# Regarding N1 and N2, what does the “N” stand for?

I initially phrased this question in a comment to another question regarding what N1 and N2 mean, hoping it would be that sort of low-hanging fruit that is easily answerable and not worth a proper question in its own right. But then I starting searching and came up short.

This Yahoo Answers page has lots of guesses on it, from "nominal" to "Newell". (And we all now are reminded why nobody goes to that site for real answers.) Many other pages explain what N1 and N2 are, but not where the "N" part comes from.

I'm wondering if it might have its origin in German, as a lot of early developmental work on jet engines was done in Germany. Or was it simply an unused letter that fit?

• N stands for an unknown number, and since RPM is given as 1/min, the N is simply the number of revolutions per minute. Doing this is common in Germany; whether it originated in Germany is unknown to me. – Peter Kämpf May 13 '15 at 13:45

As far as I can tell, the N comes from the physics behind turbines in general, whether they be water pumps or wind turbines, a subset of mathematics called fluid dynamics. Many thanks to ROIMaison's answer for steering me in the right direction.

In Turbomachinery: Basic Theory and Applications, Second Edition, Earl Logan, Jr. provides a symbol reference list at the end of each chapter starting in chapter 2, defining $N$ as rotor speed, in units of rad/s; an angular change per unit time, and $N_s$ as the specific speed, a dimension-less quantity derived from a ratio of the flow and head coefficients.

N1 and N2 seem to be derived from both. Wikipedia mentions the speed as a percentage paradigm as a human factors consideration, though as of 5/14/2015 there are no references to support this. However, there may be a scientific basis behind this as well, since a change in N is proportional to the resultant change in airflow (i.e. thrust produced):

• I would say $N_C = \frac{N}{\sqrt{\frac{T}{T_{ISA}}}}$ is proportional to thrust, not $N$ itself (which is why those values/percentages are shown to the pilot). – JulianHzg May 14 '15 at 7:57
• i'm not suggesting (for example) a 10% increase in N means 10% more thrust. i'm saying that as one increases, so does the other. – Erich May 14 '15 at 10:31
• Ok, if all other variables stay the same, that's certainly true - but that doesn't mean that they are proportional. The great thing about $N_C$ is precisely that it is approximately proportional to thrust. – JulianHzg May 14 '15 at 12:14

Here at Tech ops, they say it comes from specific speed. However, it does not explain why the letter N was chosen, but perhaps this knowledge might help lead to an answer.

This source mentions:

N is the symbol for "specific speed". Specific speed is defined as "the speed of an ideal pump geometrically similar to the actual pump, which when running at this speed will raise a unit of volume, in a unit of time through a unit of head".

• interesting from the mcnally source... i'd never thought of it from an airflow standpoint. – Erich May 13 '15 at 23:04

For rotational speed, $n$ is a common symbol. While the English Wikipedia article uses $\omega_{cyc}$, I can find many English-language sites using the symbol. To be honest, $\omega_{cyc}$ is a really combersome symbol for something that is used as often as rotational speed is.

In German (see the corresponding Wikipedia article), it is definitely the standard way of representing rotational speed in revolutions per time unit (as already mentioned by Peter Kämpf above). The origin of this is probably harder to determine, but I imagine that it has something to do with the number of revolutions always being a natural number. After all, $n$ is the go-to symbol for any unit-free integer value in engineering and physics, in my experience.

The usage of the capital letter, which is inconsistent with this, is a little more dubious in my opinion. But I have a theory for that, too: The majority of all software working with the value has, for the last 50 years, probably been written in Fortran. Fortran variable names are, by convention, capitalized. So anyone working with the value or displaying it might have just adopted the name of the variable as the symbol for N1 and N2.

Any pre-Fortran occurence of the terms might disprove that theory.

• Fortran is more than 50 years old by now, and still used by Real Programmers! – Peter Kämpf May 13 '15 at 22:18
• Thanks, corrected the age. And yes, it's still used in many companies, if not in most, in the engine manufacturing industry. – JulianHzg May 14 '15 at 7:48
• Fortran by default isn't sensitive to case. – mins Feb 12 '16 at 15:48
• @mins: As described in the Fortran 77 standard, sections 3.1.1 and 3.2 (see fortran.com/F77_std/f77_std.html ), no lowercase letters are allowed in Fortran code with few exceptions. – JulianHzg Feb 13 '16 at 16:43
• @JulianHzg: Lowercase letters were usually converted into uppercase by the compiler. I think in F90 or F95, the compiler got an option to preserve the case to deal with external library names in C (for instance). Note that extensions to F77 existed to allow lowercase use in some cases, but the problem was also the punched cards didn't support lowercase characters. – mins Feb 13 '16 at 17:03