Two different total lengths
Finished projection P is the horizontal end-to-end distance, including both straight ends. Stock S is the developed base length of those same ends and the sloped middle section. Enter the known total and choose the quantity to solve. The independently entered tail is included in both totals.
Equations
For rise H and angle θ, sloped length = H / sin(θ), slope reach = H / tan(θ). Their difference is H × tan(θ / 2). Thus S = P + H × tan(θ / 2), or P = S − H × tan(θ / 2). Lead-in = P − tail − slope reach.
Worked example
For H = 150 mm, θ = 30° and P = 1000 mm, the developed stock is 1040.19 mm. Solving in reverse from that stock returns a 1000 mm projection.
Reference and limits
This is a base-reference offset calculation. It does not add material bend allowances. Negative lead-ins or overlapping cut envelopes are rejected; the totals cannot simply be accepted when the resulting geometry does not fit.
Scope
Ideal geometric solver. Excludes kerf, bend radius, material allowance and connection specifications. Reference-product modes remain separately under review.
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