Research Reports

Dual-path exhaust — sizing sheets

A split-exit muffler bypass with a cable-operated valve, sized for depth rather than for power. The architecture is one wye, one valve and one extra tailpipe; what changes between engines is only the diameters and one length. Every figure here is modelled, not measured.

Master sizing & tip-profile reference — one table, every platform

Master sizing & tip-profile reference — one table, every platform Consolidates 16-UNIVERSAL-PH-PETROL-STOCK-MAIN-BYPASS.svg, 17-UNIVERSAL-PH-DIESEL.svg and the per-engine build examples into one sizing table and one tip/bypass reference · split-exit muffler bypass, cable valve, Deep Open tip · all diameters Ø mm, lengths mm · 2026-09-22 1 · Architecture — one build, every platform Letters match the platform table below: A = main run, B = bypass (loud branch main diameter), C = stub, D = reducer cone, E = tip. Read Ø and mm off the tables — the picture never changes. MAIN A stock / sized per table 30° WYE quiet → stock muffler, own tip (unchanged) stub C build / max cable valve straight (∝ B) FREE LENGTH — sets f₁ MIN or MAX — §4 cone D, 7° half-angle DEEP TIP E §3 sets Ø from B own exit — no rejoin 2 · Master platform table — Main A, and B/tip for every profile SPORT-RASPY steps bypass −1 ladder rung from Deep; AERO steps −2 (or "already at floor"). Tip in each column = nearest ladder rung to 1.5×that column's bypass, capped Ø102 (§4). Diesel has no derived Sport/Aero step yet — shown as "—, not derived" rather than guessed. PLATFORM cc REDLINE MAIN A DEEP · B / TIP SPORT-RASPY · B / TIP AERO · B / TIP STUB build/max A · TRIPLES Suzuki Multicab F6A 660 6,000 rpm Ø38 38/57 at floor at floor 100/512 Toyota Wigo 1KR-FE 998 6,000 rpm Ø45 45/63 38/57 at floor 109/512 Mitsubishi Mirage G4 3A92 1,193 6,000 rpm Ø45 45/63 38/57 at floor 109/512 B · 1.3–1.5 FOURS Mitsubishi Lancer CB 4G13 1,298 6,500 rpm Ø45 45/63 38/57 at floor 109/355 Mitsubishi Lancer CK 4G15 1,468 6,500 rpm Ø45 45/63 38/57 at floor 109/355 Honda Civic EG/EK D15B 1,493 6,800 rpm Ø51 51/76 45/63 38/57 117/339 Toyota Vios 1NZ/2NR-FE 1,497 6,400 rpm Ø45 45/63 38/57 at floor 109/360 Honda City L15 1,497 6,500 rpm Ø45 45/63 38/57 at floor 109/355 Kia Rio DC A5D 1,493 6,500 rpm Ø51 51/76 45/63 38/57 117/355 C · 1.6–1.8 FOURS Toyota Corolla AE92/101 4A-FE 1,587 6,300 rpm Ø51 51/76 45/63 38/57 117/366 Honda Civic EK D16 1,590 6,800 rpm Ø51 51/76 45/63 38/57 117/339 Mitsubishi Lancer CK 4G92 1,597 7,000 rpm Ø45 45/63 38/57 at floor 109/329 Toyota Corolla AE101 7A-FE 1,762 6,300 rpm Ø51 51/76 45/63 38/57 117/366 Mitsubishi Lancer CK 4G93 1,834 7,000 rpm Ø45 45/63 38/57 at floor 109/329 D · HIGH-REV FOURS Toyota Corolla AE111 4A-GE 20v 1,587 8,000 rpm Ø51 51/76 45/63 38/57 117/288 Honda Civic EG/EK B16A 1,595 8,200 rpm Ø51 51/76 45/63 38/57 117/281 A · NA DIESEL 2.4–2.8 — jeepney/L300 class Isuzu C240 2,369 3,000 rpm Ø51 45/63 —, not derived —, not derived 101/610 Isuzu 4JA1 2,499 4,000 rpm Ø57 51/76 —, not derived —, not derived 109/457 Hyundai D4BA 2,476 4,000 rpm Ø57 51/76 —, not derived —, not derived 109/457 Nissan TD27 2,663 4,000 rpm Ø63 57/89 —, not derived —, not derived 116/457 Isuzu 4JB1 2,771 3,800 rpm Ø57 51/76 —, not derived —, not derived 109/482 Toyota 3L 2,779 4,000 rpm Ø63 57/89 —, not derived —, not derived 116/457 B · NA DIESEL 3.0–3.9 — light truck / Canter class Toyota 5L 2,986 4,000 rpm Ø63 57/89 —, not derived —, not derived 116/457 Nissan QD32 3,153 3,800 rpm Ø63 57/89 —, not derived —, not derived 116/482 Isuzu 4BC2 3,268 3,800 rpm Ø63 57/89 —, not derived —, not derived 116/482 Mitsubishi 4D30 3,298 3,500 rpm Ø63 57/89 —, not derived —, not derived 116/523 Isuzu 4BE1 3,568 3,400 rpm Ø63 57/89 —, not derived —, not derived 116/538 Toyota 14B 3,661 3,400 rpm Ø63 57/89 —, not derived —, not derived 116/538 Mitsubishi 4D34 3,907 3,200 rpm Ø63 57/89 —, not derived —, not derived 116/572 (unofficial) Isuzu 4BA1* 2,776 3,800 rpm* Ø63 57/89, floor —, not derived —, not derived 116/482 C · TURBO / COMMON-RAIL 2.4–2.5 Mitsubishi 4N15 2,442 3,500 rpm Ø89 76/102 —, not derived —, not derived 140/523 Mitsubishi 4D56T 2,477 4,200 rpm Ø89 76/102 —, not derived —, not derived 140/436 Toyota 2KD-FTV 2,494 3,600 rpm Ø89 76/102 —, not derived —, not derived 140/508 Isuzu 4JK1 2,499 3,600 rpm Ø89 76/102 —, not derived —, not derived 140/508 Hyundai D4CB 2,497 4,000 rpm Ø89 76/102 —, not derived —, not derived 140/457 D · TURBO / COMMON-RAIL 2.8–3.2 Toyota 1GD-FTV 2,755 3,400 rpm Ø89 76/102 —, not derived —, not derived 140/538 Mitsubishi 4M40 2,835 4,000 rpm Ø102 89/102 —, not derived —, not derived 156/457 Toyota 1KD-FTV 2,982 3,400 rpm Ø89 76/102 —, not derived —, not derived 140/538 Isuzu 4JJ1 2,999 3,600 rpm Ø89 76/102 —, not derived —, not derived 140/508 Mitsubishi 4M41 3,200 3,800 rpm Ø102 89/102 —, not derived —, not derived 156/482 * Isuzu 4BA1 not in the official 24-platform table — sourced from 18-BUILD-D15B-UNIVERSAL.svg, redline unverified. 