Radians per second to Hertz conversion incorrect

[sdonnan]

> 6rad/s -> hertz

    6Hz

Expected result: 0.9549Hz

[itdaniher]

Not even a sig figs issue:

> 6.01 radians / second -> hertz
6.01Hz

[itdaniher]

units does the same thing:

You have: 6 radians per second
You want: hz
        * 6
        / 0.16666667
You have: 6 radians
You want:
        Definition: 6 radian
You have: radians
You want:
        Definition: radian = 1 radian

Radians is apparently a base unit as far as insect and units is concerned. We both expected radians as 2pi, but this could also be expressed in degrees. No idea what's technically correct - if insect did base unit decomposition as units does, it would be fairly trivial for an end user to observe that rad resolves to a base unit, rather than a constant of 2pi (tau) or a degrees angle conversion.

Also, your test case is semantically ambiguous, as 'rad' in the context of dimensional analysis is a depreciated unit of measure proportional to (radiation) energy in joules per kilogram:

You have: 1 rad
You want: 0.01 J / kg
        * 1

edit: markdown

[itdaniher]

Even more interestingly - gnu units (and insect) are technically correct here, since 1995 "radian" is a unitless "SI-derived" parameter, so the shortcut taken by insect seems to be radian = 1.

Current behavior might violate the principle of least astonishment, but this doesn't seem to be a bug per-se. Obviously, interesting observation nevertheless!

[sdonnan]

Thanks for looking into this! I agree the behavior is definitely unexpected and can be explained by your interpretation of the radian unit definition.

Here is another surprising example which is related:

> 360 degrees/sec -> Hz
  6.28319Hz

which doesn't really seem to make sense (I'd expect it to be 1Hz), but can be explained by the radian behavior.

As a user that does a lot of conversions with radians it would be more useful if the conventional radian conversions worked as expected. However, I will have to do some more digging to convince myself one way or the other is technically correct based on the unit definitions.

[sdonnan]

It seems like one would need to assume that any quantity measured in radians per second is an angular velocity in order to invoke the expected conversion (2 pi radians / s = 1 Hz). Pure dimensional analysis fails because (as you mentioned before) they technically have the same units (1/s).

So perhaps this should be a feature request for the calculator to abandon what I assume is a nice and tidy dimensional analysis approach to invoke a useful conversion in this corner case.

[sharkdp]

I would argue that the current behavior is not only technically correct, but also the expected behavior 😄.

The confusing part is that rotations per second and angle per second (= rotational speed / angular velocity) have the same dimension (1/time), and can both be expressed in Hz. The reason is that both number of rotations and angle are dimensionless quantities.

If I am interpreting correctly, you are interested in rotations per second. If something rotates by 720° in 1s, you want the answer to be 2Hz, because it rotates twice per second (correct me if I'm wrong). On the other hand, the quantities you entered (6rad / s or 360° / s) are expressed in angle per second.

If you want rotations per second, you would have to compute the number of rotations first (720° / 360° = 2) and then divide by the time (1s):

> (720°/360°)/s -> Hz
2Hz

Same thing in radians: In your first example, you would need to compute the number of rotations (6 rad / 2pi rad = 0.95493) and then divide by 1s:

> (6 rad / 2pi rad) / s -> Hz
0.95493Hz

Even more interestingly - gnu units (and insect) are technically correct here, since 1995 "radian" is a unitless "SI-derived" parameter, so the shortcut taken by insect seems to be radian = 1.

Yes, exactly: https://en.wikipedia.org/wiki/SI_derived_unit#Derived_units_with_special_names

360° = 2π rad = 2π

[sharkdp]

@sdonnan Can this be closed?