Closed-form relationships

\mathbf{[V][GG][BB][RR][R]}

\mathbf{0\ 261\ 20\underbrace{[X]}_{\text{Hardware Generation Tier}}\ \underbrace{[XXX]}_{\text{Specific Silicon BOM / Assembly ID}}}

\mathbf{DOC\_[Index]\_[Subsystem\_Name].md}

\mathbf{[ECU\_Part\_Number]\_v[Major].[Minor].[Patch].[ext]}

\mathbf{[Project]\_[Target]\_v[Major].[Minor].[Patch]\_[YYYYMMDD].zip}

P_{\text{abs}} = (V_{\text{in}} \times \mathbf{DSLGRAD}) + \mathbf{DSLOFS}

\mathbf{DSLGRAD} =\frac{\Delta P}{\Delta V} =\frac{3000\text{ hPa} - 200\text{ hPa}}{4.65\text{V} - 0.40\text{V}} =\frac{2800\text{ hPa}}{4.25\text{V}} = \mathbf{658.8235\text{ hPa/V}}

\mathbf{DSLOFS} = P_{\text{min}} - (\mathbf{DSLGRAD} \times V_{\text{min}}) = 200\text{ hPa} - (658.8235 \times 0.40\text{V}) = 200 - 263.529 = \mathbf{-63.53\text{ hPa}}

\mathbf{DSLGRAD} =\frac{\Delta P}{\Delta V} =\frac{4000\text{ hPa} - 500\text{ hPa}}{4.50\text{V} - 0.50\text{V}} =\frac{3500\text{ hPa}}{4.00\text{V}} = \mathbf{875.0000\text{ hPa/V}}

\mathbf{DSLOFS} = P_{\text{min}} - (\mathbf{DSLGRAD} \times V_{\text{min}}) = 500\text{ hPa} - (875.0000 \times 0.50\text{V}) = 500 - 437.500 = \mathbf{+62.50\text{ hPa}}

\text{Gear Ratio} =\frac{n_{mot}}{v_{fzg}}

\mathbf{\text{Telegram: } [0\text{x}81, \ 0\text{x}11, \ 0\text{x}F1, \ 0\text{x}81, \ 0\text{x}04]}

\mathbf{[0\text{x}83, \ 0\text{x}F1, \ 0\text{x}11, \ 0\text{xC1}, \ 0\text{xEA}, \ 0\text{x8F}, \ 0\text{x7F}]}

\text{File Offset} = \text{DAMOS Address} \land \text{0x0FFFFF}

\text{PIN}_{\text{decimal}} = \text{Byte}[0\text{x}32] + (\text{Byte}[0\text{x}33] \times 256)

\text{Hex Word} = \text{0x1A0B} = 6,667 \longrightarrow \text{Login PIN} = \mathbf{06667}

\text{Sum} = \sum_{i=0}^{13} \text{EEPROM}[\text{offset} + i]

\text{Sum} = \text{Sum} + P

\text{If } (\text{Descriptor}[P] \land \text{0x0040}) eq 0 \implies \text{Sum} = \text{Sum} - 1

\text{Checksum} = (-\text{Sum}) \pmod{2^{16}}

\text{EEPROM}[\text{offset} + 14] = \text{Checksum} \land \text{0xFF}

\text{EEPROM}[\text{offset} + 15] = (\text{Checksum} \gg 8) \land \text{0xFF}

\text{Sum}_{16} = \left( \sum_{i=0}^{N-1} \text{Word}_{16}[i] \right) \pmod{2^{16}}

\text{Word}_A + \text{Word}_B = \text{0xFFFF} \quad (\text{or } \text{Word}_B = \text{Word}_A \oplus \text{0xFFFF})

P(x) = x^{32} + x^{26} + x^{23} + x^{22} + x^{16} + x^{12} + x^{11} + x^{10} + x^8 + x^7 + x^5 + x^4 + x^2 + x + 1

\mathbf{\text{Telegram: } [0\text{x}80, \ 0\text{x}11, \ 0\text{x}F1, \ \text{Length}, \ 0\text{x}2\text{C}, \ 0\text{x}01, \ \text{Definitions}\dots, \ \text{Checksum}]}

