DaVinci Aerial Screw

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My own rough scribbling of the famous DaVinci aerial screw, circa 1493. The Wikipedia article on Leonards’s inventions has more information.

Back in December, when I got the parts for my first 250 sized quadcopter that we built for the UK Drone Show, I said that I wanted to build something unique which people would look at and go, “Wow, what is that?”. In other words, a quadcopter that doesn’t look like an all carbon killing machine straight out of a Terminator film. I had know about Leonardo DaVinci’s Aerial Screw drawing for a while and had always wanted to try it out. Now with some time on my hands, I finally managed to give it a go.

I like the smaller quacopters as they’re just right for experimenting with and I had a lot of parts for the HubSan H107 which we used for the Royal Institution “Coding for Year 9s” project in March. The main thing was a 3D printed H Frame with blade guards, which I could use for the aircraft. My own HubSan has flown so much I’ve worn it out, so the 3D printed frame, 4 new motors and new flight controller electronics were needed to get it back to flight status again. OK, I know, that’s a completely new set of kit, but to me it’s still my old version 1 HubSan.

I’ll have to upload the 3D printer CAD file later, but I had a few issues with the holes being too small for the motors, despite the measurement on the computer being 7mm exactly. I ended up having to ream and drill the holes out so that the motors were a tight enough interference fit. I’ve done this with all the 3D printed frames we made as none of the holes were the right size, so I’ve had plenty of practice.

My attempt at the Air Screw looked something like this:

What I like about this is that it’s all held together with cardboard strips, sellotape and double sided foam tape. I had originally cut myself some Depron parts to fit between the four blade guard rings and make a full circle base (you can see it on the drawing if you look carefully), but weight proved to be an issue.

All up weight for the DaVinci prototype is 42g, which is a 8g over what I would recommend for the kit being used here. As my HubSan was the original one with the 7mm motors, it’s not as powerful as the camera version with the 8.5mm motors which we used for the Royal Institution project and the 3D printed butterfly and dragonfly frames. My H Frame was the prototype designed to work with the smaller motors, so I can’t change it. It is quite a bit lighter than the later frames which we made, though, as it was built a lot thinner (2mm thick instead of 3mm).

My biggest problem was building the screw. You can see from the pictures that the vertical structure holding the screw is made from four 10mm cardboard strips which are sellotaped to the underside of the H Frame. The flight controller sits on top in the middle of the frame, held on with double sided foam tape, which also holds the battery underneath. I wouldn’t recommend this as a good solution, but, for a prototype where you can remove the battery just by unsticking it, this does make things easier. A wooden skewer (2.5mm diameter) fits through holes in the cardboard structure and the air screw fits on top. There is a piece of Depron stuck in the top of the skewer to add effect.

On the underside you can see how the sellotaped cardboard attaches and the foam sticky pad used to hold it and the motor in place.

Now, making the actual air screw itself proved to me more complicated than I thought. Originally, I assumed that it was just two 3/4 segments of a circle stuck together. I now realise how naive this was after cutting up lots of paper circles. It’s a spiral of course, so I ended up drawing a circle with 60 degree spoke lines and drawing a spiral on top which I then made into a template. The picture should make things a bit clearer.

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The template for the Air Screw. All measurements are in millimetres and all spoke angles are 60 degree segments. Note that the ‘B’ section is drawn upside down.

My first air screw was on ordinary paper, which was useful for getting the dimensions right and for enabling me to cut around it with scissors to get the spiral nice and smooth. Then I transferred the design onto the thicker grey paper which is used in the photo and videos later.

All along, the key design criteria has been that the air screw must rotate as the quadcopter flies. At this point I could claim that it was my extensive aerodynamic knowledge from designing and building radio controlled aircraft over the last 30 years. Or that I had evolved the design using complicated computational fluid dynamics software on the computer. In truth, I just figured that with all that air moving around the four rotors, anything above them which was vaguely a helical screw just had to rotate (maybe that is experience?).

