## 4 Results
### Combinations  
It has been shown that the chemical system is fast but heavier, while the drag sail is simple and efficient at low altitudes. It is interesting to combine these two technologies, using the chemical system to rapidly move a spacecraft out from a crowded region and displace it at a lower altitude where the drag sail can perform more efficiently. As an example, the deorbit from an 800 km initial circular orbit has been considered. A chemical propulsion system performs a Hohmann transfer from 800 km to a certain lower altitude called release altitude. The corresponding mass budget is calculated. Then, from the final parking orbit, a drag sail is sized in order to complete the deorbit in a certain prescribed amount of time. Three cases have been considered: 3 months, 12 months/1 year (\(\times\)4) and 4 years (\(\times\)4 again), together with two techniques for the chemical system, a full Hohmann transfer to the release altitude and a half Hohmann transfer that lowers only the perigee to the release altitude. The results are presented in Figures 40-42. Figure 41: Deorbiting with the serial combination of a chemical propulsion system and a drag sail, mass fraction vs. release altitude, 1-year total duration: (**a**) full Hohmann; (**b**) half Hohmann. Figure 40: Deorbiting with the serial combination of a chemical propulsion system and a drag sail, mass fraction vs. release altitude, 3-month total duration: (**a**) full Hohmann; (**b**) half Hohmann. In all cases, the chemical propulsion system mass is zero if the release altitude is the initial altitude (i.e., the deorbiting is performed only by the drag sail) and grows linearly as the release altitude is reduced. On the contrary, the mass of the drag sail is zero if the maneuver is completed only by the chemical system down to the corresponding natural decay altitude and increases exponentially as the release altitude is lifted up. The mass of the chemical system is dependent only on the release altitude while the mass of the drag sail is dependent on the inverse of the total decay time as less area is required. The sum of the two masses has a minimum for a certain release altitude. The minimum mass altitude shifts to the right if the decay time is increased as the required sail mass is decreased. For the same reason, the benefits of a combined solution compared to a propulsive-only solution increase as the decay time is extended. On the contrary the benefits of a combined solution compared to a sail-only solution vanish as the decay time is extended. Obviously, the half Hohmann technique guarantees lower masses and shift the optimum toward the chemical propulsion side (left). The combination of a drag sail with a chemical propulsion system is surely more complex than a single solution but becomes particularly interesting if a propulsion system is already on board and the drag sail operate in a full passive and efficient mode (regarding attitude) after deployment. Figure 43 shows the altitude behavior with time of an optimal combined solution vs. the two single-system solutions. As already shown earlier, the initial displacement by a chemical thruster is favorable to rapidly moving the spacecraft on a less crowded orbit (unless the opposite occurs, as could be in some cases). Moreover, the huge mass savings of the half Hohman technique are balanced by the drawback of sweeping continuously a wide range of different altitudes during the decay. Drag sails combined with tethers or electric thrusters are less attractive as the complexity starts to become relevant, and all three systems suffer from long decay times that will overlap in the mass budget. A combination of a chemical system with a simple electrodynamic tether can be conceived in case a controlled re-entry is foreseen, but the total mass budget constraints do not allow for a full chemical solution. Figure 42: Deorbiting with the serial combination of a chemical propulsion system and a drag sail, mass fraction vs. release altitude, 4-year total duration: (**a**) full Hohmann; (**b**) half Hohmann.