The Gravity of the Situation

 

 

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Mobile Suit Gundam: High Frontier

Life In The Universal Century


The Gravity of the Situation

Gravity is simulated by radial acceleration, which creates some interesting side effects. Since weight is a function of acceleration, walking to the east (downspin) with the spin actually increases one’s apparent weight, as the tangential velocity of one’s forward motion is added to the radial acceleration of the colony itself. Conversely, walking west (upspin) against the spin decreases one’s apparent weight, as the tangential velocity of one’s forward motion counteracts the radial acceleration of the colony hull. The first prograde (downspin) or retrograde (upspin) step might feel like a step upward or downward, due to the initial change in apparent weight, but the sensation will pass if the motion continues for more than one or two steps at a steady speed—until the next change in direction or speed again alters one’s radial acceleration and thus one’s apparent weight.

Moving “up” (toward the axis) also reduces one’s apparent weight, such that people residing in a two-story building are ½% (5‰) “lighter” upstairs than they are downstairs. As noted in my description of life inside an O’Neill “Island Three” habitat, the drop-off is linear, so a building would have to be over 500 stories tall for this effect to become really significant, although penthouse apartments and other lofty structures would display some bizarre properties due to exaggerated Coriolis effects.

The “Coriolis effect” is an inertial force described in 1835 by Gustave-Gaspard de Coriolis (1792–1843). Coriolis showed that, if the ordinary Newtonian laws of motion of bodies are to be used in a rotating frame of reference, an inertial force—acting to the right of the direction of body motion for counterclockwise rotation of the reference frame or to the left for clockwise rotation—must be included in the equations of motion.

The effect of the Coriolis force is an apparent deflection of the path of an object that moves within a rotating coordinate system. The object does not actually deviate from its path, but it appears to do so because of the motion of the coordinate system.

Coriolis

The Coriolis effect is most apparent in the path of an object moving longitudinally. On the Earth an object that moves along a north-south path, or longitudinal line, will undergo apparent deflection to the right in the Northern Hemisphere and to the left in the Southern Hemisphere. This phenomenon occurs for two reasons. First, the Earth rotates eastward. Second, the tangential velocity of a point on the Earth is a function of latitude, such that the velocity is essentially zero at the poles and it attains a maximum value at the equator.

The Coriolis deflection is therefore related to the motion of the object, the motion of the Earth, and the latitude. For this reason, the magnitude of the effect is given by sin(Φ)v, in which v is the velocity of the object, Ω is the angular velocity of the Earth, and Φ is the latitude.

The angular kinematics relating the Coriolis force are expressed in terms of the mass of an object (m), the angular velocity of the rotating frame of reference (ω) and its velocity in a rotating frame (vr), thus: FCoriolis = -2 m (ωVr).

Centripetal (centrifugal) force is not the same as real gravity, because your head is closer to the axis of rotation than your feet and the two ends of your body are therefore subject to tidal forces due to the difference in their radial accelerations.

Simple movements become complex and the eyes play tricks. Nodding or shaking one’s head produces an illusory feeling of movement, similar to the feeling one gets standing in the surf as a wave goes out, the direction of which is dependent on one’s orientation relative to the direction of the spin.

Coriolis forces also create cross-coupled angular accelerations in the semicircular canals of the ear when the head is turned out of the plane of rotation. Any sudden movement of the head, such as a simple nod or headshake, may cause vertigo and motion sickness.

According to Space Settlements: A Design Study (1977, NASA SP-413), these Coriolis forces are such that a person jumping to a height of 55 centimeters (22 inches) would land about 5.3 centimeters (two inches) upspin—an approximate 10% spatial displacement.

Normal-G

The “hop and drop” diagrams created by Dr. Theodore W. Hall for his dissertation The Architecture of Artificial-Gravity Environments for Long Duration Space Habitation (1994, University of Michigan) illustrates the difference between gravity and pseudogravity simulated by radial acceleration. The two curves in each diagram represent the trajectories of two balls: one launched from the floor with an initial velocity of two meters per second (6.6 feet per second) and the other dropped from an initial height of two meters (6’6”).

Under Terrestrial gravity, both trajectories are straight up and down, with the “hop” reaching a maximum height of 20.4 centimeters, indicated by a short horizontal line, and the “drop” indicated by dots at 0.1-second intervals.

In an artificial gravity system, the ball trajectory is not straight up and down, but curves relative to the observer, due to the Coriolis deflection of the rotation that produces the simulated gravity. The larger the habitat, the less the resulting curve.

Hop-Drop

Everyday activities, such as sports, become complicated. A ball thrown in any direction will veer upspin, as will any free-falling liquids. (“You don’t spit into the spin!”) One can’t jump straight up and down due to this upspin veer. A jump downspin might land one back where one started, while a jump upspin might carry twice as far as one along the axis of rotation, toward either of the cylindrical colony’s end caps.

The effects on free-standing or flowing water are more complicated. In any body of water of significant size, the water level on the leading (downspin) edge might be as much as 20% lower than on the trailing (upspin) edge, due to a combination of the aforementioned upspin veer, friction and inertia, but this won’t be apparent in smaller bodies, although it may literally tip the balance as to which direction might offer the path of least resistance.

(On 15 September 2004, Dr. Hall wrote to comment on the effect on ground water. “A puddle of water on a circular floor won’t have any particular tendency to flow upspin or downspin. Tilt that piece of ‘floor’ and the water will flow from a smaller radius to a larger one. It will flow either upspin or downspin depending on which way the surface tilts. … A uniformly sloping surface in the plane of rotation has the form of a spiral. The spiral can be built to wind in either direction, independent of which way it spins. Water will flow from the inner to the outer part of the spiral, whichever way it winds, whichever way it spins.”)

Ground water, such as artificial rivers and streams, may have a general tendency to flow upspin, causing it to occasionally behave in a counterintuitive manner. All other things being equal, water seeping down through soil will also tend to deflect in that direction but, as Dr. Hall notes, where there’s different porosity or other obstructions in the upspin or downspin directions, it’ll follow the path of least resistance from a smaller radius to a larger radius and never flow toward the center unless forced by something other than the pseudogravity.

Due to the change in “elevation” (distance from the axis) and the resulting changes in its position relative to the hull, and thus to the “stationary” observer, falling water will always veer upspin, while water shooting up into the air will always veer downspin for the same reason, making for weird-looking (from our mundane perspective) cascades and fountains.

The dynamics of the airflow within the cylinder resulting from Coriolis forces and, consequently, the resulting weather, are not so straightforward.


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Last Update: 01 January 2017

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