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The Masy Joule Balance:

A new look at NIST’s LEGO Watt Balance

Cesar (Jun) Bautista Ph.D., Jared Zhao, William Faulkner

September 17, 2016

Abstract

Many units of measure have previously been defined in terms of physical artifacts. These

physical artifacts are the only references defined with zero uncertainty. In mass metrology, the

International Prototype Kilogram (IPK) has been used to define the kilogram since 1879. However, with

the passing of time and the effects of the environment in which it is stored, it has been discovered that the

IPK has been losing and gaining mass. Since this discovery, a global effort has been made to redefine the

International System of Units (SI) kilogram. In the redefined system, the kilogram will be defined as a

fixed value of the Planck constant h.

I. INTRODUCTION

Many units of measure have previously been

defined using physical artifacts, which are the only

references defined to have zero uncertainty.

However, due to the passing of time and the effects

of the environment in which the artifact is stored, it

is impossible to guarantee that the artifact remains

in its original condition. In mass metrology, the

International Prototype Kilogram (IPK) has been

used to define the kilogram since 1879. However, it

has been discovered that the IPK’s mass has been

changing. Since this discovery, a global effort has

been made to redefine the International System of

Units (SI) kilogram. In the redefined system, the

kilogram will be defined as a fixed value of the

Planck constant h.

To accomplish this relationship between mass

and the Planck constant h, the gravitational force of

an object will be balanced with the electromagnetic

force generated by a current-carrying solenoid using

the Watt Balance, thus providing the relationship

between mass and electrical constants.

Our Masy Joule Balance, on the other hand,

equates the energy dissipated by the current-

carrying solenoid and the change in the gravitational

potential energy of the mass, and was developed at

Masy BioServices’ Mass Calibration Laboratory,

hence the name, “Masy Joule Balance”. Like the

NIST Watt Balance, the Masy Joule Balance finds

the relationship between mass and electrical values

by balancing the different forces acting on each side

of the balance arm, but differs in its calculations and

implementations. On the surface, both arms seem

very similar, but when we examine the calculations

used to explain our implementation, we will quickly

see the differences.

FIG. 1. Picture of completed Masy Joule Balance. The electronics are

hidden on the underside of the base.

Like NIST, we were able to build our balance

using LEGO for under $650. The parts required for

our balance are very similar to those of NIST’s

LEGO Watt Balance and the differences are noted

throughout this journal. We encourage others to

improve upon our design and increase its sensitivity

and functionality, or even design a balance entirely

different, like what we have done with NIST’s

LEGO Watt Balance.

II. BALANCE THEORY

As the name implies, the LEGO Masy Joule

Balance balances the different energies. The change

in gravitational potential energy of the mass being

measured is balanced against the energy consumed

by the current-carrying solenoid.

!"#$% & '()*++

(1)

Energy is the integral of two different forces

acting on the opposite ends of the balance arm from

0, the “down” position of the Masy Joule balance,

to D, the “balanced” position of the Masy Joule

balance, with respect to distance. The energy

dissipated by the current-carrying solenoid is the

integral of the Lorentz force it produces and the

change in gravitational energy experienced by the

mass is the integral of the gravitational force it

experiences.

,-./01/

2

3

& ,

4

2

3

./01/

(2)

The magnetic force of the current-carrying

solenoid and the gravitational force experienced by

the mass are substituted in, and the constants are

brought out of the integral.

5$6789: ;./01/

2

3

&<= 1/

2

3

(3)

The issue with Eqs. (3) is that it is very difficult

to accurately determine the integral of the magnetic

field as a function of distance with respect to

distance. To solve this, we will introduce the

equation that describes the voltage induced in a wire

of length L when it is moved through a magnetic

field B at a constant velocity in a separate mode of

operation that we will call “charge mode”.

>

$6?8"@?.A0 & ;./0: 1/

1A

(4)

By rearranging Eqs. (4) and taking the integral

of both sides, we get Eqs. (5).

>

$6?8"@? A1A

B

3

& : ; / 1/

2

3

(5)

By substituting Eqs. (4) into Eqs. (3), we can

eliminate the magnetic field from our equation.

5$6789 >

$6?8"@? A1A &<= 1/

2

3

B

3

(6)

Now, although our equation no longer contains

the integral of the magnetic field, we now must find

the integral of the induced voltage. We can do this

by substituting current in using Ohm’s Law.

Voltage as a function of time is related to current as

a function of time with constant resistance through

Ohm’s Law.

>.A0 & 5.A0C

(7)

Then by substituting Eqs. (7) into Eqs. (6), we

get Eqs. (8).

5$6789C 5$6?8"@? A & <= 1/

2

3

B

3

(8)

Then, by completing the integrals on both sides

of Eqs. (8), we get Eqs. (9).

5$6789CD$6?8"@? &<=E

(9)

Where D$6?8"@? is the total charge that

accumulates from the current passing through the

current-carrying solenoid during “charge mode”.

