Artificial gravity is now known to be needed for
long-duration space travel, because (1) decades of experience in orbiting space
stations has shown that there are limits to the effectiveness of our countermeasures
to microgravity disease, (2) there are many recently-discovered but initially-unanticipated
ill effects with no countermeasures yet available at all, and (3) the sum of
all that experience points to a time limit of about 400 days for exposure to
weightlessness, and still have a decent chance to recover acceptably. That
trend is in the wrong direction for planning to use long-duration weightless
spaceflight. This is listed in Table 1.
There is only one set of physics that we have available for
the production of artificial gravity: centripetal acceleration acentr
(that some call centrifugal force), produced by spinning around some center at
some spin radius Rspin, and at some spin rate N. Those 3 variables
are related as shown in Figure 1 below. For purposes of units
conversion, be aware that there are 3.2808333 feet per meter. Everything else
anyone might want to know is already in the figure.
The very first question that comes to mind is “how much
artificial gravity is enough?”, meaning what rim gee do we need to supply? The
right answer is very unclear, since humans have never ever experimented with
partial gee in rotating space stations in Earth orbit. We only have
experience with 1 full gee down here on Earth, and at 0 gee (weightlessness) in
orbit. There is nothing, no experiences at all, in between those two
extremes!
This is further complicated by time limitations, and by
short-duration exposures of crews to high mission gees for the transients of
rocket braking, entry deceleration, and so forth. We went into our roughly 5
decades of 0-gee orbiting space station experiences, expecting to find muscle
atrophy and bone density loss, and looking for countermeasures to both
problems.
Figure 1 – Using Spin for Artificial Gravity
We found a lot more adverse effects than initially expected,
and have found no countermeasures yet for most of those. The countermeasures
for muscle atrophy and bone density loss are exercises and drugs as expected,
but we have found definite time limitations, even for those: about 400 days max exposure time to
weightlessness. And those experiences are limited further to entry aerobraking
gees in the 3 to 4 gee range, returning to Earth from low orbit.
The only other actual-experience data we have at all, are
from the Apollo lunar missions. Those crews were fully Earth-fit at launch, and
exposed to weightlessness for no more than about 2 weeks during their missions.
They experienced very near 11 gees during entry braking, in those free returns
from the moon. They did just fine, enduring those gee levels at that level of
fitness.
The net result is that for partial-gee spin gravity, be
it lunar at 0.165 gee, or Martian at 0.382 gee, we must observe the same
limitations as for weightlessness exposures, meaning no more than 4 gee transient
exposures, after any long exposures to low gravity. There is no data to
support any other conclusion! Further, the total mission duration must
match the weightless max mission duration limit of about 400 days, again
because there are no data to support any other conclusion.
Violate either limit, and we must supply about 1 full gee’s
worth of spin gravity, in order to be fully Earth-fit, and so able to take a
transient of 11+ gees during the mission. Further, interruptions in artificial
gravity likely should not exceed the 2 weeks demonstrated during Apollo. This
is summarized in Figure 2.
Figure 2 – What Artificial Gee Level Do We Need?
There are only 3 variables interacting to provide artificial
gravity: rim gee, spin radius, and spin rate. Mathematically, any two determine
the third, per the first figure.
The limits on supplied gee were just discussed above: either
weightlessness for no more than 400 days and exposures to no more than 4
transient gees, or else full 1 gee artificial gravity, able to endure 11+ gees
transient exposure, and likely limited to no more than 2-week-long
interruptions with weightlessness.
The limitations on spin rate and spin radius are shown in
Figure 3, to the extent that any of this is known, and supported by any actual
experiences or data. There is a long-standing but anecdotal-in-nature
perception that 3 to 5 rpm, or really maybe only 3 to 4 rpm, is tolerable for
essentially steady-state exposures to spin rate. The 5 rpm figure, coupled with
partial gee, is the genesis of the centrifuge design depicted in the 1968 movie
“2001, A Space Odyssey”. None of this is
supported by hard test data, though. Those tests were never run because of
the presumption that the countermeasures for weightlessness would allow weightless
long-term space travel. That has proven to be an error, as this
article indicates.
Much more recently, NASA has funded some efforts at academic
institutions to investigate some aspects of the limitations to spin gravity.