\mathbf{KRKTE} =\frac{V_{\text{h\_cyl}} \times \rho_{\text{air\_std}}}{14.7 \times Q_{\text{inj\_g/min}} \times \frac{1}{60000}} \times \text{Scaling Factor}

V_{\text{h\_cyl}} =\frac{1781\text{ cm}^3}{4} = \mathbf{445.25\text{ cm}^3} = 0.44525\text{ dm}^3

Q_{\text{inj\_g/min}} = Q_{\text{inj\_cc/min}} \times 0.735\text{ g/cc (Heptane density)}

\text{Air Mass Multiplier} = \left(\frac{D_{\text{new}}}{D_{\text{stock}}} \right)^2

t_{\text{start}} = t_{\text{base}} \times \mathbf{FST}(T_{\text{mot}}) \times \mathbf{FKST}(T_{\text{mot}})

m_{\text{fuel\_injected}} = m_{\text{fuel\_target}} + \mathbf{\alpha} \cdot m_{\text{fuel\_target}} - \mathbf{\beta} \cdot m_{\text{film}}

\dot{m}_{\text{fuel}} = C_d \cdot A_{\text{nozzle}} \cdot \sqrt{2 \cdot \rho_{\text{fuel}} \cdot \Delta p_{\text{inj}}}

\Delta p_{\text{inj}} = p_{\text{rail}} - p_{\text{manifold}} = 3.0\text{ bar} - 1.5\text{ bar} = 1.5\text{ bar}

\frac{Q_{\text{actual}}}{Q_{\text{rated}}} = \sqrt{\frac{1.5\text{ bar}}{3.0\text{ bar}}} = \sqrt{0.50}\approx 0.707 \quad (-29.3\%!)

\Delta V = 15.0\text{A} \cdot 0.14\ \Omega = \mathbf{2.10\text{ V Drop!}}

V_{\text{G187}} + V_{\text{G188}} = \mathbf{5.00\text{V}} \pm \mathbf{0.20\text{V}}

E\% = f_{\text{signal}}\text{ (Hz)} - 50

\text{Temperature (°C)} = (t_{\text{high}}\text{ (ms)} \times 41.25) - 81.25

\mathbf{KRKTE}_{\text{active}} = \mathbf{KRKTE}_{\text{gas}} +\alpha \times (\mathbf{KRKTE}_{\text{E85}} - \mathbf{KRKTE}_{\text{gas}})

\mathbf{KRKTE}_{\text{active}} = 0.05670 + 0.70 \times (0.08535 - 0.05670) = \mathbf{0.07675\text{ ms}/\%}

\mathbf{KFZW}_{\text{active}} = \mathbf{KFZW}_{\text{gas}} +\alpha \times \mathbf{\Delta KFZW}_{\text{E85}}

\mathbf{LDRXN}_{\text{active}} = \mathbf{LDRXN}_{\text{gas}} +\alpha \times (\mathbf{LDRXN}_{\text{E85}} - \mathbf{LDRXN}_{\text{gas}})

r_l = \mathbf{FRLFN}(N_{\text{mot}}, \ \alpha_{\text{dk}}) \times \left(\frac{P_{\text{ds}}}{P_{\text{ambient}}} \right) \times \mathbf{FTBR}(T_{\text{ans}})

\mathbf{FTBR} =\frac{293.15\text{ K}}{273.15 + T_{\text{ans}}\text{ (°C)}}

f_{\text{knock}} =\frac{1.841 \times c_s}{\pi \times D_{\text{bore}}} =\frac{1.841 \times 900\text{ m/s}}{\pi \times 0.081\text{ m}}\approx \mathbf{6.51\text{ kHz}}

\text{EGT}_{\text{modeled}} = f(N_{\text{mot}}, \ r_l, \ \lambda_{\text{actual}}, \ \Delta ZW_{\text{retard}}, \ T_{\text{ambient}})

I(t) =\frac{U_{\text{batt}}}{R_{\text{pri}}} \left( 1 - e^{-\frac{t}{\tau}} \right) \quad \text{where } \tau =\frac{L_{\text{pri}}}{R_{\text{pri}}}

\text{Detonation Flagged if: }\frac{V_{\text{measured}}}{\mathbf{KRMX}(N_{\text{mot}}, \ T_{\text{mot}})} > \text{Knock Ratio Threshold}

