# Integrated Flight Control System Characterization Approach for Civil High-Speed Vehicles in Conceptual Design

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Studies on Flight Control System Design for High-Speed Vehicles

## 3. STRATOFLY MR3 Vehicle and Mission Concepts

_{2}. Particularly, the STRATOFLY MR3 vehicle was originally conceived to cover missions featuring a global distance of around 18,000 km. A first mission analysis was carried out to identify a draft trajectory and profile (Figure 2), connecting Brussels to Sydney, as described here. During the first part of the mission, six Air Turbo Rocket (ATR) engines are used [22], with an available thrust at sea level of about 233 kN per engine. The vehicle flies at subsonic speeds during the subsonic climb. Then, the acceleration up to around Mach 0.90 is supposed to take place, reaching an altitude between 11 km and 13 km. At this point, the vehicle performs the subsonic cruise. This phase is needed to avoid a sonic boom [23] while flying over land. A constraint on the distance flown from the departure site is introduced to fulfil this requirement. In fact, the subsonic cruise phase ends when the vehicle is 400 km from the departure airport. During the next phase, the vehicle performs a second climb, until reaching Mach 4 (supersonic climb). At the end of this phase, the ATR engines are turned off and the Dual Mode Ramjet (DMR) [24] is activated to accelerate up to Mach 8, reaching an altitude of 32–33 km (hypersonic climb). Here, the cruise starts at Mach 8, with a total thrust of 664 kN available for the DMR. During the first part of the cruise, the vehicle flies over the arctic region towards the Bering strait, between Asia and North America. Then, the vehicle continues to cruise over the Pacific Ocean towards Sydney. The waypoint at which the cruise phase is concluded depends on the type of descent considered, i.e., powered or gliding descent. The first mission concept developed within the precursor LAPCAT II Project [25] involved a gliding descent [26]. However, since the aerodynamic performance is supposed to be very low in engine-off conditions, a powered descent has been considered for an updated mission concept. The sketch provided in Figure 2 is just a first mission layout, while the final performance over the reference mission, in terms of fuel consumption and aerodynamic efficiency, will be updated after introducing the control surfaces and fuel depletion strategy.

## 4. Flight Control System Integrated Design Methodology

#### 4.1. Methodology Overview

#### 4.2. Step 1: Geometrical Definition of Flight Control Surfaces

#### 4.3. Step 2: Stability Analysis for the Clean Configuration

_{My}(Equation (1)) has a decreasing trend for an increasing Angle of Attack (AoA, defined as the angle between the reference longitudinal aircraft axis and the relative wing). It is worth noting that all the subsequent analyses refer to the vehicle angle of attack, already taking into account that the wing sees a higher angle with reference to the incoming flow because of its layout (incidence).

#### 4.4. Step 3: Aerodynamic Characterization of Control Surfaces and Trim Analysis

#### 4.5. Step 4: Evaluation of Hinge Moment

#### 4.6. Step 5: Detailed Estimation of Power Demand

## 5. Conclusions and Future Works

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

AoA | Angle of Attack |

ATR | Air Turbo Rocket |

CoG | Center of Gravity |

DMR | Dual Mode Ramjet |

EIS | Entry Into Service |

FCS | Flight Control System |

L/D | Lift-to-Drag ratio |

MTOM | Maximum Take-Off Mass |

$\mathrm{c}$ | $\mathrm{mobile}\mathrm{surface}\mathrm{chord}\left[\mathrm{m}\right]$ |

${\mathrm{l}}_{\mathrm{flap}}$ | selected mobile surface length [m] |

$\mathrm{p}$ | static pressure [Pa] |

${\mathrm{p}}_{\mathrm{flap}}$ | static pressure on selected mobile surface [Pa] |

${\mathrm{w}}_{\mathrm{flap}}$ | selected mobile surface width [m] |

${\mathrm{C}}_{\mathrm{D}}$ | drag coefficient |

${\mathrm{C}}_{\mathrm{L}}$ | lift coefficient |

${\mathrm{C}}_{\mathrm{m}}$ | hinge moment coefficient |

${\mathrm{C}}_{{\mathrm{m}}_{0}}$ | hinge moment coefficient at angle of attack equal to zero |

