natural illumination solution for rotating space settlements

Natural illumination solution for rotating space settlements

Pekka Janhunena,∗

aFinnish Meteorological Institute, Helsinki, Finland

Abstract

Cylindrical kilometre-scale artificial gravity space settlements were proposed by Gerard O’Neill in the 1970s. Theearly concept had two oppositely rotating cylinders and moving mirrors to simulate the diurnal cycle. Later, theKalpana One concept exhibited passively stable rotation and no large moving parts. Here we propose and analyse aspecific light transfer solution for Kalpana One type settlements. Our proposed solution is technically reliable becauseit avoids large moving parts that could be single failure points. The scheme has an array of cylindrical paraboloidconcentrators in the outer wall and semi-toroidal reflectors at the equator which distribute the concentrated sunlightonto the living surface. The living cylinder is divided into a number of ϕ-sections (valleys) that are in different phasesof the diurnal and seasonal cycles. To reduce the mass of nitrogen needed, a shallow atmosphere is used which iscontained by a pressure-tight transparent roof. The only moving parts needed are local blinders installed below theroof of each valley. We also find that settlements of this class have a natural location at the equator where one canbuild multi-storey urban blocks. The location is optimal from the mass distribution (rotational stability) point of view.If maximally built, the amount of urban floorspace per person becomes large, up to 25,000 m2, which is an order ofmagnitude larger than the food-producing rural biosphere area per person. Large urban floorspace area per personmay increase the material standard of living much beyond Earth while increasing the total mass per person relativelylittle.

Keywords: cylindrical space settlement, O’Neill type space settlement, solar system colonisation

Nomenclature

A⊥ Cross-sectional areaau Astronomical unit, 149 597 871 kmFy Wall tension forceg Acceleration due to gravity, 9.81 m/s2

h Wall thicknessK Concentration factorLz Settlement lengthm Massp Half slitwidth (semilatus rectum) of concentratorR Radius of the living wallx, y, z Cartesian coordinatesρ Radial cylindrical coordinate, ρ =

√x2 + y2

ϕ Angular cylindrical coordinate, ϕ = atan(y/x)ρw Wall mass density (kg/m3)σ Wall tension (Pa)

∗Corresponding authorEmail address: [email protected] (Pekka Janhunen)URL: http://www.electric-sailing.fi (Pekka Janhunen)

1. Introduction

Gerard O’Neill was among the first to propose thatpeople could live on the insides of kilometre-scalespinning cylindrical settlements, located in space andconstructed from asteroid or lunar materials [1, 2].O’Neill’s original concept had two cylinders rotatingin opposite directions and mechanically connected toeach other to make a system with almost zero total an-gular momentum so that it can be turned to track theSun. The drawback of such design is the existence oflarge rotary joints and moving mirrors that are poten-tial sources of single-point failures. Later, the KalpanaOne model was proposed [3], which consisted of a sin-gle cylinder whose axis of rotation is perpendicular tothe orbital plane, thus eliminating much of the mechan-ical complexity.

It has been pointed out [1, 2, 3] that unlike Moon andMars, artificial rotating settlements are able to providean earthlike 1g gravity environment for the inhabitantswhich ensures that children grow as strong as on Earthso that they are free to visit or move back to Earth asadults if they wish. Also, in the long run, there is enough

NSS Space Settlement Journal September 14, 2018

small body material in the asteroid belt, and even morein the Kuiper belt and beyond, that the total living areaof settlements could eventually exceed the surface areaof Earth by a large factor. This is understandable be-cause a settlement needs only ∼ 104 kg/m2 of radia-tion shielding mass per sunlit living wall area, while anearthlike planet needs a million times more. The settle-ment technology allows one to build 1g living space inthe solar system by using the mass per area equivalentto Earth’s atmosphere only, rather than the entire planet.

On Moon and Mars it is possible to build radia-tion shielded and pressurised living space undergrounde.g. in existing caves or lava tunnels, with low expendi-ture of processed structural materials such as steel. Incontrast, rotating cylindrical settlements in free spaceneed more structural materials and therefore they de-pend on the existence of scaled-up asteroid mining,space manufacturing and low-cost in-space propulsionsuch as electric sail [4] for moving the materials andequipment. However, there seems to be no reason whyasteroid mining and space manufacturing, once started,could not scale up exponentially.

While O’Neill’s groundbreaking idea of rotatingcylindrical “inverted planets” received significant pub-lic attention and gave rise to conferences and workshopswhere different settlement geometries were considered(for a review, see Marotta [5]), the peer-reviewed liter-ature on cylindrical rotating settlements is rather small.In addition to the references already mentioned, an ex-ample of this literature is a study of the ultimate limit insettlement radius with advanced materials [6].

