Formula Reference

Every closed-form relationship in the manual

Lifted from the chapters so the maths can be checked in one sitting. Symbols are Bosch engineering German; the chapter link carries the surrounding explanation.

Chapter 2 — 2.1. The Bosch 8-Character ASAP2/DAMOS Naming Grammar

[V][GG][BB][RR][R] 0 261 20[X]Hardware Generation Tier [XXX]Specific Silicon BOM / Assembly ID DOC_[Index]_[Subsystem_Name].md [ECU_Part_Number]_v[Major].[Minor].[Patch].[ext] [Project]_[Target]_v[Major].[Minor].[Patch]_[YYYYMMDD].zip

Chapter 3 — 3.9. Manifold Absolute Pressure (MAP) Sensor Linearization Architecture (DSLGRAD & DSLOFS)

Pabs = (Vin × DSLGRAD) + DSLOFS DSLGRAD =Δ PΔ V =3000 hPa - 200 hPa4.65V - 0.40V =2800 hPa4.25V = 658.8235 hPa/V DSLOFS = Pmin - (DSLGRAD × Vmin) = 200 hPa - (658.8235 × 0.40V) = 200 - 263.529 = -63.53 hPa DSLGRAD =Δ PΔ V =4000 hPa - 500 hPa4.50V - 0.50V =3500 hPa4.00V = 875.0000 hPa/V DSLOFS = Pmin - (DSLGRAD × Vmin) = 500 hPa - (875.0000 × 0.50V) = 500 - 437.500 = +62.50 hPa

Chapter 5 — 5.6.1. The Five Silicon & Physical Board Gating Constraints

Gear Ratio =nmotvfzg Telegram: [0x81, 0x11, 0xF1, 0x81, 0x04] [0x83, 0xF1, 0x11, 0xC1, 0xEA, 0x8F, 0x7F]

Chapter 6 — 6.1. Bosch Flash Address Mirroring

File Offset = DAMOS Address ∧ 0x0FFFFF

Chapter 10 — 2. Pages 3 & 4: Secret Key Code (SKC / Login PIN) & RFID Key Store (0x030–0x04F)

PINdecimal = Byte[0x32] + (Byte[0x33] × 256) Hex Word = 0x1A0B = 6,667 ⟶ Login PIN = 06667 Sum = ∑i=013 EEPROM[offset + i] Sum = Sum + P If (Descriptor[P] ∧ 0x0040) eq 0 ⟹ Sum = Sum - 1 Checksum = (-Sum) mod 216 EEPROM[offset + 14] = Checksum ∧ 0xFF EEPROM[offset + 15] = (Checksum ≫ 8) ∧ 0xFF

Chapter 11 — 1. Tier 1: 16-Bit Multipage Additive Checksums (Simple Word Sums)

Sum16 = ( ∑i=0N-1 Word16[i] ) mod 216 WordA + WordB = 0xFFFF    (or WordB = WordA ⊕ 0xFFFF) P(x) = x32 + x26 + x23 + x22 + x16 + x12 + x11 + x10 + x8 + x7 + x5 + x4 + x2 + x + 1

Chapter 35 — 35.1. KWP2000 Service $2C Protocol Mechanics & Memory Packet Definition

Telegram: [0x80, 0x11, 0xF1, Length, 0x2C, 0x01, Definitions…, Checksum]

Chapter 15 — Physical Definition

KRKTE =Vh_cyl × ρair_std14.7 × Qinj_g/min × 160000 × Scaling Factor Vh_cyl =1781 cm34 = 445.25 cm3 = 0.44525 dm3 Qinj_g/min = Qinj_cc/min × 0.735 g/cc (Heptane density) Air Mass Multiplier = (DnewDstock )2

Chapter 21 — 1. Stage 1: Cranking Enrichment (FST & FKST)

tstart = tbase × FST(Tmot) × FKST(Tmot)

Chapter 42 — 42.2. The Bosch ME7.5 Dynamic Wall Film Model

mfuel_injected = mfuel_target + α · mfuel_target - β · mfilm

Chapter 56 — 56.1. Hydraulic Physics: Why Returnless Systems Restrict High-Boost Fueling

˙mfuel = Cd · Anozzle · 2 · ρfuel · Δ pinj Δ pinj = prail - pmanifold = 3.0 bar - 1.5 bar = 1.5 bar QactualQrated = 1.5 bar3.0 bar = 0.50≈ 0.707    (-29.3%!) Δ V = 15.0A · 0.14 Ω = 2.10 V Drop!