3 · Branch length — fixed segments by bypass class, MIN/MAX totals by class straight = 3.5×B · cone = Δradius/tan 7° half-angle, 14° incl. (B→tip) · tip length = 3.5×tip. Only stub build differs between fuels at the same B (different valve-body constant — a known, logged discrepancy, not re-unified here). f₁ = c/2L; taper +9% central is a working correction (02-SYNTHESIS.md §3), not measured — re-verify against a built branch. CLASS (fuel · bypass) STUB STRAIGHT CONE TIP Ø / LEN MIN TOTAL f₁ MIN raw/taper MAX TARGET f₁ MAX raw/taper Petrol · B=Ø45 109 158 73 Ø63 / 220 560 mm 464 / 506 Hz 3 500 mm 74 / 81 Hz Petrol · B=Ø51 117 178 102 Ø76 / 266 663 mm 392 / 427 Hz 3 500 mm 74 / 81 Hz NA diesel · B=Ø45 (C240) 101 158 73 Ø63 / 220 552 mm 453 / 494 Hz 3 000 mm 83 / 91 Hz NA diesel · B=Ø51 109 178 102 Ø76 / 266 655 mm 382 / 416 Hz 3 000 mm 83 / 91 Hz NA diesel · B=Ø57 116 200 130 Ø89 / 312 758 mm 330 / 360 Hz 3 000 mm 83 / 91 Hz Common-rail · B=Ø76 140 266 106 Ø102 / 357 869 mm 305 / 333 Hz 3 400 mm 78 / 85 Hz Common-rail · B=Ø89 156 312 53 Ø102 / 357 878 mm 302 / 329 Hz 3 400 mm 78 / 85 Hz MAX targets are round, chosen figures — not derived per platform — chosen to clear the taper-corrected 100 Hz floor with 9–19 Hz margin (recomputed 2026-09-22; was 4–11 Hz at the old manifold-station c) (see 03-PREDICTIONS.md §2 P3). 4 · Changing the tip vs changing the bypass — they are not the same lever Changing the TIP diameter (E) Does NOT change radiated power (F2, withdrawn a⁴ claim) — tip radius cancels out of the power equation entirely at fixed volume velocity. Does NOT change firing frequency (f = (cyl/2)×RPM/60, set by the engine, not the pipe). What it DOES do: lowers exit velocity → less flow-generated hiss, and reflects more HF content back upstream. Psychoacoustic — bass sounds relatively louder because treble is suppressed, not because bass increased. Never cite a dB figure for it. Changing the BYPASS diameter (B) This is the real profile lever — SPORT-RASPY and AERO in §2 are nothing but a smaller B. Smaller B at the same flow rate raises velocity — table 2's whole −1/−2 ladder is exactly that. What it DOES do: raises broadband flow noise and edge/turbulent hiss (genuinely, this time — velocity actually went up). Also resets the tip target, since tip = 1.5×B capped Ø102 (§2) — step B down and the "deep" tip target shrinks with it, e.g. Ø51→Ø76 becomes Ø45→Ø63 one step down. Ladder and cap: tip = nearest rung to 1.5×B, capped Ø102 — the withdrawn a⁴ formula's multiplier, kept as a practical target (not a dB one) after F2. Corrected 2026-09-22: the Ø51-bypass petrol class's tip was previously given as Ø89, read off a one-off prose example rather than this ladder rule. It is Ø76. DEEP OPEN TIP — the profile used throughout Large unobstructed smooth bore, radiused lip, no internal edges, no slots/perforations. Suppresses exit-velocity hiss and reflects HF content upstream — psychoacoustic depth, not a radiated-power gain (F2, withdrawn a⁴ claim). Never cite a dB figure for it. This sheet supersedes the per-engine schematics in the prior revision of 32-BUILD-EXAMPLES-DEEP-PETROL-DIESEL.svg (6 groups, one schematic each) — same source numbers, now one continuous table plus one shared schematic. C240 and Suzuki Multicab F6A remain the only true singletons (no ladder partner at their exact B/tip). Sources: sizing from 16-UNIVERSAL-PH-PETROL-STOCK-MAIN-BYPASS.svg and 17-UNIVERSAL-PH-DIESEL.svg's own published tables, not re-derived. Dimension formulas from 15-SIZING-RULE-OF-THUMB.md §6 and 14-HANDOFF-TO-PETROL.md §2g. Deep Open tip from 29-CATALOGUE-DIESEL-TIP-PROFILES.svg card 1. Architecture from 11-/13-/31-. Taper correction from catalogue-audit-2026-09-21/02-SYNTHESIS.md §3 (working correction, not measured — P4). Diesel Sport/Aero profile columns are a genuine gap, not yet derived — shown as "—", never guessed. All figures modelled, not measured. This project is sound-only: nothing here is a restriction warning. Bypass velocities were removed 2026-09-22 — see the correction band. 32-BUILD-EXAMPLES-DEEP-PETROL-DIESEL.svg · master sizing & tip-profile reference · 2026-09-22 5 · What never changes — same on every engine in the table ◆ One wye, one valve, one extra tailpipe. Split-exit muffler bypass, no rejoin. The stock muffler and tailpipe are untouched, so the quiet path is the car's original exhaust. ◆ Cable to a cabin lever — butterfly position sets volume. The valve is the