FORCE EXERTED ON A DRIVE COIL DUE TO NEIGHBORING DRIVE COILS

During the passage of a bucket coil, a sinusoidal current flow described by the equation

will appear in each drive coil. The angular frequency,
of the flow will be
2/period, where the period
equals 4* _{m}*
/

Coil no.1 | |

Coil no.2 | |

Coil no.3 | </</TD> |

Coil no.4 | |

Coil no.5 | |

Coil no.6 | |

Coil no.7 |

The force experienced by any two active coils will be given by
the product of the instantaneous current in each coil multiplied by
the gradient of their mutual inductance (*dM*/*dx*) at
the distance of their separation:

This force will be attractive between coils with currents of the same sign, and repulsive between coil currents of opposite sign.

Refer again to figure 1 and
consider the forces acting on the reference coil no. 4. During its
first quarter-cycle (-
*t* - /2),
coil no.4 will interact repulsively with coil no. 1, repulsively
with coil no. 2, and attractively with coil no. 3. At exactly
*t* = - /2, a weakly felt coil no. 1(a
distance 3* _{m}* away) will turn off and a much
closer coil (coil no. 5 only a distance

The program listed below is designed to calculate the reaction force on a drive coil due to all other active drive coils in its neighborhood as a function of the time from which that coil was turned on. It is written to be run on a Hewlett-Packard HP-67/HP-97 calculator.

It is assumed that bucket velocity may be taken as constant during the passage of the bucket through any four successive drive coils (a distance of only a few centimeters). Hence the angular frequency will be constant.

The program is initialized by the input of three pieces of
information: key in the *dM*/*dx* between drive coils
separated by a distance _{m}; ENTER; key in the _{m}at a distance of
2_{m}; ENTER;
key in the *dM*/*dx* for a distance of 3_{m} (ref.4). Initiate the program by pressing the
button labeled [A]. Program execution will begin. Very quickly, the
program will pause for a second and the display will show "1.0."
During this pause, key in the maximum drive coil current. (this
value will default to 1.0 of no entry is made; in this case, all
final answers will actually be
*F*/*i _{a}i_{b}*.)

The program will then loop, displaying a zero for a second and
then blurring for a second. At any instant when the machine has
paused with a zero showing, key in a value of *t* and the reaction force of the drive
coil at that instant will be calculated. The program accepts values
of *t* expressed in
degrees rather than radians. The range of values
-180^{o} *t*
180^{o}.

Once a force has been calculated, the answer, (in Newtons) is
displayed for 10 sec. the program then branches to the zero/blur
input mode, ready to have the next value of *t* keyed in.

001 | *LBLA | 034 | RCL5 | 067 | x |

002 | DEG | 035 | 9 | 068 | RCL3 |

003 | ST03 | 036 | 0 | 069 | x |

004 | R | 037 | - | 072 | ABS |

005 | STO2 | 038 | X<0? | 071 | x |

006 | R | 039 | GTOB | 072 | ABS |

007 | STO1 | 040 | GSBc | 073 | RTN |

008 | CF3 | 041 | STO | 076 | SIN |

009 | 1 | 042 | GSBb | 075 | RCL5 |

010 | STO4 | 043 | ST-0 | 076 | SIN |

11 | PSE | 044 | GSBa | 077 | X^{2} |

12 | PSE | 045 | ST-0 | 078 | RCL2 |

13 | F3? | 046 | GTO3 | 079 | x |

14 | X^{2} |
047 | *LBLB | 080 | RCL4 |

15 | ST04 | 048 | GSBc | 081 | x |

16 | CF3 | 049 | ENT | 082 | ABS |

17 | *LBL1 | 050 | + | 083 | RTN |

18 | CLX | 051 | CHS | 084 | *LBLc |

19 | PSE | 052 | STO | 085 | RCL5 |

20 | F3? | 053 | GSBb | 086 | SIN |

21 | GTO2 | 054 | ST-0 | 087 | RCL5 |

22 | GTO1 | 055 | *LBL3 | 088 | COS |

23 | *LBL2 | 056 | RCL0 | 089 | x |

24 | X<0? | 057 | F2? | 090 | RCL1 |

25 | SF2 | 058 | CHS | 091 | x |

26 | ABS | 059 | PRTX | 092 | RCL4 |

27 | STO5 | 060 | PRTX | 093 | x |

28 | 1 | 061 | GTO1 | 094 | ABS |

29 | 8 | 062 | *LBLa | 095 | RTN |

30 | 0 | 063 | RCL5 | 096 | *LBLe |

31 | - | 064 | SIN | 097 | CLX |

32 | X>0? | 065 | RCL5 | 098 | 1/X |

33 | GTOe | 066 | COS | 099 | RTN |

100 | R/S |