A meter is defined as the distance traveled
by light in 3 billionths of second. A second is defined as the time it takes for
about 9 billion cycles of radiation of the cesium atom. But the definition of the kilogram is a little
bit more approachable: it’s literally the mass of a particular chunk of metal in Paris
called the International Prototype Kilogram or just IPK. And even though it’s easier to understand,
having an artifact as a definition comes with its own particular set of challenges. Measurements are so important to us, they
have their own specific branch of science: metrology. And metrologists have come up with a pretty
clever way of redefining the kilogram. Hey I’m Grady. Today on Practical Engineering, we’re building
a watt balance. And put on your asbestos pajamas, because
last time I played with electricity, Hackaday awarded me with the fail of the week. The kilogram is the only SI base unit currently
defined by an artifact instead of a fundamental physical constant. But the kilo is part of the definition of
twenty other units, including three other base units. It shows up in Amp, the Watt, the Newton,
the Joule, the Candela, the Ohm, the lumen, lux, and mole, not to mention any of the imperial
units which are officially defined based on their metric equivalents. In other words, basically the entire world’s
system of measurements can be traced back to this single object in a vault in France. And you know they gave it another bell jar
just to make sure it was extra safe. Here’s the issue: We made lots copies of
the IPK to be used around the world, and we periodically hold kilogram reunions, so to
speak, where all the facsimiles come back together for comparison. And despite our utmost diligence and care,
it seems that the mass of each copy is drifting over time, gaining or losing fractions of
a gram probably due to handling and/or long-term exposure to air. But one of the masses hasn’t changed: the
IPK. Not because it has the same mass as it started
with, but because it is literally the definition of a kilogram. You can put it on one side of the scale, but
there’s nothing to put on the other side. But the inconvenient truth is that all its
copies are changing in mass over time, so we are pretty confident that the IPK is too. The linchpin of our entire system of measurements
has some wiggle room that is impossible to characterize, because there’s nothing more
constant to compare it to. And that’s bad. So, scientists are working to redefine the
kilogram to be based on a fundamental physical constant, and they’ve come up with a pretty
cool way to accomplish this: the watt balance. Fundamentally, the watt balance is a scale
that uses an electromagnetic force to balance the weight of the object it’s measuring. But, it has a trick up its sleeve that allows
it to measure with extreme accuracy and precision. I built a model to help illustrate how it
works. This watt balance is based on a design created
by a few scientists at the US National Institute of Standards and Technology, and there’s
a link to their paper in the description. Their design used legos, but I really like the juxtaposition of a precision scientific instrument made with a natural material, so I made it out of wood. And I made a separate video all about how
this was built that I’ll link below so you can check it out after this. Before we reveal the secret to the watt balance’s
extreme precision, we need to perform the initial alignment and calibration, which is
a perfect opportunity to show the different parts of the model. At first glance, the watt balance looks like
a standard beam balance you’d see in a classroom or in practically any motif related to justice. But you’re looking at a sophisticated scientific
device capable of measuring to within an error of approximately 1%, or at least that’s
what the scientists said. The real watt balances have accuracies up
to 2 parts in 100 million. Each of the two platforms includes a wound
coil of wire. The platforms are hollow so that they can
move freely up and down around a pair of opposing permanent magnets on each side. To measure the position of the arm, the watt
balance uses a shadow sensor which consists of a photodiode and a laser line. As the balance moves, it gradually obstructs
the path of the laser, changing the intensity of light hitting the sensor. Another laser on top of the arm provides an
optical lever for calibration. A small movement of the arm creates a large
movement of the laser dot on an adjacent wall. By measuring the distance the optical lever
moves for a few different arm positions, and comparing those to the corresponding readings
from the shadow sensor, we can calibrate the watt balance so it knows the precise position
of its arm. Now we can start measuring. The secret to the watt balance’s extreme
precision is its dual mode operation which utilizes some interesting properties of electromagnetism. In the first mode, the watt balance applies
