Re: [Phys-l] backwards units : entrenched usage

[John Denker <jsd@av8n.com>]

On 05/19/2008 06:59 AM, Jeff Radtke wrote:

> Writing as an engineer, I suspect that the nameplate is the way it is  
> to save on resources used to convey the relevant specifications ...

Well, that may explain something about the nameplate ... but I
didn't want the thread to be about nameplates.  I was hoping the
thread would be about backwards units.  The nameplate is only
one illustration among many.

Here's another illustration, taken from page 13 of _Marine Engineering_ 
by Reno C. King Jr. (Prentice-Hall, 1948). 

         C = 5/9 (F - 32)
         F = 9/5 C + 32

This is manifestly an example of what I am talking about, using 
the unit of measurement as a stand-in for the thing being measured.  
I have argued
  http://www.av8n.com/physics/units.htm
that this is a Bad Idea and that it is diametrically inconsistent 
with modern notions of unit-analysis.

======================

Here's a trickier example,from page 190 of _Marine Engineering_
For a steam engine:

            P L A N
  IHP  =  -----------
            33,000

I wish to make two different points about this.  Please let's
not confuse the two points.

1) First, I call attention to the LHS, which is "indicated horsepower".
 This LHS is another an example of using the unit of measurement as a
 stand-in for the thing being measured.  

2) Secondly, let us turn to the RHS.  The book says:
  average pressure = P pounds per square inch
  stroke = L ft.
  area = A sq ft.
  there are N power strokes per minute

which is interesting because in some sense those four statements are
dimensionally correct, if we consider P, L, A, and N to be "pure numbers"
(unitless and dimensionless) numbers standing in front of explicit units.

This is, however, still not recommended.  Even though it is not wrong
in any deep sense, it is not recommended.  The problem is that the
numerical value of (say) A is tied to the units in use.

In contrast, modern practice is to do algebra using variables that 
have not had units factored out, for example
  yes:  A = area (in *whatever* units)
  yes:  area = A (in *whatever* units)
  no:   area = A sq. ft.

At this point you may be wondering about an interesting issue, namely 
that when doing a practical calculation it has always been necessary 
(with rare, recent exceptions) to calculate using pure numbers.  
  (Nowadays you can find software that will keep track of the units 
  while doing algebra, but this was not the case in 1948, and is still 
  quite rare today, and in particular not widely available in the physics 
  classroom.)

So you could argue that a formula involving pure numbers has value for
practical computations.

That is a valid argument, but there is a stronger counterargument.  The
need for pure numbers can be accommodated within the formalism of modern 
unit analysis.  One could write:

                            (P/psi) (L/ft) (A/ft^2) (N/spm)
  indicated power/HP   =  -----------------------------------
                                         33,000

(where spm means power strokes per minute).

which has the advantage of being absolutely true no matter what units the
variables are measured in.  If L is measured in some units other than ft,
then the problem is obvious and more importantly _the solution is obvious_ 
if you follow the factor-label method.