Physics · 5 min read
How Intake Air Temperature Changes Your Velocity Stack Estimate
C ≈ 331.3 √(1 + T/273.15) — warmer air, longer Ls at the same RPM
The wave in the runner travels at the speed of sound in the intake air. Hotter air raises C, and Ls scales with C, so a stack sized in a cold garage sits a few percent long once the bay is hot. This tutorial uses C ≈ 331.3 √(1 + T/273.15), the 0 °C versus 40 °C swing at 6000 rpm, and a temperature slider. The Velocity Stack Calculator uses the same C(T).
Written by the My Calculator Stack editorial team. About our methods
C(T) is a dry-air teaching fit, not a humidity-corrected lab speed. Under-hood air is often warmer than the shop. The length change is a few percent, not a reason to skip the dyno.
1.Why temperature shows up at all
Ls = (C × 60 × S) / (4 × N × O) is linear in C. If C rises 3%, the estimated tract rises 3% at the same RPM, stroke, and order. The trumpet does not expand that much; the wave speed does. A stack that was a quarter-wave at 20 °C is a slightly short quarter-wave in 40 °C air unless you add length. The reverse is true in winter. This is still the same quarter-wave estimate — temperature does not add cam timing or a plenum model.
2.C from Celsius
Dry air is taught as C ≈ 331.3 √(1 + T/273.15) with T in °C. At 0 °C, C = 331.3 m/s. At 20 °C, C ≈ 343.21 m/s. At 40 °C, C ≈ 354.73 m/s. The Velocity Stack Calculator uses that fit unless you type a manual C greater than zero, which replaces C(T). The form’s 343 m/s override is a rounded 20 °C value, not a second formula. Humidity and fuel vapor move C a little; this page does not model them.
\[ C\approx 331.3\sqrt{1+T/273.15} \]
3.Worked example: 0 °C versus 40 °C
Hold four-stroke S = 2, N = 6000 rpm, O = 3. Then Ls = C / 600 meters (because 60 × 2 / (4 × 6000 × 3) = 1/600). At 0 °C, Ls = 331.3 / 600 = 0.5522 m = 552.2 mm. At 40 °C, Ls ≈ 354.73 / 600 = 0.5912 m = 591.2 mm. That is about 39 mm, or roughly 7%, between a cold shop and a hot bay. With the typed C = 343 override you get the familiar 571.7 mm. Type temperature when you care about the swing; type 343 when you want the documented golden.
\[ L_s=C/600\quad(N=6000,\,S=2,\,O=3) \]
4.Temperature playground
Move intake air temperature to recompute C and the 6000 rpm / O = 3 four-stroke length. This widget does not include the manual C override, end correction, or an existing runner — those live on the calculator. Use it to see that a 20 °C guess is a starting point, not a lab measurement of the air in the port.
Inline playground
Speed of sound C
343.21 m/s
Effective length Ls
572.0 mm
C ≈ 331.3√(1+20/273.15) ≈ 343.21 m/s → Ls ≈ 572.0 mm
C ≈ 331.3 √(1 + T/273.15), then Ls at 6000 rpm, four-stroke S = 2, O = 3. Teaching widget — not a dyno, no C override.
Open the full Velocity Stack calculator →5.Use C(T) or the override on the calculator
On the Velocity Stack Calculator, leave the override at 0 (or clear it) to follow temperature, or type 343 to match the worked examples on that page. Solve-for-C is a sanity check on a measured length and RPM, not a thermometer. A few percent of length from heat is real; it is still smaller than the gap between this estimate and a dyno pull.
Try it yourself
Open the related calculator and put these formulas to work.