Dream 2700 | A Tailless Tale
Part II: Design Optimization and the Bell-Shaped Lift Distribution
Those who have not yet done so may want to read the first part of this series, then continue with this article — Ed.
In this second part of the journey, I will guide you through the main aerodynamic design challenges of a tailless sailplane. Nowadays, several calculation tools are available to the hobbyist and — with some effort — it is possible to run a preliminary validation of a concept, minimizing the risk of a maiden flight crash. Computational Fluid Dynamics (CFD) tools are today much easier to use, and a home workstation can deliver usable, qualitative results. However, this requires a lot of time and dedication. I’ve spent endless nights refreshing my knowledge on CFD, and fine tuning the calculation models, but this has paid-off well when you are able to see your design ‘flying’ in a virtual environment.
Wing Design Optimization In XFLR5
Most of the wing aerodynamic design has been done using XFLR5 (see Resources below). This is a wonderful tool to try different configurations, and run comparisons. My first design attempt focused on getting as close as possible to an elliptical lift distribution, since I wanted to optimize efficiency. In that configuration, winglets were placed at the wing tips, to further optimize the wing, and to give lateral stability.
The choice of the wing section profile required many iterations. The decision needs to be based on several factors: it should be a good section for low Reynolds Number (that for this design is varying from 50.000 to 400.000), should have a decent maximum Cl, and a low moment coefficient (Cm). An higher Cm will require an higher wing twist to reach the desired stability. The Reynolds Number (Re) is non-dimensional and can be described as the ratio between inertia forces and viscous forces. The lower the Re, the higher is the viscous effect of the air. Low Re usually lead to higher risk of separated flows and laminar bubbles. This can produce bad aerodynamic characteristics.
The final choice went for a section developed by Thorsten Lutz, the TL-54. This wing section offers a good maximum Cl, a quite low Cd and low zero lift moment coefficient (Cm0).
XFLR5 was used extensively at this stage to optimize the wing twist and planform. This tool allows you to test various configurations and make comparisons, by changing several parameters. I will not go into all details of XFLR5 calculations, since this has been already published in legacy RCSD in various great articles. All aerodynamics parameters were optimized, including a rough stability calculation.
At this stage, I was quite happy with the wing design, and I was ready to start the construction drawings.
The Bell-Shaped Lift Distribution
When I was close to freezing the design, I got to know about Albion Bowers, and his experiments with the Prandtl-D design. In a nutshell, Albion studies are demonstrating that, for a given payload, the lift distribution that gives the lower induced drag and the lower structural weight is the bell-shaped one. And, not to be neglected, this lift distribution gives the advantage of a coordinated roll-yaw motion, resolving one of the biggest issues we always had on flying wings, the adverse roll/yaw coupling. To better explain it, an aileron roll input to the left, will at first produce a yaw moment to the right, making the turn manouvre somewhat un-coordinated. I was so excited about this study, that I decided to modify my wing accordingly, and give it a try. With some suggestions coming from Albion Bowers, some support coming from Marko Stamenovic, the Horten Flying Wing Believers Facebook group (see Resources for links to all of these) and again a long series of XFLR5 simulations, I came out with my final wing design!
In the picture below, you can see the design evolution.
And this is the local lift distribution I got in trimmed conditions:
I fell in love with that design, for several reasons:
- There’s no reason anymore to implement winglets. They are very nice, but their location at the wingtips generates heavy loads on the wing, and increased risk of flutter.
- Vertical fins located where the downwash vortex roll-up core is found. Theoretically, a flying wing with BSLD, does not need fins for stability. Nevertheless, if you want a good amount of lateral control, you need some form of rudder somewhere. Not really a must for a scale RC model, but if your aim is to build a full scale one, think about yaw control authority during take-offs and landings.
- Wingtips are unloaded, and this allows for a lighter wing structure.
As a final design choice, I wanted to explore the ‘seagull’ dihedral, in conjunction with a special shape for the elevons. Elevons are located after the fins, towards the wingtips, and the local elevon chord increases from fin to tips. Those two features, should further improve pro-verse yaw.
Another special feature I wanted to try are the pitch neutral flaps: if the flaps extension is correctly positioned against the wing neutral point (NP), we should be able to get no pitch moment when flaps are extended.
Fuselage Pod Design Optimization
As you may recognize from the first article, the fuselage cross section is quite big, if compared to what would be really required for a radio-controlled model. This comes from the fact that I wanted to accomodate a real pilot on the full scale airplane, keeping as well enough space for the electric motor and batteries, retracting gear, and various accessories. Therefore I decided to draft the fuse at full scale, and after to scale it down to the 1:5-scale model.
