'*********************ROCKET SIMULATION/DESIGN*************************** ' GEORGE WESTROM ' 8/21/96 ' THIS IS A WATER /AIR ROCKET DESIGN PROGRAM FOR FUTURE SCIENTISTS ' AND ENGINEERS OF AMERICA.IT IS COPY WRITE PROPERTY OF FSEA AND ' MAY BE FREELY USED BY STUDENTS TO EXPERIMENT WITH VARIATION IN ' ROCKET DESIGN.IT WILL COMPUTE THE BASIC ROCKET PARAMETERS ' SUCH AS THRUST,ACCELERATION,VELOCITY AND MAX ALTITUDE. DESIGN ' PARAMETERS ARE SIZE OF THE ROCKET,PRESSURE,AMOUNT OF WATER, ' SIZE OF THE NOZZLE,MASS OF THE ROCKET AND DENSITY OF THE WATER. GOSUB 1000 'INITIALIZE PRINT "DO YOU WANT INSTRUCTIONS Y/N" INPUT a$ IF a$ = "Y" OR a$ = "y" THEN GOSUB 2000 'INSTRUCTIONS END IF PRINT PRINT " DO YOU WANT A SAMPLE PROBLEM Y/N" INPUT b$ IF b$ = "Y" OR b$ = "y" THEN GOSUB 3000'SAMPLE INPUT PROBLEM END IF IF b$ = "Y" OR b$ = "y" THEN GOTO 50 END IF GOSUB 4000 ' INPUT INITIAL VALUES 50 GOSUB 5000'CONVERT TO ALL VALUES TO METRIC UNITS GOSUB 6000 'COMPUTE DRAG COEFFICIENT GOSUB 7000 'COMPUTE NOZZLE AREA GOSUB 8000 'STEP WISE COMPUTATION UNTIL WATER "BURNOUT" GOSUB 11000 'PRINT WATER BURNOUT PARAMETERS GOSUB 12000 'STEPWISE COMPUTATION UNTIL AIR "BURNOUT"(PRESSURE AMBIENT) GOSUB 12500 'COMPUTATION OF TIME TO DESCEND WITH PARACHUTE GOSUB 13000 'PRINT AIR BURNOUT VALUES AND FINAL HEIGHT GOTO 50000 'FINISH 1000 DIM vn(3000), f(3000), a(3000), vr(3000), h(3000), v(3000) K = 20 * 10 ^ -2.5'experimental value based on bottle shape Kp = 8' experimental value based on shape of parachute kf = 5 * 10 ^ -3'experimental value based on nozzle turbulence PI = 3.1416 g = 9.8 1010 DATA 1, 200,1,30,50,1,70,3,1500 RETURN 2000 PRINT "THIS PROGRAM IS THE COPY WRITE PROPERTY OF FSEA" PRINT "IT IS A DESIGN PROGRAM TO DESIGN AND OPTIMIZE A LIQUID" PRINT "AND AIR PROPELLED ROCKET. THE ROCKET IS MADE BY PUTTING " PRINT "FINS ON 1,1.5 OR 2 LITER PLASTIC WATER BOTTLE. A RUBBER" PRINT "STOPPER ON THE LAUNCHER IS USED TO KEEP THE WATER IN THE" PRINT " BOTTLE. A BICYCLE PUMP IS ATTACHED TO THE TUBE ON THE LAUNCHER" PRINT "THE PUMP SHOULD HAVE A GAGE SO YOU CAN TELL HOW MUCH PRESSURE" PRINT "IS IN THE PLASTIC BOTTLE. IF THE STOPPER IS TIGHTLY SECURED " PRINT "PRESSURES FROM 50 TO 100 POUNDS/SQ INCH CAN BE REALIZED BEFORE" PRINT "THE CORK POPS OUT OF THE BOTTLE AND THE ROCKET TAKES OFF" PRINT "ALTITUDE WELL OVER 100 FEET CAN BE ACHIEVED. WITH THE FSEA" PRINT "ROCKET LAUNCHER , THE ROCKET CAN BE LAUNCHED AT ANY DESIRED" PRINT "PRESSURE. PRESSURES MUST NEVER EXCEED 80 POUNDS." PRINT "HIT ANY KEY TO CONTINUE" INPUT D$ PRINT " ********WARNING****WARNING****WARNING*********" PRINT PRINT "YOU MUST WEAR SAFETY GLASSES IN CASE THE PLASTIC BOTTLE" PRINT "SHOULD RUPTURE. IT IS ALSO OPTIONAL TO HAVE A SHIELD" PRINT "AROUND THE ROCKET FOR ADDED