Homemade masks w/ wire nosepieces

So, masks have been in the news a lot recently for some strange reason. Probably most interesting; in the Czech Republic masks were made mandatory, but as there wasn’t enough existing masks in the supply chain, people had to create their own. Their president is crediting the widespread use masks as one of the main reasons they’re doing so well right now.

There are a number of organizations online that have provided instructions on how to make your own mask, and, in areas which are much more severely affected, some hospitals have been requesting people produce homemade masks for them to use. Thankfully, there’s groups of volunteers around the world which have been stepping up and making them en masse. (This whole situation is something that we likely would have considered ludicrously implausible just 6 months ago)

Luckily, here in Australia the supply for medical professionals seems to be holding out, and I haven’t heard of any hospitals which need the public to make stuff for them.

But masks as a whole seem like a great idea, and they are certainly easy to make. So, my friend Kate and I decided to stitch up a bunch of masks for ourselves and others.

Making the mask:

We used the pattern and instructions from here:


and made the following modification so that you get a much better fit:

First, grab some 1.6 mm diameter armature wire . (This is the sort of thing they use inside clay puppets so they can hold position while being filmed for stop-motion animation.)

We cut 190 mm of wire, and put it in inside the mask, at the bridge of the nose, with a stitch underneath to keep it held in place.

After assembly, here’s what it looks like:

Finished mask - crop v01.JPG

Stylish fabric optional

The fit is very comfortable. As a test, I wore my one for several hours straight while we were cutting and stitching the others, and I had no issues.

Also, the armature wire in the nose is a godsend. When I put the mask on, I can press down and ensure shape the wire so the top part of the mask sits tight against my face. Most importantly, no matter how hard I exhale, I can’t fog my glasses. I don’t think I’ve ever had a mask that I could easily wear glasses with before. (This probably just means I’ve been wearing dust masks incorrectly for years, but hey)

Some tips I’d recommend if you make your own:

  • If you’re using ribbons and not elastic to hold it on, then use fairly thick ribbons, (~10-20 mm?). The thin ones we made (~6mm) have a tendency to be hard to tie in a bow, and tricky to undo if stuck. (I ended up with one double-knotted behind my head and needed another pair of hands to rescue me, which kind of defeats the point of social distancing with a mask)
  • Use two different colours of fabric, with a boring fabric inside, so it’s obvious how to put it on.
    • Some sources say to use non-absorbent material such as (polyester or poly-cotton blend) for the outside of the mask, and absorbent material (such as pure cotton) for the inside. Others don’t specify, or just use the same material for all layers. If you have a choice of materials maybe do non-absorbent on the outside.
  • Make more masks than you think you’ll need, and that way you can give (a washed) one away or have spares if needed.


Do they work?

There’s the question of whether homemade masks work. I’ve seen some people say that masks for uninfected people are a bad idea, and other say they’re great, and everyone should be wearing them. My inner [socratic dialog/shower thoughts/ shoulder angels discussion] ran something like this;

A: Now I’m confused. Hmm… What do we think?

B: Well, the argument is that while a mask might intercept an incoming droplet from someone else, in doing do it then traps the virus right next to your mouth, where you’ll just breathe it in later

A: That logic seems weird to me. I think surely more would still be stopped than make it through? I mean, how can the steady state be worse than the no-mask case?

B: Hmm… good point. But then there’s the effect that the mask stays warm with exhaled breath, so is that giving trapped particles a boost? Like a mini incubator?

A: But what about touching your face? We’ve all learned recently just how often everyone does that. A mask completely stops you touching your mouth and nose. And makes you more aware if you try and touch your eyes.

B: So in a sense, a mask makes your hand washing more effective?

A: I’d wager so. But what about that ‘incubator’ idea? Is it a real effect? And if so, does it cancel out the benefits?

B: Hmm… How the hell would we test that?

