Vahana Design Process Part II: Preparing for Lift-Off
Since we first sketched Vahana on a napkin, we’ve eagerly looked forward to the day we would see our vision become a reality as occurred just a few weeks ago with our first successful full-scale test flights. Here we’ll take a look back at our aerodynamic design process so you can join us in our journey.
Following our vehicle sizing process, which we outlined in our first design-related blog post, we dove deep into aerodynamic and structural design and validation.
The first aspect to tackle was the aerodynamic surfaces on the vehicle — fans, wings, winglets, and landing gear. We used a multi-disciplinary design approach that tied together aerodynamic performance estimates with an open-loop dynamics model and structural weight estimates. In the end, we needed to select a blade radius that would keep the footprint of the vehicle small, while ensuring the aircraft has the power required to carry its own weight (motors, fans, wings, etc.). The following figure shows an example trade off between fan radius and both the hover power required and the hover figure of merit, while holding total thrust fixed. The figure of merit is a hover efficiency measure that is equal to the ideal hover power required from momentum theory divided by the actual hover power required. The red point indicates the chosen fan radius to balance vehicle size with power requirements.
Figure 1: Shaft Power and FOM as a function of blade radius.
As a reminder, some of our original key vehicle design parameters include fan diameter, total disk area, mass, fuselage length, wing airfoil, wing tilt range, etc. After a great deal of analysis we were able to gauge performance specs that ended up being similar to tilt rotors or heavy helicopters, such as the UH-60 Blackhawk, when it comes to hover disk loading and power loading.
Figure 2: Power loading vs. disk loading for different VTOL vehicle types, including Vahana. (Original from NASA SP-2000–4517).
With this in mind, we began looking at non-planar wing designs. In keeping with our small footprint goal, we chose to utilize a smaller wingspan (even though we knew this would lead to higher induced drag). We settled on the non-planar tandem configuration with winglets to both lower the induced drag and reduce the interactions between the canard and wing mounted fans. The following figure shows the optimal load distributions for our lifting surfaces to minimize drag.
Figure 3: Optimal Trefftz plane loading with e = 1.35
When choosing the wing, canard, and winglet airfoils, we focused on balancing competing requirements. For example, following our testing of several designs, we settled on a relatively thick airfoil that allows for efficient spar structure and internal volume for routing wires and mounting systems. The following pictures show canard, wing and winglet airfoil sections:
Figure 4a: Vahana canard airfoil
Figure 4b: Vahana wing airfoil
Figure 5: Vahana lower winglet airfoil
One of our initial design targets was to have Level 1 and Level 2 open-loop dynamic modes in the cruise configuration. This provides some level of assurance that the vehicle dynamics will be well behaved and easy to control, which is especially important when considering management of failure modes. To support this, we developed tools to estimate the open-loop dynamic modes from stability derivatives, which were calculated using MIT’s open source AVL fixed wing analysis tool. With this we were able to quickly test a variety of geometric configurations, while giving us the assurance that both the vehicle performance and stability were meeting our targets. Ultimately, these targets were met by modifying the winglet geometry and tuning the size and position of the rear landing gear fairings to increase Dutch roll damping.
Figure 6: Open-loop longitudinal dynamic modes in cruise configuration. White background indicates level 1; yellow, level 2; and red, level 3
Figure 7: Open-loop lateral directional dynamic modes in cruise configuration. White background indicates level 1; yellow, level 2; and red, level 3
After our initial testing of various wing configurations, we looked at motor sizing. One of the major concerns and biggest challenges with our multirotor approach was achieving sufficient yaw authority during hover. There are three methods by which Vahana can generate yawing moments: differential torque from the motors rotating in different directions; canting the motors away from vertical, so that motor thrust generates a yawing moment about the CG; and deflecting control surfaces immersed in the induced flow below the fans.
We approached motor sizing as a hierarchical, multi-objective optimization problem. We took into account high-level design variables including: wing and canard tilt angles at hover, fan rotation directions, and fan mounting angles relative to the wing. Our goal was to minimize the maximum motor thrust required to trim the vehicle in hover with any single failed actuator. After automatically running hundreds of configurations, we were able to produce a Pareto front that allowed us to select which configuration best balanced motor sizing (i.e. weight) and yaw authority in hover.
Figure 8: Parametric design results showing the effect of wing and canard tilt angles, fan rotation directions, and motor tilt angles on the required motor size to handle failed motors/fans and maximize the hover yaw authority
We determined that the motors needed to be designed with additional thrust capability to account for uncertainty in the models and to maintain margin for maneuvering and disturbance rejection. In the end, each motor is capable of generating 1.7 times the average motor thrust required in a steady hover.
Transition Trimline Analysis
With 22 actuators, there are many feasible ways to trim at a given airspeed. Leveraging an optimization routine wrapped around our medium fidelity aerodynamic analysis tool, we are able to trim the vehicle for minimum power at each airspeed while simultaneously operating within the limitations of the actuators (e.g. don’t exceed the maximum motor speed). Once the trim conditions were identified, we generated linearized aerodynamic models at each airspeed to use for simulation and control system design.
Figure 10: Actuator layout. Variable pitch fans are 1–16, tilting wings are 17–18, control surfaces are 19–22
Once we settled on the preliminary aerodynamic design we began the extensive process of testing the performance of the vehicle.
The overall configuration was validated with extensive subscale testing. The first Vahana model was built at 17% scale using a foam board to qualitatively evaluate the cruise handling qualities.
Figure 11: 17% scale foam model with our pilot, Norio Eda
The second subscale model was built to 22% scale, making extensive use of additive manufacturing to quickly build parts that match the full-scale OML.
Figure 12: 22% dynamically scaled model prior to first hover flight.
Our third and fourth subscale models were built at 24% scale. The goal here was to test the same flight control software as the full-scale vehicle and log high-rate sensor data for control system validation. In the third phase of testing, we introduced the level of autonomy that was used in the full-scale vehicle that flew in Q1 2018.
Figure 13: 24% scale model with self-pilot capabilities.
It’s incredible to look back and see how far we’ve come since our paper napkin sketch less than two years ago — especially as we just successfully completed our first full-scale test flights. This blog post merely covers the original aerodynamic design process, but as we look to the sky to provide a quick and easy solution for today’s congestion issue, we’ll continue to provide project and process updates.
- Geoffrey Bower, Giovanni Droandi, and Monica Syal