ABSTRACT
A new propulsion technique has been dis
covered which allows manned missions to ANY
planet in the solar system. Travel time will
vary from 5 weeks to Mars to 6 months for the
outer planets(radiation hazards prevent visits
to Mercury or Venus). This technique employs
a form of propulsion where momentum is trans
ferred from "smart" projectiles to the space
ship by catching the projectiles with an EMPL.
The projectiles would be thrown from another
EMPL located at the north pole of the Moon.
Both EMPLs would be driven by nuclear power.
The specific impulse of the system, which will
be 3400 seconds initially, can be increased to
any desired value by increasing the power.
With this propulsion system we can visit
all the other planets within our own lifetime!
It is envisioned that the full scheme will re
quire 30 years to implement. The spaceships
will be reusable, so the one which takes us to
Mars can also take us to Jupiter and Saturn.
INTRODUCTION
Momentum transfer can be used as a propulsion system to
move heavy spaceships between Earth and ANY of the other
planets at much higher speeds than can be attained using
other current methods of propulsion. This scheme,in contrast
to other momentum transfer schemes such as those suggested
by G.K. O'Neill or C.E. Singer, permits fast manned round
trip missions.
Many authors have suggested using EMPLs to throw things
into space either from Earth or from the moon. Only a few of
these authors have suggested that their schemes amounted to
spaceship propulsion systems. Among those who have are G.K.
O'Neill and C.E. Singer.
In his 1977 book, "The High Frontier", Gerald O'Neill
described what he called a "reaction engine". This was a
massdriver which used electromagnetic fields to accelerate
buckets filled with surplus mass which would be thrown out
into space [p.141]. This would then accelerate the mass
driver and whatever it was attached to in the opposite
direction according to Newton's third law of motion. O'Neill
suggested that such a reaction engine could be attached to
an asteroid and could push the asteroid back to Earth by
chewing up part of the asteroid and spitting it out the
back. Of course, he conveniently forgot to tell us how the
reaction engine would get from here (or the moon or L5) to
the asteroid in question.
Although O'Neill's scheme uses an EMPL to move the
asteroid or spaceship, it still requires the huge onboard
reaction mass which must be thrown away to move the ship. It
is clear that this method will not work efficiently to move
people from one planet to another. For example, in order to
go from the moon to Mars, you would have to lift reaction
mass from the moon to the ship just so you could throw it
away from the ship to push you toward Mars. You would have
to carry a lot of extra material to throw away when you got
to Mars in order to enter a stable orbit around Mars. The
only advantage of this scheme over a conventional rocket
departure from Earth is that the reaction mass coming from
the moon would be much cheaper than rocket fuel that would
have to be lifted from Earth.
In 1979, Clifford E. Singer proposed a momentum
transfer scheme which used a stream of high velocity pellets
weighing only about 3 grams each to propel an interstellar
probe. The idea was to use a very long EMPL deployed in
interplanetary space to accelerate the tiny pellets. They
would impact the starship and transfer their momentum to it
thus accelerating it to very high (0.12 c) velocity. The
specifications of Singer's scheme are given in the center
column of Table 1, below. Apart from the ludicrous nature of
his plan, it suffers from several fatal deficiencies.
The Singer proposal fails for all of the following
reasons:
1. Any pellet which hits the spaceship will destroy it.
The energy of a 2.8 gram pellet moving at 0.25 c is
about 7.875e+12 joules which is equivalent to 1.884
kilotons of TNT (i.e. a 2 kiloton atomic bomb).
2. The spaceship can't carry enough fuel to adjust its
position to enable it to catch pellets which are out
of alignment.
3. The spaceship can't carry enough electric power
generating capacity to generate a magnetic field
strong enough to stop the pellets. The mass of a 15,000
gigawatt generator would be at least 3,000,000 MT at
0.2 MT/MW.
4. The pellet dispersion due to the influence of Jupiter,
Saturn, Uranus, Neptune, the Oort cloud, other objects,
and unknown interstellar dark matter would cause many
pellets to miss the ship or to collide with the electro
magnet (of 3.) if one existed.
The Singer proposal is useless for humans because:
1. It is not intended for interplanetary travel.
2. It is not capable of roundtrip missions.
The Singer proposal is highly impractical for at least
the following several reasons.
1. Here on Earth it takes us years to build a bridge just
a couple of kilometers long. How long would it take to
build a facility in the orbit of Jupiter which would be
100,000 kilometers long?
2. How much would such a facility cost? Who would want
to pay for it? Certainly no taxpayers I know!
3. Who would want such a facility that wasn't capable of
launching manned missions?