And I just got tied up in knots trying to imagine stuff I don’t have enough experience to predict well. But thankfully we don’t have to mentally simulate everything from first principles to find the likely answer. For example, this study:

Click to access radonovich2019N95masks.pdf

did a randomised controlled trial of just under three thousand doctors that interacted with patients with influenza. The doctors were issued at random either an:

  • N95 mask (roughly equivlant to a ‘P2’)
    • These are specially designed to stop aerosolized particles, have a material with guaranteed effectiveness stopping particles of a certain size & are tested rigorously
    • Are a pain to fit properly. You can be ruled out from wearing particular sized masks because of your head shape, or if you have a beard.
    • Depending on your area, may periodically require special procedures for a Fit Test, involving wearing the mask while an aerosolized chemical is sprayed directly at your face. If you can’t smell it at all, while vigorously breathing in and out, (you can’t cheat by holding your breath, they make you read out loud long sections from a book), then your mask fits.
  • Surgical mask
    • These aren’t remotely air tight, they’re designed to be comfortable and easy to use
    • These have no special requirements relevant to stopping viruses. (at least for the couple of models I looked at). The only specs and standards I saw were: 
      • BFE > 98%  – this only applies to bacterial filtration ability, not relevant to much smaller viruses like coronavirus
      • EAN14683: Type II – this specifies that :
        • It has a low differential pressure. I.e. it’s easy to breathe through, and
        • specifically not required to have any splash resistance, and
        • specifically not required to have any sub-micron particulate filtering ability
    • The particular surgical masks used in the study were better than ordinary cloth masks, however.
      • They had fluid resistance ratings of 160 mmHg, indicating it needs approx 1/5th of an atmosphere pressure difference to force liquid through,
      • They had particulate filtering ability at 0.1um of 98% (this is about the size of coronavirus particles)

So the study describes a comparison between basically a ‘gold standard’ mask and a quite good mask, but which is not guaranteed to be airtight , tested by people wearing them whenever they were:

routinely positioned within 6 feet (1.83m) of patients”.

And they found no significant difference in the number of doctors contracting influenza.

Of course, the influenza-A & B from the study obviously isn’t the same as coronavirus, so perhaps it might turn out that there’s a true difference in PPE effectiveness. But, I mean, they’re pretty similar. Both are small, airborne, viruses made of RNA, and if significant amounts could traverse an improperly fitted mask so easily, then we would probably have seen that reflected in the study, which we didn’t.

The next study I looked at was this one: https://bmjopen.bmj.com/content/5/4/e006577 (Also note that the authors of the study made a recent response in light of coronavirus )

The study follows 1607 healthcare workers in Hanoi who used either:

  • locally produced cloth masks,
  • locally produced surgical masks,
  • or their normal procedures (which would likely have some form of surgical mask).

The study covers a four week period, and covers seventy four wards of varying types (including emergency & infectious/respiratory disease wards) specifically selected because they were high-risk.

Looking at the results of the study, at first glance the Relative Risk level of 13 to 1 seems terrible.  i.e. wearing a cloth mask is 13 times more risky than wearing a surgical mask, as far as Influenza Like Illnesses goes.

But when you look at the actual outcomes, the numbers don’t look so scary:

  • Surgical mask: 580 people, 1 got Influenza-Like-Illnesses
  • Cloth masks:  569 people, 13 got Influenza-Like-Illnesses

[Edit: Screw it, I decided the picture from the journal article didn’t convey it well enough, so here’s my own plot instead. Edit2: I removed the ‘control arm’ section as it was confusing and not relevant as it was their old procedure. The numbers here just show surgical masks vs cloth masks]

infographic pic v01.png

Yes, technically the cloth mask is 13x worse, but at this stage you probably don’t give a shit.

When you consider that these numbers are specifically selected from front line healthcare workers, in high-risk areas, and still indicate that you can wearing cloth masks for a month and still only have a 7.6% chance of catching a CRI, or 2.3% chance of ILI, that would seem to indicate cloth masks are still pretty fuckin’ awesome. 

Don’t get me wrong, I’m sure surgical masks are better, (and they should be mandated in any countries that haven’t yet), and if you’re a healthcare worker you should absolutely use them if you have access. But it looks like we’re talking about fairly subtle differences in safety here. If it were a car, it’d be the difference between having airbags with extra side-impact cushions, and just regular airbags. Whatever you have, it’s far better than nothing. 

Now pretty much none of the extreme scenarios in either of those studies apply to me, or anyone likely to get a mask from me.  I’m not the worst-case of someone spending all day next to a contagious patient, I’m just some schmuck making a quick trip to the shops. Or getting drive-through. I just want a little more protection when I have some short interactions with others, and that’s that.

