Measuring The Planck Constant With Lego

For nearly 130 years, the kilogram has been defined by a small platinum and iridium cylinder sitting in a vault outside Paris. Every other unit of measurement is defined by reproducible physical phenomenon; the second is a precise number of oscillations of a cesium atom, and a meter is the length light travels in 1/299792458th of a second. Only the kilogram is defined by an actual object, until NIST and the International Committee of Weights and Measures defines it as a function of the Planck constant. How do you measure the Planck constant? With a Watt balance. How do you build a Watt balance? With Lego, of course.

A Watt balance looks like a double-armed scale where one weight can be compared to another weight of known mass. Instead of using two arms, a Watt balance only has one arm, brought into balance by a current flowing through a coil. The mechanical power in the balance – brought about by whatever is on the balance plate – can then be compared to the electrical power, and eventually the Planck constant. This will soon be part of the formal definition of the kilogram, and yes, a machine to measure this can be made out of Lego.

The only major non-Lego parts in the Lego Watt balance are a few coils of wire wound around a PVC pipe and a few neodymium magnets. These are placed on both arms of the balance, and a pair of lasers are used to make sure both arms of the balance are level. Data are collected by measuring the coils through a few analog pins on a Labjack and a Phidget. Once the voltage and current induced in each coil is measured, the Wattage can be calculated, then the Planck constant, and finally how close the mass on the balance pan is to a real, idealized kilogram. Despite being made out of Lego, this system can measure a gram mass to 1% uncertainty.

The authors have included a list of Lego parts, most of which could be found in any giant tub of Lego in an 8-year-old’s closet. The only really expensive item on the BOM is a 16-bit USB DAQ; apart from that, it’s something anyone can build.

Thanks [Matt] for the tip.

45 thoughts on “Measuring The Planck Constant With Lego

      1. No they are not. A meter is a measuring device and the metre is a unit of length. Just because one country is confused by its adopted language doesn’t change that language…

  1. The Plank constant, as distinct from the Planck constant, is I believe approximately two by four. (Which equates to 1.5 by 3.5 after correction for relativistic effects, shrinkage, and planing.)

    I think you may have given your spellchecker slightly too much credence.

    1. And this is a case where surely, SURELY, people can’t claim “Oh, you know what I mean” like they usually do when anyone criticises grammar or spelling on here!

      That apart, very neat mechanism. Note how there’s two different operating modes – one where a steady force is applied to balance out the mass, and the other is where the mass falls under gravity, inducing a signal in the coil.

    2. The Plank constant is actually variable depending on the nominal width of the board in inches:

      The actual width of the board can be represented by W[dry] = W[nominal] – P.
      If W[nominal] <= 2", then P=0.25.
      If 2 < W[nominal] 7″, then P=0.75.

      This is true at least up to 16 inches. A section that big from most trees would be difficult to predict anyway.

      Source: and a bunch of home improvement projects.

  2. Minor correction: it’s the meter that’s defined by the length of a platinum rod. The kilogram is defined as 1000 grams, the same mass as 1 liter of water. Of course, measuring 1 cc of water is dependent on the meter standard. However, it’s the meter stick that was cut to an arbitrary length.

    1. Actually I believe the original metre was supposed to be 1/1000000th of the distance from the equator to the geographical north pole on a meridian through Paris, but the people assigned to figure out what that distance screwed it up, but it wasn’t found out until the government had produced a bunch of platinum metre bars, so they said “F*uck it”, saved the money it would cost to make new bars and said the incorrect bar WAS a metre. And they say the metric system is based on logic. :p

      1. There’s a really good book about it, too.

        They started work on it because of the French revolution in which all things are supposed to be rational (and because they wanted one standard to replace the 250,000 or so in French regional use at the time), so they tasked two guys to take astronomy readings at various points – measuring the angles using a tool called a “Repeating Circle”. Later they measured the distance from point A to B using yardsticks. The idea was to draw triangles over France, measure the length of one side, and use trig functions to calculate the total height of France (and thus, the meter).