4. The realworld engineering problems are simply
insurmountable.
5. Vastly superior methods for launching of interstellar
probes exist  such as: matter  antimatter propulsion
or the Daedalus project of the British Interplanetary
Society.
SPACESHIP PROPULSION BY MOMENTUM TRANSFER
For years space scientists the world over have sought a
propulsion system which could significantly reduce the time
needed for interplanetary travel. My colleague, Albert Wu,
and I have discovered such a propulsion system. This scheme
works by transferring momentum from a series of "smart"
projectiles (launched from an EMPL located at the north pole
of the moon) to the spaceship by catching the projectiles
with another EMPL on board the spaceship. A spaceship with a
crew of 1000 can now travel to Mars in under two months and
to Jupiter in six.
The prime mover is nuclear power which converts mass to
energy according to Einstein's equation and drives the
EMPL's which launch the projectiles. As these fast moving
projectiles are caught by the spaceship's EMPL, their
momentum will be transferred to the spaceship according to
Newton's third law of motion. This reaction will accelerate
the spaceship in the desired direction by an amount
proportional to the ratio of the mass of the projectile to
the mass of the spaceship. As each projectile is caught, the
combined mass will be increased by the mass of one
projectile. This means that some of the momentum of
subsequent projectiles will be used to accelerate projec
tiles that have already been caught. That energy is wasted.
For that reason, the projectiles will be launched toward the
spaceship in groups  each projectile separated by the time
and distance required by the EMPL on board the spaceship to
charge up its capacitors to catch the next projectile. Once
the spaceship has caught all of the projectiles in one
group, it will proceed to launch them again in the direction
opposite to the desired trajectory of the spaceship. In this
manner each projectile will contribute two small accele
ration pulses to the spaceship.
Since the moon is locked in its orbit about the Earth,
the same part of the moon always faces Earth. This means
that as the moon rotates there are only two points on its
surface from which an observer should be able to constantly
observe the Sun (ignoring the moon's inclination)  namely,
the north and south poles. Due to the fact that there are
few maria in southern lunar regions (and for other good
reasons) the north pole has been selected for the site of
the lunar EMPL. The capacitor driven EMPL will be about 10
kilometers long and will be capable of launching one metric
ton projectiles at velocities of up to 20 kilometers per
second. This will require something on the order of 200,000
MJ of energy for each launch  which will be supplied by a
2500 MW nuclear power system. The reactor will require about
two minutes to charge the capacitors between the launching
of each projectile. The launcher itself will be mounted on a
series of circular tracks, so that it can be rotated between
each launch to compensate for the orbital motions of the
Earth and the moon. The Earth orbits the Sun in a prograde
direction at about 29.8 kilometers per second and the moon
orbits the Earth also in a prograde direction at about 1.02
kilometers per second. Thus for launches two minutes apart,
the launcher would be rotated in the retrograde direction by
5 to 10 meters depending on the final velocity of the
projectile.
In order to accelerate the spaceship to cruising
velocity it will be necessary to throw several thousand
projectiles from the moon to the spaceship (assuming none is
reused). Since each individual projectile will be separated
by about two minutes and each group by several hours, this
process will take several days. Thus the moon will rotate
significantly during the launching of the projectiles 
perhaps as much as 45 degrees. The tilt of the orbital axis
of the moon relative to a normal to the ecliptic plane may
prevent launching of projectiles during part of the moon's
orbit, but this will be only a small percentage of the time
and will not interfere with our plans.
The spaceship itself will have three major components:
an electromagnetic projectile launcher/catcher, a nuclear
power system to provide the electricity to drive the EMPL
(and everything else), and the crew's quarters. The entire
spaceship will be rotated axially about the long axis of the
EMPL to provide gyroscopic stabilization and artificial
gravity for the crew. In order to make the artificial
gravity relatively uniform, the crew's quarters will be
constructed in the shape of a ring. The ship's EMPL will be
about 6 kilometers long and the on board nuclear power
system will be rated at about 500 MW. These capabilities
should allow the spaceship to launch or catch one metric ton
projectiles at up to 10 kilometers per second at roughly two
minute intervals. Of course it could handle higher velocity
projectiles at the cost of longer capacitor charging times.
The anticipated mass of the spaceship will be 3000
metric tons. This includes 1900 tons for the EMPL (317
kg/meter), 100 metric tons for the nuclear power system (0.2
MT/MW), and 1 metric ton per crew member for each of the
1000 crew members. The allocation per crew member includes
everything: the crew member, his clothes, his space suit,
his furniture, his food production facilities, his equip
ment, his living quarters, air, water, and so on.
