1976 R.Lo Propulsion by Laser Energy Transmission

8/14/2019 1976 R.Lo Propulsion by Laser Energy Transmission

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PROPULSION BY LASER ENERGY TRANSMISSION(Considerations to Selected Problems)

R.E.Lo* (DFVLRInstitute of Chemical Rocket Propulsion, Hardthausen-Lampoldshausen,

Federal Republic of Germany

AbstractThe rewards of laser propulsion are substantial payload gains for missions with high velocity

increment. Laser-assisted chemical propulsion is an effective means to reduce required laser

powers. Payload gains of this new mode of propulsion can be calculated as functions of ratio

of laser power to chemical power, structural mass fraction and velocity increment. Payload

mass fraction can be optimised for minimum laser power requirement. Deep space missions

require very high laser power and/or very small beam divergence. For near-earth missions, the

simultaneous input of laser and solar-power is worthwhile and can be optimized.

I. Mission Considerations

When a spacecraft receives its propulsive energy by laser- or other energy-transmission from

the outside, a gain over chemical propulsion system can only be obtained, if the effective

exhaust velocity is increased above chemically achievable values. The mass of the energy

transmitted is zero for all practical purposes and the on-board propellant mass would have to

be the same for a given propulsion requirement V and a given exhaust velocity, whether it

contains chemical energy or not. For this reason, all missions requiring larger than chemical

exhaust velocities are the only candidates of real interest for laser-propulsion.

However, many of these missions require also large absolute amounts of power. Typical

examples are

- single-stage-to-orbit missions- two-way tug missions servicing geostationary orbit- fast perigee-apogee delivery of payloads.

Therefore, aside of pure laser-propulsion with chemically inert propellants, mixed mode laser-

assisted chemical propulsion should be considered as an effective means to reduce required

laser power. If the take-off mass Mo of a spacecraft is simply split into payload Mn, structural

mass Ms and propellant mass Mp

psno MMMM (1)

o

n

M

M(2)

o

s

M

M(3)

the basic Ziolkowsky equation

a

lLncV (4)


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shows (see Fig. 1) that perigee-apogee missions with a typical V of 4000 m/s and in

particular single-stage-to-orbit missions ( V about 10.000 m/s) suffer from a very steep

decrease of the payload mass fraction with c.

Single-stage-to-orbit propulsion with 1 to 5 % of payload is in the tantalizing region of

marginal feasibility with exhaust velocities of 4500 to 5000 m/s, if structural factors of 0.1

or better can be obtained. This may be the example, where some additional beamed energy

may make all the difference between tiny payload fractions of uncertain feasibility andcommercially interesting percentages. Total exhaust jet power P would thus have to consist of

a chemical and a laser contribution.

:LCh PandP

LCh PPP (5)

Its absolute value depends upon thrust F or massflow rate mwhich, in turn, are determined

by the chosen vehicle accelaeration g:

2

5.0 cmP (6)

cmF (7)

12

5.0

n

VFcFP

(8)

a

gMgMF no (9)


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- 0.1 for attitude control- 1.0 for perigee-apogee missions- 2.0 to 3.0 for single-stage-to-orbit and two-way trips.

For any given structural factor , the gain in payload fraction is obviously increasing with.

For a given it increases dramatically with V/CCh. No significant gain is obtained for lowenergy missions. On the other hand, additional laser-power of 10 to 50 % of chemical power

may raise the fraction available for masses other than propellants from 0.1 with zero payload

to feasible values.

This can more clearly be shown if payload gain in terms of % of pure chemical propulsion is

calculated as a function of and V/CCh :

0

)(100/,%

a

aCVfa Ch (19)


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Fig. 4 shows as a function of ; for high energy missions payload gain increases steeply

with .

Therefore, it may be concluded that the application of beamed energy is worthwhile only in

missions with large V , with ratios V/CCh above 1. Single-stage-to-orbit missions are

considered as an example in the next chapter, however, very similar results could be obtainedfor a two-way tug. Most of the mathematical relations derived hold for any V .

II. Laser-Assisted Single-Stage-to-Orbit Vehicles

Such vehicles fall under two restrictions:

- laser power limited design- limited design.

The following Table 1 gives the values for a single-stage-to-orbit vehicle with and Mn alittle better than the present space shuttle design (for Table 1, see Page 4).

The following conclusions can be drawn from the results:

- Lifting of 30 t of payload into orbit is not a question of megawatts, as they may be

available within several years, it is a question of gigawatts.

