This study builds on a previous tool comparison, using NDARC (NASA Design and Analysis of RotorCraft) -and SUAVE, an open-source design tool originally developed out of Stanford University [3]. In the prior study there was broad agreement in terms of overall gross takeoff weight of this configuration when selected for a prescribed mission. However, when observing design sensitivities and tradeoffs, the toolchains predicted opposing choices would result in lighter aircraft. These results acted as a guide and starting point for the more detailed comparison performed here.

Three tools are used in the present comparison: NDARC, CREATION, and HYDRA. NDARC is a rotorcraft design tool that leverages tunable parametric equations that can be fit to a combination of substantiating data and higher fidelity analysis [4]. NDARC has been used as the basis for a variety of generic reference models utilizing features common within the emerging eVTOL industry to inform technology development [5, 6]. A version of this NDARC model has also been utilized as a reference case for newly developed cost parametrics [7, 8]. CREATION (Concepts of Rotorcraft Enhanced Assessment Through Integrated Optimization Network) is a design toolchain developed by ONERA that utilizes a suite of low, medium and some higher fidelity tools, among them DynaPyVTOL [9]. DynaPyVTOL can model any aircraft combining rotary and/or fixed wings for the study of their flight dynamics (trims, failures, stability, controls etc.). HYDRA (Hybrid Design and Rotorcraft Analysis) employs a combination of parametric and physics-based subsystem weight models, with variable fidelity rotor and wing aerodynamics [10, 11]. All three codes have a recent history of investigation of aircraft configurations pertinent to electric distributed propulsion rotorcraft [3, 5, 6, 11, 12, 13].

A standardized set of basic vehicle and mission characteristics (Fig. 2, Table 1) has been modeled in each team’s respective design tool. Range credit for the climb, descent, and loiter segments was not assumed. Mission specifications were derived from a simplified version of a notional Uber Elevate profile [14]. Power requirements included an allocation of 14.9 kW of accessory power for environmental conditioning in hot climates and modern avionics equipment for integration into a crowded airspace.

Table 1

Mission profile definition including speed, time, and rate of climb specified for each segment

Segment | type | time (min) | speed (m/s) | ROC (m/s) |

1 | hover | 0.5 | 0 | 0 |

2 | climb | 0.08 | 0 | 2.54 |

3 | climb | 0.52 | 28.3 | 2.54 |

4 | loiter | 1 | 36.0 | 0 |

5 | climb | 1.4 | 30.9 | 2.54 |

6 | cruise | 32.73 | 49.2 | 0 |

7 | descent | 1.4 | 30.9 | -2.54 |

8 | loiter | 1 | 36.0 | 0 |

9 | descent | 0.52 | 28.3 | -2.54 |

10 | descent | 0.13 | 0 | -1.52 |

11 | hover | 0.5 | 0 | 0 |

Each tool requires a unique set of inputs; a rigorous adjudication process was consequently needed to ensure a consistent geometric representation of the aircraft. The common sets of geometric inputs used for this study can be seen in Tables 7–12 in Appendix A. Cant angle is considered positive when the inboard section of the rotor mid-plane is tilted above the fuselage and negative when tilted below the fuselage.

There were 18 available control inputs for this vehicle:13 propeller rpm settings, 2 wing flap deflection angles, 2 rudder deflection angles, and 1 elevator deflection angle) in addition to body pitch and roll. This yields 20 control variables for 6 Degree of Freedom (DoF) rigid body dynamics, resulting in an overactuated system. When trimming a single main rotor helicopter, there are traditionally four controls and two attitude angles (pitch and bank) corresponding to the six equations of rigid body dynamics. Under a single main helicopter control scheme, there is a single trim solution. When more than six control inputs are introduced, there are infinite solutions for this system of equations. In these situations, either new control laws must be developed, or trim must then be treated as an optimization problem. Many other proposed eVTOL concepts are similarly overactuated; this is a conscious decision to respond to emergency situations via redundancy instead of autorotation as in conventional rotorcraft. Control insights discovered on this configuration may be applicable to other concepts. The trim strategies utilized by each tool in this analysis are shown in Table 2.

NDARC utilized the VTOL trim strategy in segments 1, 2, 10, and 11, the Airplane strategy in segment 6 and the Compound strategy in segment 3–5, and 7–9. The wing lift fraction was set at 50% for segments 3 and 5 and 70% in segments 4 and 7–9. This differs from the approach in [3], which utilized an Airplane trim strategy for segments 3–9.

