SOLAR SAIL STARSHIPS: THE CLIPPER SHIPS OF THE GALAXY
Journal of the British Interplanetary Society, Vol. 34, pp. 371-380, 1981.
GREGORY L. MATLOFF*
Department of Applied Science, New York University, 26-36 Stuyvesant Street, New York, New York 10003, USA.
* Currently on leave of absence with the Systems and Applied Sciences Corporation, Riverdale, Md. 10840, USA.
Astronomy New England, 215 Highland Street, Holliston, Mass. 07146, USA. '
The utility of 10-8-10-7 meter (m) thick space manufactured solar sails for interstellar mission launch is considered. An interstellar solar sail is assumed to be partially or completely deployed behind a much more massive chunk of asteroidal debris with similar dimensions to the sail and utilized as an occulter. The sail is released from the occulter and exposed to sunlight, during a 1.5 x 109 m perihelion pass in a near-parabolic or hyperbolic orbit. Robot probes would be deposited as thin films on the spaceward side of the sails; larger habitats with human crews would be suspended by diamond or copper cables behind the sails. Stress problems in the cable and sail, the applicability of giant-planet rebounds, sail deployment strategies, thermal problems and preliminary mission design are all considered. Near term technology may be capable of launching small robot probes that could reach Alpha Centauri within about 350 years. Much larger human-occupied habitats, constrained to lower peak accelerations, may eventually be able to utilize the solar sail to reach Alpha Centauri within 900-1400 years. Eventually, when our Sun enters its giant phase about 4 x 109 years in the future, the performance of the solar sail as an interstellar booster will greatly increase.
ALTHOUGH THEORETICAL ANALYSIS of solar sails have been performed for several decades  this propulsion system required several advances in materials science before it could be considered for interplanetary missions. Recently state-of-the-art solar sails were considered to propel the 1986 Haley's comet probe  and more advanced space-manufactured sails are now under consideration for application to space industrialization and colonization .
The use of solar sails for expeditions into interstellar space has not yet been subjected to detailed analysis, but sails have been proposed as receivers of beamed laser energy for interstellar missions [4, 5]. Forward has suggested that thin-film remote probes might be deposited on the spaceward side of very thin solar sails, which would use the gravity whip principle and solar sail deployment near the Sun, for interstellar boosting . Viewing et al speculated that solar sail boosted "innocuous starships" from other civilizations might, for reasons of economy, be more prevalent in the Galaxy than the much faster ships using thermonuclear or antimatter propulsion .
Interstellar missions utilizing the solar sail will be length) A large space colony, suspended by diamond sails behind a solar sail, would be, constrained by human acceleration tolerance and sail/cable stressing, to interstellar flight times of about 1000 years.
Such long transit times may not be unreasonable because automated, miniaturized scientific probes with great long longevity may eventually become feasible  and mobile space habitats such as those proposed by O'Neill may be sociologically reliable enough to withstand long interstellar journeys . Also, if we evolve into a solar-system-wide civilization which survives for some four billion years, conditions for solar-sailing will improve and will drastically reduce interstellar flight times, when the Sun becomes a red giant star . As described below, the solar sail may indeed be the "appropriate technology" to allow a Type II civilization  to escape the dire consequences of it expanding parent star.
In the sections below, sail kinematics, stressing, deployment strategies, aspects of mission design, interstellar cruise, and deceleration will be considered. We will first consider the kinematics of fully and partially deployed solar sails.
Figure 1 presents a solar-sail/payload configuration for thin-film robot probes and mobile habitats.
In Fig. 2, we present a possible method of sail deployment near the Sun.
The sail, either partially or completely unfurled, is manoeuvred into a parabolic or hyperbolic orbit with a perihelion approach 0.01-0.03 AU from the Sun's centre. The sail is deployed behind a much more massive occulter of similar dimension which is descarded at perihelion. According to Ehricke, a 0.01 AU perihelion approach is the closest feasible . For a near parabolic orbit, the perihelion velocity V0 ≤ √2*Vcirc, where Vcirc is the velocity required to maintain a circular orbit at the perihelion distance. For r0 = 0.01 AU, V0 ≤ 0.0014 C, for r0 = 0.03 AU, V0 ≤ 0.0008 С. If an 18-24 km/sec manoeuvre is performed near Saturn, the hyperbolic velocity at r0 = 0.01 AU will be V0 ≈ 0.002 C, relative to the Sun .
For the probe and habitat boosting systems shown in Fig. 1, the total mass at time of occulter release can be expressed for a sail of circular cross section:
where σs is the sail areal mass loading (kg/m2), σpa is the thin-film probe's areal mass loading (kg/m2 ), Rs (m) is sail radius (cross-sectional radius presented to Sun), ρc (kg/m3) is the cable material density, Lc (m) is the cable length (Lc > Rs , as shown below), Ac (m2 ) is the total cable cross-sectional area, and Mp is the payload mass in kg.