The most notable of these (Reference 1) determined that with sufficient individualized
acclimatization training, many persons could tolerate spin rates up to perhaps
20 rpm, in terms of the “cross-Coriolis” effect. That is the
sudden-onset (and often severe) nausea induced by sudden head movements out of
the spin plane. This was work done by the University of Colorado Boulder in
cooperation with Arizona State University, and funded by NASA.
There are other possible effects, and those have yet to be
tested. One possibly serious effect is the gee gradient along the spin
radius, which induces a significant
difference in gees as felt at the head, versus the “rim gees” felt at the toes,
while standing. This is also indicated in the figure. There are two serious
effects to be anticipated from the gee gradient: (1) blood pooling in the legs
which could lead to fainting if a so-called “gee suit” is not worn, and (2)
long term weakening of the heart or vascular system, from the heart not having
to work so hard, pumping blood back up from the feet to the heart at lower
average gee. These are unexplored risks at this time.
There is also a sort of practical lower limit on spin
radius. The numbers quickly get entirely ridiculous if the spin radius does not
exceed about 2 or 3 man-heights. The more-or-less-average height of a standing
human is about 1.65 m (65 inches, or about 5 feet 5 inches). That puts the
practical geometric minimum spin radius (exclusive of health effects) at around
3 to 5 meters.
The upper limit on spin radius depends entirely upon what
might be practical to build. That is an entirely separate topic, not covered
here. Just be aware that bigger is always more expensive.
As for higher spin rates,
that depends upon how long a training and acclimatization interval one
can afford, but there is still an ultimate limit, of about 20 rpm after about
40-50 days of training, as depicted by the plot in Figure 4 below, obtained from Ref.1. For lower spin
rates, those training intervals are shorter, as depicted, but there was still
training needed at 5 rpm.
Figure 3 – What Are the Limits on Spin Rate and Spin Radius?
However, it would be wise to use increased intervals and
decreased spin rates, versus those shown in the figure, as the same reference
indicated a large confidence interval, meaning a lot of scatter in the data.
Even so, there were no spin rates higher than 20 rpm that proved trainable at
all. Anecdotally, something like 3 or 4 rpm may need no training at all, but
that is below the range of rpm that was tested, in the cross-Coriolis study.
Figure 4 – There Are Actual Experiments for the
Cross-Coriolis Effects
Conclusions
There are known, and still unknown, limits on the spin
gravity design problem. What we know, or can surmise, follows. Each of
the 3 variables needs to fall within the appropriate limits, or else the design
must be deemed infeasible. These are also briefly summarized in
Table 2 below.
Level of gee supplied
Until we actually know better, the gee level to be supplied
can be either 1 full gee, or a lower value,
including zero gee. At present, there is nothing known in-between those limits,
so that partial gee cannot be supposed as any different from weightlessness, in
order to take a conservative approach with respect to health risks. Zero or
any level of partial gee is OK, if (1) the transient gee exposure does not
exceed about 4 gees, and (2) the low-gee exposure does not exceed
about 400 days. Note the “both-and” coupling of the two limits!
But if the transient gee exposure does exceed 4 gees or
the mission exposure time exceeds about 400 days, the only currently-supportable
choice is supplying near 1 full gee, with a demonstrated capability of
resisting transient 11 gee exposures. There is also a relevant-but-different time
limit: no more than about a 2-week zero-gee transient interruption to the near-1-full-gee
artificial gravity. That was demonstrated during Apollo, but may actually be
longer. We just do not know. Note the “either-or” coupling of these limits.
That reflects the necessary conservatism, relative to the “both-and” coupling
of the limits to the low gee case.
Spin
rate limits
It is known from Ref. 1 that for the cross-Coriolis
problem, training can raise the max spin rate tolerable, to (at the very most) about
20 rpm, with something like at least 40-50 days training. There is enough
scatter in their data to justify reducing this to about 15 rpm with an increase
to about 60 days’ training. Lower spin rates require shorter training, down to
about 5 rpm with very little training. However, this is the one and only effect
so far evaluated, and it was tested in short-term centrifuge tests. Therefore, this
limit is probably subject to future revision. Further, the training had
to be very individualized: there is no general rule-of-thumb to use! That
is likely to be expensive training!