In this paper we study a class of Kalpana One typesettlements [3], but with a specific arrangement fortransferring sunlight to mimic earthly diurnal and sea-sonal cycles without large moving parts. The O’Neilland Kalpana One cylinders were assumed to be filledwith breathable atmosphere, but here we assume a rel-atively shallow (50 m) atmosphere under a transparentpressure-holding roof in order to reduce the amount ofnitrogen required. Nitrogen is a relatively rare elementon asteroids and on the Moon. Although humans couldalso survive in a reduced pressure oxygen atmosphere,such atmosphere would introduce an elevated risk offire. Furthermore, flying insects and birds would havechallenges in keeping aloft in a reduced pressure pureoxygen atmosphere, because the mass density of suchatmosphere would be much lower than at sea level onEarth. Flying animals play important roles in the inter-nal ecosystem, for example flying insects are responsi-ble for pollination of fruits and berries. In addition tobeing more affordable in terms of nitrogen, eliminationof a cylinder-filling pressurised atmosphere reduces the

tensile strength requirement of the walls significantly.For the location of the settlement, we assume a 1 au

orbit, for example the Earth-Moon L4 or L5 Lagrangepoint or the Earth-Sun L4 or L5 Lagrange point. Moregeneral orbits would be possible, but their study is notin the scope of this paper. We assume 1g artificial grav-ity, 1 bar atmospheric pressure and earthlike radiationprotection provided by 104 kg/m2 thick walls.

The focus of the paper is a future where – we as-sume – common engineering materials such as steel,aluminium and carbon fibre composites are available inscaled-up abundance from asteroid or lunar resources,and where the question of the preferred settlement size(the unit size of large-scale solar system settling) is rel-evant. Most inhabitants likely prefer a large settlementif given the choice. However, the tensile strength re-quirement of the settlement wall grows linearly withthe settlement radius. Thus for a larger settlement, alarger fraction of the wall mass must be structural ma-terial instead of biospheric payload like soil, vegetationand people. On the other hand, the radiation shieldingrequirement sets a minimum areal mass density for thewall which we assume to be 104 kg/m2. Then there ex-ists a settlement size – the sweet spot – where the wallthickness driven by structural requirements also pro-vides the right amount of radiation shielding. Smallersettlements would need equally thick walls because ofthe radiation shielding requirement and thus they wouldhave the same cost per inhabitant, if cost is measured bythe needed asteroid or lunar mass. Larger settlements,on the other hand, would need thicker walls because ofthe structural requirements, and thus higher mass expen-diture per person.

Concerning settlement scale, in this paper we adopt 5km settlement radius as representing an order of mag-nitude relevant for long-term future, see Appendix A forwall tensile calculations. There exists the timely ques-tion of which size of settlements one should build innear future [7], but such question is outside the scope ofthe present paper. Indeed, we stress that our choice of5 km radius should not be taken as a recommendationfor the first settlement. Our lighting solution is indepen-dent of the settlement size, however, and thus it could beapplicable also for smaller settlements in near future.

An overarching motivation of the paper is to find along-term reliable settlement architecture which enablesnatural sunlight and earthlike (and configurable) diurnaland seasonal illumination cycles. We take the long-termreliability requirement to imply that large moving partsand single failure points must be avoided and that therotation must be passively stable. As we will find outbelow, a lighting solution and the associated settlement

2 NSS Space Settlement Journal

2. LIGHT CHANNEL

architecture exists that satisfies the requirements.The structure of the paper is as follows. We describe

the settlement geometry, present a ray-tracing simula-tion to calculate how sunlight photons are distributedinside the settlement, then discuss the placement of ur-ban blocks1. We find that the naturally buildable urbanfloor area per inhabitant is large, which tends to promotethe standard of living. We close the paper by discussion,summary and conclusions. The focus of the paper is onthe lighting solution; other features of the settlement areconsidered as needed. The software used to compute theresults is available at [8].

2. Light channel

Directional light such as sunlight can be concentratede.g. by a parabolic reflector or lens. If the concentratedlight is directed into a box (light channel) whose innerwalls are perfectly reflecting, the concentrated light fillsthe entire box because photons can only exit throughthe same slit where they entered (Figure 1). If the con-centration ratio is increased, the light intensity insidethe box increases proportionally to it, until reaching thesurface brightness of the Sun.

In reality the light intensity is lower because the wallsare not ideally reflecting, and the light intensity also de-pends on the size and shape of the box. For our settle-ment application, we prefer a light intensity in the lightchannel which is a few times solar. This is because forsafety reasons we want to impose a constraint that if thelight channel contains some dark object or dark region(which might be necessary during servicing, for exam-ple), the local temperature must not go too high.

Sunlight into the settlement is concentrated by fixedcylindrical paraboloid concentrators into the light chan-nel (Fig. 2). The light channel has a geometric shapethat distributes light around the settlement, in particu-lar delivering light also to the antisunward side. Thecylindrical rural wall surface (the living cylinder wherethe biosphere exists) taps its illumination from the adja-cent light channel through windows that form the localroof of the rural surface. Local controllable blinders areused in the windows to implement desired diurnal andannual light cycles, in each ϕ-zone of the rural wall sep-arately. When closed, the blinders reflect light back tothe light channel where it remains usable for other ϕ-zones whose blinders are open.