only restriction; there is no separate dB-killer component. Return spring closed, so it fails quiet. ◆ Firing frequency f = (cylinders / 2) × RPM / 60 — RPM/30 for a four, RPM/40 for a triple. Nothing in the pipe changes it. Diameter sets character; the tip sets how much bass you hear. ◆ Stub: build to the mechanical floor — about 1.25 × bypass Ø for the crotch, plus half a valve body. Where the λ/4 notch lands on the 2nd harmonic is a check, never a target. ◆ The tip ladder caps at Ø102. Above Ø89 the 1.5×B rule would ask for ~Ø133, which is not a standard rung. ◆ MIN branch is a floor, not a target. It is only the fixed segments added up; at that length f₁ sits far too high to be deep. Every extra metre you can route drops it. ◆ f₁ is the same for every diameter — open-open resonance depends on length alone, f₁ = c/2L. Diameter does not appear in it. 6 · The cabin band — why “longer is deeper” is a trap 100–160 Hz is the cabin band. Passenger-cabin structural and air-cavity modes sit there. The obvious advice — longer branch, deeper tone, run it to the bumper — aims f₁ straight into it. Length still sets f₁, so choose a length that AVOIDS 100–160 Hz rather than one that maximises depth. The diesel branch already hit this at 67 Hz (07-DESK-ANALYSIS-DIESEL.md); the same trap reappears at petrol frequencies. The MIN/MAX targets in §3 are chosen to clear the band on both sides — that is what they are for. 7 · Cat / DOC delete — the numbers barely move, the tone does not survive Sizing: a petrol cat is exothermic, so gas downstream runs 50–100°C cooler once it is gone — under half a size step. NA diesel columns already assume no cat. A diesel DOC is only mildly exothermic, so deleting it costs ~30°C and moves two common-rail rows down one rung (4N15 Ø89→Ø76 · 4M40 Ø102→Ø89). Everything else is unchanged. ⚠ The tone does not survive, even though the numbers do. On petrol the cat is the dominant HF filter; without it the rasp it was absorbing reaches the tips. That is the single worst change you can make to a deep build. Diesels have little HF filtering to begin with, so the same geometry rasps harder there. ⚠ Turbo engines: the turbine sits upstream of everything you can modify and has already flattened the pulse edges. A cat-back valve changes far less than on an NA engine — test before spending. A DPF is a different matter again: it is an enormous filter and removing it transforms the system. Not modelled here. ⚠ RECOMPUTED 2026-09-22 — two corrections applied to this sheet, both from cross-model audits in this repo 1 · All 62 bypass velocity figures are REMOVED, not corrected. They were computed from TOTAL engine flow. The bypass never receives total engine flow — the stock muffler path stays open, and parallel branches divide flow by their resistances. The split cannot be derived without modelling both paths, so no honest velocity exists for this column. Diameters are retained; the velocities are gone. Bypass Ø is now a fabrication heuristic, not a derived value. 2 · Every f₁ in §3 is recomputed at MID-PIPE temperature. The published c values implied manifold-station gas: petrol 615 m/s → 941 K, common-rail 592 → 872 K. This repo's own exhaust-sizing-method-audit-2026-09-14 found unanimously (A3) that a mid-chassis wye sees 620–720 K. Corrected: petrol 520, NA diesel 500 (was 488 — already mid-pipe-like, nudged to its own stated 350°C), common-rail 530 m/s. Petrol and common-rail f₁ drop ~11%; NA diesel rises ~2%. No build advice reverses. Every MIN/MAX branch target still clears the 100–160 Hz cabin band after recomputation (worst case 91 Hz). The §2 diameter ladder, the tip rule and §4's tip-vs-bypass distinction are unaffected — none of them depended on the flow split or on c. Record: _meta/CONTRADICTIONS.log MERGE-03 / MERGE-07 · research-reports/exhaust-merge-audit-2026-09-22/02-SYNTHESIS.md · c remains NOMINAL until an IR reading exists. ⚠ CORRECTION 2026-10-12 — diesel loud path and the D4BA row, from the D4BA deep + loud audit in this repo 1 · Cat-less NA diesel rows: the bypass needs high-frequency stages. “The valve is the only restriction” holds only where a catalytic converter, DOC or turbine is stage one (petrol, common-rail and turbo diesels). An old NA diesel has none of them, so the open bypass passes its 0.5–4 kHz injection clatter unfiltered: louder, not deeper. Desk estimate for a packed straight-through can (Ø124 × 350 mm, 350 °C): 1.9–3.4 dB lost at 67–100 Hz against 7–8.5 dB at 250 Hz–1 kHz, so leaving it out tilts the balance ~5 dB towards harsh. Fix: a packed straight-through can upstream of the wye (serves both paths) plus a packed can on the bypass, both flanged for soot. Never an open dump. Valve within 110 mm of the wye crotch, so the closed bypass is not a soot dead end. “Two stages, not one” rests on field reports (weak). 2 · The D4BA row is stale. Ø57 main with a 51/76 bypass is the generic ladder. D4BA spec R1 §6 picks one build bore for every part (Ø57 / Ø60 / Ø63.5) from the stock downpipe ID measured with callipers, and never mixes sizes. Unchanged: every petrol and turbo-diesel row, and the diameters, lengths and f₁ of the other NA diesel rows. Only the loud-branch content moves. Record: _meta/audits/d4ba-deep-loud-exhaust-audit-2026-10-12/01-BUILD-SPEC-R1.md §1, §6 · 08-DUAL-PATH-OPTION.svg · SVG-INDEX.md