Food will be grown on board in a hydroponic production
facility. Each of these goals will be difficult to achieve,
but ingenuity and perseverance will triumph. Some latitude
is also possible  i.e. 4000 tons would be manageable.
Due to the artificial gravity, the crew will be able to
move about relatively normally  to eat, to sleep, and to
accomplish simple bodily functions normally. In addition,
human muscles should not atrophy and extensive daily
exercise programs will not be necessary. Perhaps most
importantly, the artificial gravity should be sufficient to
inhibit the bones of the crew from decalcifying  a known and
very dangerous consequence of weightlessness.
There are numerous reasons for carrying a large crew.
Among them are the following:
1. It will transform the first Mars mission into the
greatest international expedition of all time.
2. It will cause an exponential increase in public
interest and political support for the project.
3. Actual participation, in the form of on board seats,
can be sold to the public worldwide to raise funds
to support the project.
4. The cost per person will be greatly reduced from
that which would occur if a crew of fewer than 10
were sent on a similar mission.
5. The knowledge and experience to be gained from a
large crew is clearly much greater than could be
accomplished with a small crew.
6. The crew will not be a small elite group selected
in some obscure suspicious way by unknown and
untouchable bureaucrats.
7. Crew members need not be special in any way (except
perhaps in not being seriously ill); however, since
weight will be important, women may have a preference.
THE FIRST EXPEDITION TO MARS
The first expedition to Mars can be sketched out in the
following paragraphs. Using materials derived from the moon,
a 10 kilometer EMPL will be built at the north pole of the
moon. From there it will be possible to launch objects into
the plane of the orbit of the moon and to either of the
Lagrangian points, L4 or L5. Again using materials derived
from the moon, a spaceship will be assembled in orbit around
the Earth at L4 or L5. This will be an unmanned spaceship
consisting primarily of a 6 kilometer EMPL and a 500 MW
nuclear power system to drive it. The fissionable material
for the nuclear power system will be supplied from Earth.
This spaceship will carry a cargo of several thousand
"smart" projectiles, which will be produced on the moon and
lifted to the spaceship. The ship will break away from the
Earth's gravity by launching a few hundred of the projec
tiles in the opposite direction. Next, the Lunar EMPL will
launch more projectiles toward the spaceship. These will be
caught and saved by the spaceship, but they will accelerate
the ship on its way to Mars. After a leisurely trip it will
approach Mars. By launching several hundred of its projec
tiles, the ship will enter a circular orbit about Mars.
There it will locate and match orbits with Phobos, the
larger satellite of Mars. It will then attach itself to
Phobos and await the arrival of the next (manned) spaceship.
The second spaceship will be assembled in a similar
manner at L4 or L5. But this ship will have a crew of 1000,
who will be lifted from Earth by one of the various ground
to space planes currently being developed such as Hotol or
Spacebus or Space Van or the German Sanger project. They
will be lifted from the Freedom space station (or Mir, if
Freedom is cancelled) to L4 or L5 with the same space plane.
A few hundred projectiles will also be carried on board
the spaceship. They will be used to break out of Earth orbit
as the first ship did. Once on its way, the Lunar EMPL will
begin launching groups of projectiles toward the spaceship.
It will require about 160 projectiles to increase the
velocity of the ship by one kilometer per second. After the
ship catches and relaunches 20 groups, the ship's velocity
will be about 19 kilometers per second. Cruising time to
Mars will be about 41 days. When the second ship is still
several days from Mars, the first ship will launch projec
tiles to slow down the second ship. It will then be
maneuvered into orbit around Mars. Actual landing on Mars
and return to Martian orbit will be accomplished with the
usual LOXLH2 produced from water present on Phobos.
The return trip will be similar, beginning with
breakaway from Martian orbit and the launching of more
groups of projectiles from the EMPL now on Phobos. As the
returning ship approaches the moon, projectiles will be
launched from the Lunar EMPL to slow down the ship and help
maneuver it into high Earth orbit again.
Note that Phobos has a very low gravitional field so
that the first ship will be able to attach itself to Phobos
without damage. (This may require partial disassembly and
reassembly of the EMPL.) Conversely, Phobos is large enough
that the launching of several thousand (or even millions)
projectiles will not disturb its orbit.
COMPARISON WITH C.E. SINGER PROPOSAL
The following table compares the specifications of the
C.E. Singer proposal with those of this scheme.
