Sunday, March 2, 2025

Spin Gravity Requirements

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.

 


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