With the perspective of a full-scale glider, more requirements needs to be taken into account:
- Wing spar intersection with fuselage: you need enough space to accommodate pilot legs, wing spar and control systems
- Wing tips should be high enough on the ground, not to touch down during take-offs and landings (remember that we have a swept wing)
- Fuselage to be streamlined considering the wing trim angle, to minimize flow separations
- Fuselage/wing junction shall be optimized to reduce interference drag and again potential separation
- Pilot visibility should not be heavily limited by the wing
- Enough space for the retractable gears
- Being an electric motor glider, we need space for the battery compartment
The picture below gives you an idea of how much space is necessary to accommodate the wing spar joiners. Swept flying wings are subject to heavy torsional loads, and flutter can easily occurr if the wing structure is not rigid enough. Since the wing thickness was quite limited (wing section at the root is 10% thick), the only solution was to extend longitudinally the main spar box, as much as I could.
During the development, I was able to run some CFD simulation, that allowed me to optimize the wing blending with the fuselage. Running it on a home workstation, you cannot expect miracles, but nevertheless it was very interesting to highlight some potential design flaws.
When it comes to aerodynamic drag, one of the worst enemies comes from adverse pressure gradients. You usually have no issues until the air flow on a surface is accelerating: this produces a stable and potentially laminar flow. On this scale model, considering a trim speed of circa 10 m/s, we get Re = 300.000 on the fuselage. For such a low Re and if the surface finish is smooth enough, laminar flow is likely to happen, which is good, but at the same time there’s an higher risk of getting a laminar separation bubble, which is bad. On the other way around, a higher Re number will produce less separation issues, but most probably a turbulent flow.
On the Dream 2700, it looks like we have a potential separation issue at the back of the fuselage. Let me explain the physics with the help of some pictures:
In the area highlighted in blue, the flow speed is close to zero, and this is a clear sign of flow separation, highlighted as well by the chaotic flow in that region. This is due to the poor pressure recovery, caused by the abrupt cross section change in that area. Additionally, as can be see on the next picture, the wing is producing a strong energetic flow, from top to bottom and from outboard to inboard. The strong curvature at the bottom of the fuselage creates a low energy flow with few possibilities to keep it attached to the surface. Practically I designed a perfect ‘diffuser vortex generator’. One of the reasons is connected with the need to position the propeller far away from the ground during takeoff and landing: this is the main reason why the curvature of the fuse is very mild at the top, and very pronounced on the bottom part.
Unfortunately, those results were available only after the fuselage had been already manufactured, so I will have to stay with that. During flight testing, I will try to run some experimental flow visualizations to confirm this phenomena.
In any case, I’m quite happy with the wing/fuselage blending, where the CFD analysis did not show any special problem.
A very interesting phenomena is highlighted in the pictures below. Swept wings are characterized by a cross-flow, a component of the air flow going from root to tip. This happens on the top surface of the wing, generating a deterioration of the boundary layer towards the wing tips. In that specific design, the cross-flow is more evident before we reach the vertical fins, and less evident from the fins to the tips: vertical fins are acting as wing fences, reducing cross flow at the tips. The negative twist at the tips counteracts cross flow, as well as the fins.
In a last picture, there is something somewhat funny. Have you ever wondered where lift and drag comes from? Well, CFD analysis helps in visualizing lift and drag in a very intuitive way. In the following images, red areas are representing high pressure volumes, while blue areas represents low pressure volumes.
And this brings me to the end of Part II of the Tailless Tale. The next part coming up next month in the New RCSD will be dedicated to the construction, where I will share all the steps of the process, with pictures and videos.
Let me close with the rendering of the full Dream 2700, with the final colour scheme I will use.
©2022 Domenico Bosco
Resources
- XFLR5: A Powerful Tool for Preliminary Design by Francesco Meschia. — “XFLR5 is an analysis tool for airfoils, wings and planes operating at low Reynolds Numbers…”
- On Wings of the Minimum Induced Drag: Spanload Implications for Aircraft and Birds by Albion Bowers et al — “For nearly a century Ludwig Prandtl’s lifting-line theory remains a standard tool for understanding and analyzing aircraft wings. The tool, said Prandtl, initially points to the elliptical spanload as the most efficient wing choice…”
- Flying Wing Designer: A Tool to Create Your Own Flying Wing Model by Marko Stamenovic. — “This is for persons who want to make a flying RC model and are already a bit deeper into the knowledge of flying wings…”
- Horten Flying Wings Believers on Facebook. — This group is a good source of inspiration: “Place your Horten work here and tell about the positive yaw instead of adverse yaw. Tell about the lightness of the spar, tell about the great looks, tell about test you have done…”
- AeroDesign.de by Hartmut Siegmann. — “Aerodynamics, design, layout, construction, construction, further development and optimization of conventional flight models and flying wings is really an interesting thing…”
All images by the author. Read the next article in this issue, return to the previous article in this issue or go to the table of contents. A PDF version of this article, or the entire issue, is available upon request.
