‰  NOW 35 WPM  ‰  TEXT IS FROM MARCH 2014 QST  PAGE 50‰

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 35 WPM TEXT  ‰  QST DE W1AW  ƒ