Design of a vertical broadcasting tower

Description

For the design of a vertical broadcasting tower, radio engineer Ann Tenor wants to find the angle from the tower at which the relative field intensity is most negative. The relative intensity created by the tower is given by:
       cos(2πhθ) - cos(2πh)
   E = ————————————————————
        (1 - cos(2πh)sinθ

Where E is the relative field intensity, h is the antenna height in wavelengths, and θ is the angle from vertical in radians. The height is 0.6 wavelengths for her design. The desired angle is one at which the derivative of the intensity with respect to θ is zero.
To save program memory space and execution time, store the following constants in registers and recall them as needed:

r0 = 2πh and is stored in register R0 ,
r1 = cos(2πh) and is stored in register R1 ,
r2 = 1/(1 − cos(2πh)) and is stored in register R2,

The derivative of the intensity E with respect to the angle θ is given by
    dE                        cos(r0 cosθ)-r1
    —— = r2[r0 sin(r0 cosθ) - ———————————————]
                              sinθ tanθ

In Radians mode, calculate and store the three constants.
g RAD
2 g π ×
.6 × STO 0
COS STO 1
CHS 1 +
1/x STO 2

The relative field intensity is maximum at an angle of 90° (perpendicular to the tower). To find the minimum, use angles closer to zero as initial estimates, such as the radian equivalents of 10° and 60°.

10 f →RAD
60 f →RAD
f SOLVE 0
R↓ R↓
g R↑ g R↑
g →DEG

The relative field intensity is most negative at an angle of 28.0680° from vertical.

Program Resources

Labels

Name Description
 0 Main program

Storage Registers

Name Description
 0 2πh
 1 cos(2πh)
 2 1/[1 − cos(2πh)]

Program

Line Display Key Sequence Line Display Key Sequence
000 013 10 ÷
001 42,21, 0 f LBL 0 014 16 CHS
002 24 COS 015 34 x↔y
003 45 0 RCL 0 016 24 COS
004 20 × 017 45 0 RCL 0
005 24 COS 018 20 ×
006 45 1 RCL 1 019 23 SIN
007 30 020 45 0 RCL 0
008 34 x↔y 021 20 ×
009 23 SIN 022 40 +
010 10 ÷ 023 45 2 RCL 2
011 34 x↔y 024 20 ×
012 25 TAN 025 43 32 g RTN