Everything below in one sheet: a single architecture schematic, one continuous table for all 40 petrol and diesel platforms (Main A, and bypass/tip for Deep, Sport-Raspy and Aero profiles side by side), the fixed-segment lengths and MIN/MAX branch targets by bypass class, and a plain explanation of what changing the tip actually does versus what changing the bypass does — they are not the same lever. Open full size

Universal DEEP — valved branch on an untouched stock exhaust

Universal DEEP — valved loud branch on a stock exhaust PH petrol platforms · v2, rebuilt 2026-09-22 after cross-model audit · three independent columns, no universal diameter-for-depth claim v1's bypass column is WITHDRAWN: it sized diameter from TOTAL engine flow, which the bypass never receives. v1 kept as universal-deep-petrol.v1-BANDED.svg. 1 · Method — leave the stock system alone, add one branch One formed wye ahead of the stock muffler, one valve, one branch, one tip. Quiet path never cut, so valve-shut is genuinely stock and the whole thing is reversible. stock main — untouched formed wye — 30° or 45° STOCK MUFFLER stock tip valve tip valve shut → stock valve open → two parallel paths ↑ the split is unknown without    modelling both paths 2 · Platform table — three INDEPENDENT columns. Do not collapse them into one diameter. platform cc rpm Q tot L/s f₁ Hz stub ≤mm bypass Ø — heuristic, not derived FLOW · input only ACOUSTIC · c-derived, transferable PACKAGING · measured per car Toyota Vios 1NZ-FE14976400156213≤305measure host ID → that, or +1 rungCorolla AE92/101 4A-FE15876300163210≤310measure host ID → that, or +1 rungCorolla AE111 4A-GE 20v15878000206267≤244measure host ID → that, or +1 rungCivic EG/EK D15B14936800165227≤287measure host ID → that, or +1 rungCivic EK9 B16B15958400218280≤232measure host ID → that, or +1 rungLancer CB 4G1312986500137217≤300measure host ID → that, or +1 rungLancer CK 4G92 MIVEC15977500195250≤260measure host ID → that, or +1 rungHonda City L1514976500158217≤300measure host ID → that, or +1 rungMirage G4 3A9211936000116200≤325measure host ID → that, or +1 rungKia Rio DC A5D14936500158217≤300measure host ID → that, or +1 rung ACOUSTIC column is safe. f₁ = (cyl/2)×rpm/60 is set by the engine; stub and length bands by c and geometry. Neither depends on the flow split. FLOW column is an INPUT, not an answer. Q is TOTAL engine flow at VE 0.85, mid-pipe 673 K. The bypass receives an unknown fraction — see §4. BYPASS Ø is a fabrication heuristic. Start at the host pipe's measured ID, or one nominal rung up where packaging and flow margin allow. It is not a depth rule. 3 · Branch length — the actual depth lever, and the only acoustically transferable number here Open-branch fundamental f₁ = c/2L. Longer = lower. Cabin modes sit at 100–160 Hz, so "run it to the bumper" aims straight at the drone band. SHORT ≤ 1.63 m   ·   AVOID 1.63–2.60 m   ·   LONG ≥ 2.83 m (taper-corrected, unmeasured) On most of these cars only the short side packages. Take it, and accept a higher f₁ rather than chasing depth into the drone band. 4 · What this sheet will not tell you ◆ How much flow the bypass gets. Parallel branches divide by resistance. Without modelling both paths the share is unknown — so no bypass velocity is quoted here. ◆ A diameter that produces depth. There isn't one. Velocity predicts flow noise and restriction, not depth. Depth comes from branch length and from removing treble. ◆ Anything about your car's upstream spectrum. Branch after a restrictive factory resonator and the valve dumps pre-muffled air. Check what sits upstream of your wye station. ◆ A dB figure from tip area. Tip radius cancels from radiated power at fixed volume velocity. Bigger tips cut hiss; they do not add bass. ◆ Your real c. 520 m/s is a nominal sheet constant at 673 K, not a measurement. Every length above scales with it. IR-check the wye station. v2 rebuilt after research-reports/exhaust-merge-audit-2026-09-22 (GPT + Gemini; Groq rejected). Reconciles four workspaces across two design tracks. See PLAN.md · _meta/CONTRADICTIONS.log MERGE-01…08.
