Calorie (th) to Inch-Ounce

The thermochemical calorie (cal th) is defined as exactly 4.184 joules; the International Table calorie (cal IT) is exactly 4.1868 joules — a difference of 0.066%. The thermochemical value was fixed by the US National Bureau of Standards in 1935 for chemistry; the IT value was adopted for steam tables. In nutritional contexts, the difference is irrelevant, but in precise calorimetry it can matter.

Decades of published thermochemical data — heats of formation, bond energies, combustion enthalpies — are recorded in cal th and kcal th. Converting every reference table to joules would be error-prone and disruptive. Biochemistry textbooks still quote ATP hydrolysis at ~7.3 kcal/mol and glucose oxidation at ~686 kcal/mol. The convention persists because the existing literature is too vast to rewrite.

A dried, weighed food sample is sealed in a steel vessel filled with pure oxygen, submerged in a known mass of water. An electric spark ignites the sample, which burns completely. The temperature rise of the surrounding water — measured to 0.001°C — gives the total heat released. One degree rise per gram of water equals one calorie. Corrections for the heat capacity of the bomb itself, the ignition wire, and acid formation give results accurate to ±0.1%. Atwater then applied digestibility factors to convert bomb values to usable food energy.

Hydrogen releases about 34,000 cal th per gram; methane about 13,300 cal th/g; ethanol about 7,100 cal th/g; and glucose about 3,720 cal th/g. These values appear throughout chemistry textbooks as standard reference data. The higher the cal/g value, the more energy-dense the fuel — which is why hydrogen is attractive despite being hard to store.

Before 1935, the calorie was defined by water's heat capacity, which varies with temperature — the 15°C calorie, 20°C calorie, and mean calorie all differed slightly. The US National Bureau of Standards ended the ambiguity by defining the thermochemical calorie as exactly 4.184 J, a round value close to all the experimental variants. This gave chemists a fixed, reproducible conversion factor independent of water's quirky temperature-dependent heat capacity.

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.