(Note: the following is one of various posts that were copied here from the Moonwards.com forum for the sake of preserving the early days of the project. It was originally posted there on Feb 16th, 2016. An updated version of this will be posted soon.)
Okay, finally we have a reasonable design for a sunny space that uses spaced beams that are quite tall to limit radiation exposure to a livable amount even if you are hanging out there up to half the time.
Alright, suppose the little rectangle with the rays emanating from it is you. The beams start 4 m above you for a nice sense of space. In this version, the beams represented by the grey rectangles are 6 m high by 50 cm wide. The complete analysis was done using beams 4 m high by 50 cm wide. In both cases, each beam is separated by 1 m. The orange rays shows a representative set of paths radiation that passes through your body can take.
In the model of Cernan's Promise, the beams will look roughly like this:
See how it works? Straight up, there is very little material blocking radiation, you get a full dose. But because the spaces that have only glass or a transparent membrane are separated by lots of tall beams, starting a short angle away there is enough material that the dose is lowered to a small amount, and when you average the two you are a fair bit better off than if there had only been a membrane. Especially when you get into the details - those beams also protect against all micrometeorites except the ones coming straight down, which is rarely what they do. And unlike if you just dug down and put a membrane, the whole volume is usable. You don't have to stay down low in order to get a low dose.
Here is a map of how the doses work out. It bears a lot of contemplation. Because the energy in cosmic radiation is so incredibly high, it causes atomic nuclei to explode when struck and the bits that fly off have enough energy to cause other nuclei to explode too, and it takes a while before that process causes the original energy to be dispersed enough that you are getting net protection from the material shielding you instead of actually getting a lot more radiation because of the atomic shrapnel flying around.
So the map shows the area of a dome around a person through which the heightened doses due to an insufficient blocking thickness would pass. Those areas are in pink and red. The orange part offers some protection, and the yellow is better protection, good enough for permanent habitation. The green is as low as sea level on Earth. The area this dome examines is an angle of 60 degrees, roughly. Beyond where the mapping ceases, the protection has a fringe of yellow and then quickly turns to green for all the rest.
So imagine if the tall east-west sides of the beams were covered with a mirror surface. If you stand between two and look up you see nothing but stars. The are angled just slightly so that here at the equator the sun tracks around over the long day and the beams are always parallel to its rays of light, the shadows stay minimal. The Earth would be visible much of the time between the beams. When it isn't, it is still coming in from the south end, where there is a mirror pool outside the sunken hall for that very purpose. And the north wall reflect that image from the mirror pool so it is visible from inside the tunnel where people will spend most of their time.
If you'd like a few numbers, here are the basic ones (and please remember the previous post - these numbers are estimates):
Pink - covers 556 triangles, of which a half sphere has 10,240 - radiation between 0.5 and 0.13 Sv/yr. Average taken as 1 Sv/yr, cautiously on the high side. Dose of this area with constant exposure 0.027 Sv/yr
Red - covers 1120 - between 0.2 and 0.5 Sv/yr, average used is 0.4 Sv/yr (The unfilled triangles along the central axis are assumed to be red and counted in this number.) Dose of this area with constant exposure 0.022 Sv/yr
Orange - 2024 tris, average of 0.13 Sv/yr. Dose of this area with constant exposure 0.013 Sv/yr
Yellow - 964 tris, 0.07 Sv/yr. Dose of this area with constant exposure 0.003 Sv/yr
Green - 248 tris, Earth sea level equivalent, taken as 0.01 Sv/yr. If the rest of the half sphere is all green, that is another 0.003 Sv/yr. I padded that to 0.005 Sv/yr.
Which gave a round number of 0.07 Sv/yr total if you were always in that space. Spend half your time there, that's 0.035 Sv/yr. The maximum allowed for nuclear plant workers is 0.05 Sv/yr. So we're good. And we can soak up some sun and see the actual sky, and have healthy growing plants. Ahhhh....
Now let us remember what we don't know. Humans have never spent extended periods of time exposed to galactic cosmic rays. Never. The Apollo astronauts got the biggest doses in history but weren't exposed for more than 9 or 10 days each. These rays are actually particles, and they really aren't like radiation as we know it. In fact their name is a hold-over from when we thought they were radiation because they seemed like it, but actually they are protons, neutrons, and sometimes entire atomic nuclei stripped of their electrons, whipping through space at incredibly high speeds, coming from god knows where but it isn't from around here. Probably from supernovas. Our bodies repair damage from radiation if it is a small enough amount and happens slowly enough. It would in all probability react exactly the same way to cosmic rays. So we just have to keep our exposure down to levels our body can repair as part of its normal daily routine of cleaning, patching, and sprucing up. But we need to know much more before our first buff astronauts bathe in the sun in their hammocks among the tomato plants.