Table 1
COMPARISON OF MOMENTUM TRANSFER PROPULSION SCHEMES
C.E. Singer C.R. Willis
EMPL length 100,000 km 10 km
EMPL power requirement 15,000 GW 2,500  40,000 MW
EMPL deployment interplanetary north pole of moon
space & onboard spaceship
Projectile mass 3100 gms 13 MT
Projectile velocity 0.25 c 10  300 km/sec
Projectile guidance none complex
Projectile acceleration (0.3  4)e+6 g (0.5  20)e+3 g
Spaceship mass under 1000 MT 3000  5000 MT
Spaceship velocity 0.12 c 10  300 km/sec
Spaceship crew none 1000
( EMPL = Electromagnetic projectile launcher )
SPECIFIC IMPULSE COMPARISONS
The total delta velocity of the outward bound leg of the
Mars mission is about 40,000 meters per second or 40 km/sec.
This corresponds to a mass ratio of about 5393 for a rocket
using LOXLH2 for fuel and having a specific impulse of 475
seconds. For a nuclear thermal rocket with specific impulse
of 950 seconds it corresponds to a mass ratio of about 73.
For a specific impulse of 2000 seconds the mass ratio = 7.4.
However, since the fuel, i.e. the projectiles, are not car
ried on board, the (fuel) mass is about 7000 MT. This gives
a mass ratio of about 3.33 (10000/3000) which corresponds to
a specific impulse of about 3390 seconds. Thus the effective
specific impulse is much higher than the exhaust velocity
divided by 9.8.
This scheme offers readily attainable specific impulses
in the range of 2000 to 10,000 seconds  or spaceship
velocities of 20 to 100 km/sec. But, best of all it requires
carrying almost no fuel! Small amounts of fuel will be car
ried for limited maneuvers. What is the primary tradeoff?
The faster you want to go, the more nuclear power you need
to drive the EMPLs. How much?
POWER REQUIREMENTS
Table 2
POWER NEEDED BY THE EMPLS FOR VARIOUS VELOCITIES
Mars mission:
Launch Lunar polar EMPL Relative Spaceship's EMPL
velocity (10 km long) velocity (6 km long)
20 km/s 2500 MW 10 km/s 500 MW
Jupiter mission:
Launch Lunar polar EMPL Relative Spaceship's EMPL
velocity (10 km long) velocity (6 km long)
40 km/s 10000 MW 20 km/s 2000 MW
Saturn mission:
Launch Lunar polar EMPL Relative Spaceship's EMPL
velocity (10 km long) velocity (6 km long)
80 km/s 40000 MW 40 km/s 8000 MW
MISSIONS TO MARS, JUPITER, AND SATURN
Now let us look at missions to Mars, Jupiter, and
Saturn. The velocity to Mars will be 20 km/sec, the velocity
to Jupiter will be 40 km/sec, and the velocity to Saturn
will be 80 km/sec. The following table was prepared to show
sample departure dates and arrival times. Note that 'Travel
time' is ROUND trip. One way is about half. All times are in
Earth days.
Table 3
FAST MISSIONS TO MARS, JUPITER, AND SATURN
Missions to Mars: outward velocity = 20 km/sec
Outbound Inbound Travel+Mars =Total
Depart Arrive Depart Arrive time time trip
6/ 3.2/01 7/11.0 8/15.3/03 9/17.9 71.35+765.30=836.65
8/22.2/03 9/24.4 10/22.3/05 12/ 2.0 74.08+758.78=832.86
10/28.7/05 12/14.2 12/ 3.9/07 1/24.4 97.91+719.74=817.65
12/11.2/07 2/ 7.7 1/ 5.1/10 3/ 4.7 117.14+697.39=814.53
1/13.6/10 3/17.5 2/ 6.8/12 4/ 7.8 123.95+691.27=815.22
2/16.0/12 4/16.7 3/14.9/14 5/11.6 118.41+697.21=815.62
3/24.3/14 5/16.7 5/ 1.9/16 6/18.9 101.35+716.28=817.62
5/10.1/16 6/21.5 7/12.7/18 8/17.1 77.82+751.16=828.97
7/19.4/18 8/21.2 9/29.3/20 11/ 5.1 69.56+770.10=839.66
10/ 5.9/20 11/15.2 11/19.0/22 1/ 5.6 87.89+733.82=821.71