In NDARC, rotor rpm settings were collectively controlled with flaps deflected 15 degrees at airspeeds lower than cruise (49 m/s). CREATION and HYDRA each used optimization-based approaches to solve the overactuated trim problem with total power required acting as the objective function. Vehicle pitch angle was limited to +/- 8 degrees for each tool. In NDARC, this was achieved via trim strategy selection, flap deflection, and wing lift fraction. CREATION and HYDRA restricted pitch attitude via a formal optimization constraint. The pitch constraint was relaxed for segments 3 and 5 in the HYDRA model to allow for convergence in the absence of a flap model.

Table 2

Control strategy summary listing control inputs and unknowns for each conceptual design tool.

Trim Strategy | VTOL | Airplane | Compound |

NDARC Inputs | rotor rpm differential-rpm | pitch pusher rpm elevator | rotor rpm pusher rpm elevator pitch |

NDARC Unknowns | force z moment z | force x force z moment y | force x force z moment y wing lift % |

CREATION Inputs | pitch rotor rpms | pitch pusher rpm wing flap and stabilizer deflections | VTOL & Airplane controls (All) |

CREATION Unknowns | force x force y force z moment x moment y moment z | force x force y force z moment x moment y moment z | force x force y force z moment x moment y moment z |

HYDRA Inputs | pusher collective pitch | pusher collective pitch | pusher collective pitch |

HYDRA Unknowns | force x force z | force x force z | force x force z |

In CREATION each of the 20 potential inputs were individually controlled via an optimizer. For CREATION, a variety of optimization algorithms were attempted, including Sequential Least Squares Quadratic Programming (SLSQP), Constrained Optimization BY Linear Approximation (COBYLA), and trust region methods to solve this trim problem, but all were found to have difficulties in solving the problem robustly (Refs. 15–17). Optimal trim minimizing the required power for each flight case was finally computed within DynaPyVTOL by utilizing a custom algorithm using successive trim computations with the application of linear programing in order to find the global optimum. HYDRA’s trim strategy used an optimizer to find the values of pusher propeller thrust, rotor collective, and aircraft pitch that minimize power required. RPM control and flap modeling within HYDRA are areas of future code development.

A description of the component-level weight models for each toolchain can be seen in Table 13 in Appendix B. The structural weight estimation in NDARC relied on NASA Revolutionary Vertical Lift Technology (RVLT) assumptions which are described as “consciously optimistic” [3, 5, 6]. The model from [3] has been updated to utilize thermal management weight estimation methods implemented in NDARC 1.16. A new high torque-to-weight motor regression was utilized [12].

In CREATION the structural weight of the wing and booms were calculated by accounting for the maximum thrust needed to cope with the concurrent failure of two of the 12 lifting rotors (see [13]. This maximum thrust produces bending and torsion loads which size the wing structure. The demanding failure assumption was considered in the event that this aircraft experiences a failure in VTOL mode over populated areas. This condition was also used for the rotor and electric motor weight estimates. Composite structures were assumed for the wing, booms, and rotor blades. The NDARC and HYDRA models, in contrast used fixed thrust margin and motor power margins at the vertical climb condition (segment 2 of Table 1).

The HYDRA model leveraged the AFDD weight parametrics from NDARC. AFDD parametrics were uncalibrated for the HYDRA modeling in this paper, meaning the baseline equations were used without additional tuning for vehicle archetype or features [4]. Other methods for estimating structural weight are available and are detailed in [11]. Semi-empirical weight models were used for the motor, battery, and wiring [18, 19]. An empirical method was used for estimating the electric speed control (ESC) weight.

Weight estimation was performed by employing successive substitution to solve a fixed-point iteration problem for all three tools by iterating on Design Gross Weight (DGW). Table 14 in Appendix B summarizes the performance estimation methodology employed by each tool for this effort.

For NDARC performance modeling, the following tools and performance assumptions were used; finite wing theory models for lift and induced drag were calibrated to Athena Vortex Lattice (AVL) computations [20]. Rotor performance was calibrated to analysis performed using CAMRAD II [21]. NASA RVLT aerodynamic assumptions beyond current state of the art were used for parasite drag.

For CREATION, rotor performance models for the DynaPyVTOL tool were calibrated to Aero Multi Body (AMB) results. AMB is a lifting line code with a free wake model. Wing and empennage performance were estimated using separate wing polars computed with the aspect ratio and selected airfoils from Table 7, Table 11, and Table 12 in Appendix A.

In HYDRA, rotor performance was computed using momentum theory with profile corrections. Blade Element Momentum Theory (BEMT) is also an option for rotor performance. Wing loads were calculated using finite-wing theory with numerical lifting line theory as an alternative option. Parasite drag estimates from both CREATION (implemented in DynaPyVTOL) and HYDRA were informed by Computational Fluid Dynamics (CFD) computations using a visual OpenVSP model of the aircraft geometry, see Appendix A). The CFD data for CREATION and HYDRA were generated from separate models using Reynolds Averaged Navier Stokes each with a Spalart-Allmaras turbulence model [22].