Finally, by using Ohm’s law from Eqs. (7)

again, we can substitute for the input current and

reduce the equation even further

>

$6789D$6?8"@? &<=E

(10)

Now we have completed the Masy Joule

Balance equation. However, there are still issues in

measuring these variables found in the equation

accurately.

>

$6789, E, and = can all be measured direcly,

and < is what we are looking for. What remains is

an accurate method to measure the total charge Q

that passes through the current-carrying solenoid

during “charge mode”. We can do this with

Riemann Sum approximations. By taking the ratio

of the difference between the D"*%"8%*9@? and the

D*77F#G and the D"*%"8%*9@? , we can determine the

number of samples we need to take for a given time

to obtain the total accumulated charge D$6?8"@?

with acceptable accuracy.

H I

5 A 1A JK

L5.A$0

6

$M3

B

3

5 A 1A

B

3

NOPPQ

(11)

Where L is the number of samples required for

this desired % accuracy H, A$ is the time at which the

current is being measured, and K is the total time of

the experiment. For our purposes, we will be setting

our desired % accuracy H to 1%.

The issue with Eqs. (11) is that we are not able

to take the integral or Riemann Sum of the unknown

function 5.A0. We must find a way of representing it

as a function of time A, so we can numerically

determine L.

Again, Ohm’s Law from Eqs. (7) is used to to

replace the current 5.A0 in the equation to voltage

>.A0 to enable further substitution and eventual

calculations.

H I

O

C> A 1A JO

C

K

L>.A$0

6

$M3

B

3

O

C> A 1A

B

3

NOPPQ

(12)

Now we must observe the relationship between

the voltage induced >.A0 and time A in order to

complete our integration and Riemann Sums.

By observing the relationship between the

induced voltage and the magnetic field from Eqs.

(4), we can conclude that voltage >.A0 is

proportional to the magnetic field ;./0.

> A RSR;./0

(13)

And the magnetic field B decays according to

the Inverse Cube Law, since the magnet is a dipole

source.

; / RSR O

/T

(14)

And because the current-carrying solenoid is

moved at a constant velocity during “charge mode”,

we can use the relationship between velocity, time,

and distance.

/ & UA

(15)

We finally get our relationship between desired

% accuracy H, the total time of the experiment K,

and the number of samples required L in Eqs. (16).

H I O

C

O

AT1A

B

3JK

L

O

/$T

6

$M3

O

AT1A

B

3

NOPPQ

(16)

Thus, we are able to take the integral and

Riemann Sums and determine the number of

samples L that we need over an experiment time K

for our desired % accuracy H. From Eqs. (16) and

the Masy Joule Balance equation from Eqs. (10), we

can effectively find the relationship between our

measured mass and a voltage supplied to the

current-carrying solenoid.

III. BALANCE MECHANICS

Because the Masy Joule Balance is made of

LEGO bricks, it is much more easily influenced by

imperfections. Thus, we decided to adjust our Masy

Joule Balance equation and absorb all constants into

a single constant V. By doing this we can find the

linear relationship between the mass < and the

voltage U, and the slope of the trendline of our

dataset would be that constant V.

The Masy Joule Balance was initially modeled

after NIST’s LEGO Watt Balance. Thus, the Masy

Joule Balance shares many features of NIST LEGO

Watt Balance. However, several changes have been

made to improve the accuracy and stability of the

device.

Firstly, we decreased the mass of the arm itself

to decrease the rotational inertia of the balance. This

allows us to measure much smaller masses with

increased resolution. Also, rather than using a

symmetrical design, the Masy Joule Balance utilizes

a single coil immersed in a radial magnetic field

while the opposite arm of the balance utilizes two

weighing pans, one on top of the other. This

decreases the possibility of magnetizing our test

weights since the distance from the neodymium

magnets to the weight pans has increased. The top

weighing pan is used to hold tare weights to balance

out the arm when measuring lower masses, while

the bottom pan holds the actual item or mass being

weighed. The use of tare weights improves the

range of masses that the balance can accurately

measure from 0-13g to 0-105g.

The coil was made using a standard 1-inch PVC

coupling with a 1.25-inch PVC cap secured on one

end. The wire was wound onto the PVC pipe using

a low-speed electric hand drill and secured with

epoxy. A counter was created using an Arduino Uno

to count the number of winding around the coil. The

coil had approximately 3000 windings of AWG-36

magnet wire, and the total resistance of the coil was

approximately 450Ω. A pair of neodymium (N48)

ring magnets was secured to the base with a brass.

The magnets are oriented on the bolt so that they are

touching each other and are attracted to each other.

The specific orientation (North up or south up) does

not matter. Nuts were placed on either side of the

bolt securing the magnets to ensure they remain

stationary throughout our experiments.