a current to one of the coils around the platform, creating an electromagnet. The coil reacts to the existing magnetic field,
generating an upward force, also known as the Laplace force. This setup is similar to how many electric
motors work: applying a current to a coil of wire within a magnetic field. The control software written by the NIST scientists
includes a control algorithm that can do this automatically, but I’m just manually
adjusting the current in the coil in my bench power supply until the upward force is exactly
equal to the weight of the object. I do this once with no object, once with the
object, and then once again without it to get an accurate value of just the current
required to balance the object alone. Let’s take a look at this system expressed
as an equation. The weight of the object is simply its mass
times the gravitational acceleration. The Laplace force is the product of the magnetic
field strength of the permanent magnets, the length of the wire in the coil, and current
in the coil. If the beam is static, that means the two
forces are equal. Remember, our goal is to find the mass of
the object. We can measure gravity and current to very
high accuracy, but length of the coil and especially the magnetic field strength are
very difficult to measure with extreme accuracy. Without those values, we can’t solve this
equation for mass… yet. This is where the ingenuity of the watt balance
comes into play. You may know that many electric motors can
be used in reverse to generate electricity if you apply a mechanical input force. In other words, the electromagnetic principle
is reversible. The watt balance takes advantage of this for
its second mode of operation. Instead of applying a current to the coil,
we simply move it through the magnetic field. We know from Faraday’s Law of Induction,
when you move a conductor through a magnetic field, you generate a voltage. This is the reason our watt balance has two
coils. Applying a varying current to coil B moves
the beam in an up and down motion. The shadow sensor measures the velocity of
this motion, and we also measure the voltage induced in the coil A. The software samples
both the voltage and velocity as the coil moves through the magnetic field. From Faraday’s law, we know the voltage
is equal to the product of velocity, magnetic field strength, and the length of the conductor. Remember from the first mode that we couldn’t
accurately measure the magnetic field strength or the precise length of the conductor, but
we’re using the same coil around the same pair of permanent magnets. In other words, even though we don’t know
what they are, we do know that these two variables are exactly the same in both equations. As the software samples the velocity and voltage,
it generates a best fit line. The slope of this line represents the quantity
of this BL that we couldn’t measure directly. With a little bit of algebra we can rearrange
these equations and perform a substitution to completely eliminate those variables. And take a look at the units: Current times
voltage is power, and force times velocity is power. Both are measured in watts, hence the name
of the instrument. Rearranging a bit more, now we have an equation
for mass which only consists of the parameters we’re capable of measuring accurately. We measured the current required to hold up
the object in the first mode. Then we measured the voltage over velocity
in the second mode. We know the acceleration due to earth’s
gravity, so we have everything we need to determine the mass of the object. It’s so simple that you almost don’t notice
how big of a deal this really is. Traditionally, an instrument that measures
mass would be calibrated using known artifacts that themselves were calibrated using known
artifacts and so on and so on in a chain all the way back to the IPK, but I haven’t done
any of that. I know this mass is about 20 grams because
it says so right on top, but if I didn’t know that and had nothing to compare it to,
I could still get an accurate measurement out of the watt balance. And here’s the most important part: Since
voltage and current are defined in terms of fundamental physical constants, the watt balance
makes it possible to define the kilogram in terms of these absolutes, eliminating the
need for a physical artifact. Trace them back far enough and you’ll find
that all measurements are relative, they’re a comparison. Sometimes a comparison to something immutable,
but in the case of the kilogram, not yet. Redefining the kilogram to be based on a fundamental
physical constant means not only that we have more confidence in our measurements, but it
also makes metrology more democratic by metaphorically setting the standard free from its vault and
bell jars so that anyone with a garage workshop and a little bit too much free time has access. Measurements are the language of science engineering
and metrology makes sure that we’re all speaking the same one. Thank you for watching, and let me know what
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