guardian.co.uk: While sailing remains a purely Earth-bound pursuit for now, it could one day be the means of propulsion for hitherto impossible space missions.
Speaking at the British Science Festival in Guildford, Colin McInnes of Strathclyde University described the physics and feasibility of solar sailing, which harnesses the "pressure" of the sun's radiation.
Karl Schroeder summarizes his excellent concepts for Stellar Cycler manned starships at his website http://www.kschroeder.com/my-books/permanence/interstellar-cyclers
The Stellar Cycler would essentially reach a significant percentage of the speed of light at which point a charged member or other electrodynamically active member would be deployed wherein the Lorentz force imposed on the space craft by the background interstellar magnetic field would cause the craft to undergo a cyclical orbiting like path within the interstellar medium.
Imagine a Stellar Cycler that could utilize the Sun’s magnetic field or the solar magnetic field in such a manner that a Stellar Cycler craft would repeatedly dive in toward the Sun and approach the Sun within about 0.015 to 0.02 AU.
As the craft reached is closest point to the Sun, the light sail would be deployed thus giving the craft a good boost for each outward bound cycle.
As the craft velocity increased, the amount of electrical charge on the charged member could be increased to maintain the same radius of curvilinear tracking or the radius of curvature could be allowed to increase thus reducing the charging requirements for the craft.
It is interesting to consider the degree of relativistic velocity for a first solar sail pass that can be obtained using the ambient pressure of star light alone, or sunlight, in consideration of the case where the drag from the solar or stellar wind and interplanetary dust is neglected. It is also assumed that the pressure is exerted on a solar or stellar sail that is sufficiently reflective to the sun light or star light, and which is also sufficiently refractive with respect to the star light within the environment that is located within an order of magnitude or less greater distance from the star than the radius of the star; a tall order when once considers the use of Blue Super Giant or Blue Hyper Giant stars for propulsion since these stars can have a luminosity over 6 orders of magnitude greater than the Sun and are effectively black body emitters with surface temperatures of several tens of thousands of Kelvins. Any known materials in existence today would be immediately vaporized by such close proximity to these highly luminous hot stars.
Assuming fraction f of the starlight is reflected straight back and the sail moves radially outward,
the equation of motion is
B[(1 + (B EXP 2)]dB/[(1 − B)EXP 2] {[1 − (B EXP2)] EXP 3/2} = p (R0/x) EXP 2
where B = v/c, v is the speed of the sail, x is the distance from the star, R0 is the initial distance from the star,
P = 2fA(u0)R0/[Mo(C EXP 2)]
Where;
A is the area of the sail, m0 is its rest mass, and u0 is the energy density of starlight at x = R0; thus, u(x) = (u0)[(R0/x) EXP 2]
Adopting f = 1, a value of M0/A = (10 EXP −8) kg/(meter EXP 2) = the effective mass specific reflecting area of the sail craft, and u0 ~ L/[4(pi)(Ro EXP 2)C] with L the Sun’s luminosity and R0 = 0.03AU, I find p ~ 5 × (10 EXP −2).
Note also that the equation of motion can be integrated analytically to find the terminal speed.
Just integrate from zero to its terminal value and x from R0 to infinity.
This yields for the terminal velocity:
{[(1 − (B EXP 2)] EXP (1/2)} [7 − 14B + 11 (B EXP 2) + 2(B EXP 3)]/(1 − B ) EXP3 = 7 + 15p
With p = 5 × (10 EXP −2), the terminal velocity = 0.251 C.
The nature of the sail proposed in this dive and fry scenario is of a mass saving nearly perfectly reflective grid composed of some yet to be developed carbon nanotube material(s) that might be metalized with the most refractive and reflective elemental metals or metallic compounds known.