Graham Bell formulas used
Wave speed
c = 20 √(T + 273) [m/s]
T = exhaust gas temperature in °C. Hotter gas = faster waves = shorter pipe for the same RPM.
Tuned length
Lₜ = (θ × c × 1000) / (6 × N) [mm]
θ = exhaust duration ÷ 2 (degrees). N = target RPM. Lₜ runs from the flange to the baffle end; stinger L₂ extends past it.
Header diameter
D₁ = √(4 × Aport × k / π)
k ≈ 1.15–1.20 per Jennings. Port area = width × height.
Cone lengths
L = (Dlarge − Dsmall) / (2 tan A)
A = half-angle of diffuser (A₁) or baffle (A₂). Belly L₅ fills the remainder of Lₜ. Use the powerband peak slider to bias toward a sharp narrow RPM window (steep cones, short belly) or a broad usable band (gentle cones, long belly).
Stinger
L₂ = 12 × D₃
D₃ ≈ 0.5–0.6 × D₁. Bleeds average pipe pressure.
How to read the drawing
The side-view profile matches the classic expansion-chamber layout: constant-diameter header, expanding diffuser, parallel belly, contracting baffle, and narrow stinger. At true scale a 50cc pipe is roughly 1 meter long and 80–120 mm across the belly — so it will look like a wide panorama, not a chunky silencer. Labels L₁–L₇, D₁–D₃, A₁–A₂, and Lₜ follow the same convention used on moped tuning nomographs.
Pair this tool with the exhaust duration calculator for your port height, then plug that duration here. After metal is cut, fine-tune peak RPM by shortening or lengthening the header in small steps — roughly 25 mm shifts peak RPM a few hundred revs on a 50cc pipe.
Before you weld
- This is a starting-point design — secondary waves, silencer back-pressure, and multi-cone stages are not modeled.
- Automatic-clutch mopeds need conservative blowdown — do not pair a race pipe with wild port timing without clutch work.
- Always jet and plug-chop after any pipe change. A pipe without matching carburetion seizes pistons.
- See staged build paths in the Performance Building Database.