Missions to Jupiter: outward velocity = 40 km/sec
Outbound Inbound Travel+Jupiter=Total
Depart Arrive Depart Arrive time time trip
11/ 9.8/00 5/24.4 8/24.6/01 3/ 9.6 392.67+ 92.13=484.79
12/13.1/01 7/ 4.7 9/19.5/02 4/10.9 407.02+ 76.78=483.80
1/13.6/03 8/11.8 10/15.3/03 5/11.1 419.01+ 64.49=483.50
2/12.9/04 9/13.7 11/11.7/04 6/11.1 425.23+ 58.97=484.20
3/14.4/05 10/13.6 12/13.3/05 7/12.2 424.11+ 60.70=484.81
4/14.6/06 11/ 9.5 1/19.3/07 8/14.4 415.99+ 70.76=486.74
5/17.6/07 12/ 5.6 2/28.3/08 9/16.1 402.97+ 84.50=487.47
6/20.7/08 1/ 1.2 4/10.9/09 10/22.4 388.87+ 99.78=488.65
7/27.8/09 2/ 1.4 5/22.2/10 11/28.1 378.46+109.83=488.29
9/ 3.8/10 3/ 9.6 6/29.5/11 1/ 4.5 375.79+111.90=487.69
Missions to Saturn: outward velocity = 80 km/sec
Outbound Inbound Travel+Saturn=Total
Depart Arrive Depart Arrive time time trip
3/11.9/10 9/19.6 11/ 8.7/10 5/19.6 383.29+ 50.09=433.38
3/24.8/11 10/ 5.1 11/19.7/11 5/31.7 388.32+ 45.57=433.89
4/ 5.6/12 10/19.2 11/29.0/12 6/13.4 393.02+ 40.82=433.84
4/18.2/13 11/ 2.3 12/ 9.6/13 6/26.1 397.19+ 36.74=433.93
4/30.6/14 11/17.0 12/20.7/14 7/ 8.9 400.67+ 33.70=434.37
5/12.8/15 11/30.5 12/31.6/15 7/20.2 403.33+ 31.04=434.36
5/24.3/16 12/12.6 1/11.2/17 8/ 1.7 405.06+ 29.58=434.65
6/ 5.2/17 12/25.1 1/22.8/18 8/13.8 405.82+ 28.78=434.60
6/17.3/18 1/ 6.0 2/ 4.4/19 8/26.2 405.57+ 29.35=434.92
6/29.5/19 1/17.6 2/17.8/20 9/ 7.1 404.32+ 31.24=435.56
ADVANTAGES OF MOMENTUM TRANSFER PROPULSION SYSTEM
What are the advantages of this scheme compared to
current spaceship propulsion systems?
1. Crew safety. Due to the provision of artificial gravity,
which is in turn due to the large size of the spaceship,
the crew will experience normal gravity throughout the
trip rather than the very dangerous microgravity of all
past or currently planned missions.
2. Crew size. Due to the very large crew (of 1000), the per
sonnel will not be a small elite group selected in some
obscure and suspicious way by unknown and untouchable
bureaucrats. Ordinary people will be able to buy a seat
or seats.
3. Crew comfort. Due to the large size of the spaceship,
each crew member will enjoy 75 cubic meters of living
space. Crew members will be invited to help design their
own quarters.
4. Short trip duration. The momentum transfer propulsion
system can transport the spaceship to Mars in as little
as 35 days or 5 weeks (assuming a velocity of 20 km/sec).
As can be seen from table 3 above, the trip duration
varies from about 35 days to about 62 days, depending on
the date of departure. The current Mars Observer will
take 337 days to fly to Mars.
5. Reusability. The spaceship will be reusable because it
will be assembled in free space and will never land at
any of its destinations. This means that the spaceship
which we take to Mars can also take us to Jupiter and
then to Saturn, or it could become a shuttle simply going
back and forth between lunar orbit and Mars.
6. Low cost. Since one spaceship can make several or even
many trips, the average mission cost will drop with each
mission. The primary fuel, i.e. the projectiles, will be
manufactured on the Moon and therefore should be rel
atively low cost. Once the lunar polar EMPL and spaceship
are built, the system will be paid for and subsequent
missions to Mars will cost almost nothing.
