On Tue, 19 Aug 2003 06:07:19 -0400, wrote:

How do you know when the reduced units of one computation mean the
same thing as another?

They are ALWAYS fungible. You can certainly munge up operations to
prove otherwise, and it is easy to do with some really long chain of
computations.

I would suggest you investigate any of the several really good
Mathematics programs, one being Mathcad which offers a huge repository
of such Units tools that it uses to the enormous and enthusiastic
response by engineers and scientists. There greatest asset is in
allowing, you, the user, to enter your measurement in whatever Units
your profession is comfortable with, and marry them into a novel
situation at the interface to another discipline. How much horse
power generator is needed to supply electrical power that is required
to move a speaker cone how many inches to compress air to what sound
pressure level for it to be just barely discernable to the average
listener? That standard could be described as the force necessary to
move the eardrum the same distance as the diameter of an Hydrogen
Atom.


An example:
The reduced units of modulus of elasticity (in/in/psi - psi) is
the same as the units for stress (psi) and yet modulus of elasticity
is clearly not stress. And in this case, the unreduced units are
much more descriptive than the reduced units. Reducing discards
information.

The Elasticity Modulus is described in kg/mm² which is not quite MKS,
but performing the necessary operation to make it so does not remove
any information whatever. If we stick with electronics and discuss
the stress mechanics of piezos (crystals), then stress can be
described in terms of
(volts/meter) / (newtons/meter²)

On the other hand, Torque (Newton*metres) when multiplied by
Radians (metre/metre) does give Energy (N*m*m/m - N*m), but only
after reduction.

This is negative evidence? It is more a clouded argument.

And for sure, Torque (N*m) is not the same as
Energy (N*m).

You are confusing Work and Rotational Statics as being different.
Can you distinguish between Kinetic Energy and Potential Energy
described in mechanical units? If so, both are used to describe the
complete Work equation:
(KE2 - KE1) + (PE2 - PE1) = 0

So sometimes it is appropriate to say the reduced results are the
same and some times it is not. Is there a way to know when it is
legal?

Strictly speaking from the point of legality, it is demanded of
Professional Engineers by the National Institutes of Science and
Technology (what was called the National Bureau of Standards or NBS
years ago).

This means that ANY P.E. that describes a physical relation that does
not conform to these scientific concepts, and damage results to that
Professional Engineer's customer, then that P.E. is liable in a court
of law. This form of legality is the whole point of being P.E.s and
the government making the demand that P.E.s be part of describing
engineering codes and performing design review.

Anyone here who has put up a tower has had to jump through this hoop.
One of their principle concerns is found in the CM or Center of
Moment. The employment of Units transformation and reduction is part
and parcel to their activity (How tall? Length. How heavy? Mass and
the constant of Gravity).

The ONLY reason the city, or county insists on this report is to have
someone take the insurance hit if there is an error in meeting code.
Was your tower too tall for the weight of that long lever arm (your
antenna boom and elements) that also created a torque? Did it snap
with wind load? Did the guys snap through poor tensioning? Every one
of these uses Units that eventually boil down to one of the
tower/beam/guy specifications expressed in identical Units. There is
no other way for anyone to put their name to a report qualifying your
tower otherwise - why would they want to jack up their malpractice
payments? And it would be their insurance, not the city's if your
tower fell on a citizen and their heirs sued because of the city's
permission to you to erect it. This is called negligence and is why
your homeowner's insurance would walk away from you for a tower
collapse where the tower was not inspected to code.

If the P.E. met the standards of transforming between various systems
and observed the Physical Constants defined by NIST, then the P.E. is
NOT liable. If the P.E. is not liable, neither is the city/county.
If the P.E. and government are not liable, you have a problem.


What rules have you used to conclude that reducing V/m/A/m to V/A
is appropriate?

...Keith

Hi Keith,

You probably have no concern for the monolog about P.E.s or you put it
behind you long ago. Or so you and others might presume. That's fine
and this divergence off into mechanics may help some see the relations
but to answer your last question and keep it within the context of the
subject line, we should look at another reference that is less remote
than NIST and closer to antennas:
"Fields and Waves in Communication Electronics," Ramo, et al.

From page 3 (yes, pretty up front):

"Various systems of units have been used, but hat to be used in
this text is the International System (SI for the equivalent in
French) introduced by Giorgi in 1901. This is the
meter-kilogram-second (mks) system, but the great advantage
is that electric quantities are in the units actually measured:
coulombs, volts, amperes, etc."

This reference proceeds to describe those Physical Constants and their
relations that define Permittivity that I have already fully revealed
in a recent posting. If we were to proceed to page 71:

"The quantity known as the magnetic field vector or magnetic
field intensity is denoted H [sound familiar folks?- rwc] and
is related to the vector B define by the force law (2) through
a constant of the medium known as the permeability, µ:
B = µH
...
"In SI units, force is in newtons (N), Current is in amperes (A)
and magnetic flux density B is in tesla (T), which is weber per
meter squared or volt second per meter squared and is 10^4
times the common cgs unit, gauss. Magnetic field H
is in amperes per meter and µ is in henrys per meter. ...
The value for µ for free space is
µ0 = 4 · pi · 10^-7 · H/m"

So, there you have it. Absolutely identical to my other posts. The
RF engineering community's usage of free space Z is in full compliance
with the standards established and maintained by NIST. Both these
sources and standards are employed by commercial engineers and
Professional Engineers alike. It makes no sense to do otherwise
unless you want to start your own system of measurement that allows a
CFA to be 110% efficient. We get many efficiency claims that can ONLY
be judged through these associations described.

The chain of relationships proves that the "ohms" described by the Z
of free space are identical to the "ohms" used for ANY electrical
measurement, among which are the resistance determination of an
antenna (for any feed), or the resistance presented by a carbon
composition resistor.

73's
Richard Clark, KB7QHC