Re: Expressing physical units (Was: Reprise: 'in out' parameters for functions)

["Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de>]

Russ wrote:

> "Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de> wrote in message
> news:<c5dr33$gkic$3@ID-77047.news.uni-berlin.de>...
>> Russ wrote:
>> 
>> > By the way, I work in the field of air traffic management (ATM), and
>> > I'd really like to see a practical way to guarantee units consistency.
>> > The general mks system is inappropriate for ATM. The traditional units
>> > for ATM are nautical miles (nmi) for horizontal length, and feet (ft)
>> > for altitude. That won't change in our lifetimes -- and probably
>> > never. As for time, it can be in seconds, minutes, or hours.
>> > Horizontal speed in usually given in terms of knots (kn), which is
>> > nmi/hr, but altitude rate is usually given in terms of ft/min. Heading
>> > is normally given in degrees.
>> > 
>> > In my experience, the most common units problem is confusion between
>> > degrees and radians. Radians are preferable for use inside programs,
>> > but degrees are preferable for I/O. This problem really needs to be
>> > licked once and for all.
>> 
>> It does not differ from [m] vs. [ft]. The dimension of radian is [1] =
>> m**0*A**0*s**0... The dimension of degree is [Pi/180]. No magic here.
>> More difficult is Celsius degree vs. K, which AFAIK cannot be solved
>> using C++ templates.
> 
> I know it can be done in C++, but I thought we were talking about doing it
> in Ada.
> 
> By the way, what the heck is "m**0*A**0*s**0..."?

Any unit system is built upon some standard set of measures (base units).
This set is pretty arbitrary from a physics point of view, but in SI it was
selected to be m, A, s, kg, K, cd, mol. A dimension of any derived unit is
then a product of powers of the base units. For example, the dimension of
acceleration is m*s**(-2). When all powers are 0, we have a "dimensionless"
unit, like radian is.

Now to templates and C++. You are wrong thinking that units can be properly
done in C++. What indeed can be, is a tiny part of what is really
necessary. Consider the following issues:

1. Shifted units, like Celsius degree.
2. Dealing with units unknown at compile time. How would you communicate
with a data base, or develop a gauge widget, or write a unit calculator?
How to write a unit I/O package?
3. Dealing with multiple unit systems. The C++ solution actually works in
SI. It means that a measure in [ft] has to be converted to [m]. It is OK as
long as:
3.a. There is no range problems. In an emedded system one could use a fixed
arithmetics with would overflow if the distance is measured in [m], but
work fine for [km].
3.b. One can ignore inevitable precission loss caused by unit conversions.
This might be critical for some applications.
5. How to handle logarithmic units and other non-linear scales?
6. Container problem. Surely a vector, matrix etc of dimensioned values
should have a dimension. Possibly it could be handled by templates, but I
am afraid it would not be so easy.
7. Any generic (template) solution would make everything based upon it also
generic.

-- 
Regards,
Dmitry A. Kazakov
www.dmitry-kazakov.de