‰  NOW 40 WPM  ‰  TEXT IS FROM MARCH 2014 QST  PAGE 50‰
THAT USE THE LM3914 DOT/ BAR DRIVER, SUCH AS QUALITYKITS MODEL FK939, BUT
THEY HAVE THE SAME PROBLEM, WHICH IS EXCESSIVE CURRENT DRAIN.  ANOTHER VERY
WELL THOUGHT OUT KIT IS THE BVM1 FROM CIRKITS.  COM.  HERE, THE DESIGNER
PULSES THE CIRCUIT ON FOR A LOW DUTY CYCLE, RESULTING IN AN AVERAGE DRAIN
OF ONLY 6 TO 7 MA.  I HAVE ONE OF THESE, AND WAS ABLE TO REDUCE THE AVERAGE
CURRENT DRAIN TO ABOUT 5 MA BY EXTENDING THE DUTY CYCLE.  WHEN ALL IS SAID
AND DONE, HOWEVER, THE SIMPLEST APPROACH

EDITION, REPEATED IN THE FEBRUARY 2013 ARTICLE.  IN THAT EXAMPLE, THE
WEIGHT OF THE WIRE W IS GIVEN AS 0R011 POUNDS PER FOOT AND THE SPAN S,
BEING THE TOTAL DISTANCE BETWEEN SUPPORTS, WOULD BE 420 FEET.  NOTE THAT
THE CURRENT EDITION OF THE ARRL ANTENNA BOOK DEFINES A HALF SPAN AS HALF
THE HORIZONTAL DISTANCE BETWEEN SUPPORTS, WHICH WAS 210 FEET.  THIS IS
CONSISTENT WITH THE NOMOGRAPH.  NOTE 2 OF THE NOMOGRAPH INSTRUCTIONS IN THE
FEBRUARY 2013 ARTICLE ALSO DEFINES SPAN AS ONE HALF THE DISTANCE BETWEEN
SUPPORTS.  FOR THE ABOVE EQUATIONS, HOWEVER, SPAN IS DEFINED AS THE TOTAL
HORIZONTAL DISTANCE BETWEEN THE SUPPORTS.  THE WIRE TENSION T USED IN THE
EXAMPLE IS 50 POUNDS.  SUBSTITUTING W, S, AND T INTO EQUATION 1, THE
COMPUTED RESULT FOR SAG IS 4R852 FEET.  USING THE MUCH MORE CONVENIENT
EQUATION 2, THE RESULT IS 4R851 FEET.  THE SIMPLER FORMULA IS CERTAINLY
ADEQUATE.  NOTE THAT THE RESULT GIVEN BY THE NOMOGRAPH, WHICH GOES BACK TO
THE JANUARY 1966 ARTICLE IN QST, IS 4R7 FEET.  THIS IS AFTER SORTING OUT
AMBIGUITIES IN THE DEFINITION OF SPAN.  IT IS CLEARLY A SUFFICIENTLY
ACCURATE RESULT, AND THE SMALL DIFFERENCE REFLECTS THE INEVITABLE

WHEN THIS NOMOGRAPH WAS GENERATED IN 1966, THE POCKET ELECTRONIC CALCULATOR
HAD BARELY BEEN INVENTED AND FEW, IF ANY, RADIO AMATEURS POSSESSED ONE.
TODAY, MOST RADIO AMATEURS OWN COMPUTERS AND PERHAPS QUITE SOPHISTICATED
SCIENTIFIC CALCULATORS.  THE EQUATIONS TO CALCULATE WIRE SAG ARE FAIRLY
TRIVIAL BY TODAYS STANDARDS, AND NOW IT IS EASY TO USE A SIMPLE CALCULATOR
TO DETERMINE THE WIRE SAG.  THE EQUATION DESCRIBING THE CATENARY THE CURVE
OF A ROPE OR CHAIN HELD HORIZONTALLY BETWEEN TWO SUPPORTS WAS FIRST SOLVED
IN 1691 BY JOHANN BERNOULLI AND OTHERS.  THE EQUATION IS NOW FOUND IN MANY
ENGINEERING AND MATHEMATICAL TEXT BOOKS.  ONE FORM OF THE SOLUTION IS GIVEN
BY EQUATION 1.  WHERE T IS THE TENSION IN THE WIRE IN POUNDS, W IS THE
WEIGHT OF THE WIRE IN POUNDS PER FOOT, AND S IS THE SPAN OF THE WIRE, HERE
DEFINED AS THE TOTAL HORIZONTAL DISTANCE IN FEET BETWEEN THE TWO SUPPORTS
OF THE WIRE.  THE TERM COSH IS THE HYPERBOLIC COSINE FUNCTION.  SOME
SCIENTIFIC CALCULATORS INCLUDE HYPERBOLIC TRIGONOMETRY FUNCTIONS AND SO CAN
COMPUTE THIS DIRECTLY, BUT THERE IS A MUCH SIMPLER APPROXIMATION THAT IS
VALID IN ALL CASES LIKELY TO BE OF INTEREST TO AMATEUR RADIO OPERATORS.
EQUATION 2 IS EXACTLY THE ONE GIVEN IN EDMUND LAPORTS RADIO ANTENNA
ENGINEERING, IN CHAPTER 4, WIRE STRINGING.  I WILL USE THE EXAMPLE FROM THE
ORIGINAL QST ARTICLE AND GIVEN ON PAGE 25 3 IN THE ARRL ANTENNA BOOK 22ND
‰  END OF 40 WPM TEXT  ‰  QST DE W1AW  ƒ