support structure ACDTopCoreThickness + 2 * ACDFaceThickness Figure 1 Top ACD tileThickness = 10 mm ribbonGap 2.5 mm sideOverlap 30 mm topOverlap 15 mm topTileXEdgeExtra_l side tiles X ribbonOverlap= 15 mm connector topTileSupportStandoff topTileXEdge_l topTileXEdge_l topTileXMid_l topTileXMid_l topTileXCentral_l Ribbon continues to the bottom of the 4th ACD side row tileCentralThickness 12 mm ribbonThickness = 4.5 mm towersTotalX =1495.5 mm support structure ACDTopCoreThickness + 2 * ACDFaceThickness ACDTKRStayClear 25.8 mm Enclosing volume for side tiles Figure 1 provides a view of the top tiles, displaying the overlap in this direction. Also note that the edge top tiles are curved on the end – which is not necessary to simulate at this point. Rather we extend the last top tile to cover this area. Extend top tiles by a distance topTIleXEdgeExtra_l to reach edge of red box. Total length of simulated edge tiles is called topTileXTotal_l. The boxes in yellow represent the ACD support structure. The boxes in magenta are the connectors that hold the tiles to the support structure. At this time, it is not necessary to simulate these objects. The blue boxes represent the ribbons which are underneath the ACD tiles – between the tiles and the support structure. Note that all tiles are 10 mm, except for the middle row of top tiles – which are 12 mm thick. 3.) Do we know the location of the TKR edge relative to the top ACD tiles? Given the 1576 mm width of the base – I estimate that the TKR edge is 1576 – 2x(2.5 + 1.5) = 1568 mm (subtracting off 2 wall gaps and wall thickness). However, this estimate seems inaccurate, as the curved top tiles would not come close to the start of the side tiles – leaving a large gap. TKR wall side support ACDSideCorethickness + 2* ACDFaceThickness PMTFiberGap 41.6 mm Z Neiter vertical pieces of ribbon nor connectors will be simulated. See following slide for a more accurate picture of simulated elements and their relative positions. X Enclosing volume for top face of ACD Not to Scale 4 November 2002 ACD Simulated Geometry

ACD Simulated Geometry Figure 1 details tileThickness = 10 mm ribbonGap 2.5 mm topOverlap 15 mm topTileXEdgeExtra_l side tiles ribbonOverlap= 15 mm ribbonGap 2.5 mm X topTileXEdge_l topTileXEdge_l topTileXMid_l topTileXMid_l topTileXCentral_l Seg 1, face 0 Seg 5, face 0 Seg 0, face 1 Seg 2, face 0 Seg 4, face 0 Seg 3, face 0 ribbonGap 2.5 mm TKRACDSupportGap = 45mm Needed to increase from old number of 10 mm to avoid overlap of ACD and grid. Seg 0, face 3 Some constants: topTileXCentral_l (primary) 334 mm topTileXMid_l (primary) 338 mm topTileXEdge_l (primary) 300 mm topTileXEdgeExtra_l (derived, computed so that tile almost extends to side tile; gap = ribbon thickness + ribbon Gap ) topTileXEdgeTotal_l (derived, sum of previous 2) topTileSupportStandoff (primary) 25.4; distance from bottom edge of central tiles (col 2) and top of support Not to Scale Figure 1 provides a view of the top tiles, displaying the overlap in this direction. Also note that the edge top tiles are curved on the end – which is not necessary to simulate at this point. Rather we extend the last top tile to cover this area. Extend top tiles by a distance topTIleXEdgeExtra_l to reach edge of red box. Total length of simulated edge tiles is called topTileXTotal_l. The boxes in yellow represent the ACD support structure. The boxes in magenta are the connectors that hold the tiles to the support structure. At this time, it is not necessary to simulate these objects. The blue boxes represent the ribbons which are underneath the ACD tiles – between the tiles and the support structure. Note that all tiles are 10 mm, except for the middle row of top tiles – which are 12 mm thick. 3.) Do we know the location of the TKR edge relative to the top ACD tiles? Given the 1576 mm width of the base – I estimate that the TKR edge is 1576 – 2x(2.5 + 1.5) = 1568 mm (subtracting off 2 wall gaps and wall thickness). However, this estimate seems inaccurate, as the curved top tiles would not come close to the start of the side tiles – leaving a large gap. Vertical ribbon pieces are not simulated. Ribbons extend beyond corresponding tile’s edge by ribbonOverlap, except for edgemost ribbons, which go only as far as tile. Transvers gap between ribbon and adjacent tile is ribbonGap, same as vertical gap between tile and ribbon below. Assume gap of 10 mm between top of towers and lower face of top support. Side support structures not shown. Z X 4 November 2002 ACD Simulated Geometry