A second, simpler route to the same idea: leave the factory system completely alone and add one branch. Its three columns are deliberately kept apart — flow is an input, the acoustic figures are the only transferable numbers, and bypass diameter is a fabrication heuristic rather than a derived value. It quotes no bypass velocity at all, because the branch only receives a share of total flow that cannot be derived without modelling both paths. Open full size

Build sheet — the Ø51 → Ø76 petrol tail from commodity parts

Universal petrol DEEP tail — Ø51 → Ø76, commodity parts The tail of the loud branch, after the valve · Ø51-pipe petrol class (Vios, Corolla, Civic, City, Lancer, Mirage, Rio) · v1 2026-09-28 after cross-model audit · modelled, not measured Packed liner WITHDRAWN at the tip (Ø76 core, 12 mm of wool). The tail stays hollow. Packing comes back as §8 — on the stub, Ø51 core in a Ø102 shell, 24 mm of wool. 1 · Geometry — from the master sheet's petrol B = Ø51 row, unchanged Smooth Ø51 → Ø76 cone into an open Ø76 tip with a clean square lip. "Deep" here means treble removed at a low-velocity exit. No bass is added and no decibel figure is claimed. VALVE flange Ø51 optional straight, plain Ø51 (packaging only) cone 7° half-angle Ø76 — open, nothing inside lip STUB 117 178 — optional CONE ~100 TIP 266 (3.5 × Ø76) installed valve-to-lip ≈ 485 mm (663 with the straight) — measure it after fit-up; that is the acoustic length. Branch f₁ ≈ 400 Hz nominal, ±10 %. 7° is the HALF-angle (14° included). A 100 mm commodity Ø51→Ø76 reducer is 7.1° half / 14.3° included — the sheet part. 80 mm is 8.9° half: still acceptable. Segment lengths are not additive: reducers slip 20–30 mm over each pipe. Cut list comes from the received parts (step 3). Lip finish outranks angle error. Square, single-wall, deburred, no weld bead standing into the bore. No drain hole. 2 · Parts — Shopee.ph, list prices scraped 2026-09-28 · parts ≈ ₱1,000–1,150 before welds # part spec — what to accept Shopee search phrase ₱ 1conetapered reducer Ø51→Ø76 stainless, ≥ 90 mm, smooth bore — inspect on receiptexhaust reducer 51 76 stainless326–400 2tip tubeØ76 × 1.2–1.5 mm wall, 300 mm (cut to 266 + insertion), 201 or 304not on Shopee — local dealer [ESTIMATE]200–350 3stub tubeØ51 × 1.2–1.5 mm, 150 mm (cut to 117 + flange seat + insertion)stainless tube 202 51mm · 304 tube 2 in120–376 4flange pairØ51 two-bolt with gasket, so the tail unbolts at the valveexhaust flange 51mm stainless264–290 5hangeruniversal rubber hook + a welded bracket on the tip tubeexhaust hanger rubber bushing universal87–156 Fallback for #1 if the reducer fails inspection: two-step Ø51→Ø63 + Ø63→Ø76 (₱319–330 each). One-part shortcut for #1 + #2: a "2-inch inlet / 3-inch outlet" tip, ₱581–894 — accept only if, on receipt: (a) the inlet slips onto the host pipe; (b) bore after the step measures ≥ 76 mm; (c) ≥ 266 mm of that bore exists after the step, not overall; (d) the step is a continuous cone, not a flat shoulder — a shoulder is disqualifying; (e) lip is single-wall and square, not rolled inward. Most such tips are shorter than (c). Expect to fail it. Upstream of this sheet, for scale only: Ø51 vacuum cutout valve set ₱1,089–1,262; cable valve ₱2,125; "Y type 3-way tee 51/57/63/76" ₱534 — angle unstated, must be a formed wye at 30–45°, never a saddle. Shopee listing IDs (shop/item) for every price above are in the audit spec, 04-BUILD-SPEC-R1.md. 3 · Tools — fit-up at home, four welds at the shop 4-inch angle grinder, 750–1200 W — the one purchaseangle grinder 4 inch 1200W · DCA · Lotus765–1,091 1 mm stainless cut-off wheels, 25–50 pcs (Lotus 1.0 ultra-slim is the right one)cutting disc 4 inch 1.0mm ultra slim89–379 80-grit flap disc — faces every cut squareflap disc 4 inch inox #80, per piece23–35 Vernier caliper — the incoming-inspection tool; without it step 2 cannot be donevernier caliper 150mm stainless120–418 Tape, marker, paper strip, round file, bench vise or two G-clamps, gloves, goggleson hand~100 Shop welds: flange–stub, stub–cone, cone–tip, hanger bracket — four seams, dressed flush insideany muffler shop [ESTIMATE]300–600 Own welder not recommended for one tail: MMA inverters ₱1,249–2,743 and gasless MIG ₱1,098–2,388 both burn through 1.2 mm stainless unless already competent, and flux-core wire rusts at the seam. For §5: IR thermometer gun −50~530 °C ₱325–364 (BSIDE, ANENG TH202). Tools subtotal with grinder, 50 discs, flap, caliper, IR gun ≈ ₱1,670. 