I can then carefully take off the mask (without touching the outside), stick it in a plastic bag and boil it when I get home.  And I have a couple of masks ready so I’m still covered in case I have another errand later.

So as far as effectiveness of homemade masks goes, it looks cautiously encouraging. But at any rate, I’m working on the assumption that:

it’s a mask, not a magic wand:

  • Wearing it does not grant me magical powers.  I will not assume that I am in any way immune to infection because of my stylish facewear
  • I’m still going to keep social distancing, and not do any extra errands which I wouldn’t have done anyway.
  • I’m going to be careful taking it off, making sure I don’t touch the outside
  • I’m still going to wash my hands with soap and water, or hand sanitizer, as normal


  • If I do unknowingly have the virus, I’ve probably made it less likely for others to get it off me. Win!
  • If I do run across someone that unknowingly has the virus, I have probably made it a bit harder for them to infect me. Win!


If you’ve got a sewing machine, why not make your own? If nothing else, it’s an excuse to use up those fat-quarters of unmatched fabric you’ve had laying around for years…

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Waves at Bessel-on-Sea

This is a lasercut version of the Bessel Functions, as a handy desk ornament:

Bessel mono crop v03.JPG

The helical diffraction theory, (and hence the Bessel functions) were the major key to solving the structure of DNA.

In 1952 (well before the DNA structure was solved) Francis Crick & Bill Cochran wrote a paper explaining how the expected form of X-ray diffraction from a helix is the sum of various Bessel functions:

Quick bit of background. When you’re using X-rays & film to find the structure of something, what you get when the film is developed isn’t a picture of the structure. Instead, it’s (more or less) the Fourier Transform of the structure.

We can simulate this in python like so. Let’s say we have a simple helix, (which we’ll assume is smoothly continuous, and not made up of any yucky atoms). The pattern we get looks like this:


A continuous helix (left) has a diffraction pattern like a big X (right)

and then if we take a photo of a helix which is made up of a discrete atoms, we see a pattern like this: :


A discontinuous helix (left) has a diffraction pattern which is a series of diamonds (right)

The way the maths works out is something like this; the ‘dotty helix‘ can be thought of as the (piece-wise) multiplication of two functions:

  • H – a helix with constant radius
  • K – a function for the ‘planes’, which is zero everywhere except at a plane every ‘p’ units

Cochran crick maths - real space v01.png

and the result in the ‘Reciprocal Space’ (i.e. what the X-ray picture will look like) can be neatly expressed as the convolution of the [Fourier transform of H] with [the Fourier transform of K].

Cochran crick maths - reciprocal space v01.png

In other words, the big ‘X’ is “stamped” on the image every where the red planes are. The result looks like a series of diamonds.

Let’s make a larger diagram. If we sketch out the expected pattern for a continuous helix, we’ll see an x-shaped pattern, roughly like:

cochran crick sketch - platonic helix v01.jpg

And if the helix is made up of discrete units (atoms or rungs), then we’ll see the above pattern ‘stamped out’ multiple times on the image.

For example, if we have a helix which has 10 layer lines per twist (like real DNA),  we’d expect to see a pattern like this:

cochran crick sketch - 10 layer repeate helix v01.jpg

Expected diffraction pattern for a discontinuous helix which has one twist every 10 rungs

That’s an amazingly good match for this (terrible quality) photo of the real thing :


Source here

You can see most of the characteristic features. The double diamond (4+ diamonds, really). Note that they meet up on the 10th line, indicating that every 10 rungs the helix makes one turn.

There’s a whole bunch more cool stuff covered in the Cochran/Crick paper, like:

  • They explicitly consider cases where the number of rungs per turn isn’t a neat integer
  • They do worked examples to show how it explains features in the Pauling’s recently discovered alpha helix
  • They propose practical methods for analog computing via paper charts and movable masks in order for people to be able to quickly synthesize patterns for arbitrarily complex helicices in the future.


Side note: the mathematician Alexander Stokes had also worked out the helical diffraction theory at around the same time, but didn’t bother to publish it. He famously did the work on the train on the way home, and presented it to the lab the next morning. You can see the lovely sketch he did here:


Which Wilkins was so impressed with, that he stuck it on the lab notice board, with the name “Waves at Bessel-on-sea”.