Longer term, there may be other limitations, we just do not
know “for sure”. Anecdotally, the no-training threshold may be nearer 3-to-4
rpm (since 5 rpm needed training), for very long-term (essentially
steady-state) rotation rate exposures. No one knows for sure, as the
experiments have yet to be done.
About 4 rpm max (or maybe a more conservative 3 rpm) is
recommended by this author for the no-training threshold, until we know better.
There is no minimum spin rate limit that we know about, or can imagine.
Spin
radius limits
These are still unexplored experimentally, as best this
author can tell. It shows up in the radial gee gradient, which causes
head-to-toe gee differences, which could then cause any of a variety of health
effects. They could show up as blood pooling in the legs, or in weakening of
the heart from having to work so much less pumping blood up from the toes back
to the heart, at lower average gee. No
one yet knows for sure.
From a practical geometry standpoint, spin radii probably
ought to be at least 2 to 3 times the average height of a standing person, or
about 3 to 5 meters minimum. The unexplored health effects may well increase
that. Nobody yet knows for sure. A wild guess says keep the
head-to-toe gee difference under about 0.1 to 0.2 gees. That limits the gee
gradient down the spin radius to something around 0.1 gees per meter of spin
radius maximum.
The maximum spin radius is determined by the practicality
and expense of what can be built, more than anything else, so far as we know. Those
are not health risk issues. Accommodating large spin radii in smaller vehicle
designs will be rather challenging to say the least. That much is certain.
Final remarks
For manned interplanetary voyages, there are many vehicle
design requirements that are also necessary for unmanned missions. These
include protection from microgravity diseases (the topic here), protection from
radiation exposures, protection from excessive heat and cold, and protection
from meteoroid impacts. Those last two also apply to unmanned vehicle designs. None
of those others (besides spin gravity) are addressed in this article.
However, spin gravity and some or all of those other
protections, are integral to the design of interplanetary vehicles in general,
as a part of the larger topic of mission and vehicle design approaches to
make interplanetary travel less difficult and dangerous. The vehicle
designer must worry about all these things.
One part of that is the reduction of the departure velocity
requirement from low Earth orbit by means of a reusable space tug-assist, the
subject of Refs. 2 and 3. Another part of that is the application of
the lessons of history regarding getting from early exploration to being
truly ready to plant permanent settlements. That is the topic of Ref. 4.
These things all go together, but taken all at once, the article would be too
big to be posted, or to be presented as a paper. That does suggest a book, and
not a small one.
References:
#1. Bretl and Clark, “Improved Feasibility of Astronaut
Short-Radius Artificial Gravity Through a 50-Day Incremental, Personalized,
Vestibular Acclimation Protocol”, a paper published in 2020 as open-access by
Nature Partner Journals, in npj/microgravity as npj Microgravity (2020) 6:22 ; located
at https://doi.org/10.1038/s41526-020-00112-w;
work done by University of Colorado Boulder, in cooperation with Arizona State
University Biodesign Institute, and supported by NASA.
#2. G. W. Johnson, “Tug-Assisted Arrivals and Departures”,
posted 1 December 2024, at http://exrocketman.blogspot.com.
#3. G. W. Johnson, “SpaceX’s Starship As a Space Tug”,
posted 2 January 2025, at http://exrocketman.blogspot.com
(update added for evaluating Centaur stages as tugs).
#4. G. W. Johnson, “Exploring Mars Is Not Settling Mars”, posted
1 February 2025, at http://exrocketman.blogspot.com.
For references that are articles posted on this site, all
you need in order to find them without scrolling down (the hard way) is to jot
down the date of posting and the title. Then use the archive tool, left side of
page. Click on the year, then the month, then the title if need be (such as if
there was more than one posting that month). Anything posted here is freely available
by simple copy-and-paste.
There are lists sorted by topic of many of my technical
articles posted on the “exrocketman” site. Those were posted 21 October 2021 in
an article title titled “Lists of Some Articles By Topic Area”. I try to keep
it updated, but the very latest articles may not yet be added to it. This
includes in the radiation risk topic list my best take on NASA’s own radiation protection
data and (older) exposure limits, with 5 October 2018 “Space Radiation Risks:
GCR vs SFE”, and 2 May 2012 “Space Radiation Risks”. Both reference the same
NASA site, and identify it.
