MATLAB code page

% fixed constants pday1=102970; pday2=100955; d=.7755; %must be in cm for correct conversion of E to V/m rho=886; g=9.8; b=8.20E-3;

%% Drop2 eta2=1.858*10^-5; V2=500.8; trise2=[13.12 17.46 11.27 12.55 11.58]; tfall2=[18.17 19.46 19.86]; vrise2=(.5E-3)./trise2; vfall2=(.5E-3)./tfall2; vravg2=mean(vrise2) vfavg2=mean(vfall2)

E2=(V2/(300*d))/(3.33E-5) endterm2=(vravg2+vfavg2)/(E2*vfavg2); a2=sqrt(((b/(2*pday1))^2)+ ((9*eta2*vfavg2)/(2*g*rho)))-(b/(2*pday1)) m2=(4/3)*pi*(a2^3)*rho

q2=g*m2*endterm2

% ERROR PROPAGATION % standard deviation of mean for time data sdmtr2=sqrt((sum((trise2-mean(trise2)).^2))/(length(trise2)*(length(trise2)-1))) sdmtf2=sqrt((sum((tfall2-mean(tfall2)).^2))/(length(tfall2)*(length(tfall2)-1))) % standard deviation of mean for velocities sdmvr2=(vravg2/mean(trise2))*sdmtr2 sdmvf2=(vfavg2/mean(tfall2))*sdmtf2 % sdm of radius sdma2=((9*eta2)/(2*g*rho))*((sdmvf2)/sqrt(((b/(2*pday1))^2)+((9*eta2*vfavg2)/(2*g*rho)))) % sdm of mass sdmm2=4*pi*rho*(a2^2)*sdma2 % sdm of q sdmq2=sqrt(((g*(vravg2+vfavg2)*sdmm2/(E2*vfavg2))^2)+((m2*g*sdmvr2/(E2*vfavg2))^2)...   + ((m2*g*vravg2*sdmvf2/(E2*(vfavg2^2)))^2))

%% Drop9 eta9=1.855*10^-5; V9=507; trise9=[10.33, 9.05, 9.17]; tfall9=[10.14, 10.18, 10.05]; vrise9=(.5E-3)./trise9; vfall9=(.5E-3)./tfall9; vravg9=mean(vrise9) vfavg9=mean(vfall9)

E9=(V9/(300*d))/(3.33E-5) endterm9=(vravg9+vfavg9)/(E9*vfavg9); a9=sqrt(((b/(2*pday2))^2)+ ((9*eta9*vfavg9)/(2*g*rho)))-(b/(2*pday2)) m9=(4/3)*pi*(a9^3)*rho

q9=g*m9*endterm9

% ERROR PROPAGATION % standard deviation of mean for time data sdmtr9=sqrt((sum((trise9-mean(trise9)).^2))/(length(trise9)*(length(trise9)-1))) sdmtf9=sqrt((sum((tfall9-mean(tfall9)).^2))/(length(tfall9)*(length(tfall9)-1))) % standard deviation of mean for velocities sdmvr9=(vravg9/mean(trise9))*sdmtr9 sdmvf9=(vfavg9/mean(tfall9))*sdmtf9 % sdm of radius sdma9=((9*eta9)/(2*g*rho))*((sdmvf9)/sqrt(((b/(2*pday2))^2)+ ((9*eta9*vfavg9)/(2*g*rho)))) % sdm of mass sdmm9=4*pi*rho*(a9^2)*sdma9 % sdm of q sdmq9=sqrt(((g*(vravg9+vfavg9)*sdmm9/(E9*vfavg9))^2)+((m9*g*sdmvr9/(E9*vfavg9))^2)...   + ((m9*g*vravg9*sdmvf9/(E9*(vfavg9^2)))^2))

%% Drop11 eta11=1.861*10^-5; V11=507; atrise11=[22.67]; btrise11=[5.34, 5.70, 5.36]; tfall11=[5.31, 5.90, 5.93, 5.83]; avrise11=(.5E-3)./atrise11; bvrise11=(.5E-3)./btrise11; vfall11=(.5E-3)./tfall11; avravg11=mean(avrise11) bvravg11=mean(bvrise11) vfavg11=mean(vfall11)