PROTECTION. THE ROCKET WILL TAKE" PRINT "OFF WITH INTENSE ACCELERATION ,HENCE THE STUDENTS WILL NEED" PRINT "TO STAND BACK AT LEAST FIFTEEN(15) FEET. BY USING THE FSEA ROCKET" PRINT " LAUNCHER CORRECTLY YOU WILL NOT NEED A SHIELD, BUT BE SURE " PRINT " THAT THE LAUNCHER IS SECURELY IN THE GROUND WITH THE ROCKET" PRINT " PERFECTLY VERTICAL,. ALSO THE STUDENTS WHO ARE CLOSER THAN" PRINT " 15 FEET MUST WEAR SAFETY GLASSES. " PRINT "WITH THIS PROGRAM YOU CAN OPTIMIZE THE AMOUNT AND DENSITY" PRINT "OF THE LIQUID,BOTTLE SIZE,DRAG COEFFICIENT,NOZZLE SIZE" PRINT "PRESSURE AND WEIGHT OF THE ROCKET" PRINT PRINT "HIT ANY KEY TO COMTINUE" INPUT R$ PRINT "THE OBJECTIVE OF THE WATER/AIR ROCKET PROJECT IS TO DESIGN AND" PRINT "BUILD A ROCKET AND BE ABLE TO PREDICT AND MEASURE THE" PRINT "ALTITUDE TO WHICH THE ROCKET WILL RISE. IT MAY BE NECESSARY" PRINT "TO CALIBRATE THE DRAG COEFFICIENT EXPERIMENTALLY BY MEASURING" PRINT "HOW HIGH THE ROCKET RISES WITH SEVERAL TEST FIRINGS. IT IS" PRINT "DESIRABLE TO REACH THE GREATEST HEIGHT AND THE LONGEST TIME" PRINT "IN THE AIR." PRINT PRINT " COMPETITION" PRINT PRINT "THE COMPETITION WILL CONSIST OF THREE EVENTS THE FIRST" PRINT "WILL BE THE GREATEST ALTITUDE 30 POINTS 1ST PLACE,20 POINTS" PRINT "2ND PLACE, AND 10 POINTS 3RD PLACE. THE SECOND EVENT WILL" PRINT "BE FOR THE ROCKET WHICH IS CLOSEST TO A MAX ALTITUDE OF" PRINT " 100 FEET. 30 POINTS 1ST PLACE ,20 POINTS 2ND PLACE" PRINT "AND 10 POINTS 3RD PLACE. AN ADDITIONAL 50 POINTS WILL" PRINT PRINT "HIT ANY KEY TO CONTINUE" INPUT X$ PRINT "BE AWARDED TO THE TEAM WHICH DEVELOPS THE BEST METHOD FOR" PRINT "MEASURING THE ALTITUDE OF THE ROCKET. THE THIRD EVENT FOR" PRINT "WHICH YOU MAY NEED TO DESIGN A PARACHUTE ,WILL BE THE" PRINT "THE LENGTH OF TIME THE ROCKET STAYS ALOFT. 30 POINTS" PRINT "FIRST PLACE,20 POINTS SECOND PLACE AND 10 POINTS" PRINT "THIRD PLACE." PRINT PRINT " MATERIAL" PRINT PRINT "THE MATERIAL WILL CONSIST OF 1,1.5 OR 2 LITER WATER BOTTLE" PRINT "THIS BOTTLE WILL BE FURNISHED BY THE STUDENT. GUIDANCE FINS" PRINT "TAPE,GLUE AND HOT GLUE GUN,TIRE PUMP AND A LAUNCHER WITH A" PRINT "RUBBER STOPPER TO FIT IN THE BOTTLE WIL BE PROVIDED BY FSEA." PRINT PRINT "HIT ANY KEY TO CONTINUE" INPUT X$ PRINT " PROCEDURE" PRINT PRINT "THREE FINS ARE TO BE ATTACHED TO THE OPEN END OF THE BOTTLE" PRINT "SUCH THAT THE ROCKET WILL STAND ON THE FINS. THE HOT GLUE" PRINT "WILL BE USED BY THE MENTOR TO PLACE GLUE OF THE FINS WHERE" PRINT "THEY WILL BE ATTACHED TO THE BOTTLE. CARE MUST BE EXERCISED" PRINT "SO THAT THE HOT GLUE DOESN'T TOUCH THE SKIN AS IT CAN CAUSE" PRINT "A BURN. THE BOTTLES SHOULD BE MARKED SO THAT THE MENTOR KNOWS " PRINT "WHERE THE FINS SHOULD BE ATTACHED. THE GLUE WILL SET IN A FEW " PRINT "MINUTES. TAPE MAY ALSO BE