In the text, a difference equation is obtained from which the energy transfer from the drive to the bucket coil can be found as a function of iD , with the circuit constants n2, Lw and C, and velocity v as parameters. The program in this appendix solves the difference equations, with the help of an approximation for dM/dx. The entire program is designed to run on an HP-25 pocket calculator with 49 program steps. Given a larger calculator or computer, one could generalize the program by using a more exact expression for dM/dx or (more usefully) by including the finite cross sections of the drive and bucket coils.
The simple program consists of four subroutines:
For still higher accuracy, the curve of iD is traced point-by-point by slightly modifying the program: step 47: pause, step 48: pause.
In this program, one or two minor tricks are used to save
register space: the constant a, , which equals
a3/R, is stored as
a sequence of four key strokes in steps 31-34. Register 2 contains a constant
whose integer and fractional parts are both used in the
dM/dx subroutine. The step interval 
x appears as a sequence of
four key strokes in steps 01-04. (All constants are in MKS units.)
In detail, the registers store information as shown in table 5.
As normally used, the program calculates the energy transfer for
a half-cycle of oscillation. The total energy transfer for a
two-coil bucket, corresponding to the passage of both bucket coils
through one drive coil, is then (x)(4n2 iB ) (summation of
iDM/dx in register 5). Typically, a step
interval x of 1
mm is used, 0.001 in program steps 01-04. Each step interval
requires 3.75 sec on an HP-25, and about twice that time on an
HP-67, so a half-cycle of oscillation with D = 5 .0 cm
requires a little over 1 min (see table 6).
| RO | ao =
(x)iB
/Lwn2 |
| R1 | Initial value of position x (in m) at which
drive coil switch is closed. Zero is allowed , but con- stant should be chosen so that x update sub- routine never finishes with zero. R1 stores updated x |
| R2 | a2 =
constant used in dM/dx subroutine. For D = 5.0 cm, a2 = -184.000138 (i.e., INT = -184, FRAC = - 0.000138). For other cacalibers D, INT and FRAC are proportional to D. |
| R3 | a3 =
(x)
R/vLwn22. Drive
winding resistance R appears only in this constant |
| R4 | a4 =
(x) vC.
Resonant capacity C appears only in this constant and is equal to the sum of the capacities on two adjacent sectprs pf tje actual mass driver. |
| R5 | Initialize to zero; stores updated  i(dM/dx). |
| R6 | Peak voltage to which capicitor is charged
before drive circuit switches on; R6 stores updated capacitor voltage Vc. |
| R7 | Initialize to zero; stores updated current i. |
|
Curator: Al Globus If you find any errors on this page contact Al Globus. |
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