How to convert between imperial and SI units

Phil Black - PII Editor 28/05/2014

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With technical equipment and expertise increasingly sourced from the global market, the need to convert between imperial and SI metric units is becoming more common. Confusing the two can be disastrous, so here Bill Bertram, Managing Director of REGAL C&I Europe, looks at how to convert between the two, and the consequences of getting it wrong.

While much of the world has now moved to the metric units of measurement for distance, power, force and more, there are still important regions – most notably the USA (and regions influenced by it) – using the imperial system. For those companies importing or exporting across global regions, this can mean, at the very least, understanding both units, or possibly operating both side by side as part of a specification or tendering process.

There are many high profile examples of what happens when it goes wrong. The Mars Climate Orbiter, for example, was launched in 1998 to study the Martian climate, atmosphere and surface changes. But on September 23rd 1999, communication with the spacecraft was lost as it went into orbital insertion. It had entered the upper atmosphere at an incorrect angle and had disintegrated. The problem was found to be due to ground-based computer software that had produced output in pound-seconds instead of the expected Newton-seconds.

At a popular Tokyo theme park, an axle broke on a roller coaster train mid-ride, causing it to derail. The cause was found to be a part being the wrong size due to a conversion of the master plans from imperial units to metric units. Thankfully, no injuries were reported, as the vehicle was coming to a halt.

Then there was an airliner flying across Canada which ran out of fuel at an altitude of over 40,000 feet, about half way through its flight, due to a fuel loading miscalculation through misunderstanding of the recently adopted metric system. Fortunately the crew was able to glide the aircraft safely to an emergency landing at a military base, but the subsequent investigation revealed a chain of human errors.

There is good reason, then, to have a sound working understanding of the relationship connecting and differences between imperial and metric units. When it comes, for example, to specifying motors destined for, or sourced from, other regions of the globe, it is important to understand conversion between Horsepower and Watts, or between torque in lb-ft (pound-feet) and torque in Nm (Newton metres). So let’s look at some of the common permanent magnet motor formulae in imperial and SI units.

In imperial units for horsepower and torque (note – two equations; one for pound-feet, the other for pound-inches),

Horsepower = Torque (lb-ft) x RPM
5252

Horsepower = Torque (lb-in) x RPM
63025

By contrast, in SI units

Power (kW) = Torque (Nm) x RPM
9550

Where does that figure 9550 come from, you might ask. The SI unit for rotational speed is radians per second rather than revs per minute. One radian per second is approximately 9.550 RPM. And 2π radians per second is exactly 1Hz.

What about the time for a motor to reach operational speed? In imperial units, this is given by:

Seconds = 2.48 x (J (lb-ft2) x speed change (RPM))
308 x average accelerating torque (lbf-ft)

In SI units, the time for the motor to reach operating speed is given by:

Seconds = J (kg-m2) x speed change (RPM)
9.55 x average accelerating torque (Nm)

From these formulae, we can derive a whole suite of conversion factors for force, torque, power and rotary inertia that will help engineers in converting between imperial and SI units for motor applications.

Power

Multiply   By   To obtain
Watts   1   Jules/sec
Kilowatts   1.341   Horsepower
Horsepower   0.746   Kilowatts
Horsepower   550   Foot-pounds/sec
Horsepower   746   Watts

Force

Multiply   By   To obtain
Newtons   0.2248   Pounds force
Pounds force   4.448   Newtons

Torque

Multiply   By   To obtain
Kilogram metres   7.233   Pound feet
Newton metres   0.7376   Pound feet
Newton metres   8.851   Pound inches
Pound feet   1.3558   Newton metres
Pound feet   12   Pound inches
Pound inches   0.113   Newton metres

Rotary inertia

Multiply   By   To obtain
Kilogram cm2   0.341716   Pound inches2
Pound inches2   2.92641   Kilogram cm2

To date, three countries are yet to adopt the SI metric system as their official systems of weights and measures, with the US joined by Burma and Liberia. Clearly, the US is the most significant. There are moves afoot here for metrication, with a petition created on the White House’s on-line petitioning system to “make the metric system the standard in the United States, instead of the imperial system” garnering over 25,000 signatures, and so exceeding the threshold needed for an official response. In 2013, a bill was introduced by state Representative Karl Rhoads of Hawaii to make the metric system mandatory within his state. The bill stipulated that the law would go into effect on January 1 2018, and Hawaii would then become the first state to introduce the metric system in full. (As far back as the 1970s, then-US president Jimmy Carter considered metrification, but proposals were shelved.)

Research around the bill concluded that the cost to the United States of not switching was quickly increasing, with the trend towards globalisation. Further, it stated that the cost of switching to a metric system could be quickly outweighed by the economic benefits of global interoperability.

We can see, then, that there is growing momentum for true global stabilisation. In the meantime, however, armed with the tables above, engineers can convert with confidence between SI and imperial units, ensuring that system designs that look good on paper will never result in catastrophe in the real world.