The Gyroscopic Effect
Program Listing for Numerical Integration check program, Integral.txt
by N. O. Williams
10 CLS : REM Numerical integration program to calculate gyroscopic torque 15 REM for a rotating ring which is simultaneously tilted. 20 REM This is a check program which numerically integrates the combined trigonometric expression. 25 PRINT : PRINT: REM Filename:- Integral.txt 30 INPUT "INPUT NO. OF INTEGRATION ELEMENTS PER RING QUADRANT - USE A HIGHER NUMBER FOR GREATER ACCURACY"; Q 35 I = 4 * Q 40 K# = 3.1415926536# 45 PRINT 50 INPUT "INPUT TOTAL MASS OF RING IN KILOGRAMS"; M# 55 INPUT "RADIUS OF RING IN METRES"; R# 60 INPUT "INPUT SPIN SPEED OF RING IN R.P.M"; NS# 65 INPUT "INPUT TILT SPEED OF RING IN R.P.M"; NT#: PRINT 70 REM convert angular speeds to radians per second 75 WS# = 2 * K# * NS# / 60: WT# = 2 * K# * NT# / 60 80 REM ratio of tilt speed/spin speed"; C# 85 C# = NT# / NS# 90 REM ****************************************************************************** 95 PRINT 100 REM Calculation for the First Two Quadrants 105 T1# = 0: P1# = 0 110 FOR J = 1 TO (I / 2) 115 REM Calculate angles (Radians) Theta & Phi, at far end of element 120 REM T2# = ((J) / (I / 2)) * K# / 180: P2# = ((J) * C# / (I / 2)) * K# / 180 125 T2# = J * 2 * K# / I: P2# = C# * T2# 130 REM First End of Element 135 CINC# = COS(T1#) * (2 * COS(T1#) * COS(P1#) - C# * SIN(T1#) * SIN(P1#)) 140 REM Second End of Element 145 DINC# = COS(T2#) * (2 * COS(T2#) * COS(P2#) - C# * SIN(T2#) * SIN(P2#)) 150 REM End values averaged to represent Centroid of Element 155 CSUM# = CSUM# + (2 * (CINC# + DINC#) / 2) 160 T1# = T2#:P1# = P2# 165 NEXT J 170 PRINT "TRIGONOMETRIC EXPRESSION NUMERICALLY INTEGRATED TORQUE VALUE = ";(M# * R# ^ 2 * WS# * WT#) * CSUM# / I:PRINT 175 PRINT "FORMULA-BASED COEFFICIENT FOR GYROSCOPIC TORQUE VALUE = "; M# * R# ^ 2 * WS# * WT# : PRINT:PRINT 180 PRINT "RATIO OF NUMERICALLY INTEGRATED/FORMULA-BASED TORQUE VALUES = "; CSUM# / I: PRINT 185 END
Click here for Example Output from Numerical Integration check program, Integral.txt