Erg to Inch-Ounce

Astrophysics literature built decades of reference data in CGS units before SI became dominant. Key constants like solar luminosity (3.828 × 10³³ erg/s) and supernova energy (10⁵¹ erg, called a "foe") are baked into textbooks and databases. Switching to SI would require rewriting thousands of reference values, so the field maintains CGS by convention.

A core-collapse supernova releases roughly 3 × 10⁵³ ergs total, of which about 99% escapes as neutrinos. The visible light and kinetic energy of the ejected shell account for about 10⁵¹ ergs — a unit so common in astrophysics it has its own name: one "foe" (ten to the Fifty-One Ergs). In joules, that is 10⁴⁴ J, or the Sun's total output over 10 billion years.

An erg per second is the CGS unit of power, equivalent to 10⁻⁷ watts. Astronomers quote stellar luminosities in ergs per second because the numbers align well with astrophysical scales: the Sun emits 3.846 × 10³³ erg/s, and supernovae peak at ~10⁴³ erg/s. Using watts would give the same exponents minus seven — less tidy for a field that already juggles 40-digit numbers daily.

CGS (centimeter-gram-second) is a metric system that predates SI, formalised in the 1870s. It derives mechanical units from cm, g, and s: force in dynes (g·cm/s²) and energy in ergs (dyne·cm). CGS was standard in physics until the mid-20th century, and its Gaussian variant remains preferred in electromagnetism and astrophysics because Maxwell's equations take a simpler form.

One erg is 10⁻⁷ joules — roughly the kinetic energy of a mosquito in flight or the energy of a single grain of sand falling one centimeter. You would need about 10 million ergs to equal one joule, or 42 billion ergs to match the energy in a single dietary Calorie. The erg is useful precisely because atomic and astronomical quantities span so many orders of magnitude.

RC servo motors are rated by torque in inch-ounces (or oz·in) because the forces involved are tiny. A standard micro servo produces 40–60 in·oz, which is enough to deflect a model aircraft aileron. High-torque digital servos for 1/10-scale RC cars reach 200–400 in·oz. The inch-ounce scale gives hobbyists whole-number specs that are easy to compare.

Servo motors produce more torque at higher voltage because the motor windings draw more current and generate a stronger magnetic field. A servo rated at 60 in·oz at 4.8 V might deliver 75 in·oz at 6 V — a 25% boost. RC pilots choose voltage based on the tradeoff: 6 V gives snappier response and more holding torque for aerobatics, but draws more current and generates more heat, reducing servo lifespan. Competition flyers often run 7.4 V for maximum performance, accepting shorter gear life.

Inch-ounces give convenient whole numbers for very small torques where newton-meters would be awkward decimals (e.g., 50 in·oz ≈ 0.353 N·m). The RC hobby, miniature clockwork, and precision instrument industries in the US developed around imperial units, and the convention persists even as SI gains ground. Many datasheets now list both units side by side.

A mechanical wristwatch mainspring delivers roughly 2–5 in·oz of torque. Larger mantel clocks may have mainspring torques of 10–30 in·oz. Escapement adjustments are even finer, sometimes below 1 in·oz. Horologists use inch-ounces (or gram-centimeters) because these scales match the delicate forces in timekeeping mechanisms.

A servo's inch-ounce rating tells you the maximum force it can exert at one inch from the output shaft. A 100 in·oz servo can hold 100 ounces (6.25 lb) at 1 inch, or 50 ounces at 2 inches. Robotics designers use this to size servos for joint loads — a small robotic arm lifting 1 lb at 4 inches needs at least 64 in·oz, plus a safety margin of 50% or more.