Transition hopper: true shape of an inclined outlet and flat development
A sheet-metal shop must build one transition hopper joining a horizontal square duct, 120 mm × 120 mm, to a square outlet, 60 mm × 60 mm, whose plane is inclined. The centres of the two openings are 90 mm apart vertically, and the outlet plane is tipped 25° about a horizontal axis parallel to the front face, so its front edge lies 12 mm lower than its back edge. The job is drawn at 1:1 in front view and plan, with the cutting plane seen edge-on in the front view. The foreman needs two things: the true shape of the inclined outlet so the flange gasket can be cut, and a flat development of the four lateral faces so the blank can be marked out on 0.8 mm galvanised sheet. A junior drafter has already set out the front view and plan, and proposes to develop all four faces by laying off the edge lengths measured directly on the front view, adding 6 mm of overlap along one seam at a corner.
1. State how the tipped outlet plane appears in the front view and in the plan, then set out the construction that gives the true shape of the outlet opening. Name the change of projection plane used and say exactly which view supplies each coordinate.
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The outlet plane is tipped about a horizontal axis parallel to the frontal plane, so it is perpendicular to the vertical plane. Consequence: in the front view it collapses to an edge view - a straight line at 25° to the horizontal - and in the plan it appears as a foreshortened quadrilateral, neither a square nor a rectangle.
Because the plane is perpendicular to the vertical plane, the true shape is obtained by changing the horizontal plane: take a new projection plane parallel to the outlet plane and perpendicular to the vertical plane.
- Draw the new fold line parallel to the 25° edge-view line, at any convenient distance.
- From each of the four outlet corners in the plan, draw projectors perpendicular to the new fold line.
- On each projector lay off the distance of that corner from the old ground line, measured in the front view (i.e. its height), not the plan.
- Join the four transferred points.
Check: the outlet is square, so the true shape must come out as a 60 mm square with equal diagonals. If it does not, heights have been taken from the plan instead of the front view, or a plan corner has been projected from the wrong vertex.
2. Describe how the four lateral faces are developed. Which edges need a separate true-length construction, and how is each true length obtained from the two given views?
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Treat the faces in two pairs.
Front and back faces. Each is a plane trapezoid lying parallel to the frontal plane: the 120 mm top edge and the 60 mm bottom edge are both parallel to that plane, and the two sloping sides lie in it. All four edges therefore appear at true length in the front view, and each face can be set out directly by laying off the front view, checking that the two sloping sides are equal in the symmetrical case.
Side faces. These are not parallel to the frontal plane, so neither the sloping bottom edge nor the front-to-back top edge is true length in the front view. The top edge runs front-to-back: it appears as a point in the front view and at true length (the duct depth) in the plan. The inclined bottom edge is inclined in both views, so its true length must be constructed: take its horizontal projection from the plan and the height difference of its two ends from the front view, then build the right triangle - the hypotenuse is the true length used in the development.
Because a side face is a general quadrilateral, develop it by triangulation: draw a diagonal, find its true length the same way (plan projection plus height difference), and build the two triangles side by side. Repeat mirrored, then attach the front and back trapezoids, hinging on the true-length corner edges.
3. Critique the junior drafter's proposal to lay off front-view lengths on all four faces and to add 6 mm of overlap at one corner. What will go wrong with the finished blank?
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The proposal fails on the side faces. A length read off a view is true only when the edge is parallel to that projection plane. On the left and right faces, both the inclined bottom edge and the front-to-back top edge are oblique to the frontal plane, so the front view shows them foreshortened; laying those lengths off produces a blank that is too small, the four faces will not close on the 60 mm square outlet, and the error grows with the 25° tilt - at the steepest corner edge the foreshortening is roughly 10%, several millimetres over a 100 mm edge, far outside any weld gap.
Two further points on the 6 mm overlap:
- It must be added outside the developed pattern on one edge only, and it is added to the pattern, not distributed around it; the developed length of the seam edge itself is unchanged.
- The seam should sit on a short corner edge where the lap is least visible and where it will not disturb the flange seating face. If the piece is folded rather than built from four separate plates, an overlap is the wrong allowance altogether: the blank must use the bend allowance on the neutral axis, since outside dimensions overstate the developed length at every fold.