# What does “less than unity” mean in the following context…?

It's about wind power. Here is the context : "Few topics generate more controversy than capacity credits for wind plant. The capacity credit of any power plant may be defined as a measure of the ability of the plant to contribute to the peak demands of a power system. Capacity credit is often defined as the ratio (firm power capability)/(rated output). As thermal plant is not 100 per cent reliable, values for all plant are less than unity. To a first order, 1,000 MW of nuclear plant corresponds to about 850 MW of firm power and hence has a capacity credit of 0.85; coal plant has a capacity credit of about 0.75. These figures are, roughly, the statistical probability of the plant being available at times of peak demand."

What is meant by this sentence : "values for all plant are less than unity"? What are these "values"? I guess the "values" are the results of this "ratio (firm power capability)/(rated output)", aren't they?

Many thanks for your help.

INCIDENTALLY, what is meant by "To a first order"?

• This quote sounds like it is either translated from an original language using an unreliable translator (ergo, unity may mean one like ConfusedScientist says), or it was written by someone not fully fluent in English grammar (ergo, writing one as unity). It can be deduced that unity must mean one by the sentences prior to and following the sentence you don't understand. – Jonathan Spirit Jan 27 '15 at 19:29
• I guess "unity" means the figure "1" (one) hence 0.85 and 0.75, which indeed are less than unity, that is a figure inferior to 1, what do you think? – FrenchMan Jan 27 '15 at 19:40
• Yes, that's why I said, "It can be deduced that unity must mean one by the sentences prior to and following the sentence you don't understand." – Jonathan Spirit Jan 27 '15 at 19:42
• To first order means to "first approximation". In this case the power of a plant (1000) is equated firm power (850). Presumably this relationship is complex and contains many terms. Let's say that the relationship is actually firm_power = 0.85*power + 0.03 * power^2. To first order would mean keeping only the first power term and neglecting the second squared term (presumably because its contribution to the total is small). – Martin Krzywinski Jan 27 '15 at 20:47

## 3 Answers

"unity" here means the number 1 and the values are the values of the ratio in the preceding sentence. Any sort of efficiency ratio typically has a value of between 0 and 1.

Incidentally, I would expect:

values for all plant are less than unity

to read

values for all plants are less than unity

• Thank you. Yes I guess the plural has often been forgotten by the author throughout the article!! – FrenchMan Jan 27 '15 at 19:42

"Less than unity" usually means "less than one". In this case, I suspect it means that the ratio from the previous sentence (firm power capability)/(rated output) is less than one, or in other words that:

(firm power capability)/(rated output) < 1

(firm power capability) < (rated output)

As others have pointed out, "unity" in this case means one. Hence, "less than unity" means less than one. In my experience, phrases like "non-unity" (meaning not one, similar to "non-zero") are very common in mathematics (or applied math, as is the case here). Outside of the mathematically-dominated sciences, "unity" never appears in this sense.