Using the inverse-square law, solar irradiance on a sail at a distance r from the centre of the Sun, normal to the Sun is:
(All quantities in this paper are in S. I. system units unless otherwise specified).
From Tsu  for a sail of 100% reflectivity the radiation pressure can be written 2Sr/C, where С is the speed of light. For sail reflectivity k, the solar radiation pressure can be written [(1+ k)/2] Sr/C. Thus, a 95% sail reflectivity will reduce the solar radiation pressure by 2.5%. Therefore, the radial acceleration of the spacecraft due to solar radiation pressure can be written.
From elementary conservation of energy, the solar sail's velocity V at distance r from the Sun's centre is given by:
where G is the gravitational constant, MO is the mass of the Sun, and the "0" subscripts denote initial conditions. Two assumptions made in Eq. (4) are that the sail axis will always be directed toward the Sun and the sail is fully deployed between r0 and r. The solar sail's hyperbolic excess velocity, V∞ is obtained from Eq. (4) by letting r go to infinity:
We can analyze the performance of large solar sails by defining an effective mass thickness or areal density, σe, for the sail/thin-film payload, or sail/cable/payload combination. From Eq. (5),
Drexler has reported that a 10-7 m thickness will certainly be possible for space manufactured solar sails and that there is some possibility of producing sails as thin as 10"8m . Tsu projects sail material specific gravity to be 1.18 . Table 1 presents solutions to Eqs: (6) and (7) for a variety of final velocities and perihelion velocities. For simplicity, sail reflectivities were assumed to be 100%, in preparing Table 1.
^ = velocity at infinity, V0 = velocity at perihelion, С = speed of light, σe = effective mission mass area loading, Vsmax = maximum acceleration.
In evaluating Table 1, it is worth noting that, at 0.01 AU, from the Sun, the gravitational acceleration of the Sun is 6.01 gearth, where gearth is Earth's surface gravity. Although human beings have withstood as much as 45 gearth for fractions of a second, the record for extended high acceleration without ill effects or loss of consciousness is 17 gearth) for four minutes [12,13]. Thus, even with planetary rebounds and a 18-74 km/sec powered peri-Saturn manoeuvre for V0 = 0.002 C, the fully-deployed sail for use in transporting a human-occupied space habitat seems limited to V∞ ≤ 0.003 C, extrapolating well past this 17 gearth limit.
To further consider the kinematics of a sail-launched interstellar habitat, we will constrain solar sail radius such that the astronauts never experience more than a given acceleration. This could be accomplished by requiring Rs/r = constant, near the Sun. Further out, after maximum solar sail deployment, Rs = constant. The acceleration experienced by the crew is expressed in Eq. (3) and the acceleration of the spacecraft relative to the Sun can be calculated by subtracting the gravitational acceleration towards the Sun from Eq. (4).
Calling the maximum allowable acceleration VA [с точкой, dt] and utilizing Rs/r = constant and Eq. (3),
during the initial acceleration period. We next define Vp = velocity at perihelion (start of sail deployment), rp = perihelion distance. Once again, V0 = velocity at the time of sail full deployment, and r0 = distance from the Sun's centre to the position at which the sail is fully deployed. Now, since V[с точкой, dt] = V dv/dr,
since GMO = 1.33xl020. Integrating, we can relate initial (perihelion) conditions to conditions at the start of "fully deployed sail" operations:
where Rs(F.S.) is fully deployed sail radius.
Equation (11) and (12) can be used as input to Eq. (5), to relate V∞ to initial conditions, at perihelion. Solutions to these equations, calculated for 100% sail reflectivity, are presented in Fig. 3 for several perihelion velocities and values of σe = M/( π Rs2 ). Note the variety of configurations capable of travelling to a Centauri in 800-1300 years, with accelerations limited to 10 or 20 gearth.
Fig. 3. Performance of an Interstellar Solar Starship that has a partially deployed sail at perihelion, which deploys such that Rs/r = constant until full sail deployment. Rs = sail radius and r = distance from Sun centre. Cases А, В, С, D respectively refer to mission effective mass thickness of 1.18x10-5, 3.73x10-5, 1.18x10-4 and 3.73x10-4 kg/m . Unprimed cases have perihelion velocity 0.0014 C, primed cases have perihelion velocity 0.002 С.
It is good for possible interstellar applications of the solar sail that effective mass loadings 3-10 times Drexler's minimum are capable of such performance, even without a powered peri-Saturn manoeuvre. Because, as will be shown in the following section, considerations of sail stress dynamics will add to the projected system mass.
|Black Sabbath song taken from the Paranoid album We sail through endless skies|