${\mathrm{C}}_{{\mathrm{M}}_{0}}$ | pitching moment coefficient for angle of attack equal to zero |

${\mathrm{C}}_{{\mathrm{M}}_{\mathrm{y}}}$ | global pitching moment coefficient |

${\mathrm{C}}_{{\mathrm{M}}_{{\mathrm{y}}_{\mathrm{flap}}}}$ | contribution to pitching moment coefficient due to elevons |

${\mathrm{C}}_{{\mathrm{M}}_{{\mathrm{y}}_{\mathrm{canard}}}}$ | contribution to pitching moment coefficient due to canard |

${\mathrm{C}}_{{\mathrm{M}}_{{\mathrm{y}}_{\mathrm{bodyflap}}}}$ | contribution to pitching moment coefficient due to body flap |

${\mathrm{C}}_{{\mathrm{M}}_{{\mathrm{y}}_{\mathrm{Thrust}}}}$ | contribution to pitching moment coefficient due to thrust |

${\left({\mathrm{C}}_{{\mathrm{M}}_{\mathrm{y}}}\right)}_{\mathrm{clean}}$ | global pitching moment coefficient for clean aircraft configuration only |

${\mathrm{C}}_{{\mathrm{m}}_{\mathsf{\alpha}}}$ | $\mathrm{hinge}\mathrm{moment}\mathrm{coefficient}\mathrm{at}\mathrm{angle}\mathrm{of}\mathrm{attack}\mathrm{equal}\mathrm{to}\mathsf{\alpha}$ |

${\mathrm{C}}_{{\mathrm{M}}_{\mathsf{\alpha}}}$ | contribution to pitching moment coefficient due to angle of attack |

${\mathrm{C}}_{{\mathrm{m}}_{\mathsf{\delta}}}$ | $\mathrm{hinge}\mathrm{moment}\mathrm{coefficient}\mathrm{for}\mathrm{a}\mathrm{deflection}\mathrm{angle}\mathrm{equal}\mathrm{to}\mathsf{\delta}$ |

${\mathrm{F}}_{\mathrm{flap}}$ | force acting on the selected mobile surface [N] |

${\mathrm{M}}_{\mathrm{actuator}}$ | moment generated by the actuator [Nm] |

${\mathrm{M}}_{\mathrm{hinge}}$ | hinge moment [Nm] |

$\mathrm{M}$ | Mach number |

P | power demand to the actuator [W] |

$\mathrm{S}$ | $\mathrm{mobile}\mathrm{surface}\mathrm{area}\left[{\mathrm{m}}^{2}\right]$ |

$\mathrm{V}$ | $\mathrm{airspeed}\left[\frac{\mathrm{m}}{\mathrm{s}}\right]$ |

$\mathsf{\alpha}$ | angle of attack |

${\mathsf{\beta}}_{0}$ | oblique shock wave angle |

$\mathsf{\gamma}$ | ratio of specific heats of air |

$\mathsf{\delta}$ | deflection angle of the control surface |

$\mathsf{\eta}$ | efficiency of the transmission |

${\mathsf{\theta}}_{0}$ | wedge angle of the lower part of the vehicle |

$\mathsf{\rho}$ | $\mathrm{air}\mathrm{density}\mathrm{in}\left[\frac{\mathrm{kg}}{{\mathrm{m}}^{3}}\right]$ |

$\mathsf{\omega}$ | angular speed of the control surface [rad/s] |

${\mathsf{\Delta}\mathrm{C}}_{\mathrm{D}}$ | variation of drag coefficient due to control surfaces |

${\mathsf{\Delta}\mathrm{C}}_{\mathrm{L}}$ | variation of lift coefficient due to control surfaces |

${\mathsf{\Delta}\mathrm{C}}_{\mathrm{M}}$ | global variation of pitching moment coefficient |

${\left(\Delta {\mathrm{C}}_{\mathrm{My}}\right)}_{\mathrm{i}}$ | i-th effect of control surfaces on global pitching moment coefficient |

${\left(\Delta {\mathrm{C}}_{\mathrm{My}}\right)}_{\mathrm{T}}$ | effect of thrust vector on global pitching moment coefficient |

