A flying wing is a tailless aircraft design that achieves passive stability on roll, pitch, and yaw axes using only wing geometry, eliminating the need for a vertical tail. The bell-shaped lift curve distribution, developed by Ludwig Prandtl, provides higher efficiency than elliptical distributions by reducing bending moments, enabling higher aspect ratio wings with reduced induced drag. This design naturally eliminates adverse yaw through aggressive wing tip twist, creating proverse yaw where the rising wing experiences less drag, enabling coordinated turns without a vertical stabilizer. Stability analysis using CFD software (XFLR5) examines eigenvalues, particularly the damping factor for Dutch roll stability, which describes the coupling between yaw and roll oscillations. The final design achieved a 5° dihedral angle, -7° washout, and 31° sweep, demonstrating that careful geometric optimization can produce efficient, stable tailless aircraft.
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Engineering a Tail-less Flying WingAjouté :
This is a flying wing, a high-efficiency UAV design meant to utilize only wing geometry to achieve passive stability on the roll, pitch, and most importantly yaw axis. The topic came to mind when I discovered the works of Al Bowers and his Prandtl wing aircraft, a flying wing sailplane design that was capable of achieving proverse yaw, meaning it was able to fly without a vertical tail or complex control surfaces. Most times when we consider tailless flying wings, the first thing that comes to mind is the B-2 bomber. But, this aircraft, along with many other tailless flying wings, use split flaps or differential thrust for course correction and better directional stability. So, considering the method of just using wing geometry for stability made me quite interested in designing a small-scale UAV that could utilize this exact concept without the addition of specialized control surfaces that can increase the weight and complexity of the aircraft. The concept I'm referring to is the bell-shaped lift curve distribution created by Ludwig Prandtl, a method of distributing lift on an aircraft's wing that was said to yield higher efficiency for a given structural limit over the elliptical distribution method. This was because the bell curve distribution would reduce the bending moment, making it possible to build higher aspect ratio aircraft for the same structural weight, which would lead to reduced induced drag. This method would also be able to get rid of adverse yaw in flying wings, since the aggressive twist in the wing tips made the downwash deflecting elevon experience upwash rather than downwash, making the side of the wing that's rising experience less drag, which makes natural coordinated turns possible. And by having proverse yaw, there's no need for a vertical stabilizer, which removes more structural weight and drag from the aircraft. a research project for a science fair, me and my friends wanted to see how we could design such an aircraft at a much smaller scale and much smaller Reynolds numbers. And although this was just supposed to be a one-off project, I've become way more interested and confused in this whole concept and design process than I thought I would be. So, I thought it would be really fun to continue this project in the future videos where I try to make better and more refined versions of this wing design, cuz this aircraft is certainly not perfect. For optimizing and designing this aircraft, we use XFLR5, which is a CFD software. And with this, we were able to determine our airfoils and also analyze the efficiency and stability of the aircraft itself.
And by running a stability analysis, we were able to get animations and also eigen values, which help us determine whether our aircraft is stable or not.
For the eigen value, we mainly paid attention to the real number, which is the damping factor. And our goal was to get that number as close as we can to negative on the Dutch roll stability, which describes how the yaw and roll are coupled to each other.
Ultimately, I don't want to get too technical in this video because there's a lot of stuff I still need to learn, and I'm hoping to provide more detailed information in my next video on designing version two of this wing. But one of the examples of the mistakes we made while optimizing this aircraft through CFD was not paying attention to these numbers and frequencies, which provide a lot of useful info about how the aircraft behaves when recovering after a disturbance and stuff like that.
And you'll see later how this gets translated into real flight. But anyways, after a lot of fiddling and looking back and forth through efficiency graphs and eigen values, we ended up with this wing design, which had a dihedral angle of 5°, washout of -7°, sweep of 31°, a root chord of 6.3 in, and a tip chord of 1.9 in.
After that, the models were replicated in Onshape and configured to include all the holes and cavities for the servos, carbon spars, and the main electronics.
Originally, I was going to have a hatch to increase the efficiency and cover up the electronics, but because of how thin the wing is and for the sake of just stability testing, I just ended up keeping it a wing without any cover.
Since the design relies heavily on the geometry of the wing itself and because of the time restraints, we decided to 3D print the whole aircraft. 3D printing can be pretty amazing because although the aircraft needs to be made out of a material that can keep it lightweight, I'm able to use a specialized lightweight PLA and print all the components I need in just two to three days. If you also want 3D printed parts for your projects or want to get your hands on custom CNC carbon fiber and metal pieces that you don't have the machinery for, I highly recommend using PCBWay. PCBWay is a full-service prototyping and fabrication of fully custom PCBs and allows you to specify details like the number of layers, material, solder mask color, service finishing, and much more, making your custom circuit board fit for any type of project. Along with their PCB manufacturing, they also include services like 3D printing, CNC machining, sheet metal fabrication, and injection molding. And with its varieties of materials to choose from, options for post-processing, and its instant quote feature, it's perfect for acquiring any sort of complex component for a project without needing any multi-thousand-dollar machine in the garage. If you're interested, check out the link in my description to get a free $5 coupon to get started with PCBWay today. Again, thank you to PCBWay for sponsoring this video. After all the parts were printed, I began gluing and assembling everything with the servos and the 1806 brushless motor. Then I began soldering and connecting everything to a Flying RC F-4 flight controller. And you can see here, I added this body fuselage part on the nose. And the reason for that was because I made a fatal mistake of measuring the CG place incorrectly and not looking back at the CFD simulations to double-check. I just assumed it was in the right place since this wing design had a lot more wash up than normal. I really should have realized based on the wing shape alone that I would have balanced out at the correct CG spot without needing any extension.
