Physics · 5 min read
How End Corrections Affect Velocity Stack Sizing
An open mouth behaves a little longer than the wall — L_eff ≈ L_phys + kD
An open pipe reflects slightly outside the physical lip, so the acoustic length is a bit longer than the wall you can measure. This tutorial uses the teaching correction L_eff = L_phys + kD, a 50 mm mouth at k = 0.3, and the stack split after a 350 mm runner. The Velocity Stack Calculator leaves the correction off until you turn it on.
Written by the My Calculator Stack editorial team. About our methods
k is a teaching factor in a typical 0.3–0.6 band, not a measured discharge coefficient. Diameter here is only for kD. Confirm the length on the engine.
1.Why the mouth is “longer” than the metal
A pressure wave does not reverse exactly in the plane of the flare. The antinode sits a fraction of a diameter outside an open end. Acoustics texts write that extra piece as kD, with D the mouth diameter and k a factor that depends on the flange or flare. A sharp unflanged pipe can sit near k ≈ 0.6; a flanged or well-radiused stack is often taught around 0.3–0.4. The Velocity Stack Calculator defaults k to 0.3 when the correction is On. It does not size the bore for flow; D is only the length tick.
2.Where kD sits in the budget
The quarter-wave formula already reports an effective length L_eff. If that L_eff includes the end effect, the physical wall you cut is shorter: L_phys ≈ L_eff − kD. After you subtract the existing runner, the trumpet piece is L_stack ≈ L_eff − L_existing − kD. Leave the correction Off when you want a wall-length budget with no extra theory. Turn it On when you want that extra diameter of length pulled out of the stack rather than out of the runner.
\[ L_{\mathrm{stack}}\approx L_{\mathrm{eff}}-L_{\mathrm{existing}}-kD \]
3.Worked example: 50 mm mouth, k = 0.3
Defaults again: L_eff = 571.7 mm at 6000 rpm, S = 2, O = 3, C = 343 m/s. Existing runner 350 mm. Correction off, stack = 221.7 mm. Turn On, D = 50 mm = 0.050 m, k = 0.3. Then kD = 0.015 m = 15 mm, and L_stack = 571.7 − 350 − 15 = 206.7 mm. At k = 0.6 the correction is 30 mm and the stack budget is 191.7 mm. Fifteen or thirty millimeters is a real cut on a short race trumpet; it is still smaller than picking the wrong odd order. If existing plus kD already exceed L_eff, the remainder goes negative — shorten the runner or change O or RPM.
\[ kD=0.3\times 50=15\,\mathrm{mm} \]
4.What end correction is not
kD is not a flow coefficient, not a filter-screen model, and not a reason the formula will match a dyno. A mesh, a rain cap, or a velocity-stack sock moves the reflection and the discharge; none of those appear in k. Diameter in this identity does not tell you whether the ITB is too small for the cylinder. If two websites disagree by about one diameter, check whether one of them baked in an unstated k.
5.Turn the correction on only when you mean it
The Velocity Stack Calculator hides D and k until end correction is On, then subtracts kD from the stack contribution. Compare Off versus On at the same RPM before you trim a trumpet. The 15 mm in the example is a teaching tick at k = 0.3, not a measured lab end correction for your flare. Cut metal after you have measured the runner; believe the dyno over k.
Try it yourself
Open the related calculator and put these formulas to work.