ACD Simulated Geometry Figure 2 Top Tiles Not to Scale Y-ribbon top segment is min. distance above top support.. ribbonGap + ribbonThickness ribbonGap = 2.5 mm ACDSidesGap 334 mm 334 mm 318 mm 334 mm 334 mm Face 0, fMeasure = Y, fRibbon = 1 Face 0, fMeasure = Y, fRibbon = 3 Face 0, fMeasure = X, fSegment = 1 Face 4, fMeasure = X, fSegment = 0 topTileGap = 3.5 mm Face 2, fMeasure = X, fSegment = 0 towersTotalX =1495.5 mm Figure 2 The typical top tile has a width of 334 mm. We know that the distance between the inner edge of the side tiles is 1670 mm. 1670 – (4 x 334) = 334 mm But then we must account for the gaps between the tiles and the gap between the edge of the top tiles and the side tiles. 334 – (4 x 3) – (2 x 2) = 318 mm ACDSidesGap= max of (tile y-dimensions) + 4*(topTileGap) + 2*ribbonGap + 2*(ribbonThickness) = 4*334 + 318 + 4*3.5 + 2*2.5+2*4.5 = 1684 mm. and towersTotalX + 2*ACDTKRStayClear + 2*sideSupportThick + 2* PMTFiberGap = 1495.5 + 51.6 + 52.832 + 83.2 = 1683.132 side support as in Fig.1 Z Y ACDTKRStayClear 25.8 mm PMTFiberGap 41.6 mm 4 November 2002 ACD Simulated Geometry

Not to Scale Side Tiles Figure 3 X Z 331 mm 210 mm 160 mm 150 mm Row 0 sideHorizontalGap = 3 mm Z X 344 mm 334 mm 322 mm 334 mm 344 mm 331 mm Row 0 sideVerticalGap = 0 mm 210 mm Row 1 160 mm Row 2 150 mm Row 3 Leave side_vertical_gap == 0 mm until we can insert tilt in the side tiles. Figure 3 ribbonWidth = 11 mm Side tile height in row 0 artificially reduced to 331 since in simulation side tiles neither overlap nor slant. X-dimension of middle column set to 322 mm to get total X-extent to be 1690. 4 November 2002 ACD Simulated Geometry

Side Tiles another view Not to Scale Z X Row 0 Height = 331 mm Ribbon width 11 mm, 4.5 mm thick. This is +x side so identifier has fFace=3, fMeasure=Y , fSegment=0 Row 1 Height = 210 mm 851.0 mm ACD side support Row 2 Height = 160 mm Along the sides – it is probably easiest to model the scintillating tape in segments. Row 3 Height = 150 mm Figure 4 4 November 2002 ACD Simulated Geometry tileThickness = 10 mm

ACD Simulated Geometry Not to Scale One more Top View Face 4 (+y) Side tiles Face 1 (-x) Face 3 (+x) Y ribbons Side length = ACDSidesGap + tileThickness – dovetailGap = 1690 The ribbons are underneath the tiles. X Figure 5 ribbonGap + ribbonThickness = 2.5 + 4.5 = 7 mm Face 2 (-y) dovetailGap = 4 mm 4 November 2002 ACD Simulated Geometry

Support pieces jigsaw puzzle, top view y Pieces || to X axis are longer Top support covers sides x Pieces || to Y axis are shorter Not to Scale Figure 6 4 November 2002 ACD Simulated Geometry

Support pieces jigsaw puzzle, side view Top z Short side || to y-axis y Pieces || to Y axis are short Not to Scale Figure 7 4 November 2002 ACD Simulated Geometry

ACD Simulated Geometry Identifiers Tiles FIELD NAME fLATObjects fACDFace fACDCmp fRow fCol Symbolic Value eLATACD eACDTopFace, etc. eACDTile - - Numeric Value 1 0- 4 40 0-4 0-4 Example: /1/0/40/2/2 (top center tile) Ribbons FIELD NAME fLATObjects fACDFace fACDCmp fMeasure fRibbon fSegment Symbolic Value eLATACD eACDTopFace, etc. eACDRibbon eMeasureX,..Y - - Numeric Value 1 0- 4 41 0, 1 0-3 Side faces: 0 Top face: 1-5 Example: /1/2/41/0/2/0 (segment of third “x-measuring” ribbon which runs along the –y face) Supports FIELD NAME fLATObjects fACDFace fACDCmp Symbolic Value eLATACD eACDTopFace, etc. eACDSupport Numeric Value 1 0- 4 42 Example: /1/4/42 (side support on +y side) 4 November 2002 ACD Simulated Geometry