THE PHYSICS AND MATHEMATICS OF THE INVENTION
No fancy equations or physics are required to explain
this invention. Simple concepts will do. Table 4 shows the
acceleration required in thousands of Earth gravities (KG)
to achieve the given velocity, V, in kilometers per second
for electromagnetic projectile launchers of various lengths
from 2 kilometers to 10 kilometers. The columns labeled by T
give the time in seconds necessary to achieve the given
velocity. Recall from basic physics that velocity equals the
product of acceleration times time for a constant rate of
acceleration. Also for a constant rate of acceleration,
distance traveled equals one half of the product of that
acceleration times the square of the time. Expressed in
equations we have:
V = A * T (1)
D = 0.5 * A * T * T (2)
By squaring the first equation and substituting into the
second equation we get:
D = V * V / ( 2 * A ) or (3)
A = V * V / ( 2 * D ) (4)
Equation (4) was used to calculate the results of table 4
which were converted to KGs by dividing the result by 9800
meters per second per second. By substituting for A in
equation (1) from equation (4) we get:
T = 2 * D / V (5)
Table 4
ACCELERATION REQUIRED FOR SPECIFIED PROJECTILE VELOCITY
LENGTH OF EMPL IN KILOMETERS
4 6 8 10
V KG T KG T KG T KG T
5 0.32 1.60 0.21 2.40 0.16 3.20 0.13 4.00
10 1.28 0.80 0.85 1.20 0.64 1.60 0.51 2.00
15 2.87 0.53 1.91 0.80 1.43 1.07 1.15 1.33
20 5.10 0.40 3.40 0.60 2.55 0.80 2.04 1.00
25 7.97 0.32 5.31 0.48 3.99 0.64 3.19 0.80
30 11.48 0.27 7.65 0.40 5.74 0.53 4.59 0.67
35 15.62 0.23 10.42 0.34 7.81 0.46 6.25 0.57
40 20.41 0.20 13.61 0.30 10.20 0.40 8.16 0.50
45 25.83 0.18 17.22 0.27 12.91 0.36 10.33 0.44
50 31.89 0.16 21.26 0.24 15.94 0.32 12.76 0.40
It is important to know how many of these smart
projectiles are required to propel the spaceship. Table 5
shows the number of projectiles required (N) to increase the
velocity of the spaceship by approximately one kilometer per
second. The column labeled V is the velocity of the
projectiles as they leave the first electromagnetic projec
tile launcher in kilometers per second. Of critical impor
tance here is the ratio of the mass of the spaceship to the
mass of the projectiles. Let that ratio be denoted by R,
then we have:
R = mass of spaceship / mass of projectile (6)
Let us define the following variables:
m = mass of projectile
v = velocity of projectile
p = momentum of projectile
M = mass of spaceship
V = velocity of spaceship
P = momentum of spaceship
M' = new mass of spaceship
V' = new velocity of spaceship
The momentum of the projectile as it approaches the
spaceship will be given by the product of its relative
velocity and its mass:
p = ( v  V ) * m (7)
The momentum of the projectile will be transferred to the
spaceship ( plus the projectile ) when the electromagnetic
projectile launcher on board the spaceship catches the
projectile. We can calculate the velocity change for the
spaceship from the law of conservation of momentum.
dV = p / M' or (8)
dV = ( v  V ) * m / ( M + m ) or (9)
dV = ( v  V ) / ( R + 1 ) (10)
Notice that the mass of the projectile cancels out in
equation (10) leaving us with the ratio. Now we have the
following:
M' = M + m = m * ( R + 1 ) (11)
dV = ( v  V ) * m / M' (12)
V' = V + dV (13)
By iteratively recalculating equations (11),(12), and (13)
we can find a number N such that the final mass and velocity
of the spaceship are given by:
M' = M + N * m (14)
V' >= V + 500 (15)
The spaceship has now caught N projectiles and next we will
throw them back. In a similar manner we find the following:
dV = v * m / M (16)
M' = M  m (17)
V' = V + dV (18)
Notice that in equation (16) there is no subtraction of the
velocity of the spaceship. This is because the velocity of
the spaceship relative to itself is zero. After we have
thrown all the projectiles, we find that the mass of the
spaceship is back to its original value and the velocity of
the spaceship is at least one kilometer per second faster
than when we started. The columns labeled VEL give the
actual calculated velocity increase of the spaceship in
meters per second. These numbers are shown for various
values of R, the mass ratio.
Table 5
NUMBER OF PROJECTILES FOR 1 KM/SEC INCREASE IN SHIP VEL
MASS RATIO IN THOUSANDS
1 2 3 4
V N VEL N VEL N VEL N VEL
5 112 1004.25 223 1000.09 334 1000.37 445 1000.50
10 53 1009.51 106 1004.64 158 1000.17 211 1000.07
15 35 1008.02 69 1001.39 104 1003.68 138 1001.45
20 26 1019.92 52 1000.06 77 1000.59 103 1000.49
25 21 1008.53 41 1009.39 62 1000.86 82 1003.21
30 17 1006.93 34 1007.06 51 1007.10 68 1007.12
35 15 1003.11 29 1003.97 44 1003.77 58 1004.04
40 13 1029.71 26 1009.85 38 1003.73 51 1000.29
45 12 1025.16 23 1003.54 34 1011.33 45 1003.97
50 11 1040.79 21 1016.69 31 1008.65 41 1004.63
Now we wish to calculate the acceleration of the
spaceship during the catching and throwing of the projec
tiles. This is important because humans are fragile and
cannot tolerate very high accelerations. For this calcu
lation we have selected a electromagnetic projectile laun
cher 6 kilometers in length. We assume it is capable of
launching projectiles according to table 4. Therefore the
time to catch (or launch) a projectile will be the same as
in table 4. Again V is in kilometers per second and T in
seconds. It is clear that the more massive the spaceship,
the less will be its acceleration. The deceleration (or
acceleration) of the projectile is given by equation (4).
