The Physics of Solar Sailing - Revision history

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The Physics of Solar Sailing

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

← Older revision		Revision as of 15:17, 30 June 2009
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	neufeld@physics.utoronto.ca		neufeld@physics.utoronto.ca
		+
		+	[[Category:Sailing]]

← Older revision		Revision as of 20:58, 16 February 2006
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−	Copyright © ~~1991~~ by Christopher Neufeld. Republished with permission of the author.	+	Copyright © 1995 by Christopher Neufeld. Republished with permission of the author.

← Older revision		Revision as of 20:46, 16 February 2006
Line 1:		Line 1:
	Copyright © 1991 by Christopher Neufeld. Republished with permission of the author.		Copyright © 1991 by Christopher Neufeld. Republished with permission of the author.
		+

	A couple of years ago George Bush charged a committee with planning		A couple of years ago George Bush charged a committee with planning

← Older revision		Revision as of 20:45, 16 February 2006
Line 1:		Line 1:
		+	Copyright © 1991 by Christopher Neufeld. Republished with permission of the author.
		+
	A couple of years ago George Bush charged a committee with planning		A couple of years ago George Bush charged a committee with planning
	events to commemorate the five hundredth anniversary of Christopher Columbus'		events to commemorate the five hundredth anniversary of Christopher Columbus'

@@ Line 1: / Line 1: @@
-	The Physics of Solar Sailing
+A couple of years ago George Bush charged a committee with planning
-−
-−
-	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
@@ Line 23: / Line 20: @@
 budget.
-	One way of looking at the mass-energy equivalence expressed in
+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
@@ Line 42: / Line 39: @@
 a square as long on edge as three football fields.
-	Solar sailing will almost certainly never be used as a ground
+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
@@ Line 62: / Line 59: @@
 would be 99% fuel.
-	It might seem at first that the optimal configuration for a solar
+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,
@@ Line 83: / Line 80: @@
 metres, before putting on structure or electronics.
-	So, putting the sail at normal incidence to the sun is not the best
+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.
@@ Line 92: / Line 89: @@
 slows down the whole time it is climbing the well.
-	Well, if the only important thing is the component of the thrust
+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
@@ Line 99: / Line 96: @@
 it can travel anti-sunward.
-	The travel time to Mars for a solar sail is a strong function of the
+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
@@ Line 107: / Line 104: @@
 for sailcraft launched from the ground.
-	If a solar sailcraft is to be launched from the ground and unfolded
+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
@@ Line 117: / Line 114: @@
 sail, and this possibility has been investigated by several teams.
-	In the future, solar sails might be manufactured and deployed in
+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
@@ Line 124: / Line 121: @@
 would have essentially an unlimited fuel supply.
-	Solar sails were seriously studied by NASA in the 1960s as possible
+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
@@ Line 145: / Line 142: @@
 He can be reached at:
-=========  Addendum: June 19, 1995 =========
+<nowiki>=========  Addendum: June 19, 1995 =========</nowiki>
-	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
@@ Line 159: / Line 157: @@
 the entrants of the race.
-	The Canadian Space Society sail project is in an indefinite hold,
+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
+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
@@ Line 173: / Line 171: @@
-	Also, while the email address above works, it is probably safer
+Also, while the email address above works, it is probably safer
 in the long run to use:
 neufeld@physics.utoronto.ca