Sharing factor estimation

The settlers can share the same air revitalization system, the same water processing system, the same habitat, etc. Obviously, the scale of the systems has to be adapted to the number of individuals, but scaling up has often a small impact on the required time to develop and operate the systems. In addition, time savings are expected for a greater number of individuals thanks to specialization and productivity gains. For some activities, however, scaling up does not provide substantial time savings. For instance, the required time for picking fruits on plants is closely correlated with the amount of fruits to be collected, which is linearly correlated to the number of individuals. An important issue is to be able to calculate the sharing factor as a function of the number of individuals. If such a function were available, the minimum number of settlers for survival could be deducted from Eq. (³). Importantly, whatever the activity, the sharing factor is equal to 1 for 1 individual and then increases with the number of individuals according to a curve that follows, as a first approximation and in most cases, a logarithmic law (in a way similar to productivity gains). Such curves can be conveniently approximated by Eq. (²) with ∝ in the range [0;1].

Sometimes, this depends on the organization of the society. Imagine for instance that the settlement is split into groups of a hundred individuals with autonomous life support and energy systems. In this case, the sharing factor of activities linked to life support or energy would resemble a step function, with a monotonic growing rate below 100 and a division by a factor of 2 when 101 is reached, then another monotonic rate, etc. The most appropriate function must be used if it is known. For the sake of simplicity, and in the context of this preliminary study, it is suggested here to use Eq. (²) to estimate the sharing factor of most activities. In order to determine ∝i the proposed method is to interpolate the function with two points. The first point is given with n=1 by 1∝i=1 and the second point is given by an estimation of the sharing factor for 100 individuals. Then ∝i is chosen such that 100∝i is a good approximation of that value.

Noticeably, if the activity is completely modified for a greater number of individuals due to adaptations of technologies and procedures, it is possible to take changes into account by an appropriate modification of the sharing factor.

Let us illustrate this method with 2 examples:

The same oxygen production unit (based on water electrolysis) can be shared by all individuals of the same habitable area. The scale of that unit must be adapted to the production needs, but the sharing factor quickly increases with the number of individuals. At some point, however, other oxygen production units must be built for other habitable areas. The sharing is not increasing any more, but there is an industrial development allowing the use of better materials and more efficient processes. For large values of n, productivity gains are therefore expected and the sharing factor can still be used to take these gains into account. For 100 individuals, the sharing factor is estimated at 25. For oxygen production and n individuals, a good estimate is thus provided by n0.7.

For the construction of a new habitat, 10 individuals specialized in an activity may work 20 times faster than a single person doing everything. For 10 individuals, the total working time would therefore be divided by a sharing factor of 2. Now, in order to divide the working time by another factor of 2, the number of individuals might have to exceed 100. In this case, n0.3would be a good approximation of the sharing factor.