It was after seeing Stoke’s picture, that I decided I wanted to make my own copy of Bessel-on-Sea for my coffee table:

Bessel crop v02.JPG

Files here for anyone that wants to make their own:


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The Crystallographer’s Watch

Finished product v01.JPG

Here’s a project I made almost accidentally on the way to a later design. I’ve wanted to make my own watch for a while now. It’d allow me to pick and choose all the features I really want, and it’s a fun exercise in design to try and figure out which features work smoothly, that I’d appreciate having everyday, and which features are more ‘fads’ that I can do without.

I have a metal CNC machine, so carving the watch body from solid metal is doable (if somewhat fiddly and time consuming). And it’s really cheap to design and make your own circuit boards these days, so the electronics are fairly easy.

But it occurred to me that this is still a multi-stage process, which plenty of opportunity to loose energy or procrastinate. If I wouldn’t get that reinforcing emotional feedback/reward until WATCH_CASE_DESIGN + MILLING + ELECTRONICS + SOFTWARE are all done, that’s a very long chain with plenty of ways it can fail.

So, as a way to break the the project into chunks, I figured I’d start with the circuit board only.
I bought a large men’s watch 2nd hand watch on gumtree and pulled out the guts, this left me with a big empty enclosure I can fill with my custom electronics.
Unmodified watch v01.JPG

I measured up the internal space I can use, and I lasercut a couple of ‘dummy’ cylinders of the same size:

Internal case dimensions v01.JPGdummy cylinder v01.JPG

The idea is that as long as whatever electronics I come up with are smaller than the dummy cylinders, I’ll have no surprises when it comes to assembly.

At that point I realised that the empty watch was essentially a wrist mounted display case.

The other day I’d been playing around with small ball bearings, to make a ‘bubble raft’ style display like those popularized by Sir Lawrence Bragg.

I figured that with a bit of fiddling, I could make a watch mounted version I could take anywhere. So I laser cut another plug, and some circular rings hold off the wood from the glass, which allowed the balls to move freely.

Ball bearing insert v02.JPG
It took a bit of tweaking to ensure the balls didn’t have enough space to ‘double pack’ when tilted. Brett and I had to have several rounds of taking it apart, sanding the ring down carefully, then reassembling before it worked nicely.

There’s a lot of interesting structure in the raft. You can see how the balls pack in regular order at a local scale, but don’t line up on a global scale.

Raft coloured v01.JPG

Grain boundaries and sphere packing

(Also note the red areas with square packing, everywhere else seems to be the more efficient hexagonal packing).

Every time you look at your wrist you’ll see a different pattern. Sometimes regular, sometimes chaotic. And by tapping and jiggling, you can often ‘anneal’ the structure into a lower energy state. Here’s one pattern that’s been annealed a bit.

Raft coloured v02.JPG

The watch annealed into a much more regular shape

(Note the lovely grain boundary, and two large grains which have steadfastly refused to merge together).

The semi-randomness of the pattern is quite appealing. The eye has no problems picking up the detail, and you can often see grain boundaries more easily than the individual balls. And with a quick flick, you can get a whole new arrangement. Sort of a wrist mounted I-Ching.

I’ve been wearing it for two days now, and it’s rather soothing. In fact it’s an anti-watch.
(Since a regular watch tells you the time and makes you stressed. This tells you absolutely nothing, but makes you calmer)




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The Dichroic Confuse-O-Scope

This is the ‘Confuse-O-Scope’, a device which allows you to enjoy all the fun of having mis-aligned RGB in real life! Guaranteed to cause both confusion and irritation in anyone that’s worked in TV, printing or theatre lighting!

Example view 01.JPG

If only I could make a telescope that messed with Kerning.

It uses the same dichroic beamsplitter cubes as my previous project, but arranges 3 in a row:

case inside 02.JPG

With the result that; while any colour light from the world can get to your eye, the red, green and blue colours all travel via different paths. And because of parallax effects the view of each will be slightly different:

example view 02.JPG

You can also flex the frame a bit and change the RGB alignment, making it overlap or separate.

