The Gyroscopic Effect
Program Listing for QuickBASIC Numerical Integration Program, GyroTorque.txt
by N. O. Williams
10 CLS : PRINT: REM Numerical integration program to calculate gyroscopic
torque for a rotating ring which is simultaneously tilted. 15 REM Filename:- GyroTorque.txt 20 INPUT "INPUT NO. OF INTEGRATION ELEMENTS PER RING QUADRANT - USE A HIGHER
NUMBER FOR GREATER ACCURACY"; Q 25 I = 4 * Q 30 INPUT "INPUT TOTAL MASS OF RING IN KILOGRAMS"; M# 35 INPUT "RADIUS OF RING IN METRES"; R# 40 INPUT "INPUT SPIN SPEED OF RING IN R.P.M"; NS# 45 INPUT "INPUT TILT SPEED OF RING IN R.P.M"; NT#: PRINT 50 REM convert angular speeds to radians per second 55 K# = 3.1415926536#: WS# = 2 * K# * NS# / 60: WT# = 2 * K# * NT# / 60 60 REM ratio of tilt speed/spin speed 65 C# = NT# / NS# 70 REM ********************************************************************** 75 PRINT "PHI-DIRECTION, ACCELERATIONS NORMAL TO SPIN PLANE" 80 REM set initial values for near end of first element 85 MO# = 0: T1# = 0: P1# = 0: D1# = 0: V1# = 0: A1# = WS# ^ 2 * 2 * C# * R# 90 FOR J = 1 TO I / 2 95 REM Calculate angles (Radians) Theta & Phi, at far end of element 100 T2# = J * 2 * K# / I: P2# = C# * T2# 105 REM calculate displacement at far end of element 110 D2# = R# * SIN(T2#) * SIN(P2#) 115 REM calculate velocity at far end of element 120 V2# = WS# * R# * (COS(T2#) * SIN(P2#) + C# * SIN(T2#) * COS(P2#)) 125 REM calculate acceleration at far end of element 130 A2# = WS# ^ 2 * R# * (-SIN(T2#) * SIN(P2#) + 2 * C# * COS(T2#) * COS(P2#)
- C# ^ 2 * SIN(T2#) * SIN(P2#)) 135 REM calculate force at middle of element (= mass x acceleration) 140 DF# = M# * (A1# + A2#) / (2 * I) 145 REM calculate gyro-moment at middle of element (= force x offset) 150 DM# = DF# * R# * COS((T1# + T2#) / 2) 155 REM summation of moments and set initial values for next element 160 MO# = MO# + DM#: T1# = T2#: P1# = P2#: D1# = D2#: V1# = V2#: A1# = A2# 165 NEXT J 170 REM torque = mass x rad^2 x w(spin) x w(tilt) 175 TT# = M# * 4 * R# ^ 2 * K# ^ 2 * NS# * NT# / 3600: CM# = 2 * MO# 180 PRINT "CALCULATED TORQUE DUE TO FORCES NORMAL TO SPIN PLANE = "; CM#;
"Nm":PRINT 185 PRINT "RATIO OF CALCULATED NORMAL FORCES ONLY TORQUE/FORMULA TOTAL TORQUE
= "; CM# / TT#: PRINT 190 REM ********************************************************************** 195 PRINT "THETA-DIRECTION, ACCELERATIONS PARALLEL TO SPIN PLANE" 200 REM set initial values for near end of first element 205 NO# = 0: T1# = 0: P1# = 0: E1# = R#: U1# = 0: B1# = WS# ^ 2 * -R# 210 FOR J = 1 TO I / 2 215 REM Calculate angles (Radians) Theta & Phi, at far end of element 220 T2# = J * 2 * K# / I: P2# = C# * T2# 225 REM calculate displacement at far end of element 230 E2# = R# * (1 - COS(T2#)) 235 REM calculate velocity at far end of element 240 U2# = WS# * -R# * (SIN(T2#)) 245 REM calculate acceleration at far end of element 250 B2# = WS# ^ 2 * -R# * (COS(T2#)) 255 REM calculate force at middle of element (= mass x acceleration) 260 EF# = M# * (B1# + B2#) / (2 * I) 265 REM calculate gyro-moment at middle of element (= force x offset) 270 EM# = EF# * R# * SIN((T1# + T2#) / 2) * SIN((P1# + P2#) / 2) 275 REM summation of moments and set initial values for next element 280 NO# = NO# + EM#: T1# = T2#: P1# = P2#: E1# = E2#: U1# = U2#: B1# = B2# 285 NEXT J 290 REM torque = mass x rad^2 x w(spin) x w(tilt) 295 TT# = M# * 4 * R# ^ 2 * K# ^ 2 * NS# * NT# / 3600: CN# = -2 * NO# 300 PRINT "CALCULATED TORQUE DUE TO FORCES PARALLEL TO SPIN PLANE = "; CN#;
"Nm":PRINT 305 PRINT "RATIO OF CALCULATED PARALLEL FORCES ONLY TORQUE/FORMULA TOTAL TORQUE
= "; CN# / TT#: PRINT:PRINT 310 REM *********************************************************************** 315 PRINT "SUMMING TORQUES DUE TO FORCES IN NORMAL & PARALLEL DIRECTIONS":PRINT 320 PRINT "SUM OF CALCULATED TORQUES = "; CM# + CN#; "Nm" :PRINT:PRINT 325 PRINT "FORMULA-BASED TOTAL GYROSCOPIC TORQUE = "; TT#; "Nm":PRINT:PRINT 330 PRINT "RATIO OF TOTAL CALCULATED/FORMULA TORQUES = "; (CM# + CN#) / TT# 335 END
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