4 · Procedure 1 · Measure the host. Caliper the valve outlet OD. "51 mm" parts slip over a 50.8 mm pipe; they do not fit 52. 2 · Inspect the reducer on receipt. Inlet ID, outlet ID, cone length, insertion depth each end. half-angle = atan((ID out − ID in) ÷ 2 ÷ cone length). Accept ≤ 8°. Reject > 9°, any internal shoulder, or a seam standing proud inside. Fall back to two-step. 3 · Cut list from the received parts, not from §1: stub = 117 + flange seat + insertion; tip = 266 + insertion. Write down the installed valve-to-lip length. 4 · Cut with the 1 mm disc, marking square with a wrapped paper strip. Face every cut square with the flap disc. Deburr inside with the round file. 5 · Dry-fit under the car: flange, stub, cone, tip. Mark where the hanger lands and which way the tip points — slightly down, clear of bodywork. The cone should drain toward the exit. 6 · Shop welds: flange–stub, stub–cone, cone–tip, bracket. Full circumference, then dress every internal seam flush — a bead in the bore is an edge-tone source. Do not let the shop neck the exit down "for sport". Exit stays Ø76. 7 · Lip: face the outlet square, deburr inside and out, no weld intrusion, no inward roll. 8 · Do not drill a drain. 9 · Fit via the flange; hang; check clearance by hand through full suspension travel. 10 · Verify against §5: cold leak-by check with the valve shut; hot IR reading at the wye after a loaded pull; phone FFT valve shut vs open at 2,500 / 3,500 / 4,500 / 5,500 / 6,500 rpm; listen for a whistle at part throttle. 5 · What should happen — and what it means if it doesn't ◆ FFT, valve open vs shut: engine-order peaks rise more than the > 2 kHz broadband floor. Floor up ≥ 6 dB more than the peaks = cone stalled or lip ragged. Check the lip first. ◆ No discrete whistle at part throttle. A whistle = an internal edge or the lip, not a length problem. Dress before changing anything else. ◆ IR at the wye after a loaded pull reads 350–450 °C (c ≈ 500–540 m/s). Outside that = every length on every sheet moves ≥ 10 %. ◆ Owner hears less hiss, "fuller", no bass claim. No change, or more hiss = Deep Open is not delivering on this car. Revisit a Ø102 packed variant, not a smaller exit. 6 · What this sheet will not tell you ◆ A dB figure. Tip radius cancels from radiated power at fixed volume velocity. Ø76 cuts hiss; it does not add bass. No diameter produces depth. ◆ How much flow the branch gets. Parallel paths divide by resistance; the share is unknown without modelling both. That is why §5 is measured on the car. ◆ Anything from packing. Both reviewers independently dropped the Ø76 packed liner. A packed variant needs a Ø102 shell, three transitions and 150–300 g/L of basalt or stainless wool. The same shell on the Ø51 stub gives 24 mm — that is §8. Or buy the resonator, §7 step 3. ◆ A branch that is acoustically inert. The ~400 Hz mode crosses the 2nd firing harmonic near redline on a 6,500 rpm four. Inherent in any short branch; not a defect of this one. 7 · What actually makes it deeper — in order of effect 1 · Branch length. f₁ = c / 2L. This tail alone (0.49–0.66 m) sits near 400 Hz; a branch ≥ 2.83 m sits near 80–90 Hz. That is the whole depth lever. Take the longest run that packages under the car; never land in 1.63–2.60 m (cabin drone). Measure the run before buying anything. On most of these cars only the short side fits — accept it. 2 · Treble removal at the exit: this sheet's open Ø76 tip. 3 · Still hissy? Build §8, or buy a factory straight-through resonator, Ø51 in/out, weld it inline directly before the cone (Shopee ₱1,935–2,050, HKS-style 2 in × 15 in). Cuts 0.8–2 kHz a few dB; nothing below. Never pack at the tip (Ø76 core). 