Here’s what the view looks like from the other side:

image split v01.JPG

Files here for anyone that wants to make their own:


case overview v02.JPG

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Dichroic Moving Sculpture

This is a quick project I made to explore dichroic filters. I just love the colours that can be produced, and wanted a way to display it easily.

In the last few years, these dichroic cubes have appeared on eBay. They’re used inside projectors to combine red, green & blue colour channels into a full image. And, apparently making them isn’t a perfect process, so a bunch of defective ones regularly end up for sale.


I used a couple of stepper motors to allow the cubes to be rotated at a slow yet precise speed, and used the same unwise technique from before to simplify wiring. I then used some high power LEDS to provide illumination:

Side note: The ‘unwise technique’ still seems to be paying off surprisingly well. Everything you see in the video is running straight off the arduino, via USB with no other power supply.

To collimate the light from the LED I used some lenses from eBay jeweller’s loupes (which were so terrible that their main value is for parts), and made a lasercut holder for the lens. The light assemblies are mounted on thin brass shims to allow bending and positioning them by hand:

box behind v01.JPG

Files up here for anyone that wants to make their own:



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A Planetary/Harmonic Hybrid Gearbox

I recently saw this amazing idea from Darren Schwenke on Hackaday.io:


Which is (so far as I know) a brand new type of gearbox, inspired by a well known concept called a  “Harmonic-Drive“. Harmonic drives have been around for years and were used whenever light weight or small size was required (on the moon rover, for example). They work via the deformation of a flexible ‘strain wave gear’ to enforce the meshing between two gears with nearly matching numbers of teeth. This allows very small reduction ratios, in a compact space:


Image from Wikimedia Commons, here

The red strain wave gear is where output goes. The downside is that a strong and really flexible gear like that is hard to make, and also difficult to couple the output from easily. Most designs I’ve seen require custom spring steel ‘cups’ which are precision manufactured via electro discharge machining or similar. (Although there are several awesome 3D printed versions out there. )

Darren’s idea with the MPRT gearbox is to take the basic concept of the harmonic drive, but remove the complicated strain wave gear and instead substitute ordinary planetary gears, which then do the same job of enforcing the meshing of the two outer rings at several key points:

Gear sketch v01.jpeg

The final gear ratio for this is around 66:1 reduction, which is amazing for a single stage:


I liked his design, but didn’t want to wait a long time to 3D print it, so I drew up this one for my laser. I created the gears just using the involute generator in inkscape, then added all the bits and bobs to hold it on the motor and mount reliably. I laser cut the pieces out of bamboo ply, and screwed them together with M3 fasteners.

A NEMA 17 stepper motor sits underneath and drives the whole assembly:


Also, I’d like to mention one of my favourite construction techniques, using M3 nylon standoffs as thumbscrews. I’ve had to put various bits of the gearbox together and pull them apart half a dozen times while prototyping, and being able to fasten bits securely by hand is a huge time saver.

I used a few dollops of furniture wax, which seemed to make it run smoother:


The torque is large but not ridiculous, and I can make it stall by hand if I really try, but overall it’s still remarkable for a single stage gearbox. (Also, not many moving devices have sliding wood-on-wood surfaces, so if you made this out literally almost any other material you’d likely have better results. )

Files up here for anyone that wants to make their own:



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Unwisely driving 17 stepper motors from a bare arduino

This is a quick and dirty way to get a whole bunch (up to 17) small stepper motors working off a single arduino, with no extra circuitry whatsoever.

Why would you want to do that? Maybe you want to make a wall display, a clock or some other interactive object, and you can’t afford thousands of dollars for motors, and hundreds of hours spent wiring up boards for ‘proper’ drivers.

(Side note, the back story to this is for a while now I’ve been wanting to make a big-ish display simulating vector fields, and I was scratching my head trying to come up with a way to do it that wasn’t ridiculously expensive. I ended up finding one that was not only cheap, but lazy too!)

Anyway, here’s the finished display:

finished display.JPG

The main ingredient is the 28BYJ-48 stepper motors, which is a geared motor which is dirt cheap. They’re mass produced and apparently designed for air conditioning louvres?

Ordinarily when you use a stepper motor you need a dedicated constant-current driver to avoid damage. The essence of this project is how to avoid the cost and complexity of a driver.

