The Physics of Solar Sailing

Copyright &copy; 1995 by Christopher Neufeld. Republished with permission of the author.

A couple of years ago George Bush charged a committee with planning events to commemorate the five hundredth anniversary of Christopher Columbus' departure from Europe for the Americas. Among the ideas which were implemented by the Christopher Columbus Quincentenary Jubilee Commission was the Columbus 500 Space Sail Cup. Spacecraft are to launch on conventional chemical rockets around Columbus day of 1992 and have to go to Mars using only light pressure. Among the serious competitors are the Canadian Solar Sail Project, the Aeritalia Team from Italy, Cambridge Consultants from Great Britain, and the World Space Foundation from the United States. There are also teams from Japan, Israel, and the Soviet Union, though the status of those projects is less clear. There are numerous criteria for winning, such as shortest transit to Mars orbit and the closest approach to the planet. In order to be recognized as a winner the sail must receive no government funding, but may receive money from the Columbus Commission. The Commission is subsidizing the efforts of three ships to match the three ships Columbus took to the new world (there was a fourth, but it had to turn back). One team from each of the Americas, Europe, and Asia, will receive whatever money becomes available. The World Space Foundation sail is the official Americas sail, and will receive some of the money, if it ever is granted in the budget.

One way of looking at the mass-energy equivalence expressed in Einstein's famous equation, E = m * c^2, is that any time energy moves from one place to another, it behaves in part as if mass is moving that way. If a mass is moving into another body, it pushes on it. The same is true of light. The momentum flux associated with light is very low, equal to the power flux divided by the speed of light. At Earth orbit, above the atmosphere, the solar power flux is roughly 1400 watts per square metre. This corresponds to a momentum flux of 4.7 micronewtons per square metre. If a square metre of a perfectly absorbing material is put in direct sunlight above the atmosphere, and the light hits it perpendicularly to the surface, it feels a force of 4.7 micronewtons, or roughly one two thousandth of the weight of a paper clip at the Earth's surface. A perfectly reflecting material would feel double that force. Compare this to the three space shuttle main engines (SSMEs), each of which generates 1.67 meganewtons of thrust at sea level, and 2.1 meganewtons of thrust in vacuum. Even a 100000 square metre sail would not generate a millionth the thrust of a single SSME, though it would be a square as long on edge as three football fields.

Solar sailing will almost certainly never be used as a ground launcher, though a variant, a laser launcher, could be constructed in the next five or ten years. Solar sailing becomes attractive as a means of thrust on long voyages through interplanetary space. The three space shuttle main engines and the two solid rocket boosters together provide, very roughly, 8 km/second of delta-velocity before they burn out after 8.5 minutes. A shuttle which masses 2 million kilograms on the pad delivers itself and cargo, about a hundred thousand kilograms in total, to orbit. 95% of the mass goes out as rocket exhaust gas, or is dropped into the sea in the form of spent boosters and empty external tank. Compare this to a solar sail. The propellant is sunshine, there is no fuel, and the thrust is continuous. The spacecraft does not have to be made to be 95% fuel by mass. While it might be fifty percent or more sail by mass, that material is not expended. A sail can be reused, or the material melted down for use at the destination. If a rocket were used in a round trip to Mars, and it had to carry its fuel for the return journey, it would have to be huge at launch. If the fuel for the engines massed 9 times as much as the payload, which must include the fuel for the return trip, then the initial mass of the rocket would be 99% fuel.

It might seem at first that the optimal configuration for a solar sail is one in which the light hits the sail at normal incidence (perpendicular to the surface). This doesn't turn out to be the case, though. A sail oriented this way exerts all its thrust along the line away from the sun. Because the intensity of the light from the sun falls off as the square of the distance, the magnitude of this outward thrust must fall off also as the square of the distance. In this way it is exactly like gravity. In fact, putting the sail at normal incidence to the sun has the same effect as would have reducing the mass of the sun. It places the sail into an elliptical orbit which moves farther away from the sun for a while, but must return to its starting point after one complete revolution about the sun. This is not a particularly useful configuration. The only way to avoid this with a sail at normal incidence is for the solar pressure to exceed the force of gravity, so that the sail goes into a hyperbolic escape from the solar system. In order to do this, for the power output and mass of our sun, the sail would have to mass no more than one kilogram for every 600 square metres of sail area, including the mass of payload and electronics. This is not practical for ground-based construction. The sail material for the Canadian Solar Sail Project will mass about a kilogram per hundred square metres, before putting on structure or electronics.