USED TO ATTACH THE FINS INSTEAD OF" PRINT "OF THE GLUE. IN PREPARATION FOR LAUNCH SOME WATER IS PUT IN" PRINT "IN THE BOTTLE(AMOUNT DETERMINED BY THE TEAM),THE RUBBER STOPPER" PRINT "IS THEN INSERTED SECURLY INTO THE BOTTLE. THE LAUNCHER IS PUSHED" PRINT "INTO THE GROUND SO THAT IT WILL HOLE THE BOTTLE SECURELY UPRIGHT." PRINT "IF YOU TRY TO LAUNCH ON CEMENT OR BLACKTOP,YOU WILL NEED TO" PRINT "PREPARE A BLOCK OF WOOD SUCH AS A 2x4 INCH BY TW0 FEET LONG" PRINT "AND MAKE HOLES FOR THE LAUNCHER'S FEET SO THAT THE ROCKETS WILL" PRINT "SECURELY STAND UPRIGHT." PRINT PRINT "HIT ANY KEY TO CONTINUE" INPUT X$ PRINT "NEXT THE BOTTLE IS INSERTED INTO THE ROCKET LAUNCHER" PRINT "WITH THE CLAMPS HELD IN PLACE USING THE -U- SHAPED LOCK." PRINT "PUMP UNTIL THE PRESSURE IS 50 TO 80 POUNDS. BE SURE " PRINT "TO KEEP YOUR FACE&BODY AWAY FROM BEING OVER THE ROCKET. THE" PRINT "ROCKET WILL ESCAPE WITH A VERY LARGE FORCE AND CAN CAUSE" PRINT "INJURY IF IT STRIKES YOU CONTINUE TO PUMP UNTIL" PRINT "DESIRED PRESSURE IS REACHED. HAVE SOMEONE SET UP A TRACKING" PRINT "DEVICE 100 FEET AWAY FROM THE ROCKET LAUNCH SITE SO THAT THE" PRINT "ALTITUDE CAN BE DETERMINED. THIS SIMULATION PROGRAM CAN BE USED TO " PRINT "OPTIMIZE BOTTLE SIZE,AMOUNT OF WATER ETC. PARACHUTE CAN BE" PRINT "MADE FROM TRASH BAG PLASTIC MATERIAL" PRINT "k AND kf ARE EXPERIMENTAL DRAG COEFFICIENTS FOR THE ROCKET" PRINT "BODY AND THE FLUID FLOW IN THE NOZZLE RESPECTIVELY. THE VALUES " PRINT "ARE SET IN THE INITIALIZATION ROUTINE. IT IS RECOMMENDED THAT " PRINT "THE STUDENT EXPERIMENT WITH DIFFERENT VALUES OF THE COEFFICIENTS" PRINT "AND DETERMINE THE BEST VALUE SUCH THAT THE ROCKET HEIGHT" PRINT "MOST CLOSELY MATCHES EXPERIMENTAL LAUNCHES. " PRINT PRINT "HIT ANY KEY TO CONTINUE" INPUT z$ PRINT " EXPLAINATION OF UNITS OF MEASURE" PRINT PRINT "WE HAVE ELECTED TO USE THE -MKS- METER,KILOGRAM,SECOND" PRINT "UNITS IN ALL THE COMPUTATION AND IN THE OUTPUT FROM THE PROGRAM." PRINT "THE INPUTS TO THE PROGRAM ARE HOWEVER IN THOSE WHICH ARE MOST" PRINT "FAMILIAR AND EASILY AVAILABLE TO THE USER. FOR EXAMPLE THE" PRINT "BOTTLE VOLUME IS IN LITERS AS PRINTED ON THE PLASTIC BOTTLE." PRINT "THE AMOUNT OF WATER IS IN GRAMS ,WHICH IS 1 GRAM PER CUBIC" PRINT "CENTIMETER OR 1000 GRAMS PER LITER. THE DIAMETERS ARE GIVEN" PRINT "IN INCHES SINCE AN ENGLISH UNITS RULER MAY BE MORE AVAILABLE" PRINT "THE PRESSURE IS GIVEN IN POUNDS PER SQUARE INCH SINCE THAT IS" PRINT "THE NORMAL UNITS ON A TIRE PUMP. DENSITY IS INCLUDE AS GRAMS" PRINT "PER CUBIC CENTIMETER,WHICH IS ONE FOR WATER." PRINT " THE PRINTOUT IS GIVEN BOTH IN THE INPUT QUANTITIES AND IN" PRINT "MKS UNITS FOR COMPARISON. IF YOU ARE NOT FAMILIAR WITH THE UNITS" PRINT "ONE METER EQUALS 39.37 INCHES, ONE NEWTON EQUALS .2248 LB FORCE," PRINT "ONE NEWTON PER SQUARE METER EQUALS .000145 LB PER SQUARE INCH." PRINT INPUT z$ PRINT PRINT "THE VELOCITY OF DESCENT WITH A PARACHUTE DEPENDS ON THE AREA" PRINT "OF THE PARACHUTE,THE WEIGHT OF THE PAYLOAD AND THE EXPERIMENTAL" PRINT "CONSTANT Kp. THE VALUE OF Kp SHOULD BE MODIFIED BASED ON" PRINT "EXPERIMETAL ROCKET FIRINGS WITH A PARTICULAR PARACHUTE DESIGN" PRINT "IF THERE IS NO PARACHUTE ENTER ZERO FOR THE AREA" RETURN 3000 'INPUT SAMPLE CASE READ v1, m1, d1, M2, M3, d2, p, d3, a5 GOSUB 10000 'PRINT VALUES IN INPUT UNITS RESTORE 1010 RETURN 4000 'INPUT INITIAL VALUES PRINT "Input volume of rocket in liters" INPUT v1 PRINT "wt of liquid in grams" INPUT m1 PRINT "Density of liquid in gram/cc " INPUT d1 PRINT "wt of rocket (grams)" INPUT M2 PRINT "wt of payload in grams" INPUT M3 PRINT "Diameter of rocket nozzle in (inches)" INPUT d2 PRINT "Pressure (lb/sq inch)" INPUT p PRINT "Diameter of rocket in (inches)" INPUT d3 PRINT "Area of parachute in square cm" INPUT a5 PRINT PRINT GOSUB 10000 'PRINT VALUES IN INPUT UNITS RETURN 5000 'CONVERT TO PROPER METRIC UNITS(MKS) v1 = v1 * .001'volume of rocket in cubic meters m1 = m1 * .001'mass of liquid in kg d1 = d1 * 1000'density of liquid in kg/cubic meter d2 = d2 * .0254 'diameter of the nozzle in meters M2 = M2 * .001'mass of empty rocket in kg M3 = M3 * .001'mass of payload p = p * 6.895 * 10 ^ 3'pressure in newtons /sq meter d3 = d3 * .0254'diameter of rocket in meter GOSUB 9000 'PRINT INPUT VALUES IN (MKS) UNITS RETURN 6000 'COMPUTE DRAG COEFFICIENT D = K * PI * (d3 ^ 2) / 4'dependent on rocket frontal area RETURN 7000 'COMPUTE NOZZLE/ROCKET AREA AND INITIAL PRESSURE ENERGY AN = PI * (d2 ^ 2) / 4 'area of the nozzle ar = PI * (d3 ^ 2) / 4'cross section area of the rocket va = v1 - (m1 / d1)'initial volume of air EP = p * va * LOG(p / 1.013 * 10 ^ 5)'pressure energy(joules) RETURN 8000 'STEP WISE COMPUTATION UNTIL WATER IS GONE t = .001'time step IF m1 = 0 THEN GOTO 8020 END IF 8010 vw = m1 / d1'volume of liquid I = I + 1' counter hl = vw / ar'height of the liquid pd = h1 * d1 * a(I) 'pressure due to acceleration vn(I) = (SQR((p + pd) / d1)) - kf * vn(I - 1) ^ 2'nozzle velocity mr = AN * vn(I) * d1 IF m1 < mr * t THEN GOTO 8011 m1 = m1 - mr * t 'instantious mass of liquid 8011 f(I) = mr * vn(I) - (m1 + M2) * 9.81'rocket thrust a(I) = f(I) / (m1 + M2 + M3)'rocket acceleration vr(I) = vr(I - 1) + a(I) * t' - (D * t * vr(I) ^ 2) / (m1 + m2+m3)'rocket velocity h(I) = h(I - 1) + t * (vr(I) + vr(I - 1)) / 2 p = p - p * t * ((AN * vn(I)) / (v1 - vw)) IF m1 > mr * t THEN GOTO 8010 END IF tb = I * t 'time till liquid burnout 8020 vb = vr(I)' velocity at liquid burnout pb = p'pressure at liquid burnout hb = h(I) 'height at liquid burnout