The cost of the parts were:

  • $3 each for the driver and motor pair , from Little Bird Electronics.  (If you really wanted to, you could get them even cheaper in bulk, and also by not including the driver)
  • $10 for the arduino, from eBay.

I used 17 motors, so it was $61 AUD all up. Which is ridiculously cheap for something with almost twenty channels of precise motion control.

Here’s what it looks like inside:

A smarter person would have numbered them so they were correct as viewed from the front. Next time, Gadget, next time.

Also, the wiring is also about as simple as you can imagine, I basically just jammed the motor wires into the arduino’s digital pins and slammed the box shut before they could fall out again:


Here’s how to do it yourself. But, before we begin:

If you try this, you might break your arduino.

If you try this, you might break your arduino.

If you try this, you might break your arduino.

And also,

If you try this, you might break your arduino.

Everybody clear?

This approach works*, but relies on several things which might not occur all the time. Don’t assume you can get away with this in other designs.

*Actually, I’ve really no idea if this will work long term, all I can say is that my one has been running for several hours now, and the arduino hasn’t yet caught fire, appeared broken, or visibly lost steps on the motor. Win!

Trick 1: The arduino digital outputs have a non-zero resistance

This is the reason you often see people getting away with plugging LEDs in to the arduino pins directly, without a current limiting resistor.

(For years I thought it the ATMEGA chip had actual current limiting circuitry, but turns out it’s just the internal resistance or something? At any rate, don’t assume you can abuse other chips in the same way. )

I don’t know for sure this is required, but I’ve found in the past the ATMEGA/arduino is way more tolerant than microcontrollers for badly connected loads, so I’ll assume it’s relevant.

Trick 2: We convert the motor from unipolar, to bipolar,

(This has the nice side effect of doubling the resistance of the motor, further reducing it to the point where the arduino chip can drive it without circuitry).

The motor from the factory has a coil arrangement we want to change from this, to this:

We do this by:

  • opening up the back cover,
  • cutting off the centre tap ( red wire)
  • Dremelling out the circuit board to disconnect the two pairs of coils from each other

Trick 3: The 28BYJ-48 stepper motor is crap. And that’s good news for you!

Or, to be more precise, the motor has (before the gearbox) only 32 steps per rev, or 11.25 degree step size.

Why this is relevant is that we want to be able to power down each motor’s coils between movement, so that the arduino is only powering a single motor at a time. But we also want the motor to not lose steps the next time it’s powered up again.

A big 400 step NEMA17 motor (such as you might find in a good 3D printer) has 0.9 degree step size. If you power on and off a big 400 step motor repeatedly, it’ll jiggle slightly. If it jiggles more than 0.45 degrees, then when it’s started it’ll be dragged to the next notch in the rotor, and hence the wrong  location. This will happen most when under mechanical load, or the influence of belt tension, etc. So ordinarily, turning motors off translates into lost steps, and poor position accuracy. Hence for a 3D printer, they typically leave the motors powered up, or under a reduced current whenever they need it to hold position correctly.

Because the 28BY-48 motor has a huge 11 degree step size, (and it’s behind a gearbox) it’s really unlikely any mechanical jiggling is going to move it far enough to be a whole step away from where it should be. So the next time it’s powered up, it’ll be pulled back to the exact location it was before!

And that’s it. With code to carefully avoid running more than one motor at once, it can be scaled up to as many motors as you like, and you only need to stop when you run out of arduino pins.

I think am going to enjoy making displays with this technique, and it’s quite satisfying to watch the dials spin around in person.


Files and code here for anyone that wants to make their own:


Have fun, but don’t blame me if you damage stuff by trying this.

Edit: I’m still playing around, but it seems like you can get loss-free movement of at least 6,  8, 10+ motors at a time. Damn, this works way better than I have any right to expect. 


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Tangent Ruler – Draw circles passing through two points

Unintentionally I’m going to continue my tradition of making projects involving rulers.

I saw this picture online: https://imgur.com/t/aiko/mu96ohu and I thought it was too cute a technique not to try out for myself. I did a couple of minutes sketching in Inkscape, and then had it lasercut shortly thereafter.

Here’s how to use it. First, simply drive a couple of nails through your favourite table or work surface:


Then, using a pen, draw out the circle while keeping the ruler pressed against the two nails:


You should end up with a perfect(ish) circle that passes smoothly through both nails.

