Re: Being careful with dimensions

[brian whatcott <inet@INTELLISYS.NET>]

(a divergent meander)

At 09:22 9/22/99 -0400, Michael Edmiston wrote:
> I think it is amazing that the unit vector thread has produced the
> divergent views it has

> ... if you routinely write
> F = (2i - 3j) N, would you also write F = (3.61 at -56.3-degrees)
> newtons?
>
> I would not typically write that.  I would write F = 3.61 N at -56.3
> degrees.
>
> Michael D. Edmiston

Michael's angular specification reminds me of the varying presumptions
as to directionality.
 I don't suppose there was anyone here who did not imagine the
0 degree direction as being 'rightwards' or 'Eastwards' or in the
direction of increasing 'i', and increasing counterclockwise.

 But the compass has angle increasing clockwise from North,
and astronomy can sometimes offer angles progressing counterclockwise
from South.

   This comes to mind because my attention was caught by the innocent
enquiry of an Australian engineer, who asked (on a newsgroup) for a
compact explicit expression for the compass direction of Sunrise at
any latitude at any time of year.

   It happens that nautical almanacs can readily provide an expression
for 'amplitude' given lat, lon, time of day and declination
but the declination and time of day inputs lead to the requirement for
computing declination which calls for an aproximation.

   Amplitude is the difference in angle between the naive expectation
 (due East) and the actual angle. And it turns out that
dawn's sunrise bearing varies; in some places as widely as between due South
and due North. And of course, at other places and times, dawn and dusk
do not occur.



brian whatcott <inet@intellisys.net>
Altus OK