- If, however, gigawatts are available, even a small contribution to chemical power

has dramatic effects on vehicle size: with little more than 5.5 GW it can be reduced

by a factor of more than 21!

- There is a region, where vehicle mass is a very sensitive function of laser power. It isvery much worthwhile to get into this region: in the present example, an increase of

0.26 GW from 5.52 to 5.78 will result in a further vehicle mass reduction by another

factor of almost 3!

- At larger laser powers, their application becomes temperature limited. If 10 00 m/s

are considered as maximum achievable exhaust velocity (corresponding to chamber

temperatures of 6000-7000 K), no more than 5.6 GW can be applied (assuming total

conversion).

- Total power requirement goes through a minimum, while laser-power does not,

since in this particular case is marginal.

Let us consider the question of minimum power requirement as a function of payload mass

fraction . It is well known, that such a minimum exists for any thrust F, propulsion

requirement V and structural factor . However, at available exit velocities, has to be

kept far below optimum values, while on the other hand chemical power has no upper limit.

From equation (10) we derive:

a

ana

an

Va

gMdadP n 1

11

1

(20)


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)()()(2

1)( afcaFa

da

dPa

(21)

!0da

dB(22)

!01

anaa (23)

Table 1:

Data of laser-assisted chemical single-stage-to-orbit vehicles as a function of ratio of laser

power PL to chemical power PCh. There is in all cases a payload of 30.000 kg, structural factor

of 0.13 chemical exhaust velocity of 5000 m/s, take-off acceleration of 1.2 g and V of10.000 m/s (tb = thrust time).

0 0.1 0.5 1 5 10 100

0.00533 0.01854 0.1131 0.3120 0.4172 0.4172 0.6895

Mo t 5622.9 1618.4 495.1 265.2 96.16 71.92 53.51

Ms t 731.0 210.4 59.7 34.5 12.50 9.35 5.66

Mp t 4861.9 1378.0 369.4 200.7 53.66 32.57 7.85

F 104N 6619 1905 540.5 312.2 113.2 84.7 51.2

c m/s 5000 5244 6114 7071 12247 16583 50249

m kg/s13239 3633 882.6 441.5 92.43 51.05 10.19

tb s 367 379 418 455 580 638 770

P GW 165.5 49.95 16.55 11.04 6.932 7.019 12.865

PCh GW 165.5 45.41 11.03 5.52 1.155 0.638 0.1274

PL GW 0 4.54 5.51 5.52 5.777 6.381 12.7380

Table 2

Payload mass fraction cmin for minimum total power requirement as function of structuralfactor .

0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.5 0.7 0.9 1.0

amin 0.367

9

0.365

0

0.357

7

0.347

4

0.334

7

0.320

3

0.304

4

0.287

2

0.229

8

0.143

5

0.049

3

0.0

Numerical solution of equation (23) results in the minimum values for shown in Table 2.

This minimum can, of course, easily be understood in terms of masses (see Fig. 6): power

requirement increases at low values of, due to raising Mo, at high values of it increases due to

decreasing propellant mass with accordingly increasing exhaust velocity requirements.


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With a constant chemical contribution to power in laser-assisted chemical propulsion there,

too, should be minima for required laser power.

Differentiation of equation (17) gives:

V

C

an

V

aa

gM

da

dP ChnL2

2 1

1

2

(24)

)1

1(

12

an

V

C

an

V

a

Ch

),,(min ChCVfa (25)

An analytical expression in the form of equation (25) cannot be obtained by setting the factors

of equation (24) equal to zero. However, numerical solution of equation (24) or (17) gives the

desired answers (Fig. 5).


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For a V = 10.000 m/s single-stage-to-orbit mission, the results are shown in Fig. 6. From

these, minimum required laser-power results with payload and acceleration as additional

parameters.

Equation (14) may be rewritten as follows:


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)(;2

2

min

min,c

Cc

a

gMP ChnL (26)

LL

n

L PF

P

a

gMP

2,2 minmin,

(27)

min

2

'

min, 1

an

V

c

CcP ChL

(28)

min

21

an

V

CCh

'

LP being the equivalent laser-exhaust velocity. Plotted as a function of min with CCh and as

parameters (see Fig. 7), it delivers the required minimum laser power for any thurst level

(chosen according to equation (27) after selection of acceleration and payload along with

fixed min, the latter being determind by . V, CCh and .


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As Fig. 7 shows, no min occurs where a line of constant CCh does not cross a particular line of

constant . Below a certain laser power simply decreases with decreasing . This is always


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the case, when CCh alone is close to being sufficient for a particular mission, as in the example

of Table. 1.This is made more obvious by considering another sample case.