        This was supposed to take a few months – it ended up dragging on for seven years. Difficulties arose for the guy going South, because he couldn’t take some necessary measurements from Spain as France was at war with them, so he estimated from a different position. They never matched up properly because of two other systematic errors though –
        * The “repeating circle” used to take readings was Precise but not Accurate, and
        * The earth is oblong, not spherical as they thought at the time, so the computations were wrong. (Incidentally, they were able to use this to prove that the Earth is not a regular sphere)

        Of course once you’ve gone to the effort and expense, there was an uphill climb to get people in France to take the system and replace their customary units – almost didn’t happen. No way were they going to go back and retake the measurements again for the sake of correctness!

        1. Thanks, I’ll check the book out. And as for C I “invented” my own system for temp. 0C is 0 and 37C is 100, it has the logic of C, the charm of F and is sooo easy to calibrate, stick a thermometer n ice you get zero, stick it up your butt you get 100, what could be easier. (Just email me my Nobel.)

      2. They also messed up C. It should be 180 degrees between the freezing point of water and the boiling point just like F. F only messed up with the 0 point and that was because of the limits of technology at the time.

      3. In metric system, it would be silly to use 180 for full scale. Not even Fahrenheit did that.

        Fahrenheit is messed up because they use a non-repeatable 0 starting point as well as 100 point. I mean using the freezing point of a salt mixture as 0F and the armpit temperature for the upper end!? Do you want to have strangers to use the arm pit to calibrate thermometers?

        It is not like people can’t deal with decimal point if they need higher resolutions or negative numbers. When it is cold enough, you’ll see negative numbers in C or F anyways.

        So 0C as freezing point and 100C as boiling point of pure water at 1 atm is sensible. Kevin is the SI unit for temperature and it has a sensible 0K point.

      1. It is important in scientific circles to use the right terminology, units to describe things as accurate as possible. Dito for law or medicine etc. It is not like a book of god(tm) or a cooking recipe where everything is up to interpretation and tweaks.

        Failing basic stuff like that and fact checking is a failure as a *paid* writer. Might as well write for tabloids and the readers there won’t complain as much.

        1. You know education has gone to crap when a supposedly college educated AP reporter uses a phrase like “peel of laughter”. Or you can get your bad grammar SM on by browsing Craigslist for a while. Oh, it feels so good when you quit reading and the pain stops…

    1. PCV = Positive Crankcase Ventilation. PVC = PolyVinyl Chloride. Soooo many auto mechanics that call a PCV valve a PVC valve.

      Then there’s the bane of anyone who has ever done internet tech support. Symmetric Mail Transport Protocol or FMPZ, SMPT, no, say it with me Ess Emm Tea Pee. Right, FNPT.

      In other words, if you’re in charge of setting up a mail server and value the sanity of support people, do not put SMTP anywhere in server names.

  3. What are the benefits of using a watt balance compared to the round silicon sphere atom counting method?

    Unless the electrons can be counted individually, AFAIK every current measurement relies on a voltage drop over a resistor. Resistors are usually quite drifty and the best voltmeters only go up to 8 1/2 digits, which isn’t even 1ppb resolution, let alone 1ppb accuracy. I guess that using a mass spectrometer (requires a loooon time) or the X-ray diffraction atom counting method in the round silicon sphere atom counting approach gives much better results

    1. The NIST is using a voltage source accurate to 1 part per billion. It’s made of thousands of Josephson junctions connected in series.

      Using the quantum hall effect allows them to measure the resistance of a 100 ohm resistor to a few parts per billion.

      The overall measurement is made to about that accuracy.

      The silicon sphere is difficult to work with. You have to very accurately measure the roundness, and even when you do that you don’t really know what’s going on inside the device.

      Tying the measurement to quantum effects allows you to build a measuring system anywhere in the world, you don’t have to duplicate the sphere or ship it.

  4. Mass is best defined in terms of mass. At the moment they are trying to define mass as the number of atoms of a known isotope of an element. From memory I think the element is Si.

  5. Sorry I should have said more. When you are measuring current or watts or whatever, then interpreting it as mass there are too many measurements each with its errors. Every measurement has error. So you still do not define mass precisely.

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