The way the aerodynamics work is that the four quadcopter rotors all push air downwards to varying degrees, depending on manoeuvring thrust. This means that air is being sucked down from on top of the quadcopter. My first attempt with a flimsy paper screw didn’t work as the paper just got sucked downwards by the air. This is the first lesson learnt, the paper needs to be stiff enough to hold its shape under the pressure difference caused by the rotors sucking air underneath. My second attempt was using some thicker cardboard, which was almost successful. I ended up cutting this one down to experiment with a smaller screw diameter, plus whether slots in the screw made much of a difference, so ended up destroying this one. My third attempt is the grey one you see here. This was from the page of an old scrap book, so heavier than the paper, but not as stiff as the card. Crucially, it holds its shape under the air pressure and it spins fairly well. I have also been using a small Depron disk (13mm diameter, 1.5mm thick) which the air screw rests on. This enables it to spin freely without catching on the under side of the screw. I’ve also increased the hole in the centre of the screw to be about 1.5 times the diameter of the skewer that it spins on. Basically, you just need to ensure that it spins freely without binding and that it’s fairly well centred. Also, that it sits more or less straight and doesn’t lean to one side. One final feature I’ve added is a small tab of sellotape on the under side of the screw, sort of like a trim tab. You can just about see it in the flying shots, but I think it helps a bit in getting the screw to start spinning.

Flying

I could try and claim that this was the first flight, but I’ve been flying this all week with different air screw designs until I found one that worked. It was excellent fun, and this grey version of the air screw was working really well last night.

As you can see, it’s quite hard to get the air screw turning, but, when it does, it spins in a very scale-like fashion. At least, if there was a person standing on the platform underneath and walking around turning it with handles, then that’s about as fast as they could turn it. In order for it to fly using the air screw it needs to go a lot faster and that’s ignoring the torque reaction and control problem. Also, the area covered by the Nexus 4 camera phone which I’m using to film is only about 1 metre square. So, I’m flying an under-powered quadcopter that’s top heavy, is held together with stick tape and has a big thing on top which messes with the aerodynamics while trying to stay within a confined space. Like I said, it’s been excellent fun all week. The bit near the end where I bump the wall was where I tried putting in a small rudder input. The HubSan flight controller has always been a bit funny when you spin it around on the rudder. All the ones I’ve flown drift very badly in all directions and I can never get it to spin on the spot. The interesting thing when watching this video is the realisation that the spin is related to how the quadcopter is being flown.

For the second flight I curled up the air screw a bit more to make a better spiral and you can see that it does spin up a lot faster. The flight was cut short because I realised that the spin increases when it is drifting left, so I then tried to do a 360 degree left spin on the rudder. That’s when I bumped the wall and drifted out of shot.

By flight three, I’m getting the hang of it and understanding how to control the spin of the air screw by the control inputs I’m making. This is really starting to get fun – I’m flying the quad and the air screw on top. By this point I’m also wondering whether it makes any difference what angle the air screw is relative to the quadcopter frame. The flight ends when the sellotape finally gives up the ghost and the frame supporting the air screw collapses. This is not before I’ve noticed a pronounced lean to the right though. I’m not sure whether this makes a difference – left drift and right lean makes it spin better?

What We’ve Learnt

The air screw is simply a cardboard piece dropped onto the skewer and free to spin. It needs to be rigid enough not to deform, but, if you watch the flying shots, manoeuvring causes it to tilt, which stops the spin. If the air screw could be fixed to the skewer with a low friction bearing such that it was held rigid horizontally, then it might spin more reliably. The air screw shape also needs some more experimentation and the addition of the helical screw above where the four quadcopter rotors are drawing their air from significantly affects the performance. It’s definitely a successful first prototype though. The air screw spins and it is controllable in flight.

Homework

  • Investigate the mathematics of spirals.
  • Make a wooden version of the cardboard air screw frame.
  • Design a zero weight, frictionless, horizontally rigid bearing arrangement for the air screw.
  • Build a second prototype with the more powerful motors, which looks like it’s 500 years old.

Links

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