I’m going to try to remember this trick, I can see it being useful for laying out parts for machining, or to make shapes based off existing features.

Files here for anyone that wants to make their own:



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Huygens’ Ruler – Drawing Interference Patterns

Here’s a quick project to make it easier to draw examples of interference patterns and wave behaviour. I call it Huygens’ Ruler:

ruler overview v01.JPG

It’s based on the idea of Huygens’ principle, the idea that every point on a wavefront becomes the source of spherical wavelets that make up the next wavefront.

Here’s how you use it. Drive a nail or thumbtack through some cardboard, and drop the ruler on top ( I just nailed into the desk of the makerspace, because meh, that table’s already seen a lot worse):

drawing in action v01.JPG

Using the Huygens’ Ruler

There are circled markings for every integer wavelength, and also holes for half-integers. This means you can easily make diagrams with different colours for the ‘peaks’ and ‘troughs’ of a wave, and see by the intersections where they reinforce, and where they cancel out.

close up interference drawing v01.JPG

Green dots are where the two waves reinforced each other, and red dots are where the waves cancelled out. 

Here’s a few nifty demonstrations that are possible to do with the rulers. First off, we can see how changing the only wavelength of the two sources changes the interference pattern spacing:

changing wavelength v01.JPG

Left: 3cm wavelength, Right: 4cm wavelength. Sources are 10cm apart in both

Next, we can see the effect of changing the phase of one of the sources. To do that, instead of putting the nail in the first hole, we use one of the later ones:

Setting phase on ruler v01.JPG

Setting the phase of the source at 90 degrees

Here’s the effect that has on the resulting pattern:

Beamforming example v01.JPG

Top drawing: No phase difference. Centre nodes head straight to the right.     Bottom drawing: 90 degree phase shift between sources, and the resulting beam is ‘steered’ downwards.  

This is the basis behind the idea of Beamforming, and also represents the simplest possible example of a phased array.

I added markings to the body of the ruler so that it’s possible to measure what the phase is at any point. This makes it easy when a wave hits a gap in a wall, for example. In that case the wave will be re-emitted starting at that phase again. (e.g. if the ruler hits the wall at the 270 degrees mark, you would then draw the next source with the nail on the 270 degree point.)  That way a blue line always represents the same amount of distance from the source, via whatever holes or path you use (modulo the wavelength).

I’m rather happy with this project. I had a few rounds of revisions, but I’m quite pleased with the final result, and it’s pretty fun to draw with.

Double double slit drawing v01.JPG

Soothing. This is my version of those adult colouring books, with the added bonus that it involved using a hammer 

Files are here for anyone that wants to make their own:



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‘Born Ruler’ addon for Qubit/Bloch Sphere

Here’s something I was planning to make ages ago, as part of the Bloch Sphere project, but it slipped my mind.

It’s a visual demonstration of how the Born Rule, which describes how complex ‘probability amplitudes’ are related to probability.

Say we have a single quantum bit, represented as a point on the surface of the Bloch sphere. (Note: depending on how our qubit is implemented, the 3 dimensions of the Bloch sphere aren’t necessarily the same 3 dimensions of ordinary space, but let’s ignore that for now).

Let’s say we’ve recently measured the state of our qubit, so we know which way it’s pointing (the pink arrow in the model), which we’ll call ‘1’.

If we measure the state again at the same angle,  there’s 100% chance of measuring  a ‘1’. Dead certain, no ambiguity about it. Spin up v01 small.JPG

If we rotate our qubit so it’s pointing down, we have a perfect 0% chance of measuring a ‘1’. Again, dead certain, with no ambiguity:

spin down v01 smalls.JPG

But if we rotate it so it’s pointing to the side, we will have a 50% chance of measuring a ‘1’:

spin right v01 small.JPG

Another way to say this is that if we measure it at right angles to the way we measured it last time, there’s absolutely no correlation between the previous measurement and the next.

And any other angle in between those will be slightly correlated to the last result, and become more correlated as the old and new angles of measurement become closer.

Here’s the files for people that want to make their own:

Born Ruler: https://www.thingiverse.com/thing:3235423

Bloch Sphere: https://www.thingiverse.com/thing:3053421

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