1By urban blocks we refer to multi-storey floorspace that has nonatural illumination.

a)

b)

Figure 1: When sunlight is concentrated into a light channel by aparabolic concentrator, photons can only escape through the same slitwhere they entered. Light intensity inside the box in case (b) is higherthan in case (a) because the concentration ratio is higher.

Sunlight

Concentrators

Light channel

Rural wall

Figure 2: Path of sunlight onto the settlement’s rural wall living area.

3. Settlement geometry

A cut 3-D rendering of the settlement is shown inFig. 3. The overall shape is a cylinder without endcapswhich rotates so that the spin axis is orthogonal to theplane of the settlement’s heliocentric orbit, i.e. that thespin axis is perpendicular to the Sun direction. (Theillumination direction is different in Fig. 3 to aid visu-alisation of the shape.) The settlement is divided intoidentical southern and northern cylinders separated byan equatorial region. The cylinder has three walls. Theoutermost wall has an array of cylindrical paraboloidconcentrators, shown as black in Fig. 3, whose purposeis to trap sunlight into the light channel beneath. A con-centrator centred at z = z1 is the parametric surface

ρ(ϕ, z) = R+(z − z1)2

2p, ϕ ∈ [0, 2π), |z−z1| ∈ [p,K p] (1)


3. SETTLEMENT GEOMETRY

where p is the half-width of the concentrator slit (thesemilatus rectum parameter of the parabola) and K = 20is the concentration ratio.

The middle wall is the cylindrical rural wall whose ra-dius is taken to be 5 km. The inner wall reflects the con-centrated sunlight that arrives from the equatorial semi-toroidal reflector2 towards the rural wall.

The biosphere of the settlement resides on the innersurface of the cylindrical rural wall. About 50 m abovethe living surface there is a pressure-tight transparentroof equipped with 0–100 % adjustable blinders. Thenitrogen-oxygen atmosphere has not more than 50 mthickness to limit the mass of nitrogen needed. Thebiosphere is divided into 20 compartments called val-leys in the ϕ direction. The diurnal and seasonal cyclesare simulated by controlling the blinders in each val-ley separately. The neighbouring valleys have approx-imately opposite diurnal and seasonal phases so thatthe total dissipated power stays approximately constant.The yearly average insolation is 100 W/m2 at the highlatitude end of the valley and increases linearly to 160W/m2 towards the equatorial end. The values 100 and160 W/m2 correspond to yearly average insolation inHelsinki and in southern France, respectively. We as-sume average albedo of the biosphere of 0.2.

During the simulated night of the valley, the blindersof the valley are closed. Closed blinders reflect photonsback into the light channel so that the photons benefitother valleys whose blinders are open. During daytimethe blinders are opened partially to simulate the wantedlight level.

The equatorial part of the settlement has semi-toroidal reflectors whose purpose is to turn the flux ofconcentrated sunlight coming from the paraboloid re-flectors by approximately 180◦. The equatorial regionhas a belt of solar panels shown as dark blue in Fig. 3 toprovide electric power for the settlement.

The interior of the cylinder has two docking ports forexternal spacecraft. Each docking port is a cylinder withone open end. All parts rotate with the same angularspeed so the cylinder walls of the docking ports expe-rience a small artificial gravity of 0.074 g. An arrivingspacecraft flies inside the cylinder and sets its landinggear wheels into rotation that matches the rotational ve-locity of the docking port wall. Then it moves slowlyto the rotating wall, perhaps uses some amount of mag-netic attachment to prevent bouncing, and applies brak-ing to the wheels. Due to the braking, the spacecraft

2A cylindrical corner reflector made of two conical surfaces wasalso tried, but seemed to distribute light to the backside somewhat lessefficiently than the toroidal version.

gradually starts to co-move with the wall and the cen-trifugal force increases, ensuring that the wheels stayfirmly on the wall even without magnetic attachment.Finally the spacecraft comes to rest with respect to therotating wall and experiences the same centrifugal ac-celeration (artificial gravity) than the wall. The systemcan be thought of as a cylindrical landing strip wherewheeled craft of different sizes may land.

The edge of the cylinder contains one or more in-clined ramps. A departing spacecraft rolls over theedge of the landing port cylinder along a ramp, likea wheeled aeroplane that starts to accelerate downhill.After exiting the ramp and unless propulsively changed,the spacecraft follows a straight path and moves with therotational velocity of the docking port wall. The dock-ing port is placed outside the z range of other structuresof the settlement so that the departing spacecraft doesnot collide any obstacle.

The arrival and departure procedures sketched in theprevious two paragraphs are such that the spacecraftneed only low-thrust proopulsion. Impulsive chemicalpropulsion is not mandatory, which is good from thesafety point of view. If chemical propulsion is neverthe-less used for some external reason and if an accidentalexplosion occurs in the docking port, the open cylin-der shape of the docking port tends to direct the explo-sive energy away from the settlement. Existence of twodocking ports enables access to the settlement throughthe other port while a damaged port is repaired.