And unfortunately, I didn't get any footage of it in the air, but this model did crash as a result of it being too nose-heavy and unable to pitch up. But luckily, all the electronics survived and I was able to rebuild the whole aircraft in a relatively short period of time and make that CG adjustment. And after a bit of a sketchy launch, the aircraft was successfully flying and had very well coordinated turns as intended.
>> But it was clear during this flight that the aircraft had some issues with the roll axis oscillating and going into small Dutch roll oscillations. But all in all, I was pretty happy with how the aircraft flew and I was ready to try some autonomous flights and gather some data. But to do that, I needed to switch to a flight controller that could do data logging. So I used a Speedybee F405 Wing Mini stripped off an old project and this BZ251 GPS. Definitely overkill and has a lot of unnecessary weight, but those were just the leftover components I had.
During the first flight with the new flight controller, upon hitting the return to launch switch, the aircraft started climbing pretty rapidly. And that's because I forgot to change the RTL height ceiling from 100 m to 60 m in ArduPilot. And because I didn't bring my computer to change the parameters, I just ended up flying it around manually to collect some data and try the autonomous flight later. Before looking at the efficiency graph, I first wanted to see if there was data that showed any correlation between the roll and the yaw. And because the logs provide graphs for the IMU X, Y, and Z axes, I can see whether or not the roll and the yaw have any sort of correlation. And it's pretty interesting to see that the yaw does indeed seem to follow with the roll IMU data whenever it increases or decreases, which proves that this design does indeed have proverse yaw. But as I I in the first flight, this aircraft would sometimes go into some Dutch roll oscillations. And during this flight with the new flight controller, none of that really happened until towards the end of the flight where it started as just a roll oscillation, then proceeded to get worse until it got into a Dutch roll oscillation where the roll and yaw seemed to be out of sync with each other. I was wondering what it looked like in the IMU graphs, and I'm not 100% sure if this is what it is, but it does seem like the yaw axis is out of sync with the roll where the yaw axis seems to be decreasing as the roll axis has yet to reach its peak in the oscillation. I'm not sure if that is Dutch roll, but it's something interesting I wanted to point out. For the actual efficiency data, I was at first using Mavlink Explorer to get a watt hours per kilometer graph, but because I couldn't figure out how to get it to display actual numbers, I just ended up using UAV Log Viewer. And with it, I was able to get the average efficiency and also an animation of the flight itself. And with the animation, I was able to look back at the portion of the flight where the aircraft went under a Dutch roll oscillation and actually see it in the flight replay, which is just really cool. But anyways, back with the efficiency data, it seems that throughout the flight while the aircraft was cruising, its average efficiency was around 0.5 to 0.55 watt hours per kilometer, which is obviously really good, but doesn't mean much when there's not an actual comparison. So, all I really cared about with the efficiency data for this aircraft was to get it as accurate as possible. And to do that, I was going to need to get this aircraft to fly autonomously. And before I did, I tried attaching this all-in-one FPV camera to get some onboard footage, but I ended up accidentally losing all the recording from my goggles. It didn't matter too much since the video was really low quality and would always cut out, but I did end up saving this one photo from the video.
>> Ready?
It's auto.
It's working.
All right.
All right, I need a I need to let that flight stabilize for a little bit.
Walking by.
This is not good.
So, after finishing the autonomous flight, I went back to UAV log viewer to check the data. And this aircraft stayed pretty consistent at an average of around 0.52 watt hours per kilometer.
So, pretty much the exact same from the previous flight. And again, this is data I'm going to be using for when I'm designing and testing the second version of this aircraft. So, that's pretty much going to conclude the end of this project for now. But, once again, towards the end of this flight, the aircraft got into another nasty Dutch roll oscillation. As you can see here in the flight replay. So, definitely my biggest focus with the next wing iteration is improving that stability and making sure it can't get into Dutch roll oscillations as easily cuz it's definitely the biggest problem with this aircraft. Yeah, this is definitely a different project for me since it's just so heavily involved in aerodynamic principles and CFD optimization. And I've been finding it pretty enjoyable to work on. So, yeah, that's pretty much going to be it. And I'll see you when I continue this project later.
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