Centered Rectangular Funnel with Unequal Face Slopes

Define the opening centers and setbacks

Center the 800 by 600 mm upper opening above the 400 by 300 mm lower opening, with 500 mm between their planes. Both offset inputs are zero. This layout uses four planar panels and two different pairs of face slopes.

The half difference along X is (800 − 400) / 2 = 200 mm. Along Z it is (600 − 300) / 2 = 150 mm. Each face uses the setback perpendicular to its own end edges. The long faces span along X and use the 150 mm Z setback.

The short faces span along Z and use the 200 mm X setback. Although both openings share one centerline, the two pairs have different slopes because their setbacks differ. Use the general rectangular funnel tool to keep these dimensions editable as a complete example.

Calculate each face and corner

The long-face slant height is √(500² + 150²) = 522.02 mm. The short-face slant height is √(500² + 200²) = 538.52 mm. Each height lies within its panel and is perpendicular to the two parallel opening edges. Measure the 500 mm vertical height between opening planes.

The corner edge moves 200 mm along X and 150 mm along Z while rising 500 mm. Its true length is √(500² + 200² + 150²) = 559.02 mm. All four corners have this length because the two opening centers coincide.

Each long panel area is (800 + 400) × 522.015325… / 2 = 313209.20 mm². Each short panel area is (600 + 300) × 538.516481… / 2 = 242332.42 mm². Add two of each to obtain 1111083.22 mm² of ideal panel area, using full precision throughout.

Worked example dimensions

Lay out and identify all four panels

Draw the long panels with parallel 800 and 400 mm edges, separated by their 522.02 mm slant height. Center the shorter edge, leaving a 200 mm shift at both ends. Draw the short panels with 600 and 300 mm edges separated by 538.52 mm and a 150 mm shift at both ends.

Check every oblique joining edge against 559.02 mm. Label the two long and two short panels before cutting. Their adjoining edges match even though the pairs have different perpendicular face heights. Follow the numbered panel dimensions in the model to keep each measurement on its intended face.

Original and Mark show developed outlines, Cut separates the four panels and Form assembles them between the centered openings. Rotate the model to inspect both ends and all corner seams. Review actual thickness, seams, kerf and fabrication allowances when preparing the final workshop blank.

Review the fabrication detail

This layout develops ideal separate panels. Add the selected seam details and material allowances after reviewing the actual fabrication method.