The docking ports are connected with a central hubby train tubes that carry passengers and cargo. The cen-tral hub contains a recreational low-g space. It is con-nected with the cylindrical artificial gravity surface byelevator tubes.

Thick walls that play the role of a radiation shield areshown in reddish colour in Fig. 3.

A 2-D cross section of the settlement is shown inFig. 4, where the radiation shielding parts are markedred. The radiation shielding walls are positioned so thatno direct paths exist between the living wall surface andexternal space.

The main parameters of the settlement are listed inTable 1. The light transfer strategy is scalable to anysettlement size. The main underlying assumptions aresummarised in Table 2.

We adopt a population density of 500 persons persquare kilometre of rural wall area. For comparison,The Netherlands has a population density of 400/km2

and is a net exporter of food. It is a requirement that aspace settlement produces all the food that it consumesin a closed ecosystem, with sufficient margin.

The settlement length is selected by requiring, fol-



Docking port

Solar panelzone

Parabolicconcentratorzone

Ruralwall

Radiatorwall

Z

X

Y

Figure 3: Cut view of the cylindrical space settlement.



Sunlight

Rural cylinderDocking port

Elevator tube

Radiator wall

Low-g area

Train tube

Parabolicconcentratorzone

Solar panelzone

Urban blockspace

Semitoroidalmirror

ρ

z

Figure 4: 2-D cut view of the cylindrical space settlement. Thick radiation shielding parts of the walls are shown in red.

Table 1: Main parameters of the settlement.Diameter 11.5 kmLength 10.01 km*

Radiation shield wall mass 3.55 · 1012 kgTotal mass ∼ 4 · 1012 kgRural wall radius 5.0 kmRural wall length 2 × 4.255 kmRural area 267 km2

Number of valleys 2 × 20Valley width 1.57 kmValley length 4.255 kmValley area 6.68 km2

Reflector semitorus radius 750 mSun-facing solar panel area 17.25 km2 (11.5 km × 1.5 km)Electric power /w 20 % solar panel efficiency 4.7 GWArtificial gravity at rural wall 0.93 gRotation period 2.45 min* Excluding docking ports.


4. ILLUMINATION SIMULATION

Table 2: Underlying assumptions.Solar distance 1 auSolar constant after filtering out IR,UV 1000 W/m2

Inertia moment ratio Izz/Ixx 1.2Mirror absorptivity 0.02Mirror diffuse reflectance fraction 0.001Concentration factor, K 20Maximum rural time-average insolation 160 W/m2

Minimum rural time-average insolation 100 W/m2

Spatiotemporal average rural insolation 130 W/m2

Rural albedo 0.2Radiation shielding mass* 104 kg/m2

* Doubles as structural mass.

lowing the Kalpana One design choice, that the inertialmoment tensor component Izz is 20 % larger than thex and y components: Izz = 1.2Ixx. This is thought to beenough to have a passively stable rotation with sufficientmargin. Here Ixx = Iyy holds because of the cylindricalsymmetry. Only the radiation shielding walls were con-sidered when calculating the inertial moment, becausethey are the heaviest parts.

Figure 5 shows 2-D cross sections of the settlementwith the paraboloid concentrators in different scales,i.e. different semilatus rectum parameters p. In an actualsettlement one could have a large number of small con-centrators (small p, perhaps a few centimetres). Simu-lating a small p is time-consuming and in the calcula-tions we use p = 1 m (Fig. 5c). We have verified thatthe results are not sensitive to the value of p.

4. Illumination simulation

We wrote a C++14 [9] code that performs forwardand backward ray-tracing. Figure 3 was produced bythe code by backward ray-tracing. Forward ray-tracingis used to launch 4 · 106 random solar photons towardsthe settlement. Each photon typically undergoes manyspecular and diffuse reflections until it is absorbed bysome of the optical surfaces or by the settlement’s bio-sphere. The photon may also exit back to space througha paraboloid concentrator slit. The ray-tracing code sup-ports geometric shapes such as planes, cylinders, cones,tori and cylindrical paraboloids, as well as the set opera-tions union, intersection, complement and difference toform more complicated surfaces.

We start with a trial value of 0.08 for the biosphere’sabsorptivity. The absorptivity value models both theblinders and the biosphere itself. The resulting absorbedpower density is calculated as a gridded function of ϕ

and z on the cylindrical rural wall. We then calculatethe corresponding insolation (power density that wouldbe absorbed by a small piece of fully absorbing mate-rial) by dividing the actually absorbed power density byone minus the albedo of the biosphere, for which we usethe value 0.2. We compare the obtained insolation withthe wanted insolation which varies between 100 and 160W/m2 in z. Then we multiply the local absorptivity bythe ratio of the wanted versus obtained insolation andcompute the next iteration. We perform four iterations,during which the result typically converges well. As aresult, the code reproduces the wanted insolation pro-file, using some absorptivity profile that depends on ϕand z.

