Engineering units: from psi to GPa without losing a spacecraft

A number without a unit is not an answer

“The modulus is 200” means nothing on its own. In gigapascals it is steel; in megapascals it is a soft plastic a thousand times floppier. Units are half of every engineering number, and most calculation mistakes that survive to the real world are unit mistakes rather than arithmetic ones.

The habit that prevents them is simple: write the unit next to every number, convert everything into one consistent set before you start, and check the answer's size against something you know.

SI and its prefixes

The SI unit of stress, the pascal, is one newton per square metre, which is tiny. So engineers work in megapascals (millions of pascals) for strengths and gigapascals (billions) for stiffness. One megapascal is exactly one newton per square millimetre, which is why mm and N pair so neatly in hand calculations.

Typical orders of magnitude are worth memorising: epoxy has a modulus of about 3 GPa, aluminium about 70 GPa, steel about 200 GPa and standard carbon fibre around 230 GPa. If a calculation hands you a steel beam at 200 MPa of stiffness, a unit has gone missing.

US customary units, and force versus mass

Much aerospace and composites data is published in psi (pounds-force per square inch), ksi (a thousand psi) and Msi (a million psi, common for fibre moduli). One ksi is about 6.895 MPa and one Msi about 6.895 GPa, so a fibre listed at 33 Msi is roughly 228 GPa.

The pound is also two different things: a pound-mass (lb) and a pound-force (lbf), the weight of that mass under standard gravity. Mixing them silently changes an answer by a factor of about 32.17, the value of standard gravity in feet per second squared. SI avoids the trap by keeping kilograms and newtons separate.

Temperature does not convert like other units

Most conversions are a single factor: multiply inches by 25.4 to get millimetres. Temperature is different, because the Celsius and Fahrenheit scales have different zeros. A temperature converts as °F = °C × 9/5 + 32, but a temperature difference converts by the 9/5 alone.

So a part that warms by 10 °C has warmed by 18 °F, not 50 °F. The same care applies to anything measured per degree: a thermal expansion coefficient per °C is 5/9 of the same value per °F. Kelvin and Rankine avoid the offset entirely by starting at absolute zero.

Compound units carry their parts

Viscosity in pascal-seconds is often quoted in centipoise instead: 1 cP is exactly 1 mPa·s, and water at room temperature is close to 1 cP. Kinematic viscosity, which divides by density, comes in centistokes, where 1 cSt is 1 mm²/s.

Thermal conductivity in watts per metre-kelvin shows up in American data as BTU per hour-foot-degree Fahrenheit; one of those is about 1.731 W/(m·K). None of these factors needs memorising, because each follows from definitions — a BTU in joules, a foot in metres, a degree Fahrenheit as 5/9 of a kelvin — and that is exactly how a careful converter builds them.

When units go wrong

In 1999 NASA lost the Mars Climate Orbiter. Software on the ground reported thruster impulse in pound-force seconds, while the navigation software that used it expected newton seconds. Each correction was off by a factor of about 4.45, the trajectory drifted, and the spacecraft reached Mars far too low and was lost.

In 1983 an Air Canada Boeing 767 ran out of fuel mid-flight over Canada. During the airline's change to metric units, the fuel on board had been worked out in pounds where kilograms were needed, so the aircraft carried less than half the fuel its crew believed. The pilots glided it to a landing at a disused airfield at Gimli, Manitoba, and it became known as the Gimli Glider. Both are reasons to convert once, carefully, with the unit written down every time.

Check yourself

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