A Maple file for the calculation of the baffle positions

File contents

restart; 
offwall:=0.3+0.125+0.125; 
offwall := .550 
"offwall" is the distance between the tube wall and the edge of the mirror furthest off axis (i.e. the vertex mirrors, MCe and MCn). The tube radius is 30 cm, the mirrors distance to the axis 12.5 cm, and its radius 12.5 cm, giving offwall=55 cm. 
bafflelength:=0.07;\ 
"bafflelength" is the length (in the direction of the tube axis) of one half on the paired baffles. 
angle_degree:=27.5;\ Half the angle of the cone forming the baffles. 
safety:=0.003;\ A safety margin for the production of the baffles. 
angle:=(2*Pi)/360*angle_degree;\ 
h:=evalf(tan(angle)*bafflelength)-safety; 
"h" is the height of the baffles, i.e. the distance of the tip of the baffle from the wall. 
bafflelength := .07 
angle_degree := 27.5 
safety := .003 
angle := .1527777778 Pi 
h := .03343969355 

factor := offwall/(offwall-h); 
position[0]*factor**n,k=0..n-1); 
number:=(solve(300=(position[0]*factor**num),num)); 
surface:=evalf(0.3*2*Pi*(0.14+0.14/cos(angle))*number*2+2*position[0]*0.3*2*Pi); 
#plot(surface,position[0]=0..20); 
test:=diff(surface,position[0]); 

mini:=solve(diff(surface,position[0])=0,position[0]); 
position[0]:=10; 
number:=(solve(300=(position[0]*factor**num),num)); 


mini := 4.748 
"mini" gives the legth of the liner minimizing the overall surface area. 

position[0] := 10 
The compromise for convenient baffle spacing at the tube end/beginning. 

number := 54.22288271 
for i from 1 to (number+1) do 
position[i]:=(position[i-1]*factor): 
gap[i]:=position[i]-position[i-1]: 
od; 
position[1] := 10.64735314 
gap[1] := .64735314 
position[2] := 11.33661289 
gap[2] := .68925975 
position[3] := 12.07049209 
gap[3] := .73387920 
position[4] := 12.85187919 
gap[4] := .78138710 
position[5] := 13.68384962 
gap[5] := .83197043 
position[6] := 14.56967792 
gap[6] := .88582830 
position[7] := 15.51285060 
gap[7] := .94317268 
position[8] := 16.51707985 
gap[8] := 1.00422925 
position[9] := 17.58631820 
gap[9] := 1.06923835 
position[10] := 18.72477403 
gap[10] := 1.13845583 
position[11] := 19.93692816 
gap[11] := 1.21215413 
position[12] := 21.22755146 
gap[12] := 1.29062330 
position[13] := 22.60172367 
gap[13] := 1.37417221 
position[14] := 24.06485335 
gap[14] := 1.46312968 
position[15] := 25.62269919 
gap[15] := 1.55784584 
position[16] := 27.28139267 
gap[16] := 1.65869348 
position[17] := 29.04746219 
gap[17] := 1.76606952 
position[18] := 30.92785878 
gap[18] := 1.88039659 
position[19] := 32.92998343 
gap[19] := 2.00212465 
position[20] := 35.06171625 
gap[20] := 2.13173282 
position[21] := 37.33144746 
gap[21] := 2.26973121 
position[22] := 39.74811043 
gap[22] := 2.41666297 
position[23] := 42.32121684 
gap[23] := 2.57310641 
position[24] := 45.06089410 
gap[24] := 2.73967726 
position[25] := 47.97792523 
gap[25] := 2.91703113 
position[26] := 51.08379128 
gap[26] := 3.10586605 
position[27] := 54.39071655 
gap[27] := 3.30692527 
position[28] := 57.91171666 
gap[28] := 3.52100011 
position[29] := 61.66064982 
gap[29] := 3.74893316 
position[30] := 65.65227135 
gap[30] := 3.99162153 
position[31] := 69.90229175 
gap[31] := 4.25002040 
position[32] := 74.42743856 
gap[32] := 4.52514681 
position[33] := 79.24552217 
gap[33] := 4.81808361 
position[34] := 84.37550593 
gap[34] := 5.12998376 
position[35] := 89.83758080 
gap[35] := 5.46207487 
position[36] := 95.65324480 
gap[36] := 5.81566400 
position[37] := 101.8453876 
gap[37] := 6.19214280 
position[38] := 108.4383807 
gap[38] := 6.5929931 
position[39] := 115.4581733 
gap[39] := 7.0197926 
position[40] := 122.9323944 
gap[40] := 7.4742211 
position[41] := 130.8904616 
gap[41] := 7.9580672 
position[42] := 139.3636967 
gap[42] := 8.4732351 
position[43] := 148.3854494 
gap[43] := 9.0217527 
position[44] := 157.9912281 
gap[44] := 9.6057787 
position[45] := 168.2188399 
gap[45] := 10.2276118 
position[46] := 179.1085393 
gap[46] := 10.8896994 
position[47] := 190.7031868 
gap[47] := 11.5946475 
position[48] := 203.0484175 
gap[48] := 12.3452307 
position[49] := 216.1928206 
gap[49] := 13.1444031 
position[50] := 230.1881307 
gap[50] := 13.9953101 
position[51] := 245.0894316 
gap[51] := 14.9013009 
position[52] := 260.9553729 
gap[52] := 15.8659413 
position[53] := 277.8484009 
gap[53] := 16.8930280 
position[54] := 295.8350044 
gap[54] := 17.9866035 
position[55] := 314.9859763 
gap[55] := 19.1509719