Rotorcraft Sizing: Project HYDRA

Introduction

A helicopter mission is typically defined by the following segments

(1) Hover, take off and land without a runway

(2) Cruise for a certain distance 

(3) Drop or pick up a payload

(4) Loiter (e.g. to look for people or patrol)

(5) Return to the staging area

An example mission profile from the 2016 UMD design for the American Helicopter Society Design Competition is shown below. The mission was to launch from a cargo transport aircraft, deliver a relief package to a disaster-struck area and fly to a staging area for recovery.

Depending on the number of mission segments and duration of each segment, the  "best" design that meets the requirements is chosen and built. 

Challenges that must be addressed to synthesize a design

(1) Sizing a vehicle for a given set of design parameters

(2) Choosing the right combination of design parameters

Both these challenges are tackled by project HYDRA, which I developed with Bharath Govindarajan.  HYDRA is an acronym for HYbrid Design and Rotorcraft Analysis. It's an all-in-one Python framework that brings together rotorcraft sizing and the following "higher-fidelity" analyses

(a) rotorcraft comprehensive analysis, 

(b) free wake, 

(c) airframe analysis, 

(d) Blade Element Momentum Theory (BEMT) and 

(e) blade cross-sectional stress analysis 

The first problem is called preliminary sizing. The four main vehicle characteristics (weight, size, performance and fuel) are interdependent and must be determined simultaneously to ensure that the design is consistent with the parameters chosen. Given a fixed payload, mission and some combination of design parameters, an initial guess for vehicle weight is chosen, and fixed-point iterations are performed until the design characteristics converge. The process is shown in a simple block diagram below.

The second problem can be tackled with multi-variable design optimization, or parametric sweeps. The problem with preliminary sizing is that the response surface is sometimes non-convex when using higher-fidelity models, and global optimization tools add another layer of complexity and require their own specialized fine-tuning of tolerances and error bands for each problem set (solvable problems, ultimately, but problems nonetheless). Response-surface based optimization tools are typically used when evaluating the objective function is so costly that there is no choice but to resort to this middle-man type approach. 

We set out to make HYDRA so fast that we can sweep the entire parameter space of design variables. By writing the low-level code in Fortran and wrapping it with Python, distinct modules are created that can be used as plug-and-play units in the Python framework. 

A more detailed look at the various calculations that occur in preliminary sizing is given below.

In HYDRA, we use multi-fidelity performance and stress-based airframe weight models to introduce aspects of detailed design into preliminary sizing, for two reasons:

(1) Sizing a vehicle requires an empty weight model. For newer configurations like the Quadrotor Biplane Tailsitter (QBiT), legacy empty weight models based on helicopter or airplane trends are not be directly applicable, because statistical data is unavailable for these configurations.

(2) Errors in empty weight introduced by the statistical models (from other aircraft) cascade to over-designing or under-designing other components. 

A schematic of the Quadrotor Biplane Tailsitter is shown below. This vehicle was developed at UMD by Vikram Hrishikeshavan, and affords superior hover controllability through a quad-rotor design, as well as enormous cruise efficiency improvements over an edgewise flying quad-rotor by producing lift with fixed wings. At small scales up to 8 lb, it has promising performance characteristics. Building a larger-scale version (up to 1000 lb take-off weight) requires an accurate sizing analysis to determine dimensions, subsystem targets and mission effectiveness. Sizing a vehicle in turn needs an accurate empty  weight model and aerodynamic performance model. Targeting this configuration (and other unconventional looking platforms) is the driving motivation for including these physics-based weight prediction models in HYDRA.  

For calculating the weights, HYDRA uses a finite element based static analysis with safety factors. Rotor loads and wing lift/drag are applied along at the rotor mounts and along the wing. As sizing proceeds, the model is sized up or down automatically based on rotor radius and wing span. A 3d beam lattice is used to define the load-carrying members, and the cross-sections are sized based on allowable stresses and deflections in hover and forward flight. Finally, the weight of the airframe members is used (with other components) to calculate the total empty weight, and subsequently the lift, drag and rotor thrust for sizing. 

At each step of vehicle sizing, the dimensions of the airframe member cross-sections are computed in an inner loop. Even with the additional computation cost, HYDRA can evaluate 40 designs per second on one ten-year-old CPU core.

BEMT for prop-rotors with Reynolds/Mach tabulated airfoil properties is also available for use within the sizing loop. This feature reveals additional details of the rotor design, such as the best blade twist, taper, cruise RPM and root pitch travel. The additional fidelity weeds out infeasible rotor designs and also provides insight into the range of electric motor speeds or variable-speed transmissions required.

The resulting designs can also be analyzed in detail to identify the vehicle power curves, payload-range and payload-endurance trade-offs in hover and cruise. To illustrate this capability, a 50-lb quad-rotor biplane tailsitter vehicle was designed with both a Lycoming EL-005 small piston engine with an electric transmission (generator+wires+motor) as well as with Lithium-ion batteries. The mission and performance of the two vehicles is shown below.

FULL-SCALE DESIGNS

HYDRA is also applicable to intermediate-scale and full-scale designs for both conventional and unconventional rotorcraft. Some examples of high-speed winged compounds with swiveling propellers are shown below.

In the case of full-scale designs with "conventional" frames, the statistical empty weight models may be applicable (extracted from legacy aircraft). However, the need to fly at 240 knots edgewise cruise results in a slowed rotor configuration. For a slowed rotor, lift vanishes on the retreating side and momentum theory based predictions are not reliable. Further, the blades need to be stiffened to operate at lower RPMs, which then drives the weight of the blade and therefore the whole vehicle. Therefore, an accurate aero-elastic model is needed to tune the lower-fidelity performance and blade weight models to determine how stiff the blades need to be, and the impact of that stiffness on rotor performance.

Or, as we did with HYDRA, we use the aeroelastic model  within rotorcraft comprehensive analysis directly in the vehicle sizing loop as the performance module. Using techniques adapted from real-time simulation with comprehensive analysis, the trim routine was also accelerated with algorithmic and parallelization techniques to be 24 times faster. The effect of rotor lift offset and blade twist on vehicle performance and sizing was also studied in this paper and its follow-up work. Incorporating higher-fidelity models allows us to predict exactly how stiff the blades need to be to prevent excessive flapping and to carry the lift (and lift offset) at the chosen RPM. 

The resulting angle of attack, lift and drag contours are shown for each of the three vehicles below.

The effect of carrying a lift offset is seen clearly in the last column, where the thrust concentration is clearly biased towards the advancing side. Of all 3 configurations, the symmetric fixed wing compound affords the best performance.

The effect of blade weight (driven by the blade stiffness) cascades into sizing of other components. Without a basis to set the blade stiffness (the flap natural frequency parameter) for a given cruise tip speed, the resulting vehicle may be over-designed or under-designed and not meet the mission requirements.

Cross-link with real-time simulation

A UH-60A blender model was modified to add the half-wing to the visualization model for piloted real-time simulation. The design identified by HYDRA was ported over to the real-time framework with comprehensive analysis, and the 3D model is shown below. The model can be directly imported into Unity for Virtual Reality based piloted simulation.