E11=(V11/(300*d))/(3.33E-5) aendterm11=(avravg11+vfavg11)/(E11*vfavg11); bendterm11=(bvravg11+vfavg11)/(E11*vfavg11); a11=sqrt(((b/(2*pday2))^2)+ ((9*eta11*vfavg11)/(2*g*rho)))-(b/(2*pday2)) m11=(4/3)*pi*(a11^3)*rho

aq11=g*m11*aendterm11 bq11=g*m11*bendterm11

% ERROR PROPAGATION % standard deviation of mean for time data sdmatr11=0 sdmbtr11=sqrt((sum((btrise11-mean(btrise11)).^2))/(length(btrise11)*(length(btrise11)-1))) sdmtf11=sqrt((sum((tfall11-mean(tfall11)).^2))/(length(tfall11)*(length(tfall11)-1))) % standard deviation of mean for velocities sdmavr11=0 sdmbvr11=(bvravg11/mean(btrise11))*sdmbtr11 sdmvf11=(vfavg11/mean(tfall11))*sdmtf11 % sdm of radius sdma11=((9*eta11)/(2*g*rho))*((sdmvf11)/sqrt(((b/(2*pday2))^2)+ ((9*eta11*vfavg11)/(2*g*rho)))) % sdm of mass sdmm11=4*pi*rho*(a11^2)*sdma11 % sdm of q asdmq11=sqrt(((g*(avravg11+vfavg11)*sdmm11/(E11*vfavg11))^2)+((m11*g*sdmavr11/(E11*vfavg11))^2)...   + ((m11*g*avravg11*sdmvf11/(E11*(vfavg11^2)))^2)) bsdmq11=sqrt(((g*(bvravg11+vfavg11)*sdmm11/(E11*vfavg11))^2)+((m11*g*sdmbvr11/(E11*vfavg11))^2)...   + ((m11*g*bvravg11*sdmvf11/(E11*(vfavg11^2)))^2))

%% Drop12 eta12=1.862*10^-5; V12=506.5; atrise12=[8.93, 8.84]; btrise12=[3.48 3.68, 3.50, 3.65, 3.43]; ctrise12=[1.15, 1.15, 1.30, 1.21, 1.36]; tfall12=[22.00, 22.34, 25.62, 22.70, 20.45]; avrise12=(.5E-3)./atrise12; bvrise12=(.5E-3)./btrise12; cvrise12=(.5E-3)./ctrise12; vfall12=(.5E-3)./tfall12; avravg12=mean(avrise12) bvravg12=mean(bvrise12) cvravg12=mean(cvrise12) vfavg12=mean(vfall12)

E12=(V12/(300*d))/(3.33E-5) aendterm12=(avravg12+vfavg12)/(E12*vfavg12); bendterm12=(bvravg12+vfavg12)/(E12*vfavg12); cendterm12=(cvravg12+vfavg12)/(E12*vfavg12); a12=sqrt(((b/(2*pday2))^2)+ ((9*eta12*vfavg12)/(2*g*rho)))-(b/(2*pday2)) m12=(4/3)*pi*(a12^3)*rho