We show the results in Fig. 6. Figure 6a shows theincident illumination above the blinders, which is cal-culated by dividing the absorbed power density by thelocal absorptivity. (We checked that we obtain the sameresult from a transparent photon-counting detector nearthe surface.) The incident illumination represents thehighest obtainable illumination that results if all blin-ders are fully open and the roof is completely transpar-ent. For most ϕ values the incident illumination exceeds1000 W/m2. The value 1000 W/m2 corresponds to sun-shine on a cloudless day when the sun is at the zenith.The lowest illumination that occurs for ϕ ≈ 180◦ is 850W/m2. Each point on the biosphere passes through all ϕvalues in a few minutes as the settlement rotates. Hence,for each z the minimum incident flux corresponds to themaximum obtainable illumination, if one wants to avoidperiodic dimming of the daylight at the rotational fre-quency.

Figure 6b is the corresponding time-averaged absorp-tion, which includes the effect of the blinders as wellas the biosphere itself. The lowest panel Fig. 6c is theobtained insolation below the blinders. Apart from nu-merical noise originating from the finite number of pho-tons used in the calculation, the result corresponds tothe wanted insolation profiles that goes from 160 to 100W/m2 when one moves from the equatorial end to thehigh latitude end.

The cylindrically symmetric light channel distributeslight in ϕ and z. Figure 7 shows paths of photons thatenter the settlement in a particular exemplary y = constplane (y = 0.5R). To ease visualisation, views from twodirections are included. Some photons are reflected outalready when interacting with the cylindrical paraboloidconcentrator. A few photons find their way out from theconcentrator slits later after reflecting back and forth in-side the light channel. A significant amount of photonsgo to the antisunward side, some even make a full circlearound the settlement. The Monte Carlo approach was


4. ILLUMINATION SIMULATION

a) b)

c) d)

Figure 5: 2-D cuts showing the parabolic concentrators for different slit half-width parameters p of 4 m (a), 2 m (b), 1 m (c), 0.5 m (d). The valuep = 1 m (panel c) is used in the calculations. In the limit of small p (small and numerous concentrators), the parabolic concentrator zone looksdark and featureless to an external viewer, as was depicted in Fig. 3.

0

1

2

3

4

km

Incid

en

t W

m−

2

800

850

900

950

1000

0

1

2

3

4

km

Ab

sorp

tio

n

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0.05

0.1

0 100 200 300 deg

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3

4

km

Inso

lati

on

W m

−2

100

110

120

130

140

150

160

a)

b)

c)

Figure 6: Incident photon power density above the blinders (a), effec-tive absorptivity of the blinder-equipped settlement surface (b), inso-lation below the blinders. All are as function of the cylindrical coor-dinates ϕ and z. In (a), values over 1 kW are shown are white.

used in the simulation, i.e., at each reflection the photonalso has a chance of being absorbed at a nonzero proba-bility. In Fig. 7, the path of each photon was traced untilit escaped or was absorbed at an internal wall. The in-ternal walls include reflector surfaces that are part of thelight channel, blinders covering the windows betweenthe light channel and the rural wall, and the rural wallitself.

The cylindrical paraboloid concentrators are some-what sensitive to the direction of the incoming sunlight.Increasing the concentration ratio K (i.e. the total widthversus slit width of the parabola) traps light better be-cause it reduces the amount of light that escapes throughthe slits. On the other hand, increasing K increases thedirectional sensitivity. We use K = 20 as a tradeoff.Figure 8 shows the total sunlight power absorbed by therural biosphere (in the z > 0 half of the settlement) asa function of the angle between the sun direction andthe spin plane. We see in Fig. 8 that if the spin axisis controlled with better than ∼ 0.5◦ precision, then theabsorbed power is optimal, while a deviation of 2 de-grees causes up to 20 % reduction. Even a 20 % re-duction is not catastrophic for the crop yields, however,since plants are accustomed to cloudiness associated in-solation variations on Earth during the growing season.The temperature remains controllable by regulating thecooling through the blinders and the radiator wall. Wethink that the sensitivity to spin axis inclination is not


5. URBAN BLOCKS

a)

ZY

X

b)

ZYX

Figure 7: Photon paths inside the light channel from two viewing an-gles. A vertical sheet of input photons enters from the right hand sideand propagates along −x at y = R/2, while z is a random number ininterval [0, Lz/2).

a problem. The sun angle dependence (Fig. 8) is notquite symmetrical because although the southern andnorthern parts of the settlement are identical, there isno light exchange between them and the northern parttaken alone is not symmetrical in z.

The settlement is cooled radiatively through the innerconical reflector wall whose interior emits thermal in-frared into space. A glass-covered optical mirror of theinner side of the conical surface absorbs well in thermalinfrared and conducts heat away because its underly-ing support structure is metallic. To avoid using heatpumps, the radiator temperature must be lower than thedewpoint of the climate that one wants to maintain. Inour simulation, the average radiator temperature is −16◦C if one makes the approximation that the effective ra-diating areas are the open endcap areas of the cylinder(making such assumption models the effect that part ofthe emitted infrared is re-absorbed by the opposing radi-ator wall). Power generated at the rural wall is radiatedaway by the nearby radiator wall so that liquid transferof heat over longer distances is not required.

