A LEGO Watt Balance: An apparatus to determine a mass based on the new SI

A global effort to redefine our International System of Units (SI) is underway and the change to the new system is expected to occur in 2018. Within the newly redefined SI, the present base units will still exist but be derived from fixed numerical values of seven reference constants. More specifically, the unit of mass, the kilogram, will be realized through a fixed value of the Planck constant $h$. For instance, a watt balance can be used to realize the kilogram unit of mass within a few parts in $10^8$. Such a balance has been designed and constructed at the National Institute of Standards and Technology. For educational outreach and to demonstrate the principle, we have constructed a LEGO tabletop watt balance capable of measuring a gram size mass to 1 % relative uncertainty. This article presents the design, construction, and performance of the LEGO watt balance and its ability to determine $h$

💡 Research Summary

The paper presents the design, construction, and performance of a tabletop watt balance built almost entirely from LEGO® components, intended as an educational demonstration of the new SI definition of the kilogram based on a fixed value of the Planck constant h. After a brief overview of the global effort to redefine the SI (expected in 2018) and the role of the watt balance in realizing the kilogram, the authors explain the fundamental physics underlying a professional watt balance. Two operational modes are required: a velocity mode, where a coil moving through a magnetic field induces a voltage V = BL v, and a force mode, where a current‑carrying coil generates an electromagnetic force F = BL I that balances the weight mg of the test mass. By eliminating the geometric factor BL through the combination of the two equations, the mass can be expressed as m = VI / (g v). In a high‑precision laboratory this relationship is linked to quantum electrical standards – the Josephson voltage standard (V = hf/2e) and the quantum Hall resistance (R = h/e²) – which allow voltage, current, and resistance to be expressed directly in terms of h with uncertainties of a few parts in 10⁹.

Because such quantum standards are unavailable in a classroom, the authors rely on the conventional 1990 electrical units (K_J‑90, R_K‑90) to obtain a value of h from a known mass, essentially reproducing the pre‑redefinition method. The LEGO watt balance implements the same principle with far lower precision but at dramatically reduced cost and complexity.

Mechanically, the balance is a symmetric, equal‑arm device pivoting on a LEGO T‑brick “knife‑edge” bearing. Each arm carries a PVC pipe coil (≈ 3000 turns of AWG‑36 copper wire) wound around a 1‑inch diameter tube, with a small hole for a LEGO cross‑axle that suspends the coil beneath a mass pan. Two neodymium (N48) ring magnets are positioned on a brass rod to create an open‑field radial magnetic flux; the magnets are arranged to repel each other, and aluminum nuts set their separation, allowing fine adjustment of the BL factor. The coils are driven with a modest current (≈ 2.7 mA) producing about 0.1 N of upward force, sufficient to balance a 10 g test mass. The entire apparatus measures roughly 43 × 36 × 10 cm and weighs about 4 kg, including the wooden base.

Electronics and data acquisition are handled by two USB devices: a LabJack U6 for analog inputs (coil voltage, coil current, balance position) and a Phidget 1002 0 for analog outputs (±10 V, up to 20 mA per channel) that drive the coils. A relay switches which coil is the actuator and which is the sensor. Velocity is measured optically: a laser projects onto a ruler placed a few meters away, and a shadow sensor records the moving coil’s displacement, yielding v. A handheld LEGO potentiometer provides a manual tare function for demonstrations.

Experimental results show that the device can determine the mass of a 10 g standard with a relative uncertainty of about 1 %. Using the conventional electrical constants, the derived value of h differs from the CODATA value by roughly 5 %, an error attributed to magnetic field non‑uniformity, coil‑magnet misalignment, limited velocity measurement accuracy, and electronic noise. The total cost of the system is approximately $650, dominated by the data‑acquisition hardware; the mechanical parts can be assembled for well under $200.

The authors conclude that, despite its modest precision, the LEGO watt balance successfully demonstrates the core concepts of the watt‑balance method, the link between mechanical and electrical power, and the role of quantum electrical standards in the new SI. Its low cost, modular construction, and hands‑on nature make it an excellent tool for outreach, science fairs, and undergraduate laboratories, providing students with a tangible experience of how a fundamental constant can define a unit of mass.