aq12=g*m12*aendterm12 bq12=g*m12*bendterm12 cq12=g*m12*cendterm12

% ERROR PROPAGATION % standard deviation of mean for time data sdmatr12=sqrt((sum((atrise12-mean(atrise12)).^2))/(length(atrise12)*(length(atrise12)-1))) sdmbtr12=sqrt((sum((btrise12-mean(btrise12)).^2))/(length(btrise12)*(length(btrise12)-1))) sdmctr12=sqrt((sum((ctrise12-mean(ctrise12)).^2))/(length(ctrise12)*(length(ctrise12)-1))) sdmtf12=sqrt((sum((tfall12-mean(tfall12)).^2))/(length(tfall12)*(length(tfall12)-1))) % standard deviation of mean for velocities sdmavr12=(avravg12/mean(atrise12))*sdmatr12 sdmbvr12=(bvravg12/mean(btrise12))*sdmbtr12 sdmcvr12=(cvravg12/mean(ctrise12))*sdmctr12 sdmvf12=(vfavg12/mean(tfall12))*sdmtf12 % sdm of radius sdma12=((9*eta12)/(2*g*rho))*((sdmvf12)/sqrt(((b/(2*pday2))^2)+ ((9*eta12*vfavg12)/(2*g*rho)))) % sdm of mass sdmm12=4*pi*rho*(a12^2)*sdma12 % sdm of q asdmq12=sqrt(((g*(avravg12+vfavg12)*sdmm12/(E12*vfavg12))^2)+((m12*g*sdmavr12/(E12*vfavg12))^2)...   + ((m12*g*avravg12*sdmvf12/(E12*(vfavg12^2)))^2)) bsdmq12=sqrt(((g*(bvravg12+vfavg12)*sdmm12/(E12*vfavg12))^2)+((m12*g*sdmbvr12/(E12*vfavg12))^2)...   + ((m12*g*bvravg12*sdmvf12/(E12*(vfavg12^2)))^2)) csdmq12=sqrt(((g*(cvravg12+vfavg12)*sdmm12/(E12*vfavg12))^2)+((m12*g*sdmcvr12/(E12*vfavg12))^2)...   + ((m12*g*cvravg12*sdmvf12/(E12*(vfavg12^2)))^2))

%% Drop14 eta14=1.862*10^-5; V14=506.5; atrise14=[1.81, 2.00, 1.58]; btrise14=[15.53, 20.33, 15.95, 17.81, 19.33]; tfall14=[7.08, 7.63, 7.75, 7.46, 7.87]; avrise14=(.5E-3)./atrise14; bvrise14=(.5E-3)./btrise14; vfall14=(.5E-3)./tfall14; avravg14=mean(avrise14) bvravg14=mean(bvrise14) vfavg14=mean(vfall14)

E14=(V14/(300*d))/(3.33E-5) aendterm14=(avravg14+vfavg14)/(E14*vfavg12); bendterm14=(bvravg14+vfavg14)/(E14*vfavg12); a14=sqrt(((b/(2*pday2))^2)+ ((9*eta14*vfavg14)/(2*g*rho)))-(b/(2*pday2)) m14=(4/3)*pi*(a14^3)*rho

aq14=g*m14*aendterm14 bq14=g*m14*bendterm14

% ERROR PROPAGATION % standard deviation of mean for time data sdmatr14=sqrt((sum((atrise14-mean(atrise14)).^2))/(length(atrise14)*(length(atrise14)-1))) sdmbtr14=sqrt((sum((btrise14-mean(btrise14)).^2))/(length(btrise14)*(length(btrise14)-1))) sdmtf14=sqrt((sum((tfall14-mean(tfall14)).^2))/(length(tfall14)*(length(tfall14)-1))) % standard deviation of mean for velocities sdmavr14=(avravg14/mean(atrise14))*sdmatr14 sdmbvr14=(bvravg14/mean(btrise14))*sdmbtr14 sdmvf14=(vfavg14/mean(tfall14))*sdmtf14 % sdm of radius sdma14=((9*eta14)/(2*g*rho))*((sdmvf14)/sqrt(((b/(2*pday2))^2)+ ((9*eta14*vfavg14)/(2*g*rho)))) % sdm of mass sdmm14=4*pi*rho*(a14^2)*sdma14 % sdm of q asdmq14=sqrt(((g*(avravg14+vfavg14)*sdmm14/(E14*vfavg14))^2)+((m14*g*sdmavr14/(E14*vfavg14))^2)...   + ((m14*g*avravg14*sdmvf14/(E14*(vfavg14^2)))^2)) bsdmq14=sqrt(((g*(bvravg14+vfavg14)*sdmm14/(E12*vfavg14))^2)+((m14*g*sdmbvr14/(E14*vfavg14))^2)...   + ((m14*g*bvravg14*sdmvf14/(E14*(vfavg14^2)))^2))

%% Plots of time distributions

subplot(2,2,1), bar(trise2), title('Drop2 rise time') subplot(2,2,2), bar(tfall11), title('Drop11 fall time') subplot(2,2,3), bar(tfall12), title('Drop12 fall time') subplot(2,2,4), bar(btrise14), title('Drop14 rise time')