Chapter 22 — 22.1. Dual-Potentiometer Plausibility & Mechanical Limp-Home

VG187 + VG188 = 5.00V ± 0.20V

Chapter 24 — 24.1. Hardware Interfacing & Signal Physics

E% = fsignal (Hz) - 50 Temperature (°C) = (thigh (ms) × 41.25) - 81.25 KRKTEactive = KRKTEgas +α × (KRKTEE85 - KRKTEgas) KRKTEactive = 0.05670 + 0.70 × (0.08535 - 0.05670) = 0.07675 ms/% KFZWactive = KFZWgas +α × Δ KFZWE85 LDRXNactive = LDRXNgas +α × (LDRXNE85 - LDRXNgas)

Chapter 31 — 31.1. The Mathematical Mechanics of the Saugrohrmodell

rl = FRLFN(Nmot, αdk) × (PdsPambient ) × FTBR(Tans) FTBR =293.15 K273.15 + Tans (°C)

Chapter 18 — 1. Acoustic Resonance Frequency Calculation

fknock =1.841 × csπ × Dbore =1.841 × 900 m/sπ × 0.081 m≈ 6.51 kHz EGTmodeled = f(Nmot, rl, λactual, Δ ZWretard, Tambient)

Chapter 29 — 29.1. The Physics of Inductive Coil Saturation & Primary Dwell

I(t) =UbattRpri ( 1 - e-tτ )    where τ =LpriRpri

Chapter 37 — 37.2. Recalibrating the Reference Noise Baseline (KRMX)

Detonation Flagged if: VmeasuredKRMX(Nmot, Tmot) > Knock Ratio Threshold

Chapter 48 — 48.1. Compressor Pressure Ratio (Πc) & Rotational Speed (Ntc) Physics

Πc =p2,absp1,abs =pcharge_pressurepambient - Δ pintake_filter Ut =π · Dwheel · Ntc60

Chapter 51 — 51.1. Mathematical Physics of the Differential EGT Observer

Ttarget = Tbasic(Nmot, rl) + Δ Tzw + Δ Tλ + Δ Tvvt Δ Tzw = kzw(Nmot, rl) · (ZWopt - ZWact) Δ Tλ = kλ(Nmot, rl) · (1.000 - λ) dTexhaustdt = Ttarget - Texhaustτmanifold λtarget = MIN[ LAMFA ,  1.00 - Δλbts(Nmot, Texhaust) ]

Chapter 16 — 16.2. The Inversion Rule & The Cause of Electronic Throttle Limp Mode

rl = KFMIRL(N, Torque) ⟺ Torque = KFMIOP(N, rl)

Chapter 27 — 2. Electrical & Software Delete (Preventing Fault Codes)

ESKONF[2] = ESKONF[2] | 0x30

Chapter 28 — 28.3. Software Delete Protocol for Track & Clean Engine Bay Builds

ESKONF[3] = ESKONF[3] | 0xF0

Chapter 46 — 46.1. Chemical Reaction & Catalytic Light-off Physics

2CO + O2 ⟶ 2CO2 + Δ H    (Δ H = -283 kJ/mol) CnHm + (n + m4)O2 ⟶ nCO2 + m2H2O + Δ H

Chapter 47 — 47.1. The Thermodynamics of Internal Residual Gas Fraction (xr)

xr =mresidualmtotal =mresidualmfresh + mresidual p3 = pambient + Δ pcat + Δ pturbine(mexhaust, T3, wg_pos)

Chapter 49 — 49.1. Hydrocarbon Vapor Dynamics & Real-Time Observer (FTE)

Δ p = pambient - pmanifold ˙mte = f(Δ p, duty_cycleN80) FTEk+1 = FTEk + Kadapt · (1.0 - λ) ti = (rk - Δ rk,te) · KRKTE + TVUB

Chapter 50 — Cubic RPM Normalization Formula

LUEn =Tseg, n+1 - Tseg, nTseg, n3

Chapter 52 — 52.1. Physics of Catalyst Oxygen Storage Capacity (OSC) & DTC P0420

2CeO2 + CO ⟶ Ce2O3 + CO2 Ce2O3 +12O2 ⟶ 2CeO2 Ecat =∫ |dVpost / dt|∫ |dVpre / dt|

Chapter 14 — C167CR Addressing Constraints

C167 Operand Address = 0x8000 | 0x0A90 = 0x8A90

Chapter 58 — 58.1. Transmission Ratio Calculation & Algorithmic Gear Identification

Rtransmission =Nmotvfzg |Nmotvfzg - NVQUOTi | ≤ DNVQi ⟹ gangi = i LDRXNfinal = LDRXN(Nmot) · fgear(gangi)

Chapter 57 — 57.1. Alternator Terminal DF (Dynamo Field) Interface & Torque Compensation

Pmech =1330 W0.65 = 2.05 kW ⟹ Mdrag =Pmechωcrank≈ 24.5 Nm of torque at 800 rpm Idle! i(t) =UBR · (1 - e-RL · t ) Espark =12 · Lprimary · Ipeak2≈ 45 mJ

Chapter 60 — 4. Mass Airflow Power Estimation

Estimated Brake Horsepower (BHP)≈ Peak Mass Airflow (g/s)0.80

79 equations.