The acceleration of the spaceship will be approximately:
a = dV / dt or (19)
a = V * m / M / dt from (16) or (20)
a = V / R / dt or (21)
a = V / ( R * dt ) but dt = T from (5) (22)
a = V / ( R * 2 * D / V ) or (23)
a = V * V / ( 2 * D * R ) substituting from (4) (24)
a = A / R (25)
Notice that the acceleration experienced by the spaceship is
quite acceptable for velocities up to 25 kilometers per
second when the mass ratio is two or three thousand. The
columns labeled G are in Earth gravities.
Table 6
SHIP'S ACCELERATION FOR EMPL OF ** 6 ** KILOMETERS
MASS RATIO IN THOUSANDS
1 2 3 4
V G T G T G T G T
5 0.21 2.40 0.11 2.40 0.07 2.40 0.05 2.40
10 0.85 1.20 0.42 1.20 0.28 1.20 0.21 1.20
15 1.91 0.80 0.96 0.80 0.64 0.80 0.48 0.80
20 3.40 0.60 1.70 0.60 1.13 0.60 0.85 0.60
25 5.31 0.48 2.66 0.48 1.77 0.48 1.33 0.48
30 7.65 0.40 3.82 0.40 2.55 0.40 1.91 0.40
35 10.41 0.34 5.21 0.34 3.47 0.34 2.60 0.34
40 13.59 0.30 6.80 0.30 4.53 0.30 3.40 0.30
45 17.20 0.27 8.61 0.27 5.74 0.27 4.30 0.27
50 21.24 0.24 10.62 0.24 7.08 0.24 5.31 0.24
This table (7) gives the same data as table 6 except that
the length of the on board electromagnetic projectile
launcher is 10 kilometers instead of 6 kilometers as in
table 6.
Table 7
SHIP'S ACCELERATION FOR EMPL OF ** 10 ** KILOMETERS
MASS RATIO IN THOUSANDS
1 2 3 4
V G T G T G T G T
5 0.13 4.00 0.06 4.00 0.04 4.00 0.03 4.00
10 0.51 2.00 0.25 2.00 0.17 2.00 0.13 2.00
15 1.15 1.33 0.57 1.33 0.38 1.33 0.29 1.33
20 2.04 1.00 1.02 1.00 0.68 1.00 0.51 1.00
25 3.19 0.80 1.59 0.80 1.06 0.80 0.80 0.80
30 4.59 0.67 2.29 0.67 1.53 0.67 1.15 0.67
35 6.24 0.57 3.12 0.57 2.08 0.57 1.56 0.57
40 8.16 0.50 4.08 0.50 2.72 0.50 2.04 0.50
45 10.32 0.44 5.16 0.44 3.44 0.44 2.58 0.44
50 12.74 0.40 6.37 0.40 4.25 0.40 3.19 0.40
The next item of interest is the amount of power
necessary to operate these electromagnetic projectile launc
hers  especially the ones on board spaceships. The kinetic
energy of any mass is given by one half the product of that
mass times the square of its velocity.
E = 0.5 * m * V * V (26)
If the launchers could operate at 100% efficiency, this
would give us a good idea of the power required. Table 8
shows the energy of a one kilogram projectile travelling at
the specified velocity ,V, in kilometers per second. The
energy, E, from equation (26) is in megajoules. The power,
P, is given in megawatts for three different lengths of
electromagnetic projectile launchers. P is calculated by
dividing the required energy, E, by the time, T, from the
corresponding entry of table 4.
P = E / T or substituting from (5) (27)
P = 0.5 * E * V / D (28)
Table 8
POWER REQUIRED FOR A ONE KILOGRAM MASS AT VELOCITY, V
LENGTH OF EMPL IN KILOMETERS
6 8 10
V E P P P
5 12.5 5.21 3.91 3.13
10 50.0 41.67 31.25 25.00
15 112.5 127.84 105.14 84.59
20 200.0 333.33 250.00 200.00
25 312.5 651.04 488.28 390.63
30 450.0 1125. 849. 671.
35 612.5 1801. 1331. 1074.
40 800.0 2666. 2000. 1600.
