The Genius Device That Rocked F1 | An Interview With Its Inventor (YouTube, 47m) in which Professor Giordano Scarciotti of Imperial College London talks to Professor Malcolm Smith of the University of Cambridge about an innovative suspension component that Smith invented after Formula 1 motor racing rules banned the active suspensions he’d previously consulted on, and a followup: Why Everyone Gets the F1 Inerter Wrong | Explained Clearly (38m) in which Scarciotti expounds at length upon the profundity of spoons.

I’m posting this mostly because I very much enjoyed the analogy that Smith makes between mechanical and electrical design where voltage and current are taken to be the counterparts of velocity and force respectively, rather than voltage being in some sense a force and current a flow as they’re customarily explained.

Just as each terminal of a resistor, inductor or capacitor can have a voltage with respect to the other, each terminal of a damper, spring or inerter can have a velocity with respect to the other. And just as the instantaneous current into one terminal of a resistor, inductor or capacitor is always equal to the instantaneous current out of the other, the instantaneous force applied to one terminal of a damper, spring or inerter is always equal to the instantaneous force applied by the other terminal.

As Smith explains it, these facts justify describing voltage and velocity as “across” variables, and current and force as “through” variables. And if you multiply together the applicable across and through variables for any two-terminal component, be it mechanical or electrical, what you get has the dimensions of power i.e. a quantity expressible in watts: power is voltage times current, and it’s also velocity times force.

The advantage of using these analogies is that they make series and parallel connections work the same way in electrical and mechanical domains, which means that arbitrary networks of two-terminal components will work the same way as well. So if you can find mechanical analogues for resistors, inductors and capacitors, all of the extensive electrical engineering theory applicable to those components becomes applicable to mechanical designs as well.

Ohm’s Law for ideal resistors says that the current through a resistor is proportional to the voltage across its terminals. The analogous mechanical component is the damper, where the force that a damper can transmit is proportional to the velocity of its terminals with respect to each other. Like resistors, dampers dissipate energy.

Hooke’s law for ideal springs says that the force applied across the terminals of a spring is proportional to their deflection with respect to each other: that is, to the integral of their relative velocity. The analogous electrical component is the inductor, where the current through it is proportional to the integral of the voltage across it. Like springs, inductors store and release energy, ideally without dissipating any.

Capacitors also store and release energy without (ideally) dissipating it, and current through a capacitor is proportional to the derivative of the voltage applied across it. If voltage is analogous to velocity then its derivative is analogous to acceleration, so a capacitor-like mechanical component should show force proportional to acceleration. This is exactly the proportionality Newton’s Second Law describes for masses.

But the mechanical analogue of a capacitor can’t simply be a mass, because a capacitor has two well-defined terminals and a mass has only the one (or perhaps infinitely many, depending how you squint). So how does one go about constructing a component that behaves like a two-terminal (i.e. relative) mass, and what is the electrical analogue of a simple mass?

I found Smith’s answers to those two questions just absurdly pleasing, and I hope you will too.