5. Urban blocks

The population density per rural wall area is lim-ited by the biological productivity of the rural walls,we have assumed 500 persons per square kilometre, or2000 m2 of rural area per person. Additional space per

−2 −1 0 1 2 deg0

5

10

GW

Figure 8: Power absorbed by the living cylinder as function of sunangle.

person can be obtained by building urban type multi-storey blocks, and it can be done without reducing therural area. For example, urban blocks could simply existon the rural walls so that the roofs of the buildings areused for agriculture. Another possibility which is bet-ter from the mass distribution point of view is to buildurban blocks inside the volume (Fig. 4, pale red areas)that is left over by the equatorial semi-toroidal reflec-tors. Equatorial mass promotes rotational stability, andthe extra stability would enable making the settlementsomewhat longer, with a corresponding increase in ru-ral area and consequently the maximum population.

Table 3 lists population related parameters. For a set-tlement of 5 km rural wall radius, the space availablefor urban blocks between the toroidal reflectors (palered areas in Fig. 4) is as large as 15 km3. The volumescales cubically with the settlement radius. The volumecorresponds to a vast 25, 000 m2 of urban floor area perperson, which is an order of magnitude larger than therural area per person. In this paper we call this the max-imal (or naturally buildable maximal) urban area, eventhough it is not really maximum because one could buildalso additional urban spaces in the rural areas.

To have a rough estimate of the mass of urban blocks,the large luxury cruise ship “Oasis of the Seas” weighs108 kg and its total internal volume is 710.6 · 103 m3, ascalculated from the gross tonnage of 225,282 GT[10],yielding a bulk density of 141 kg/m3. If this bulk den-sity is representative of the settlement blocks as well,


6. DISCUSSION

the mass of the fully built urban blocks filling 15 km3

volume is 2 · 1012 kg, which is 50 % of the mass of therural-only version of the settlement (Table 1). If onechooses to build 10 % of the maximum urban volume,for example, it increases the settlement mass by only5 % and provides 2000 m2 of urban floor area per per-son, which is still a vast amount.

Table 3: Population parameters.Total population 134,000Population density per rural area 500 km−2

Rural area per capita 2000 m2

Electric power per capita 35 kWMax equatorial urban block volume 15 km3

Max urban floor area * 3.3 · 109 m2

Max urban volume per capita 110, 000 m3

Max urban floor area per capita 25, 000 m2

El. power per fully built urban area 1.5 W/m2

Artificial gravity in urban blocks 0.79–1.07 g* Assuming 4.5 m floor-to-floor height difference.

The available electric power is large per capita (35kW), although lowish per maximal urban floor area (1.5W). The artificial gravity in the inner and and outer ur-ban volume is lower and higher, respectively, than onthe rural walls. In Tables 1 and 3 we have selected the1g level to be reached halfway between the rural walland the outermost part of the urban blocks. For exam-ple, kindergartens might exist in the ≥ 1g parts so thatchildren grow as strong as on Earth, whereas motion-challenged old people might live in the parts were thegravity is lower than 1g.

The interiors of the urban blocks should also beshielded against radiation. We do not include mass forsuch shielding in the mass budget explicitly, becausewe consider it likely that parts of the urban blocks areused as storage area for items that do not need radia-tion protection. By placing the storage areas at the outerboundary of the urban block, their mass contributes tothe shielding of the inside of the block so that dedicatedradiation shielding might be unnecessary.

6. Discussion

We assumed a 5 km settlement radius. The value ismeant to correspond roughly to the sweet spot where thestructural walls double as radiation shields. Settlementsof all sizes up to and including the sweet spot size havethe same wall thickness and thus the same mass cost per

inhabitant3. The sweet spot size is preferred because alarge settlement is preferable over a small one. Settle-ments larger than the sweet spot size have, however, ahigher mass cost per inhabitant because of structural re-quirements. Because of this, we consider it likely thatlarge-scale settling of the solar system is undertaken us-ing settlements around the sweet spot size.

We assumed light channel width which is 15 % of therural wall radius (750 m, since the rural wall radius is5 km). A wider light channel would distribute sunlightmore evenly, but would increase the mass needed perilluminated rural area because a larger fraction of thesettlement length would be radiation shielding surface.

Periodic variation of the insolation by the rotationrate is not observable by the inhabitants because it issuppressed by continuous active controlling of the blin-ders. The diurnal and seasonal cycles are produced syn-thetically by the blinders. Failure of a small fractionof the blinders is acceptable. The blinders can be lu-bricated in a normal manner because they reside in a1 bar pressure normal atmosphere in normal tempera-ture. They can be serviced and replaced by humans androbots easily because they reside in earthlike gravity andradiation protection.

