Unit Conversion Tips

Unit Conversion Errors Can be Costly (and deadly)

• A passenger plane ran out of fuel and had to dead stick land because of a unit conversion error. Check out the story of the Gimli Glider at links below:
1. http://en.wikipedia.org/wiki/Gimli_Glider
2. http://www.answers.com/topic/gimli-glider
• A NASA spacecraft was lost because engineers used the incorrect unit. Check out the story of the Mars Orbiter lost.

How To Avoid Unit Conversion Errors

1.      Proper conversion occurs by multiplying by one, since this does not change the physical magnitude of an item. Do not take short cuts, write out each step as follows, where each fraction in parentheses is equal to a physical value of one:

 

 

 

2.      Memorize common values. This will give you a quick method of developing real world smarts! Always ask yourself if you expect the numerical values in new units to be larger or smaller than the starting units. Also check the intermediate values of unit conversions, such as the distance conversion in the speed example above, to better find errors. Guess the conversion factors for the items below then check them using the computer tools listed below. Pay attention to values in work you are doing and reports you read; it will develop your intuitive sense of values and save your neck sooner or later!

a.       A mile is larger than a km.

b.      A radian is much larger than a degree.

c.       A Kg force is larger than a pound (yes I know one is mass and the other is force; see discussion below).

d.      A Newton is smaller than a Kg weight on earth. Tip an apple on earth weighs about one Newton (remember the apple that hit Sir Isaac Newton on his head!).

e.       A Slug is much larger than a pound (see below)

 

3.      Some special cases:

 

a.       Angles: Degrees and Radians

We typically have a better intuitive sense for degrees, but it is best to perform calculations in radians. Many kinematic calculations have an angle or angular velocity multiplied by a length vector, and this calculation is only valid if performed in radians. Thus the recommended approach is to perform calculations in radians but then convert back to degrees for output and reports. Note, radians are a ratio and therefore can be represented as unitless in some cases.

 

 

 

b.      Weight Force vs Weight Mass

 

Engineering specifications will often not rigorously distinguish between mass and force. Thus one may find documentation referring to forces with units of pounds, Kilograms, or Newtons. The key to understanding these variables is the implicit assumption that all values relate to properties on Earth. A force specification given in Kilograms implicitly refers to the weight force this object generates in the Earth’s gravitational field. It is the responsibility of the end user to interpret these values correctly and convert to proper units.

 

 

Example: convert from force specification given in Kg, to proper force units of Newtons.

 

 

Example: convert from mass specification given in lbs, to proper mass units of Slugs.

 

 

Certain equations, such as for centrifugal force, require that mass values be in mass units and that units are consistent (do not use inch/second when you use g=32.2 ft/sec² in your conversion). Be safe and always use proper and consistent units.

 

Computer Tools Can Help (but do not rely solely on them!)

 

On line converter from Science Made Simple

 

Download a Free Unit Conversion Software Package (for Windows machines)