A single-stage-to-orbit ( V = 10.000 m/s) vehicle providing a chemical exhaust velocity of

CCh = 4500 m/s cannot be built with structural factors above 0.10837. In this case, it has

precisely zero payload. To design it with any other values of the sum + .requires additionalbeamed power. The situation is depicted in Fig. 8.

PL is plotted over , with as parameter. All values of above 0.1 show minima at values

between 0.1 and 0.3. For very low values of , PL again decreases monotonously with (not

shown in Fig. 8). However, vehicles with very light construction ( below 0.10837) require

smoothly raising amounts of laser power if increases beyond values where + equals

0.10837.


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The PL lines of constant in Fig. 8 are very flat in the vicinity of this critical value. This again

reflects the fact found in the example of Table 1: in these regions a small increase in PL results

in a dramatic increase of possible payload massfractions .

In closing the present consideration of laser-assisted chemical propulsion, it should be

mentioned that, of course, all PL values considered here are effective values as they mustshow up in the kinetic energy of the exhaust gases. Laser power to be transmitted from the

base power station PL,bas has to be larger according to transmission and conversion

efficiencies nT and nC, which normally will together be below 0.5:

basLCTL PnnP , (29)

III. Transmission Considerations

Even in the case of short distance laser power transmission to ascending launch vehicles or tospacecraft in low-earth orbits beam divergence, tracking and jitter may be well beyond

present-day technology. The situation is gravely worsened if transmission to geosynchronous

orbits, over lunar or interplanetary distances is considered. Due to beam divergence, power

desity is diluted by the square of the transmission distance. Since direct conversion to

propulsive power requires large total amounts of energy per second, which may not be

feasible with power-limited laser energy sources, indirect conversion by means of solar panels

might be of interest. This, as another advantage, offers the opportunity of making use of the

solar radiation as additional energy source, with which to compete any laser will have trouble

over larger distance. Electric power from the panels could then be converted to thrust with ion

or plasma engines.

Let us assume the existence of a laser-power base in low earth orbit, such that its distance

from the sun is essentially 1 AU (taken to be 1,496.1011

m).The base emits a conical laser

beam with divergence angle . The cross-sectional area of the beam at any distance from the

laser source DL will then be:

2

22tgDA L (30)

If the laser ha a power Eo at the source,its intensity will the diminish with DL:

2

22tgD

EI

L

o

L (31)

On the other hand, the solar intensity at 1 AU is ko. ko = 1,3146.103

W/m2.

The local solar intensity at any distance Ds from the sun is

22

/mWD

AUkI

s

os (32)


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The ratio of laser to solar intensity is therefore:

o

o

L

s

s

L

k

E

tgAUD

D

I

I

2

1

22

2

(33)

The solar panel shall be a planarian surface of area A and radius r (not necessarily determined

by equation (30).The angle between this surface and the line of sight to the laser base be a, the

angle with the line of sight to the sun , so that the angle between two lines is the difference

= - (34)

The effective areas of the panel surface are then the projection upon a plane perpendicular to

the respective lines of sight:

arAL sin2 (35)

sin2

rAs (36)

cossin)(sinsin aa (37)

)sincoscos(sin2

aarAs . (38)

If laser beam divergence satisfies equation (30), the laser power received by the panel is

2

22

2

rE

tgD

EI

L

o

L sin a (39)

while from the sun it receives

2

2

rDAUkI

s

os (sin a cos + (40)

+ cos a sin ).

Panel center, laser base and sun form a triangle with sides DL, AU and Ds, the angle formed

by DL and Ds. Therefore

cos2222

sLsL DDDDAU (41)

cossL

sL

DD

AUDD

2

22

(42)


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with the following abbreviations

2

2

1r

D

AUkK

s

o (43)

sL

sL

DD

AUDDK

2

222

2 (44)

sL

sL

DD

AUDDarcK

2cossin

222

3 (45)

2

224

2

r

tgD

EK

L

o (46)

the total power received by the panel becomes the following function of a:

sLto t III (47)

= .cossin)( 31421 aKKaKKK

Before studying the incluence of a, let us consider power and beam divergence requirements

as a function of distance.

For the simple case of the panel bearing spacecraft being in the direction opposite to the sun

(that is, the angle between the line of sight from base to sun and from base to spacecraft is

180 degress), the following results are obtained. It is further assumed that the panel has a size

given by local laser beam diameter and that the center line of the beam goes through the panel

center. is measured in fractions of one degree

a) Case of a 103

W laser

Fig. 9 plots I tot as a function of DL for this moderate size laser, with beam divergence asparameter. Under the optimistic assumption of a pointing accuracy and beam divergence as

low as 10-5

(= 0.036 seconds!!) being feasible, this laser contributes substantially to solar

power only below 30.000 km distance.