8 · Tier 1b — packed stub, Ø51 core in a Ø102 shell: the full Notch-Damped Deep, and how it transfers A packed section is a perforated core + wool + shell, nothing else. At the tip the core is Ø76 and the wool 12 mm: withdrawn. On the stub the core is Ø51: same Ø102 shell, 24 mm of wool. VALVE shell Ø102 × 200, wool 170–345 g core Ø51 × 250 · Ø4 holes, 8 mm pitch, 20 per ring × 20 rings ≈ 20 % open · 20 mm blank under each cap cap 1: welded first cap 2: stitch-welded after packing cone, as §1 Ø76 tip, hollow Build order (the draft got this wrong): 1 · Drill + deburr the core. Cut shell, two Ø102 discs with a Ø51 hole (1.5 mm plate; no 51→102 reducer exists). 2 · Weld cap 1 to shell and core, full circumference. 3 · Pack by weight: 150–300 g/L × 1.15 L. Not "firm". 4 · Scourer ring; wool held 15 mm back from the seam. 5 · Cap 2: 4 × 15 mm stitches, shell side then core side. 6 · Dress internal beads. Then cone, tip, lip as §4. Wool: stainless first (₱881 / 3 m), fibreglass ₱222–390 with a 2–3,000 km first inspection. Basalt, Ø102 shell, 51→102 parts: not on Shopee — dealer. Adds ≈ ₱950–2,200 to Tier 0. Bought resonator ₱1,935 is the same money. Transfer to other classes — rules carry, numbers do not. Shell OD ≈ 2 × B (annulus ≥ 20 mm), packed length 4 × B, cone 7° half, tip 3.5 × Ø. class core B shell OD wool mm packed L cavity wool g holes × rings cone tip Ø / len stub MIN Tier 0 Petrol · B=Ø45 45 89 20.8 180 0.77 L 116–232 18 × 18 73 Ø63 / 220 109 560 Petrol · B=Ø51 51 102 24.3 200 1.15 L 172–345 20 × 20 102 Ø76 / 266 117 663 NA diesel · B=Ø45 (C240) 45 89 20.8 180 0.77 L 116–232 18 × 18 73 Ø63 / 220 101 552 NA diesel · B=Ø51 51 102 24.3 200 1.15 L 172–345 20 × 20 102 Ø76 / 266 109 655 NA diesel · B=Ø57 57 114 27.3 230 1.66 L 249–499 22 × 24 130 Ø89 / 312 116 758 Common-rail · B=Ø76 76 127 24.3 300 2.30 L 345–689 30 × 32 106 Ø102 / 357 140 869 Common-rail · B=Ø89 89 140 24.3 360 3.11 L 467–934 35 × 40 53 Ø102 / 357 156 878 Diesel: soot loads packing — stainless wool, Ø5 holes, inspect at the first 2–3,000 km valve-open [INFERRED]. Lower gas temperature is already in the class f₁. Common-rail: the wye sits after the DOC/DPF, never before. Same rule as the cat on petrol; the master sheet §7 covers the delete consequences. Transfers as-is: cone half-angle · tip = 3.5 × Ø · square lip · no drain · reducer inspection thresholds · cut list from received parts · weld order · density by weight · annulus ≥ 20 mm · hole pitch. Does not transfer: any absolute length (read the row) · f₁ (c differs by fuel) · tip Ø (per-class ladder, capped Ø102) · stub build (valve-body constant) · prices (Ø89–Ø140 shells are dealer items). Transfer to other sound profiles — the flange after the valve is the boundary. Wye, valve, stub and branch length are common; the profile is what bolts on after it. profile (29-CATALOGUE mechanism names) Tier 0 · stub / cone / Ø76 tip Tier 1b · packed stub note 1 Deep Open — smooth bore, radiused lip is this sheet optional — 2 Notch-Damped Deep — Deep Open + packing as-is is Tier 1b big on NA/IDI diesel; near-nil behind a turbo 3 Jet Wash — convergent throat stub only; cone runs Ø51 → throat, no Ø76 tip as-is size by area ratio + measured backpressure 4 Deep Jet Blend — jet source beside the mouth as-is, unchanged as-is second nozzle outside the plane, never in series 5 Dry Hiss / Multi-Jet — multi-hole plate as-is; plate in the tip mouth, holes ≥ 2,040 mm² conflicts packing removes the band this adds; pick one 6 Idle Bleed — spring flapper, Ø18 as-is + disc in the tip as-is redundant: cable valve near-closed is an idle bleed 7 Drone Slicer — folded λ/4, DISPUTED as-is; slicer is a side branch off the stub as-is do not build expecting a result 8 Edge Snarl — bluff ring outside the pipe as-is; ring replaces the square lip irrelevant soot cakes the edge in 5–10 h on IDI diesel 9 Whistle — sharp edge + cavity as-is; mouth add-on irrelevant 0.5 mm soot silences it; not recommended 10 Wide Mouth / Flare nothing to add: Ø76 tip is already the deep tip — directivity only (F2); do not build Sport-Raspy — not a tip: B one rung down, Ø45 B45 row: stub 109 · cone 73 · tip Ø63 × 220 B45 row: Ø89 shell packing removes the rasp; Sport + 1b contradict Aero — B two rungs down or at floor no B38 class row; at Ø45 it is Sport — not derived for diesel v1 2026-09-28 after _meta/audits/deep-tail-51-76-audit-2026-09-28 (GPT + Gemini, independent; Groq not run). Geometry: 32-BUILD-EXAMPLES petrol B=Ø51 row. [ESTIMATE] = no listing. CONTRADICTIONS.log TAIL-01, TAIL-02.
