Physics · 5 min read
How to Compare Odd Harmonics in a Velocity Stack Length Table
Orders 1, 3, 5, 7 at one C and S — length falls as 1/O
One RPM produces four odd-harmonic lengths, not one magic trumpet. This tutorial reads the 1 / 3 / 5 / 7 table at 6000 rpm and C = 343 m/s, then lets you slide RPM so the rows update. The Velocity Stack Calculator prints the same table. Use it to compare long versus short, not to skip a dyno.
Written by the My Calculator Stack editorial team. About our methods
The table is the same quarter-wave identity at four odd orders. It is not a power band, a cam model, or a ranking of which order “makes more power.”
1.Why a table instead of one O
Once C, S, and N are fixed, each odd order is just a different divisor. O = 1 is three times O = 3; O = 5 is three fifths of O = 3. Writing them in one grid stops you from treating 571.7 mm as the only answer at 6000 rpm. It also shows why a first-harmonic tube is rarely a street ITB: 1715 mm from valve to mouth is a plumbing problem. The table does not say which row will make the most torque. It only says which length each order wants at that engine speed.
2.The same formula, four divisors
Ls = (C × 60 × S) / (4 × N × O) with O in {1, 3, 5, 7}. Flip it and the table can hold RPM at a fixed length: N = (C × 60 × S) / (4 × Ls × O). The Velocity Stack Calculator uses the length form when you solve for length, and the RPM form when you solve for engine speed. This tutorial’s grid is the length form at C = 343 m/s and four-stroke S = 2, matching the calculator defaults.
\[ L_s=\frac{C\times 60\times S}{4 N O},\quad O\in\{1,3,5,7\} \]
3.Worked table at 6000 rpm
C = 343 m/s, S = 2, N = 6000. Then Ls in millimeters is 1715 / O. Order 1: 1715.0 mm (67.52 in). Order 3: 571.7 mm (22.51 in). Order 5: 343.0 mm (13.50 in). Order 7: 245.0 mm (9.65 in). If you instead keep the 571.7 mm third-harmonic length and ask what RPM the other orders would want, O = 1 wants 18000 rpm, O = 5 wants 3600 rpm, and O = 7 wants about 2571 rpm. That inverse read is why a short stack is not “the same tune at a different O.”
\[ L_s(\mathrm{mm})=1715/O\quad(N=6000,\,C=343,\,S=2) \]
4.RPM playground
Move target RPM to rebuild the four-row length table at C = 343 m/s and S = 2. The highlighted row is O = 3, the usual street start. This widget does not subtract an existing runner or kD. Open the calculator when you want those, or when you want the table in RPM-from-length mode.
Inline playground
| Order O | Ls (mm) | Ls (in) | vs O = 3 |
|---|---|---|---|
Ls = (343×60×2)/(4×6000×O) at S = 2
C = 343 m/s, four-stroke S = 2. Length falls as 1/O. Teaching table — not a dyno.
Open the full Velocity Stack calculator →5.Read the calculator table the same way
The odd-harmonic comparison on the Velocity Stack Calculator is this grid, not a second theory. Change RPM or C and every row moves together. Pick one row as a starting cut, subtract the runner you measured, then verify the engine. Four lengths at one RPM is still one estimate times four; none of them is a dyno sheet.
Try it yourself
Open the related calculator and put these formulas to work.