Its influence at all distances beyond the earth-moon distance is negligible even if isdecreased by another order of magnitude.

Such a small laser is therefore of any interest only in the immediate vicinity of the earth, and

might assist operations of spacecraft within the shadow cone of the earth.


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b) Case of a 10

6W laser

Fig. 10: this laser is without any influence beyond lunar distances with = 10-5

. However, it

might power electrical tugs to and from geosynchronous orbit even with larger beam

divergence.

It is a true but unrealistic statement that this laser, with 10-9

degrees beam divergence could

produce an illumination intensity equal to one solar constant ko as far as the distance ofUranus. With equal pointing accuracy, the panel area required would have a diameter of 50 m.

An electrical engine with a specific impulse of 2000 s and a total panel- and engine-efficiency

of 20 % could produce a thrust of 20 N with a propellant consumption of 1 g/s.


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C Case of a 109

W laser

Fig. 11: for all greater than 10-3

degrees, the power intensity beyond lunar distance is

essentially ko, before it decreases below the level short of Mars due to decreasing solar

intensity. It would require 10-6

degrees to keep power level at 1 ko up to Mars. Jupiter distancerequires 10

-7degrees, Pluto 10

-8.

Required panel diameter at Jupiter distance (and 10-7

degrees) is 1358 m. An electrical engine

could under the same assumptions as mentioned above produce a thrust of 2000 N at a

mass flow rate of 106 g/s.


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As the above examples clearly demonstrate, the use of lasers over planetary distances is

completely unfeasible. If these cases were -limited, the situation becomes swiftly power-

limited when more realistic divergence angles are assumed.

With = 1 second (2,78.10-4

degrees), it takes 3.56 GW to produce the local solar intensity at

the distance of the moon, 64 200 GW for Mars in opposition and 516 000 for Pluto.

Since energy distribution across a laser beam as well as beam divergence are governed by

optical laws, including non-linear effects, none of the split-second divergence angles

considered above might ever become feasible. As Table 3 shows, it takes again multi-gigawatt

lasers to produce 1 ko only at the distance of the moon if an of 1.6710-2

degrees (1 minute) is

assumed:

Table 3

Range of lasers with power Eo to produce 1 ko intensity.

Eo(W) 106 107 108 109 12,2880.109

DL (km) 107 338 1070 3383 384.000

Therefore, once again, laser-powered propulsion will be restricted to short distances. At such

distances, if indirect conversion is used rather than directly laser-powered engines, the

simultaneous use of solar light is most rewarding. (For direct conversion propulsion, the

additional use of chemical power at appropriate V/CCh-missions leads to moderate laser

power requirements. See previous chapter).

Turning back to equation (47) we find:

aKKaKKKad

dEtot sincos)(31421

(48)

amax = arc tg31

421

KK

KKK(49)

amax being the angle between panel surface and line of sight to the laser base for obtaining

maximum combined solar and laser energy input.

Although equation (49) is valid for any value of the constants, the optimization of at

moderate laser powers is worthwhile only at rather short distances.

Fig. 12 shows the result for a 1000 W laser with = 10-6

(which again is unrealistic, but the

result is quite typical): for all distances above 40.000 km, the panel has always to be turned

towards the sun. It is a question of payload gain or thrust-to-weight gain, whether the required

amount of attitude control pays off.


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IV. Conclusion

Laser propulsion is worthwhile for high V missions only. With limited laser power, laser

assisted chemical propulsion can lead to very high payload gains over purely chemical

propulsion. This would require the use of chemical propellant combinations rather than inertmaterials. Long-range laser propulsion requires very low beam divergence angles. Laser

propulsion will therefore have to be confined to near-earth missions. Two-way tugs and

single-stage-to-orbit shuttles are attractive candidates.

However, these and other missions are up to several orders of magnitude beyond present-day

technology in one or several of the following areas.

Laser power output

Mirror materials for very hig intensity energy fluxes

Solar panels for very high intensity energy fluxes

Pointing accuracy

Jitter reduction

Beam divergence angle.

However, it is hoped that the arguments presented above contribute to the conviction shared

by many scientists not afraid of looking into a somewhat more distant future, that laser

propulsion is a rewarding field for further studies.

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1976 R.Lo Propulsion by Laser Energy Transmission