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I'm trying to name a measurement that is measured in reciprocal length, which is in a draft document for vehicle risk management.

It currently says:

Crash rate = number of crashes / million kilometres driven

where the measurements are taken annually. So the units are in reciprocal length.

I'm not happy with the word "rate" because that seems to imply the number of events over time, whereas the measurement is the number of events over distance.

Existing names of units of reciprocal length in various disciplines don't seem to work - it's not a measurement of any cyclic phenomenon.

Is there an better word for this measurement?

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    $\begingroup$ Usually, something that goes inverse to spatial measures and counts the presence of something is a density. e.g. linear density $\endgroup$ – alemi Jul 15 '14 at 16:15
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    $\begingroup$ I don't really see such a strong link between "rate" and temporal phenomena. We happily use, for example, "exchange rate" for the number of dollars that you'll get for each euro, so I don't really see a problem in calling "the number of crashes you expect for each Mm" a rate. $\endgroup$ – Emilio Pisanty Jul 15 '14 at 16:20
  • $\begingroup$ It's not so important which word you choose, as long as there is some fathomable relationship and you use it consistently. $\endgroup$ – Klik Jul 15 '14 at 16:43
  • $\begingroup$ What about just frequency? It is a spatial frequency, as used in Fourier analysis for instance... But I have to agree with @EmilioPisanty here. $\endgroup$ – Anael Jul 15 '14 at 16:50
  • $\begingroup$ @Anael Frequency is often (usually?) associated with things that occur regularly. It seem that johntait wants to avoid that implication. In a sense this is like the relationship between Hz = 1/s (cyclic) and Bq = 1/s (probabilistic). $\endgroup$ – dmckee --- ex-moderator kitten Jul 15 '14 at 23:57
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I like alemi's suggestion in a comment of crash density, by analogy with the linear "mass density" for a rod.

Among other advantages, this frees up "crash rate" to mean the number of crashes per million hours driven.

Alternatively you could invert the crash density to talk about the "mean distance between crashes."

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The term "Crash Recurrence" comes to mind.

http://dictionary.reference.com/browse/recurrence

  1. an act or instance of recurring.
  2. return to a previous condition, habit, subject, etc.

It captures the concept of an interval without implying that it is regular or predictable, which seems to be what you're looking for.

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Collider physicists actually use a quantity called "luminosity" which has inverse areal units, and they just quote as such (note that a "barn" is a (very small) measure of area), so when they say "inverse-femtobarns" they mean the inverse of an exceedingly small area which equates to a very high luminosity.

There is nothing fundamentally wrong with "inverse terameters" (inverse of a large distance means a small chance in any given kilometer), though it is unlikely to be familiar to your audience and will take some explanation.

Though I have to agree with Emilio Pisanty in the comments to the question "rate" does not always and everywhere imply "per unit time". However, as "per unit time" is by far the most common meaning, if you want to use another meaning you should explain clearly what you are about.

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  • $\begingroup$ I heard a story about the introduction of luminosity as the figure-of-merit for the operations engineers to maximize at Fermilab. For some time leading up to the change, you could find confused-looking engineers hunting for physicists in the hallway, collaring them, and saying "Tell me again — what the hell is an inverse femtobarn?" $\endgroup$ – rob Jul 15 '14 at 23:37
  • $\begingroup$ Watching particle physics grad students trying to wrap their heads around it the first time can be pretty amusing. It's best if you can introduce the idea at the pub after a point or so... $\endgroup$ – dmckee --- ex-moderator kitten Jul 15 '14 at 23:45
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You could use the generic/boring term ratio, and precede it with CMK for crashers per million kilometers. The entire thing then becomes the CMK ratio. Though CMK rate can also work as others have said so long as your definition is clear. Then there's CMK factor if you want to use a fancier but more ambiguous term.

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