No Frank I was careless.
When you are determining the area under a curve, the curve has an
equation
When the graph is roughly drawn out you draw a narrow vertical strip
that represents dy/dx
That strip has no specific thickness as it represents a vanishingly
thin strip.
You appear to be confused with the defininition of the integral. You
simply integrate the function over the desired range, and should not be
concerned with irrelevant concepts, such as strip widths.
If the area represented a cross section of a radiator the thickness of
that strip is then a problem.
No such strip exists in integration.
As a radiator dx could represent the skin depth or it could represent
the distance from the surface to the center line and thus the cross
Not so; "dx" simply refers to the independant variable to be integrated.
Note the first example of a "Reimann integral" at:
http://mathworld.wolfram.com/Integral.html
section would not be homogenous, same density etc
The problem then becomes what is the true skin depth density in
relation to the inner core which allows for the application of the
material resistance.
To determine the RF resistance of a conductor requires a
solution involving "Kelvin/Thompson" functions; which are
modified Bessel functions with a complex argument. See the
following for details:
http://www.st-andrews.ac.uk/~www_pa/...ect/page1.html
Also:
http://mathworld.wolfram.com/Bei.html
http://mathworld.wolfram.com/Ber.html
Now I see skin depth as the point that eddy current becomes a
contained current circuit without discontinuity. The books define skin
depth as a relation of decay which is not how I see things so we have
a difference in proving things one way or the other.
Ansoft's (
www.ansoft.com) "Maxwell" is a "Finite Element Modeling"
(FEM) program which, among other things, can accurately produce
a graphical representation of the current distribution in a cylindrical
conductor. See examples at:
http://www3.telus.net/nighttrainexpr...in%20depth.htm
These graphs are reproduced from an article in the November/December
issue of QEX magazine, pp20 - 29, by Rudy Severns, N6LF.
I then added
aunconnected problem by drifting towards integration and limits ie
travelling back from integration to the differation format which was a
silly mistake for which I have been already reprimanded by the nets
monitor who looks out for those things rather than the technical
content.
Sorry, I don't mean to be insulting, but I am baffled how you can
have such problems with elementary math; yet argue about
concepts taught in a third year electrical engineering degree
program with prerequisites in advanced calculus, partial differential
equations, and more.
I really believe that the answer lays on Maxwells laws and not with
the approximation supplied by Uda/Yagi.
I agree, but Yagi and Uda simply build experimental models. Which
is about all anybody could do in those days.
Computor programs say the same thing via the tipping radiator which
all deny so there is no possible solution to be arrived at that
satisfies all unless somebody provides answers that reflect Maxwell
and not Yagi/Uda rather than "I said so" as every thing is known and
is in the books that I own. At no time have I taken your postings as
mocking or otherwise insincere as you are the only person who used a
antenna program in conjuction with my beliefs which shows radiators as
not being parallel with the surface of the Earth where others refused
to check in any way.
Many hams interested in low frequency DX use sloping (monopole) radiators,
which gives a slight improvement in low angle radiation.
As I stated in an earlier posting one must graph
the current levels at the top of a radiator by superimposing both
graphs where both the leading and trailing currents arrive at the end
( time separation of half a period)so that current direction can be
determined since in one case there is no eddy current and the other
case does have eddy currents( flow resistance) on the surface which
thus determines current flow direction at each point.
Sorry, but you lost me again.
73,
Frank