russ
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Orion ships: Could they be engineered?
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Oct 12 00:32 UTC 1998 |
This item is an offshoot of Space.cf item #10, which is about the
feasibility of nuclear-pulse driven spacecraft. [See that item
response 0 for a definition of Orion, and the expected range of
operating conditions.] The basic scenario is that small fission
bombs explode behind the spacecraft, and the force impinging upon
a "pusher plate" is used to propel the vehicle.
Driving a ship with atomic bombs sounds like it would lead to a
pretty rough ride. The hammer-blows of the explosions would be
quite hard on delicate cargo (like people). When each "pulse unit"
(bomb) explodes, the pusher plate receives a sudden kick. In a
matter of a millisecond or so, its speed changes very suddenly.
What can be done to smooth this out?
Surprisingly, it looks like there are several possibilities which
aren't overly difficult. I will address two: spring suspensions
and compensator masses. For each possibility, I will touch on 2
operating conditions: 30 m/sec^2 acceleration at 1 pulse/sec, and
5.0 m/sec^2 at 0.1 pulse/sec. The first condition represents a
climb from a planetary surface, and the second represents a slower
acceleration to cruise speed. The mass of the pusher plate is
assumed to be either 10% or 20% of the vehicle mass.
Spring suspensions
A spring suspension is much like what you see on a car. As
a car rests on wheels which transmit force to the body through
springs, in an Orion the pusher plate would be connected to
the passenger space by springs. (These do not have to be coil
springs. They could just as easily be torsion bars or gas pistons.)
There are several ways to use a spring suspension, but I will
assume that the intent is to average the acceleration out to a
constant value over the interval between pulses. To limit the
travel of the suspension to the minimum required, I assume that
the the suspension is latched with the springs compressed until
1/2 inter-pulse intervals before the first pulse. At that time,
it is let go and the pusher plate is pushed backwards by the
springs (while the rest of the vehicle moves forwards, by
conservation of momentum). When the pulse occurs, the pusher
plate reverses direction and compresses the springs back to the
starting position at 1/2 interval after the pulse. If another
pulse follows the plate is allowed to fly backwards again.
The center-of-mass of the vehicle changes speed very suddenly,
but except for the pusher plate the change occurs at the average
acceleration rather than the instantaneous acceleration.
At 30 m/sec^2 average acceleration and 1 pulse/sec, the per-pulse
delta-V is 30 m/sec. If the pusher plate has 10% of the total vehicle
mass, each pulse changes its speed by 300 m/sec. The pusher plate is
accelerated backwards by the springs for 0.5 second to a speed of
135 m/sec, then receives a kick of 300 m/sec. In the 0.5 second
from release to the pulse, by d = 0.5 * a * t^2 the plate travels
0.5 * 270 * 0.25 = 33.75 meters from the center of mass. The remainder
of the vehicle, which is accelerating at 30 m/sec^2, travels 3.75 meters
from the center of mass in the same time. Immediately before the pulse
the two elements are moving apart at 150 m/sec; immediately afterward,
they are moving together at 150 m/sec. The situation is thus symmetrical.
The total spring travel is 37.5 meters, or about 123 feet. For the
case where the pusher plate has 20% of the total mass, the numbers are:
d(plate) = 0.5 * 120 m/sec^2 * 0.25 sec^2 = 15 m
d(ship) = 0.5 * 30 m/sec^2 * 0.25 sec^2 = 3.75 m
Total spring travel = 18.75 m = ~62 feet.
These numbers appear reasonable.
At 5 m/sec^2 average acceleration and 0.1 pulse/sec, the per-pulse
delta-V is 50 m/sec. Under these conditions, the numbers stop
looking so attractive; the distances can be expressed in
(fractional) miles without looking trivial.
For the case of the pusher plate containing 10% of the total vehicle
mass, the numbers are:
d(plate) = 0.5 * 45 m/sec^2 * 25 sec^2 = 562.5 m
d(ship) = 0.5 * 5.0 m/sec^2 * 25 sec^2 = 62.5 m
Total spring travel = 625 m = 2050 feet
At 20% pusher-plate mass-fraction, the numbers are:
d(plate) = 0.5 * 20 m/sec^2 * 25 sec^2 = 250 m
d(ship) = 0.5 * 5.0 m/sec^2 * 25 sec^2 = 62.5 m
Total spring travel = 312.5 m = 1025 feet
Could we build thousand-foot-plus long springs? I don't know; it
seems to be quite a stretch. This doesn't mean that the ship could
not be built, but perhaps building it for constant acceleration
under acceleration-to-cruise conditions isn't practical. This would
mean something like pulses of 3 G's between periods of free-fall,
repeating every 10 seconds. It might be livable, but it will never
be as comfortable as a constant push.
Compensator masses
Compensator masses are a system which uses the principle of conservation
of momentum. By F=ma, a variable force applied to a mass will cause a
variable acceleration. However, this only applies to the mass as a whole;
if it is divided into parts which move independently, different parts can
experience different accelerations. By allowing one part of the total
mass to move around more than the average, an unwanted movement in the
rest can be damped out. This part is called a compensator mass.
The compensator has to move a distance which is inversely proportional
to its mass, so to be feasible a rather large mass is required. Where
could you get it? One candidate is the on-board consumables. A manned
ship on a long mission will be carrying a large amount of air, food and
water. Figuring 1 kilo/day/head oxygen and 19 kilo/head/day water
(rehydrating freeze-dried food, drinking and washing), a crew of 150
will use about 3 tonnes a day. On a year-long mission, that's about 1100
tons. This is 11% of the mass of a 10,000 tonne ship, which seems adequate
for a compensator mass. The water alone would probably suffice.
In operation, the compensator mass would resemble nothing more than an
enormous paddle-ball. It would receive the bulk of the kick from the
pusher plate and fly forward as it slowly gave up its speed to the crew
compartment. Eventually the springs would reverse its travel, and it
would (still pulling the crew compartment ahead) return to be kicked
by the pusher plate once more.
What could you use for a spring? A gas piston is a likely possibility.
If the compensator moved inside a tube, gas pressure could provide both
the coupling between the compensator and the pusher plate and also
between the compensator and the crew compartment. Like this:
|cabin| |
________________________________ |
| |co| gas |---| <- pusher plate
| gas |mp| |---|
-------------------------------- |
|cabin| |
The cabin would be wrapped around a cylinder or cylinders. If the
compensator mass was 1000 tonnes of water, it would fill a volume 10
meters long and 100 square meters in area.
What about gas pressure? The 8000 tonnes of cabin would require 24000
tonnes of force to accelerate at the maximum level of 3 G. At roughly
10,000 N per tonne and 100 square meters of piston area, the pressure
would be 2.4 MPa, or less than 25 atmospheres. At 0.5 G, the pressure
would be about 400 KPa, roughly 4 atmospheres. A steel tube could
be built to handle this easily.
How far would the mass travel? Assuming the travel of the pusher
plate was limited, the compensator would have to move about as much
as the pusher plate in the spring-mounted scenario. If more than
10% of the total mass could be placed in the compensator, its travel
would be reduced according to the same equations. Unlike a 1000-foot
spring, a thousand-foot pipe does not appear to be difficult to make.
Miscellany
There don't appear to be any really useful side-effects of a spring
suspension system. However, the compensator-mass system might have
uses during cruise as well as boost. The long pipe may allow the
entire ship to be rotated end over end when the pulse engine was not
operating. If the crew cabin was at one end and the pusher plate
and compensator (20% of the total mass) at the other, a spin rate of
3.8 RPM would give 1 G artificial gravity in the crew sections.
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