45 1012.5 3750. 2812. 2301.
50 1250.0 5208. 3906. 3125.
In order to propel a spaceship of the expected size and
mass, it will be necessary to use much more massive
projectiles than 1 kilogram. Projectiles of about 1000
kilograms will be required. Fortunately this does not mean
that we will need 1000 times the power. The power requi
rements of table 8 were for continuous operation but such is
not required. Electromagnetic projectile launchers can be
operated or powered by capacitors which we may take as long
as we wish to charge up. This is clearly a tradeoff wherein
we can manage with less power if we are willing to accept
the penalty of lengthy capacitor charging periods between
each projectile launch. To achieve 1000 times the energy of
table 8, we can use 10 times the power applied over 100
times the time. In other words, we will take about 100
seconds to charge up the capacitors of the EMPL fully, using
10 times the power given in table 8 in order to launch (or
catch) each projectile. Table 9 shows the time, T(in days)
required to accelerate the spaceship by one kilometer per
second. The number of projectiles, N, was calculated exactly
as in table 5. The velocity of the projectiles relative to
the spaceship is V, in kilometers per second. The power of
the on board EMPL (in megawatts) is indicated by the column
headers in the table. The mass ratio, R, used was 3000, the
mass of the projectiles was 1000 kilograms, and the length
of the ship's EMPL was assumed to be 6 kilometers. The
energy of each projectile was calculated from equation (26)
 with 'm' set to 1000 kilograms. The capacitor charging
time(in minutes) is then given by:
CT = E/P/60.0; (29)
Where P is the power of the spaceship's EMPL in megawatts.
We have allowed 10% extra time between each projectile
launch. Therefore, the time between projectiles, DT (in
minutes), is given by:
DT = 1.1 * CT; (30)
The total time, T (in days), is therefore given by:
T = 2 * DT * N / 60.0 / 24.0; (31)
Table 9
TIME(T) TO ACCELERATE SPACESHIP BY 1KM/SEC (IN DAYS)
POWER OF SPACESHIP'S EMPL IN MW
200 500 1000
V N DT T N DT T N DT T
5 334 1.04 0.53 334 0.42 0.21 334 0.21 0.11
6 273 1.50 0.63 273 0.60 0.25 273 0.30 0.13
7 231 2.04 0.72 231 0.82 0.29 231 0.41 0.14
8 200 2.67 0.81 200 1.07 0.33 200 0.53 0.16
9 177 3.38 0.91 177 1.35 0.37 177 0.68 0.18
10 158 4.17 1.01 158 1.67 0.40 158 0.83 0.20
11 143 5.04 1.10 143 2.02 0.44 143 1.01 0.22
12 131 6.00 1.20 131 2.40 0.48 131 1.20 0.24
13 120 7.04 1.29 120 2.82 0.52 120 1.41 0.26
14 112 8.17 1.40 112 3.27 0.56 112 1.63 0.28
15 104 9.38 1.49 104 3.75 0.60 104 1.88 0.30
NUCLEAR POWER GENERATION SYSTEM
The weight to power ratio given above was 0.2 MT/MW
which is much better than the SP100 specification which is
about 30 MT/MW. However, Brookhaven National Laboratory has
built a gas core particlebed reactor that can produce 200MW
from a 300kg 1.0x0.56 meter package [1, p.302]. That amounts
to a weight to power ratio of 0.0015 MT/MW. The plasma from
the reactor could be run through a magnetohydrodynamic (MHD)
generator to convert the power into electricity while still
keeping the mass low. Current experiments indicate that a
power density of 40MW per liter is possible [4,p.201]. That
scales up to 40,000MW per cubic meter, which is what we need
to get to Saturn. Superconducting magnetic energy storage
(SMES) systems may be used instead of capacitors to store
the energy to drive the EMPLs, but that can be determined
at a later date.
CONCLUSION
A way to reach the planets is now available. Will any
body listen? I have written a book called "JOBS for the 21st
Century" which describes my plan to visit Mars and Jupiter
in detail. If you are interested please contact me at:
C.R. Willis, 3311 Santa Monica Dr., Denton, TX., 76205 or at
crwillis@androidworld.com
REFERENCES
1. "Guide to the Strategic Defense Initiative", ed. by R. H.
Buenneke & J.A. Vedda, ISBN 0935453113.
2. "The High Frontier", G.K. O'Neill, ISBN 0688031331.
3. "Interstellar Propulsion Using a Pellet Stream for Momen
tum Transfer", C.E. Singer, JBIS v33, 1980, p.107116.
4. "Aviation Week and Space Technology", 1/20/92.