We divided the cylindrical rural wall into (for exam-ple) 20 valleys in the ϕ direction. Each valley is in itsown phase of the diurnal and seasonal cycle. The ar-rangement enables simulating the diurnal and seasonalcycles using local blinders while keeping the total sun-light power dissipation roughly constant. Neighbour-ing valleys are isolated from each other optically, andfor safety reasons they can also be pressurised indepen-dently of each other. Division of the rural wall cylinderinto valleys also has the benefit of making the cylin-der’s curvature visually less apparent to the inhabitants,particularly if there are artificial ridges or “mountains”between the valleys.

One benefit of the proposed architecture is that thickradiation and meteoroid protecting transparent windowsare not needed.

It is noteworthy that the naturally available maximalurban floor area per inhabitant is large, 25,000 m2 underthe baseline assumptions. This floor area per person is2-3 orders of magnitude larger than the contemporaryaverage on Earth and comparable to what today’s royalfamilies have access to. If the urban blocks are max-imally built, electric power usage per urban floor areamust be limited to 1.5 W/m2. However, this does not

3The sweet spot size is a function of the radiation environment.Thus an equatorial LEO settlement would have a much smaller sweetspot size than the deep space settlement considered in this paper.


7. SUMMARY AND CONCLUSIONS

restrict the use of the floorspace in an essential way be-cause rooms where no people are present do not needenergy. Plants feeding the biosphere must be grownin the open rural areas where the light energy dissipa-tion per area is two orders of magnitude higher. Thedominant power is the sunlight dissipated in the rural ar-eas, while for a maximally built settlement the dominantfloor area exists in electrically lighted urban blocks.

The 3.3 · 109 m2 urban floor area is so large that ifarranged in rooms of 6.7 m wide, for example, a pathgoing through all the rooms must be at least 5 · 105 kmlong. A person walking 20 km per day for 70 yearscould theoretically visit every room once. Thus, a 5 kmradius settlement can have more things inside than aninhabitant can experience or explore over an entire life-time. Even so, the maximal urban volume is only ∼ 6 %of the volume of the light channels.

We calculated the length of the settlement from therequirement Izz = 1.2 · Ixx, without including the massof any urban blocks. If one decides to introduce largeurban blocks, the settlement could be made somewhatlonger while keeping passively stable rotation. It is alsopossible and perhaps likely that urban blocks are con-structed gradually by the first generations of inhabitants.In that case, the settlement length must be restricted sothat rotation is stable also without the mass of the ur-ban blocks, which is the case that was calculated in thispaper.

The inner and outer light channels are tapered, i.e. thechannel gets narrower with increasing |z| as seen e.g. inFig. 4. A tapered inner light channel works better thana non-tapered one, for multiple reasons:

1. According to numerical experimentation, a taperedinner light channel distributes light better onto therural wall. The sunlight power that reaches the ru-ral wall is higher and more uniform in ϕ and z.

2. A non-tapered inner light channel would need to beclosed by a radiation shielding end member. Theradiation shield would increase the settlement’s to-tal mass, and the extra mass would be located athigh |z| which would reduce the stability of the ro-tation. To restore stable rotation, the cylindricalrural wall would have to be made shorter, whichwould result in smaller area for the food-producingbiosphere and thus a smaller maximum population.

3. Cooling of the settlement occurs by thermal radi-ation emitted by the inner wall of the inner lightchannel4. The emitted thermal radiation is par-

4In this cooling method, heat produced at the rural wall by dissi-pated sunlight is radiated away by the adjacent inner lightchannel sur-face so that there is not much if any need for fluid-based heat transfer.

tially re-absorbed by the opposing wall. To ac-count for the re-absorption, the effective radiatorarea is approximately given by the area of the openend of the cylinder. The open area is larger if theinner light channel is tapered. Hence, tapering in-creases the available cooling power of the settle-ment, which increases the maximum tolerable sun-light power that the rural wall can be configured toabsorb by the artificial diurnal and seasonal illumi-nation cycles. Consequently, when all else is equal,the maximum biological production and the max-imum allowed human population are larger whenthe inner light channel is tapered.

Tapering is beneficial also for the outer light chan-nel because according to numerical experimentation,a tapered channel directs light towards the equatorialsemitoroidal reflector with fewer reflections, so that lesslight gets absorbed by the reflector surfaces or escapesthrough the concentrator slits back into space.

Are there other ways to design a settlement that pro-duces earthlike illumination cycles without large-scalemoving parts? One approach would be to use artifi-cial light sources instead of natural sunlight and to pro-duce the needed electric power by covering the exte-rior surface by solar panels. However, natural sunlightis expected to be visually more pleasing than artificiallight and it also has cost, lifetime, reliability and ther-mal management benefits relative to electric lighting.

7. Summary and conclusions

We have presented a cylindrical space settlementconcept where sunlight is concentrated by cylindricalparaboloid concentrators and reflected by semi-toroidaland conical reflectors and controlled by local blindersto simulate earthlike diurnal and seasonal illuminationcycles. The rural wall living cylinder is divided into 20(for example) z-directed valleys which are in differentphases of the light cycles. No moving parts are neededother than numerous and easily accessible local blindersthat regulate light input into the valleys. The settlementrotates as a rigid body and the mass distribution is suchthat the rotation is passively stable.