So, putting the sail at normal incidence to the sun is not the best configuration. It is better to angle the sail in such a way as to maximize the component of the thrust which is parallel to the direction of travel. This turns out to be when the angle between the sun and the perpendicular to the sail is about 35.3 degrees. In this configuration the spacecraft is being pushed along the direction of travel, and so it climbs the gravity well. In the counter-intuitive realm of orbital mechanics, the spacecraft slows down the whole time it is climbing the well.

Well, if the only important thing is the component of the thrust along the velocity vector, it can clearly be aligned the other way to oppose the velocity vector. This pushes against the direction of travel, dropping the sail down the gravity well, causing it to speed up the whole time. A solar sail, contrary to popular belief, can travel sunward just as easily as it can travel anti-sunward.

The travel time to Mars for a solar sail is a strong function of the mass to area ratio. It is not unreasonable to manufacture a solar sail which can be launched in the next two years to arrive at Mars in about another two years. It has been suggested that solar sail spacecraft could be used to send provisions and equipment to Mars ahead of a manned expedition. This two year time is not a fundamental limitation of solar sails, but is quite good for sailcraft launched from the ground.

If a solar sailcraft is to be launched from the ground and unfolded in space, the sail must be strong enough to withstand the stresses involved. For the solar sailcraft running in the race to Mars in 1992, the sails will be made of a strong polymer coated with aluminum for reflectivity. Once the sail is launched and unfolded, the polymer is just dead weight which has to be dragged to the destination by the sailcraft. It would be convenient if the substrate could be chosen to evaporate in the environment of space, for instance if the polymer breaks down in ultraviolet light, thus lightening the sail, and this possibility has been investigated by several teams.

In the future, solar sails might be manufactured and deployed in space, allowing square kilometres of very thin aluminum to be tethered to a cargo or passenger module. These sails could make an Earth-Mars transit in less time than a Hohmann transfer orbit. It has been speculated in science fiction that a solar sail would make an excellent asteroid surveyor, as it would have essentially an unlimited fuel supply.

Solar sails were seriously studied by NASA in the 1960s as possible manned transportation around the solar system. In those days of optimism serious plans were formed for lunar bases by 1975, nuclear launchers and interplanetary engines, and unmanned interstellar probes. None of these ever received serious funding, and they all died on the drawing boards and test beds by the early 1970s. Now, twenty years later, we will finally, to quote Arthur C. Clarke, sail the wind from the Sun.

-- Space Shuttle statistics taken from _The Space Transportation Systems Reference_ edited by Christopher Coggon, ISBN 0-920487-00-9

Christopher Neufeld is a physics Ph.D. student at the University of Toronto and a team member on the Canadian Solar Sail Project, which is an initiative of the Canadian Space Society. In his copious free time he reads science fiction or pushes buttons on his Apple ][GS.

He can be reached at:

neufeld@helios.physics.utoronto.ca

========= Addendum: June 19, 1995 =========

Several things have not happened since I wrote this article around 1990. Most notably, the solar sail race did not take place. The commercial funding was not available for us to make a private launch, and the American government decided not to pay for launch costs for three of the entrants of the race.

The Canadian Space Society sail project is in an indefinite hold, awaiting detailed design review. The team has not met in several years, and while the notes and designs are all still filed away, restarting the project would almost mean starting from scratch at this point.

My phrasing was a bit imprecise when talking about the laser launcher as a "variant" of a solar sail. When I said this, I meant that this was another example of a design which does not carry its energy source with it. A laser launcher would still have a working fluid, unlike a solar sail, but would not carry oxidizer, and would not burn the fuel to produce its thrust. Such launchers are still five to ten years off, of course.

Also, while the email address above works, it is probably safer in the long run to use:

neufeld@physics.utoronto.ca