A hole was drilled into the PVC cap and a

LEGO cross axle with two LEGO Wedge Belt

Wheels were passed through the hole. The assembly

was then bonded with hot glue. This was then

connected to another LEGO cross axle, which was

then connected to the beam using the LEGO

universal joint system.

The central pivot was a 4 by 1 technic brick

secured to the beam with a connector peg. The

technic brick was secured so that it balanced on its

edge as it sits on a smooth surface. This knife edge-

like balance point has much lateral movement due

to rotation and thus much higher precision than the

T brick used on the NIST LEGO Watt Balance. A

series of LEGO bricks were stacked on either side

of the tower to prevent the balance from moving out

of alignment.

FIG. 2. The balance rests on a knife edge created by turning a 4 by 1

technic brick on its side.

IV. BALANCE ELECTRONICS AND

DATA ACQUISITION

Similar to the NIST LEGO Watt Balance, the

Masy Joule Balance utilized a photodiode and a line

laser to determine the balance position and a

Phidgets 1002 Voltage Output to produce the

voltage supplied to the current-carrying solenoid.

However, we chose to use an Arduino Uno as our

voltage reference when reading from the photodiode

and line laser system.

The photodiode and the line laser were mounted

on opposite sides of the tower so that the arm could

swing freely between them.

FIG. 3. The line laser is projected onto the arm and the photodiode

behind.

During operation, the line laser is projected onto the

arm and a portion of the laser would shine through

to the photodiode. When the laser is half covered by

the arm and half projected onto the photodiode, the

arm is considered balanced. During operation, to

ensure the beam is in the balanced position

consistently during each run, the voltage across the

photodiode must remain constant at the balanced

voltage for a total of 20 consecutive samples

gathered at a sampling rate of 80ms.

The program provided by NIST for the LEGO

Watt Balance was not well suited for the Masy Joule

Balance due to the differences in wiring and setup.

Instead, a custom operating program was written in

Java. The program now lives on Github as an open-

source project.

FIG. 4. The program was developed in Java and is run without a GUI.

This program utilizes the feedback loop from the

laser-photodiode system to determine whether the

arm is too far left or too far right, and thus determine

whether the voltage supplied to the current-carrying

solenoid from the Phidgets 1002 Voltage Output

needs to increase or decrease.

V. MEASUREMENT

To ensure the Masy Joule Balance remains

consistent for each experiment, alignment lines are

drawn on the fulcrum and the top of the tower.

Before each experiment, the mass is placed onto the

weighing pan. When the test begins, the coil will

produce a magnetic field that pulls the coil toward

the magnets. The beam is then realigned using the

alignment dots. The entire beam is then pulled

toward the front face of the balance. This ensured

that the beam is aligned and is in the same position

for each measurement.

VI. ACKNOWLEDGMENTS

NIST’s experience in building the LEGO Watt

Balance was extremely useful in the initial design

and planning of our Masy Joule Balance. Many of

the parts used in our design were chosen due to their

inclusion in NIST’s LEGO Watt Balance physics

journal. Our balance was heavily influenced by

design choices made by the NIST in designing their

LEGO Watt Balance.

Assistance from Masy BioServices is gratefully

acknowledged. This project was completed as a

summer internship at Masy BioServices’ Mass

Calibration Laboratory, and the hospitality and help

received from Masy BioServices was a major

encouragement to this project.

VII. REFERENCES

1. B.Eng.(Hons.), Xavier Borg. "The Inverse Cube Law for Dipoles."

(2009): n. pag. Blaze Labs. Web. 18 Sept. 2016.

<http://www.blazelabs.com/inversecubelaw.pdf>.

2. Chao, L. S., S. Schlamminger, D. B. Newell, J. R. Pratt, F. Seifert,

X. Zhang, G. Sineriz, M. Liu, and D. Haddad. "A LEGO Watt

Balance: An Apparatus to Determine a Mass Based on the New SI."

Am. J. Phys. American Journal of Physics 83.11 (2015): 913-22. AIP

Publishing. Web. 13 July 2016.

3. Measure, By Default They. "Arduino - ArduinoBoardUno." Arduino

- ArduinoBoardUno. N.p., n.d. Web. 14 July 2016.

<https://www.arduino.cc/en/Main/ArduinoBoardUno>.

4. "Phidgets Inc. - 1002_0 - PhidgetAnalog 4-Output." Phidgets Inc. -

1002_0 - PhidgetAnalog 4-Output. N.p., n.d. Web. 18 Sept. 2016.

<http://www.phidgets.com/products.php?product_id=1002>.

5. Stock, M. "Watt Balance Experiments for the Determination of the

Planck Constant and the Redefinition of the Kilogram." Metrologia

50.1 (2012): n. pag. Web.

6. Scream3r. "Scream3r/java-simple-serial-connector." GitHub. N.p.,

24 Jan. 2014. Web. 18 Sept. 2016. <https://github.com/scream3r/java-

simple-serial-connector>.