BTTB
Three Centred Arch Calculator — Span & Rise Method
Calculates striking-point geometry, rise-based three-centred arch radii, and voussoir sizing using the construction method derived from span and rise.
Side sections may use odd or even brick counts. The middle section is forced to an odd brick count so there is always a centred key brick.
Side section · left and right symmetrical pair
Middle segmental section odd brick count · centred key brick
Joint rule used
Side sections: joints = bricks.
Middle section: joints = bricks + 1.
Therefore total joints = total bricks + 1.
Construction basis
The large construction arc is a quadrant struck from the centre of the span to the springing point.
The small upper construction arc is struck from the top of rise with a radius equal to the distance from the rise point to where the large arc meets the centre line.
The remaining chord from springing point to that upper-arc intersection is bisected at 90°.
Selection logic
For each section, the calculator chooses the arrangement that gets the extrados brick width as close as possible to 65 mm without exceeding it.
For the middle section, only odd brick counts are considered so there is always a centred key brick.