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**Figure 11.**Trim maps for Mach 0.5 and CoG 52.5 m—(

**a**) 3D, (

**b**) 2D for ${\mathsf{\delta}}_{\mathrm{bodyflap}}=-25\xb0$.

**Figure 12.**Trim maps for Mach 0.8 and CoG 52.0 m—(

**a**) 3D, (

**b**) 2D for ${\mathsf{\delta}}_{\mathrm{bodyflap}}=-25\xb0$.

**Figure 13.**Trim maps for Mach 1.2 and CoG 50.0 m—(

**a**) 3D, (

**b**) 2D for ${\mathsf{\delta}}_{\mathrm{bodyflap}}=-20\xb0$.

**Figure 14.**Trim maps for Mach 2.0 and CoG 49.5 m—(

**a**) 3D, (

**b**) 2D for ${\mathsf{\delta}}_{\mathrm{bodyflap}}=-20\xb0$.

**Figure 15.**Trim maps for Mach 5.0 and CoG 48.0 m—(

**a**) 3D, (

**b**) 2D for ${\mathsf{\delta}}_{\mathrm{bodyflap}}=-15\xb0$.

**Figure 16.**Trim maps for Mach 8.0 and CoG 48.0 m—(

**a**) 3D, (

**b**) 2D for ${\mathsf{\delta}}_{\mathrm{bodyflap}}=-15\xb0$.

**Figure 17.**Comparison between clean and trimmed configuration for C_L (

**a**), C_D (

**b**), and L/D (

**c**). Comparison between stable and unstable configurations in terms of L/D (

**d**).

**Figure 19.**Updated mission profile trends in trim conditions as a function of time: (

**a**) altitude (blue) and Mach number (orange), (

**b**) vehicle mass (blue) and propellant mass (orange), (

**c**) L/D, and (

**d**) AoA.

Surface Type | Ratio Movable Surface/Reference Surface [27] |
Resulting Movable Surface (Total) [m^{2}] |
---|---|---|

Pitch control devices | 0.048 | 120 |

Roll control devices | 0.022 | 55 |

Lateral control devices | 0.021 | 52.5 |

Surface Type | LAPCAT MR2.4 Movable Surfaces (Total) [m^{2}] |
---|---|

Wing trailing edge surfaces (roll) | 60 |

Canard (pitch) | 100 |

Rudders (yaw) | 32 |

**Table 3.**Control surfaces characterization for MR3 (data for single surface—one side for each category).

Surface Name | Chord (Mean) [m] | Span [m] | Deflection Limits [Deg] | Surface [m^{2}] |
---|---|---|---|---|

External Elevon | 3.00 | 5.00 | +/−25 | 15.00 |

Internal Elevon | 3.00 | 5.00 | +/−25 | 15.00 |

Canard | 5.75 | 8.70 | +/−20 | 50.00 |

Rudder | 3.05 | 6.50 | +/−20 | 19.80 |

Body Flap | 7.14 | 4.05 | −30 | 23.70 |

Single Surface Actuator Mass [kg] | |
---|---|

Elevon | 74.4 |

Body Flap | 178.3 |

Canard | 81.2 |

Rudder | 17.7 |

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**MDPI and ACS Style**

Ferretto, D.; Gori, O.; Fusaro, R.; Viola, N.
Integrated Flight Control System Characterization Approach for Civil High-Speed Vehicles in Conceptual Design. *Aerospace* **2023**, *10*, 495.
https://doi.org/10.3390/aerospace10060495

**AMA Style**

Ferretto D, Gori O, Fusaro R, Viola N.
Integrated Flight Control System Characterization Approach for Civil High-Speed Vehicles in Conceptual Design. *Aerospace*. 2023; 10(6):495.
https://doi.org/10.3390/aerospace10060495

**Chicago/Turabian Style**

Ferretto, Davide, Oscar Gori, Roberta Fusaro, and Nicole Viola.
2023. "Integrated Flight Control System Characterization Approach for Civil High-Speed Vehicles in Conceptual Design" *Aerospace* 10, no. 6: 495.
https://doi.org/10.3390/aerospace10060495