Here's a quote from Kraus' "Antennas For All Applications"
3rd Edition, page 177, section 6-4:

"The Thin Linear Antenna - In this section
expressions for the far-field patterns of thin linear
antennas will be developed. It is assumed that the antennas
are symmetrically fed at the center by a balanced two-wire
transmission line. The antennas may be of any length, but
it is assumed that the current distribution is SINUSOIDAL.
Current-distribution measurements indicate that this is a GOOD
ASSUMPTION provided that the antenna is thin, i.e., when the
conductor diameter is less than, say, lamda/100. Thus, the
sinusoidal current distribution approximates the natural
distribution on thin antennas." Emphasis mine.

So Kraus gives us permission to treat the currents on a
dipole as sinusoidal as long as the diameter of the element
is less than 4 inches on 30 MHz or less than 40 inches on
3 MHz. So virtually all HF dipoles are thin-wire antennas.

And since the current distribution is assumed sinusoidal, the
arc-cosine function will yield the number of degrees a point
is away from a current maximum point, e.g. the phase information
for the forward traveling wave.
--
73, Cecil, http://www.qsl.net/w5dxp

"Cecil Moore" wrote in message
.com...
Here's a quote from Kraus' "Antennas For All Applications"
3rd Edition, page 177, section 6-4:

"The Thin Linear Antenna - In this section
expressions for the far-field patterns of thin linear
antennas will be developed. It is assumed that the antennas
are symmetrically fed at the center by a balanced two-wire
transmission line. The antennas may be of any length, but
it is assumed that the current distribution is SINUSOIDAL.
Current-distribution measurements indicate that this is a GOOD
ASSUMPTION provided that the antenna is thin, i.e., when the
conductor diameter is less than, say, lamda/100. Thus, the
sinusoidal current distribution approximates the natural
distribution on thin antennas." Emphasis mine.

So Kraus gives us permission to treat the currents on a
dipole as sinusoidal as long as the diameter of the element
is less than 4 inches on 30 MHz or less than 40 inches on
3 MHz. So virtually all HF dipoles are thin-wire antennas.

And since the current distribution is assumed sinusoidal, the
arc-cosine function will yield the number of degrees a point
is away from a current maximum point, e.g. the phase information
for the forward traveling wave.
--
73, Cecil, http://www.qsl.net/w5dxp

i believe in this description he is refering to the current distribution of
the standing wave. that is, the classical sine curve that shows a maximum
at the feedpoint of the 1/2 wave dipole and zeros at the ends. in this case
the shape of the curve is a function of the sin or cos of the distance from
the feedpoint divided by the leg length times pi/2 or 90 degrees, which ever
you prefer.

however, that is not the phase of the forward traveling wave, that is the
envelope of the sum of the forward and reverse waves... or the standing
wave. the phase of a traveling wave is added to the omega*t value in the
sin(wt+p) representation, but in a distributed system must be referenced not
only to a time but also the location. or in simpler terms you can reference
it to the time that the current crosses zero at a given point in the forward
traveling wave. to get rid of the time dependence you must add the foward
and reflected waves to get the standing wave, then you can make the
classical sunusoidal dipole current plot.

Dave wrote:
i believe in this description he is refering to the current distribution of
the standing wave. that is, the classical sine curve that shows a maximum
at the feedpoint of the 1/2 wave dipole and zeros at the ends. in this case
the shape of the curve is a function of the sin or cos of the distance from
the feedpoint divided by the leg length times pi/2 or 90 degrees, which ever
you prefer.

Exactly, and that is the number of degrees by which the forward
traveling wave lags the source wave and therefore is the phase
angle of the forward traveling wave reference to the source wave.

however, that is not the phase of the forward traveling wave, ...

Of course it is, referenced to a source phase angle of zero.
Assuming the source phase reference is zero degrees, the phase
of the forward traveling wave is related to the distance from
the source (modified by the velocity factor). That's just simple
physics.

Given the source current is 1.0 amps at zero degrees, the
standing wave current 1/2 way to the end of the antenna element
will be 0.707 amps at zero degrees. Arc-cos(0.707) = -45 degrees.
That's the phase angle of the forward current at that point since
it lags the source current. Hint: There are very close to 90 degrees
of antenna between the source and the end of a 1/2WL dipole since
it is 1/4 wavelength. Remember 360/4 = 90 degrees.
--
73, Cecil http://www.qsl.net/w5dxp