fa = f(I)'MAX thrust aa = a(I)'max acceleration RETURN 9000 PRINT "INPUT VALUES IN MKS UNITS" PRINT v1, "BOTTLE VOLUME(CUBIC METERS)" PRINT m1, "LIQUID MASS(KILOGRAMS)" PRINT d1, "LIQUID DENSITY(KILOGRAMS/CUBIC METER)" PRINT M2, "EMPTY ROCKET MASS(KILOGRAMS)" PRINT M3, "PAYLOAD MASS(KILOGRAMS)" PRINT d2, "NOZZLE DIAMETER(METERS)" PRINT p, "PRESSURE(NEWTONS/SQUARE METER)" PRINT d3, "ROCKET DIAMETER (METERS)" PRINT a5 * .0001, "PARACHUTE AREA (SQ METERS)" PRINT "HIT ANY KEY TO CONTINUE" INPUT X$ RETURN 10000 PRINT "INPUT VALUES IN INPUT UNITS" PRINT v1, "BOTTLE VOLUME(LITERS)" PRINT m1, "LIQUID MASS(GRAMS)" PRINT d1, "LIQUID DENSITY(GRAMS/CC)" PRINT M2, "EMPTY ROCKET MASS(GRAMS)" PRINT M3, "PAYLOAD MASS(GRAMS)" PRINT d2, "NOZZLE DIAMETER(INCHES)" PRINT p, " PRESSURE(POUNDS/SQUARE INCH)" PRINT d3, "ROCKET DIAMETER(INCHES)" PRINT a5, "PARACHUTE AREA(SQ CM)" RETURN 11000 PRINT "OUTPUT VALUES AT LIQUID BURNOUT" PRINT tb, "TIME TILL LIQUID BURNOUT(SECONDS)" PRINT vb, "VELOCITY AT LIQUID BURNOUT(METERS/SECOND)" PRINT pb, "PRESSURE AT BURNOUT(NEWTONS/SQUARE METER)" PRINT hb, "ALTITUDE AT BURNOUT(METERS)" PRINT aa, "MAX ACCELERATION(METERS/SECOND SQUARED)" PRINT fa, "MAX THRUST(NEWTONS)" RETURN 12000 ' STEPWISE COMPUTATION OF AIR ONLY t = .0001 pa = 1.014 * 10 ^ 5'atmospheric pressure(newtons/sq meter) 12010 dg = (p / pa) * 1.293'kg/cubic meters I = I + 1 X = X + 1 vn(I) = SQR(2 * p / dg) mr = AN * vn(I) * dg m = dg * v1 f(I) = mr * vn(I) - (M2 + m + M3) * 9.81 a(I) = f(I) / (M2 + m + M3) vr(I) = vr(I - 1) + a(I) * t h(I) = h(I - 1) + t * (vr(I) + vr(I - 1)) / 2 p = p - (p * mr * t) / m IF p > pa THEN GOTO 12010 END IF KE = (M2 + M3) * (vr(I) ^ 2) / 2 tba = t * X'time for air burn t = .001 v = vr(I) 12020 v = v - 9.81 * t - (D * t * v ^ 2) / M2 h = h + v * t n = n + 1 IF v > 0 THEN GOTO 12020 END IF th = t * n PER = h * (M2 + M3) * 9.81'POTENTIAL ENERGY AT MAX ROCKET ALTITUDE POWER = KE / (tb + tba)'AVERAGE POWER(WATTS) RETURN 12500 t = SQR((2 * h) / g) + Kp * (a5 * .0001) / (M2 + M3) 13000 PRINT "PRINT FINAL OUTPUT VALUES" PRINT tb + tba, "TIME TO AIR BURNOUT(SECONDS)" PRINT vr(I), "VELOCITY AT AIR BURNOUT(METERS / SEC)" PRINT p, "PRESSURE AT AIR BURNOUT(NEWTONS/SQ METERS)" PRINT h(I), "ALTITUDE AT AIR BURNOUT(METERS)" PRINT f(I), "MAX THRUST(NEWTONS)" PRINT a(I), "MAX ACCELERATION(METERS/SECOND SQUARED)" PRINT h, "MAX ALTITUDE(METERS)" PRINT tb + tba + th, "TIME TO MAX ALTITUDE(SECONDS)" PRINT t + tb + tba + th, "TOTAL TIME OF FLIGHT SECONDS" PRINT EP, "ENERGY IN COMPRESSED AIR(JOULES) " PRINT PER, "POTENTIAL ENERGY OF THE ROCKET AT MAX ALTITUDE(JOULES)" PRINT KE, "KENITIC ENERGY AT BURNOUT(JOULES)" PRINT POWER, "AVERAGE POWER(WATTS)" 50000 PRINT PRINT " WARNING !!! YOU MUST WEAR GLASSES WHEN TESTING"