Low-Thrust Missions to Jupiter With SwingbyContinuation to the Outer Planets," Journal of Spacecraft and Rockets,Vol. 5, No. 9, September, 1968.

9. Handbook ofAstronautical Engineering. McGraw-Hill, 1961, p.21-42 to 21-44.

10. Schuerch, H. U., andRobbins, "Rotary, Deployable Space Solar Power Supply," NASA Contractor'sReport NASA CR-122, October, 1964.

11. McLafferty, G. H., "Survey of AdvancedConcepts inNuclear Propulsion,'' Journalof Spacecraft and Rockets,Vol. 5, No. 10, October, 1968.

12. Dickersonand Smith, "Trajectory Optimization for Solar-Electric Powered Vehicles,''Journal of Spacecraft and Rockets,Vol. 5, No. 8, August, 1968.

.... , ,. . L 10 103 1,000 1c),oon Mission Duration (Days) FIG. 1. SPECIFIC I~iDULSEVS MlSSlCN DlJRATlO11 FOR VARIr)l.lS PROPllLSIOIJ SYSTFUS OPERATING IN THE VICINITY OF THE EA4TH'S OPSIT

NASA-Langley, 1912 -28 CR-19% 9