## Sunday, July 31, 2011

### ABOUT ARTIFICIAL GRAVITY FOR LONG SPACE MISSIONS

This article discusses artificial gravity by centrifugal force for spaceflight. It supports the manned Mars mission article posted 7-25-11. This article demonstrates why “just spin the vehicle” is a naïve statement.  Update:  1-18-13 (in red):  there actually is an ship design approach not contemplated in this article that solves this problem.  See the newer article dated 7-19-12 for a rough design that uses the modular "spinning baton" approach.  I have also marked below where this concept is missing.

The concept of using a spinning design to provide a substitute for gravity (“artificial gravity”) is a very old concept, going back many decades in science fiction, and to the 1930’s and 1940’s in real scientific proposals. The late 1930’s concept of a spinning wheel space station (from the von Braun group in Germany) is an example of an early, but very real, scientific proposal.

To provide artificial gravity by spin requires a radius for the spin, a spin rate, and a design value for how much gravity (“gee”) is to be produced. These variables are related by the familiar equation from circular motion:

a = R ω^2

or:

n = R ω^2 / gc

where a is the acceleration level, R is the spin radius, ω is the angular velocity (rate of spin), n is the acceleration expressed non-dimensionally in gees, and gc is the standard acceleration of gravity. Consistent units of measurement must be used, of course. If metric, R is meters, ω is radians per second, a and gc are both meters/second2.

To find R, one must know the desired a (or n), and must have a value of ω. In other words, we need to know the answers to two simple questions: “how much gee is enough?” and “how much spin rate is too much?”

So far, we only have real human experience at one gee (here on Earth), and zero gees (out in space). There are surrogate studies, based on bed rest, but these are only surrogates, not exact models. These are no more trustworthy than dosages of drugs based on doses in mice, without human trials.

So, until real fractional gee studies are done, the design value must be one full gee. There is no other ethical, moral choice.

Tolerance of spin rate is something dependent on exposure time. I am unaware of any real long-term experimental results for this, but anecdotes based on real experiences would suggest that 4 rpm is the upper limit, perhaps plus or minus 1 rpm. People do get seriously motion sick when exposed to faster rates for long periods of time.

4 rpm = 4 rev/min = 4 rev * (1min/60 sec) * (2 π rad/rev) = 0.4189 rad/sec

There is one other issue to worry about, especially for faster spin rates. That is the gradient of gees head to toe for someone standing in an artificial gravity device. If that gradient is too large, there could be blood pooling in the legs, leading to possible fainting. We have no real criteria for this, the real human experiments never having been done. That gradient is the first derivative of the circular motion equation with respect to R:

da/dR = ω^2

or:

dn/dR = ω^2 / gc

Using the equation from circular motion in its second form above, plus the gradient equation, and using 4 rpm for the spin rate (converted to radians per second) leads directly to figure 1. Reading these curves at one gee required leads to R = 56 meters, and a very small gradient (0.0179 gee/m).

Figure 1 – Artificial Gravity Data for Spin at 4 RPM

What we learn from this is that, under these requirements, the gradient issue is of no real concern, while the size of the artificial gravity device is quite large. Size, and the weight, complexity, and expense that go with it, are extremely serious design issues for spaceflight.

There are essentially three ways to handle this dilemma: (1) cable-connected modules spinning about their common center of gravity, (2) truss-connected modules spinning about the center of gravity of the structure, and (3) simply making the entire ship (or space station) very large, and spinning it about its principal axis. These choices are shown in figure 2.

Update 1-18-13 (in red):  there is a fifth approach not shown in Figure 2 or discussed in this text that solves the "1-gee at 56 m and 4 rpm" problem.  It is to spin a slender baton configuration "head over heels",  not about the principal axis.  Otherwise,  all the physics discussed here is still true.

To adapt to the need to stage-off emptied propellant tanks,  the vehicle must be modular,  built of modules docked in orbit,  not launched from the surface all-at-once.  You simply reconfigure the docked assembly at each staging,  to maintain the same 56m (at 4 rpm) radius,  measured from the center of mass to the crew habitat.  See the newer article dated 7-19-12 for but one example of such a design study.

Figure 2 – Ways and Means to Provide 1-Gee Artificial Gravity at 4 RPM

The cable-connected module option is perhaps the simplest and lightest practical solution, except that maneuvers are impossible in the spinning configuration. This rules out mid-course corrections and collision-avoidance maneuvers. One must stop the spin and re-dock the modules to maneuver.

The truss-connected module option allows limited maneuvering of the spinning structure, as indicated, at the center of gravity. Precessional effects must be taken into account. Even so, how then does one make a major “burn” without disassembling the structure? That question has no answer at this time.

Building a ship (or space station) with a 56 meter radius is a major construction undertaking. This cannot be, and can never be, easy or inexpensive (update 1-18-13:  maybe it is not so expensive as I thought when I first wrote this) under any imaginable circumstances. It does allow maneuver easily, by simply arresting the spin. This would be appropriate for very large objects, such as colonization ships or space stations, but it is difficult to imagine how to do it with small docked modules, for something smaller overall.

We do know from space stations in Earth orbit, that exposure to zero-gee does damage to many body systems, the most well-known being bone decalcification. Unfortunately, the heart and circulatory systems also suffer. There are serious concerns about effects on the immune system as well. However, our experiences also indicate that these effects can be held to acceptable, recoverable levels by appropriate vigorous exercise, for at most about a year’s exposure.

What that says is that for journeys under a year duration, we may fly without artificial gravity, given the space and equipment to do the appropriate vigorous exercise daily. Beyond that time, we must provide artificial gravity.

We cannot count on the surface gravity of places like Mars (0.38 gee) to counter the effects of weightlessness enough to be therapeutic, simply because we have never done the experiments to find out “how much gee is enough?” That means the 1 year limit applies to the round trip, not just the one-way voyage there.

The classic min-energy Hohmann trajectory to Mars is 8.5 months one-way. We can do somewhat better than that without expending a great deal of extra energy: 6 months. But, even with a 6-month one-way trajectory to Mars, the total round trip is over a year, even with a trivial stay at the planet. Most such mission designs require a considerable stay at Mars, from months to nearly 2 years, because of orbital mechanics constraints.

CONCLUSIONS:

So, until the appropriate experiments have been done, our ethics-bound criteria must be:

Provide one full gee at no more than 4 rpm, for any round trip over 1 year

Fly without gravity for up to a one year round trip, given appropriate exercise

This poses a very severe design dilemma for manned Mars missions: either fly the men very much faster than 6 months one way, or else provide one full gee artificial gravity at enormous construction difficulty and expense.

For exploration, which otherwise requires much smaller vehicles than colonization, I favor flying faster.  (Update 1-18-13:  reconfigurable docked modules in a "slender baton" spin mode could solve this dilemma without flying faster.  With commercial launchers,  this actually can be more-or-less affordable.  Launch costs are "typically" about 20% of total program costs.)

So, as always, propulsion is the key. In my opinion, the solutions to faster propulsion will likely be nuclear. It’s past time to face up to that fact, and simply get on with it.  (Update 1-18-13:  flying faster just lowers costs further,  if you can delete the artificial gravity with round trips under 1 year.)