The tail of that branch, after the valve, as something an ordinary muffler shop can build from Shopee parts: one tapered reducer, two lengths of tube, a flange and a hanger, for roughly seven hundred to a thousand pesos before welding. It carries the parts list with search phrases, the tool list, a ten-step procedure, and the checks that tell you whether the reducer you received is the part the sheet assumes. The packed liner at the tip was dropped in audit — a Ø76 core leaves no room for wool to do anything — so the tail itself stays hollow and the sheet makes no decibel claim. It closes with the order of things that actually make the branch deeper (length first, the open exit second) and then the full Tier 1b build: the same packing moved onto the stub, a Ø51 perforated core in a Ø102 shell with the assembly order that keeps the weld heat off the wool, plus two transfer tables: one carrying the rules to the other petrol and diesel classes without carrying the numbers, and one saying which parts of the tail survive a change of sound profile, from Jet Wash to Edge Snarl, with the flange after the valve as the boundary where the profile begins. Open full size

Worked example — Kia Rio DC, A5D 1493cc

Kia Rio DC · A5D 1493cc — dual-path system, v4 Performance-first main run · bright/hard (LFA-character) loud path · stock muffler silent path · schematic, not to scale · dims mm 2026-09-22 merge: saddle-hole method WITHDRAWN · slip-on can superseded by Build A tail ROUND 3: 30° is CONDITIONAL — 45° equally valid (~0.04 hp apart). Stub band "50–110" WITHDRAWN — floor is mechanical, must be mocked up. MANIFOLD stock cast, ported CAT — flanged deleted; refit for PETC Ø50.8 (2.0") ID · 80 m/s @6500 1300 — existing straight pipe, kept 30° OR 45° MANDREL WYE formed or Y-cutout — NEVER a saddle hole STOCK MUFFLER stock tip BRANCH B — SILENT always open · unchanged · carries 100% of flow when the valve is shut length = packaging, but RECORD it — sets open-state shunting (D6) VALVE normally CLOSED stub ≤110 — MEASURE BUILD A TAIL — 215.9 (8.5") DUMP Ø50.8 · mid-car BRANCH A — LOUD Ø50.8 → Ø76.2 belly → Ø50.8 exit · 38% reflection · 0.013 hp exit = 103% of pipe area — do NOT neck down (+19 dB hiss at 1.5") Station chain, manifold outlet = 0 0 manifold 1300 wye crotch 1380 valve face 1560 tail in 1776 dump ⚠ 1776 mm total — confirm this clears the rear axle before cutting. Packaging gate. ⚠ 30° needs 260 mm longitudinal vs 45°'s 150 mm for the same offset — and a 30° wye's ~108 mm saddle may make a short stub unbuildable. Non-negotiable at the shop ◆ No saddle hole. Formed wye or Y-cutout. If fabricated: fish-mouth to measured OD, trace the aperture, borescope the inside. No inspection = wrong method. ◆ Caliper the wall first. PH mid-pipe is often 1.0–1.2 mm, not 1.5. Thin or scaled = replace the section, don't weld into it. ◆ Dump outlet faced square, fully deburred, no weld bead in the bore. A ragged lip whistles — rated above any angle error by both reviewers. ◆ Cat delete ⇒ actuator heat is now a live case. Standoff or shield, and IR-check the actuator body after a loaded pull. ◆ BLOCKING: mock up the wye + valve and caliper crotch-to-butterfly-face before ordering. The stub floor is mechanical and is currently a guess. Schematic — angles and proportions not to scale; station chain is the dimensional record. c≈520 m/s (mid-pipe). Full spec LOG-007 §v4 · reconciliation PLAN.md
The same architecture on one real car, built the opposite way round: performance-first on the main run with a bright, hard loud path instead of a deep one. Useful mainly as a counter-example — it shows which parts of the method are universal and which follow the chosen tone. Open full size

Fabricator sheet — megaphone and reverse cone

EXHAUST TAIL — BUILD A · megaphone + reverse cone 2004 Kia Rio DC · A5D 1493cc · Branch A (valved dump) · mild or stainless, 1.5–2.0 mm wall · all dims mm Total length 215.9 (8.5") Elevation 1:2 · patterns NTS SECTION / ELEVATION from valve 9.5° incl. 36.9° incl. throat ø50.8 (2.0") ø76.2 (3.0") ø50.8 (2.0") 152.4 (6") 38.1 (1.5") 25.4 215.9 TOTAL (8.5") CUT LIST 1 · Diverging cone — rolled sheet ø50.8 → ø76.2 over 152.4 2 · Reverse cone — rolled sheet ø76.2 → ø50.8 over 38.1 3 · Throat — ø50.8 tube × 25.4 long offcut from the existing 2" run 4 · Inlet joins valve outlet, ø50.8 BUILD SEQUENCE a. Roll + seam-weld both cones, dress seams flush inside. b. Butt-weld cone 1 → cone 2 at the ø76.2 belly. c. Butt-weld throat tube to reverse cone. d. Dress ALL internal weld beads flush. No intrusion. e. Face the outlet square, deburr inside and out. FLAT PATTERN DEVELOPMENT — mark out on sheet before rolling ① DIVERGING CONE outer radius 458.8 inner radius 305.9 sector angle 29.9° outer arc 239.4 inner arc 159.6 slant height 152.9 ② REVERSE CONE outer radius 120.5 inner radius 80.3 sector angle 113.8° outer arc 239.4 inner arc 159.6 slant height 40.2 Sector diagrams are schematic, not to scale. Outer arc 239.4 = π × ø76.2, so both cones share the same belly circumference — check this when marking out. CRITICAL — these drive the result more than any dimension above 1 · Outlet must be faced square and fully deburred, inside and out. A sharp or ragged lip sheds vortices and produces a whistle over the note. 2 · No weld bead may protrude into the bore anywhere. Dress every internal seam flush — belly joint, throat joint, and both rolled seams. 3 · Do not substitute a smaller outlet. ø50.8 is deliberate: matching pipe area keeps jet noise down. Smaller buys hiss, not tone.
A shop-floor drawing for the loud-path tail on that car, including flat-pattern development for both cones so the sheet can be marked out directly. Both cone outer arcs are 239.4 mm because they meet at the same belly — a built-in check before any metal is cut. Open full size

The drawings are generated as hand-written SVG and read back as rendered images before being accepted. Their source lives in the research monorepo; the copies here are rewritten at build time so the palette follows this site's light and dark themes. Scroll a sheet sideways on a portrait phone, or open it full size — the dimension chains are drawn to scale and do not reflow.