**8.2 Entry with bank angle modulation**

Aerodynamic efficiency can be varied implicitly without using AoA modulation opportunely changing the bank angle *μa*. Bank modulates the lift force into two components *Leff* ¼ *L* cos *μ<sup>a</sup>* and *Lside* ¼ *L* sin *μa*. The lateral force, *Lside*, deviates the lift vector outside the plane of trajectory, thus allowing a cross-range performance in the lateral direction. Therefore, trajectory footprint can be decomposed into two components: the down-range <sup>Δ</sup>*xp* � *<sup>L</sup> <sup>D</sup> cos <sup>μ</sup><sup>a</sup>* and the cross-range <sup>Δ</sup>*yp* � *<sup>L</sup> <sup>D</sup> sin μ<sup>a</sup>* . In **Figure 7** the effect bank modulation on vehicle trajectory is shown.

### **Figure 5.** *Entry analysis with no bank angle modulation.*


**Table 3.** *Total energy absorbed during entry.*

**Figure 6.**

*Trade-off effects of flight path angle for entry flight at ve = 3484 m/s, α = 30°, μ<sup>a</sup> = 0°.*

**Figure 7.** *Entry trade-off analysis with bank angle modulation.*

*Lifting Entry Analysis for Manned Mars Exploration Missions DOI: http://dx.doi.org/10.5772/intechopen.101993*


**Table 4.**

*Total energy absorbed during re-entry.*

Increasing *μ<sup>a</sup>* at constant AoA (i.e., constant *L=D*Þ the total range (cross-range and downrange) increases. The effective lift component *Leff* is reduced, and the vehicle attains a lower altitude at *<sup>M</sup>*<sup>∞</sup> <sup>¼</sup> 2, *<sup>μ</sup><sup>a</sup>* <sup>¼</sup> <sup>20</sup>° with respect to *<sup>μ</sup><sup>a</sup>* <sup>¼</sup> 40° as it is shown in **Figure 5c**. Therefore, control authority increases at expense of a higher terminal speed. Another effect of bank angle modulation can be observed in **Figure 7d**. The lower lift reduces the skip motion when the vehicle encounters the Martian atmosphere. Higher heat flux peaks over a shorter entry time are experienced. Therefore, at constant AoA, bank modulation improves the capability to reach the predefined landing spot.

Finally, in **Table 4** the total energy absorbed during the entry with bank modulation is computed.

From an energetic point of view, bank modulation toward higher *μ<sup>a</sup>* favors lower total energy stored but shifts trajectory toward a ballistic-like behavior.