The geometry has natural spare volume at the equatorwhere one can add multi-storey urban blocks withoutreducing the rural area. Adjacent to the urban blocksthere is natural place where to install a zone of solarpanels without reducing the amount of gathered light.

The inhabitant population is limited by the ability ofthe closed ecosystem of the sunlit rural areas to producefood. The naturally buildable total urban floorspace area


8. ACKNOWLEDGEMENT

can be an order of magnitude larger than the rural areaif the settlement radius is 5 km. The maximum urban torural area ratio scales linearly with the settlement radius.A 5 km settlement radius corresponds roughly to thesweet design spot where earthlike radiation shielding isproduced for free by the required structural mass.

Overall, the settlement concepts satisfies the follow-ing generic requirements for long-term large-scale set-tling of the solar system:

1. 1g artificial gravity, earthlike atmosphere, earthlikeradiation protection.

2. Large enough size so that internals of the settle-ment exceed a person’s lifetime-integrated capac-ity to explore.

3. Standard of living reminiscent to contemporaryroyal families on Earth, quantified by up to 25,000m2 of urban living area and 2000 m2 of rural areaper inhabitant.

4. Access to other settlements and Earth by spacecraftdocking ports, using safe arrival and departure pro-cedures that do not require impulsive chemicalpropulsion.

In particular, the proposed lighting geometry enablesa long-term reliable architecture, i.e., a design that doesnot include large moving parts, is free of single failurepoints and exhibits passively stable rotation.

As a future refinement of the concept, one could con-sider more general orbits than 1 au circular, and a rangeof settlement sizes could be analysed.

In conclusion, a requirement for settling the solar sys-tem in a large scale is that the habitats must be long-term reliable and they should provide a high standardof living compared to Earth. In the light of our anal-ysis, the goals seem possible to reach, without essen-tially increasing the total mass consumption per inhab-itant beyond what is required by radiation protection inany case.

8. Acknowledgement

The results presented have been achieved under theframework of the Finnish Centre of Excellence inResearch of Sustainable Space (Academy of Finlandgrant number 312356). The author is grateful to SiniMerikallio for suggesting a modification of the title.The author also thanks the Editor Al Globus and threeanonymous reviewers for making a large number of veryuseful constructive comments.

Appendix A. Wall tension

Consider a cylindrical settlement wall of radius R,length Lz, thickness h and wall mass density ρw, rotatingso that the centrifugal acceleration at the wall is g. Themass of the cylinder is

m = 2πRLzhρw. (A.1)

Use cylindrical coordinates ρ, ϕ and z so that the cylin-der is centred at origin and its axis is aligned with z.Let us consider the y > 0 half of the cylinder. For thissemicylinder 0 ≤ ϕ < π.

The wall tension Fy at y = 0 is equal to the y-component of the centrifugal force acting on the {y > 0}semicylinder:

Fy =

∫dFy =

∫dmg sinϕ =

mg2π

∫ π

0dϕ sinϕ =

mgπ.

(A.2)The force Fy pulls a cross-sectional wall area

A⊥ = 2Lzh (A.3)

where factor 2 comes from two edges of the semicylin-der at x = ±R. The tensile stress σ of the wall is thengiven by

σ =Fy

A⊥= Rρwg. (A.4)

If R = 5 km, ρw = 7.8 · 103 kg/m3 (steel) and g = 9.81m/s2, we obtain tensile stress σ = 380 MPa. In the formof piano wire, steel’s ultimate tensile strength can ex-ceed 2500 MPa [11]. If half of the wall mass is payload(soil, vegetation, etc.), for example, then the structuralparts must have 2 × 380 = 760 MPa of usable tensilestrength. This is 30 % of the piano steel wire ultimatestrength of 2500 MPa. In the light of these numbers,a living wall radius of 5 km seems feasible. Steel is areasonable choice for the main structural material sinceiron is one of the dominant elements on asteroids.

It is of interest to notice that the wall stress (A.4) doesnot depend on the wall thickness h. This is because wedid not include the internal atmospheric pressure of thesettlement in the calculation. Neglecting the internalpressure is a good approximation since the 50 m highatmosphere contributes only 65 kg/m2 to the wall massloading.

When the settlement radius R is increased, the walltensile strength requirement σ increases proportionally,according to Eq. (A.4). If the structural material char-acteristics remain the same, this means that for a largersettlement, a smaller fraction of the wall mass can bepayload (soil etc.). If the payload mass per area is kept


REFERENCES REFERENCES

unchanged, this implies that the wall’s total mass perarea must increase. The question of what is the sweetspot settlement size (i.e., size where radiation shield-ing and structural requirements meet) depends on therequired payload mass per living wall area. In conclu-sion, the adopted 5 km settlement radius is compatiblewith, for example, 50 % wall payload fraction and ten-sile loading which is 30 % of piano wire steel’s ultimatetensile strength.

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natural illumination solution for rotating space settlements

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