1.2 Foam-Based Method
The problem of the active debris removal of space debris has to be approached facing with the  enormous quantity of debris and with their various nature in terms of size, shape and kind (e.g.upper stages, telecommunication satellites, and so on). Any approach can be intuitively classified into one of the three following different strategies of debris removal:
• One-to-one: each debris, regardless of its size, has to be targeted and removed. Thus, a
deorbiting platform has to be developed, manufactured and launched for each single debris
to deorbit.
• One-to-many: the chosen strategy is autonomously capable to target and remove several
debris. These could be of just one kind or of multiple kinds and sizes.
• One-to-any: the chosen method affects any object in a given orbit. To this category belong those methods that rely on global physical factors or uncontrollable deorbiting strategies.
Each one of these three strategies can be supported presenting their pros and cons but, as a matter of  fact, the second one represents the most viable option. Indeed, a strategy aimed to target each one of  the millions of debris represents a huge task in terms of time and technical requirements. By means  of this kind of approach only the larger/heavier debris can be targeted in order to avoid having more costs than benefits. On the other hand, a strategy whose main effect is to decrease the lifetime of any orbiting object could be even more dangerous for all manmade spacecrafts, than for debris themselves. In this case there would be hundreds of active satellites forced to realize displacement
manoeuvres to avoid the effects of one of these global affecting methods.
Therefore, the conceived debris removal system has been identified within the one-to-many category. In this category already several methods have been proposed. The main ones are:
electromagnetic methods, capture with net-like systems, momentum exchange methods, ground  based methods, modification of material properties or change of material state.
The proposed scenario belongs to the field of the momentum exchange methods, and in particular it can be thought as a drag augmentation system. The proposed system tends to define a reliable and easy way to perform this drag augmentation. The core idea is to develop a platform able to realize a foam ball around a target debris that enlarges its area-to-mass ratio such that the atmospheric drag can exert a significant influence to decelerate the debris. In this way, debris that would have orbited for hundreds of years, will re-entry in a prescribed time. The most remarkable advantages of this method are:

• A docking mechanism is not required, thus all the technological issues related and all the
potential hazards deriving from the docking with a non-cooperative debris do not apply.
• The resulting foam structure does not require any control during the re-entry. Since the
foam will ideally expand isotropically in the space (vacuum and microgravity conditions)
[15,16], resulting in a spherical form presenting always the same cross section, an
uncontrolled re-entry (no thruster and a limited ground segment) can take place.
• The resulting foam structure around the debris is much sturdier than any tether, sail or netbased  structure.
• The momentum exchange is given only by the drag force decelerating the debris until it
burns completely up in the atmosphere.
• There are no potential hazards related to ground based systems, e.g. lasers passing through  the atmosphere (although other kind of hazards might exist, see Sec. 11).
The reliability of a foam-based strategy relies on the absence of control during the deorbiting time  and the absence of any potential impact damage. The resulting object can be thought as a ball that  offers always the same cross section; it contains in itself the target debris and can be nucleated also  at a distance from the deorbiting platform. Furthermore, as already stressed, the absence of any docking system and close approaches reduce the key technology to the specific foam employed.
If compared to other drag augmentation methods, a foam ball offers several advantages. First of all,it is not exposed to impact damages that could prejudice the goal of the whole mission. For  instance, let us think to a sail: it realizes the same drag augmentation (and, from a purely area-to mass ratio point of view, also more advantageous), but it is very likely that it will impact something during the re-entry that can tear the sail off, thus compromising the mission. Moreover, another  significant advantage is that an almost spherical form does not require any particular attitude control, while a sail-shaped object works at its best only in some configurations that should be  actively maintained. As drawbacks of this method, instead, a difficult foam nucleation, incomplete  attaching or not complete expansion in vacuum have to be mentioned; phenomena that could limit
the foam-based method performance.
By way of example, for this methods’ potential, it is possible to choose an arbitrary upper limit for  the deorbiting time. Accordingly with the IADC Guidelines it can be assumed that, after the foaming process, the debris have to re-enter within 25 years. Although this is the prescribed time since end of operations recommended to be considered for future space objects, for an active debris  removal mission, this period is here evaluated since the mission takes care of specific debris. Figure  4 shows, on a logarithmic scale, the deorbiting time as a function of the area-to-mass ratio for different values of the initial altitude.
The atmospheric model, however required to compute this deorbiting time, is based on average values as described by the Medium Density model in Sec. 2.2.


From Fig. 4, it results that an area-to-mass ratio larger than 0.07 is required at 900 km of altitude  (see the close up of Fig. 5). For lower values, regardless of the specific debris mass and area, the reentry  time exceeds this threshold.


Nevertheless, the value of the area-to-mass ratio is not enough meaningful as it can result in extremely high areas depending on the debris mass. For instance, let us think to a typical upper  stage of a launcher, it weights some 800 kg, thus an area-to-mass ratio equal to 1.5 would mean that  we have to produce a foam ball cross section of 1200 m2, i.e. a radius of 20 m, value here  considered not really realistic.
For this reason, it is interesting to observe the actual area value for different masses and for several  area-to-mass values. This is represented in Fig. 6, where an upper limit of about 314 m2, which  means 10 m radius, has been assumed. This value represents a sort of assumption and it reflects the  idea to design a realistic methodology even in quite conservative cases. Higher area values could  still be realized (and the general performance of the scenario would be better) but could require too  much time to nucleate, and so they may be considered not suitable.


As we are assuming that the foam will produce a ball-like structure, a given area represents a fixed  value of the radius of this ball, represented in the rightmost vertical axis of Figure 6. Moreover, we  stress that, also considering these reduced characteristics, appealing performances can be achieved  by this methodology.
Thus, also the upper limit on the area can be estimated. Once this specific area-to-mass ratio has  been fixed, Fig. 6 gives the maximum area that we have to produce such that a massive (2000 kg)  debris re-entry within 25 years from 900 km of altitude. This value is 140 m2, corresponding to 6.7m of ball radius. Considering, by way of example, the same value for the area-to-mass ratio (0.07), a  1000 kg debris with an initial orbital altitude of 800 km, should deorbit within 10 years with a foam  ball area of 70 m2 and then 4.7 m of foam ball radius. For the same debris, considering a deorbiting  time of 25 years, a smaller value for the area-to-mass ratio can be assumed (0.03) and thus a smaller  foam ball area (30 m2) and radius (3.1 m).
Better results in terms of re-entry time can be, however, obtained in the case of small mass debris.
Indeed, in these cases, higher area-to-mass values can be targeted, resulting in shorter deorbiting  times. For instance, considering the same 6.7 m sphere, 300 kg debris can be deorbited in  approximately 3 years, as an area-to-mass value up to 0.5 can be achieved. It is worth saying that  this analysis has been carried out neglecting the mass of the foam and that more conservative results  are shown in Sec. 4.


Authors: M. Andrenucci, P. Pergola, A. Ruggiero /2011
Affiliation: University of Pisa – Aerospace Engineering Department – Italy
ACT researcher(s): J. Olympio, L. Summerer

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