Velocity Decay Curves

This diagram visualizes centerline velocity decay from the cooking surface up to hood mounting height for the papers’ reference source, a medium gas grill (40,000 BTU, Q_c = 8.2 kW). Stronger and weaker sources — a high-output gas grill at one end, a pellet smoker in low-smoke mode at the other — shift the curve up or down without changing its shape; the full set of eight source curves is tabulated in RB-003 §3.1.

Reference readings

Representative values below are computed directly from the same centerline-velocity function (physics/plume.mjs) driving the instrument above — the Heskestad relation with the source inputs of RB-001 Tables 3.1 and 3.2; live values update as you move the distance control. The table is regenerated by scripts/generate-reference-tables.mjs, never typed by hand.

Centerline velocity over the medium gas grill falls from about 508 fpm at 6 inches to 393 fpm by a 30-inch mounting height and 350 fpm by 48 inches — an inverse cube-root decay, not a linear one [RB-003 §2.1]. At the non-standard heights (6, 12, 42, 54, 60, 72 inches) these are the cells RB-003 Table 3.1b prints; at the standard heights (18–48 inches) RB-003 v1.0 carried RB-001 Table 3.5’s hand-rounded values (453/417/392/370/337 fpm), which the paper itself noted sat 1–4% off its own formula; its Revision history (v1.1, 2026-09-26) regenerates those rows from the formula, as RB-001’s does for Table 3.5 [RB-003 §3.1]. The values here are the same recomputation from the Heskestad relation with RB-001 Table 3.2 inputs — 435/412/393/377/350 fpm — and match the printed v1.1 cells. Even at 72 inches, well beyond any standard mounting height, this plume’s centerline velocity (314 fpm) is three times the 100 fpm face-velocity figure indoor practice treats as a minimum [RB-003 §3.1]. The velocity loss from 24 to 48 inches (412 to 350 fpm, a 15% drop) is small next to the growth of plume mass flow over the same interval — the RB-008 exhaust requirement climbs as z^(5/3), from 550 to 1,518 CFM for this source under moderate exposure — which is why CFM, not centerline velocity, governs hood sizing at greater mounting heights [RB-003 §4.1; RB-008 §2.4, Table 3.2b].

Key Findings

All source types keep capture-viable velocities at standard mounting heights. Even the pellet smoker in low-smoke mode (Q_c = 1.5 kW) holds about 222 fpm at 30 inches and still about 178 fpm at 72 inches (RB-003 Table 3.1b; v1.0 printed 179), so velocity decay alone does not cause capture failure for properly sized hoods [RB-003 §3.1, §4.1].

The practical constraint is not velocity but plume width and mass flow. While centerline velocity remains adequate, the capture diameter grows at 0.48 inch per inch of rise and the plume mass flow as z^(5/3), requiring progressively larger hood coverage and higher CFM to capture the widened plume [RB-002 §3.4; RB-008 §2.4].

The velocity hierarchy is preserved at every height. At 30 inches the eight modeled sources run from about 222 fpm (pellet smoker, low) to 485 fpm (high-output gas grill), a ratio of roughly 2:1 that holds at all heights because every source follows the same (z − z_0)^(−1/3) law with a different Q_c^(1/3) prefactor [RB-003 §3.1]. The charcoal kettle’s 230 fpm at 30 inches — below a 25,000 BTU gas grill’s 342 fpm despite a comparable rating — is the charcoal paradox: only 40% of its heat goes into the plume [RB-001 §4.3].

Governing Equation

The live instrument draws the papers’ reference plume, not a separate curve per source type:

u_0(z) = 1.03 · Q_c^(1/3) · (z − z_0)^(−1/3) [m/s]

with Q_c = 8.2 kW and the tabulated virtual origin z_0 = −0.37 m for the medium gas grill (RB-001 Tables 3.1–3.2), converted to ft/min [RB-001 §2.2; RB-003 §3.1]. The inverse cube-root law produces a gradual decay — velocity falls slowly with height because the plume keeps converting buoyancy to momentum even as it entrains ambient air. Because z_0 is negative, the relation stays finite at the cooking surface itself; the per-source comparisons above use the same formula with each source’s own Q_c and z_0.

Source Papers

• RB-001: Buoyant Plume Behavior — Heskestad correlations (§2.2), source heat release rates and virtual origins (Tables 3.1–3.2)
• RB-003: Velocity Decay and Capture — Continuous velocity profiles (§3.1) and why CFM, not face velocity, governs (§4.1)