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rpm frequency unit?

ddenholm
6-Contributor

rpm frequency unit?

There is a built-in frequency unit "rpm" which I am assuming stands for "revolutions per minute".

But in MathCAD Prime 3.0 I am finding that 1 rpm is equal to 6.238/min or 0.105/sec.

But my understanding of revolutions per minute is that it shoud be equal to 1/min or 0.017/sec.

To put it differently, my feeling is that 60 rpm should be equal to 1/sec or 1 Hz but that is not what MCP 3.0 is calculating.

Am I missing something?

--Doug

6 REPLIES 6
Werner_E
24-Ruby IV
(To:ddenholm)

According to SI rpm is not a unit at all (cause revolution is not a unit).

Im Mathcad and Prime rpm correspond to angular speed and is defined as 1rpm:=2*pi/(60 sec), that is radian per minute.

There is a similar confusion with Frequency. Here Mathcad copes by providing two different Frequency units:

1Hz:=1/sec and 1Hza=(2*pi)/sec (angular frequency).

ddenholm
6-Contributor
(To:Werner_E)

Thanks for the explanation. I guess I was "missing something."

But it does seem an obvious point of confusion since a lot of folks (like me ) will assume that the "r" in rpm will mean revolution.

The MCP unit set contains lots of non-SI units (e.g. BTU, lbs, hp etc.) so the user is entitled to think that rpm as revolutions per minute (as in how many times a minute a shaft rotates through 360 degrees) might be available.

Also, if you hover the cursor over "rpm" in the Units/Frequence selection dropdown, the help tip says "revs per minute" not "radians per minute."

By fiddling around with it, I figured out that 1 "rev" is equal to 360 degrees or 6.283 radians. So MCP's "rpm" can be interpreted as either rad per minute or revs per minute but rev's is not "revolution": in the sense I would use it... MCP rev is a unit of angle equivalent to 360 degrees.

But in the "rpm" is listed under Units/Frequency.. all the other frequency units are inverse time except for the "Hza" unit you mention. My definition of rpm (e.g. number of full rotation per minute) is inverse time.

If you can clarify that for me, I would appreciate it.

Thanks again,

--Doug

Werner_E
24-Ruby IV
(To:ddenholm)

Douglas Denholm wrote:

Thanks for the explanation. I guess I was "missing something."

But it does seem an obvious point of confusion since a lot of folks (like me ) will assume that the "r" in rpm will mean revolution.

Thats indeed what it does. rpm stand for revolutions per minute and the dimension is indeed time^-1, because radians per se are unitless. The difference to the number of revolutions you (and many others) have in mind ist just a constant factor (2*pi).

The problem is the term "revolution", which according to Wikipedia is "a semantic annotation rather than a unit". The equivalent SI unit of rpm is 1/sec anyway, but in Prime its 1 rpm = (2*pi) *1/60*1/sec.

Also, if you hover the cursor over "rpm" in the Units/Frequence selection dropdown, the help tip says "revs per minute" not "radians per minute."

Yes, and thats true. As 1 rad per min would be the rpm you have in mind, but Primes rpm is 2*pi*rad per min.

Fred gave you some examples where it makes sense that rpm is defined as it is, but of course we could vote for introducing two different rpm's (rpm, rpma) like Hz and Hza. As radians are unitless (or you may call it a pseudo unit) all four could be calles units of frequency and could be converted to 1/sec.

PhilipOakley
5-Regular Member
(To:ddenholm)

Which is of course why we need to continue the 'fight' (struggle) to get Angle recognized as a an allowable 'unit' (it's a Dimension actually) both via SI and the ISO docs, and more importantly by MathCAD/PTC.

If they can add "Currency" as a Dimension (That's not SI is it !), then we can have some additional "semantic annotation" markers that have the same properties as regular units/dimensions. (revs to radians, would be like inches to centimeters).

There are many other cases where the inclusion of a few additional semantic markers would help avoid computational errors, if only they were provided. (e.g. where someone is doing Dollar - Euro block trading and wahts teh two currencies flagged separately, but still have scaling between Canadian dollars and US dollars etc within NAFTA, and similar within the EU trade area)

I work in Electro Optics where performance measures can be in Cycles per milliRadian, so that's unitless/unitless which usually simplifies to 'meaningless' SI..gh 😉

Philip

PS sorry for not using proper British English zpelling.

Werner's explanation is correct. The reason for the ambiguity is so that when you multiply torque (in Newton meters,or any equivalent unit set time shaft speed in rpm (or Hza), you get power properly in watts, kilowatts, or horsepower. You can also multiply rpm times radius to get tip speed correctly. Thes multiplications work just as written, without requiring the insertion of 2 pi.

There are two types of dashboards of cars:

  • with rpm as radian per min for Mathcad users
  • with rpm as revolution per min for others normal people.

rpm.png

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