\Pi_c =\frac{p_{2,\text{abs}}}{p_{1,\text{abs}}} =\frac{p_{\text{charge\_pressure}}}{p_{\text{ambient}} - \Delta p_{\text{intake\_filter}}}

U_t =\frac{\pi \cdot D_{\text{wheel}} \cdot N_{\text{tc}}}{60}

T_{\text{target}} = T_{\text{basic}}(N_{\text{mot}}, rl) + \Delta T_{\text{zw}} + \Delta T_{\lambda} + \Delta T_{\text{vvt}}

\Delta T_{\text{zw}} = k_{\text{zw}}(N_{\text{mot}}, rl) \cdot (ZW_{\text{opt}} - ZW_{\text{act}})

\Delta T_{\lambda} = k_{\lambda}(N_{\text{mot}}, rl) \cdot (1.000 - \lambda)

\frac{dT_{\text{exhaust}}}{dt} = \frac{T_{\text{target}} - T_{\text{exhaust}}}{\tau_{\text{manifold}}}

\lambda_{\text{target}} = \text{MIN}\left[ \text{LAMFA} ,\; 1.00 - \Delta\lambda_{\text{bts}}(N_{\text{mot}}, T_{\text{exhaust}}) \right]

r_l = \mathbf{KFMIRL}(N, \text{Torque}) \iff \text{Torque} = \mathbf{KFMIOP}(N, r_l)

\mathbf{\text{ESKONF}[2] = \text{ESKONF}[2] \mid 0\text{x}30}

\mathbf{\text{ESKONF}[3] = \text{ESKONF}[3] \mid 0\text{xF0}}

2\text{CO} + \text{O}_2 \longrightarrow 2\text{CO}_2 + \Delta H \quad (\Delta H = -283\text{ kJ/mol})

\text{C}_n\text{H}_m + \left(n + \frac{m}{4}\right)\text{O}_2 \longrightarrow n\text{CO}_2 + \frac{m}{2}\text{H}_2\text{O} + \Delta H

x_r =\frac{m_{\text{residual}}}{m_{\text{total}}} =\frac{m_{\text{residual}}}{m_{\text{fresh}} + m_{\text{residual}}}

p_3 = p_{\text{ambient}} + \Delta p_{\text{cat}} + \Delta p_{\text{turbine}}(m_{\text{exhaust}}, T_3, \text{wg\_pos})

\Delta p = p_{\text{ambient}} - p_{\text{manifold}}

\dot{m}_{\text{te}} = f(\Delta p, \text{duty\_cycle}_{N80})

\text{FTE}_{k+1} = \text{FTE}_k + K_{\text{adapt}} \cdot (1.0 - \lambda)

t_i = (r_k - \Delta r_{k,\text{te}}) \cdot \text{KRKTE} + \text{TVUB}

\text{LUE}_n =\frac{T_{\text{seg}, n+1} - T_{\text{seg}, n}}{T_{\text{seg}, n}^3}

2\text{CeO}_2 + \text{CO} \longrightarrow \text{Ce}_2\text{O}_3 + \text{CO}_2

\text{Ce}_2\text{O}_3 +\frac{1}{2}\text{O}_2 \longrightarrow 2\text{CeO}_2

E_{\text{cat}} =\frac{\int |dV_{\text{post}} / dt|}{\int |dV_{\text{pre}} / dt|}

\text{C167 Operand Address} = \text{0x8000} \mid \text{0x0A90} = \mathbf{\text{0x8A90}}

R_{\text{transmission}} =\frac{N_{\text{mot}}}{v_{\text{fzg}}}

\left|\frac{N_{\text{mot}}}{v_{\text{fzg}}} - \text{NVQUOT}_i \right| \le \text{DNVQ}_i \implies \mathbf{\text{gangi} = i}

LDRXN_{\text{final}} = LDRXN(N_{\text{mot}}) \cdot f_{\text{gear}}(\text{gangi})

P_{\text{mech}} =\frac{1330\text{ W}}{0.65} = 2.05\text{ kW} \implies M_{\text{drag}} =\frac{P_{\text{mech}}}{\omega_{\text{crank}}}\approx \mathbf{24.5\text{ Nm of torque at } 800\text{ rpm Idle!}}

i(t) =\frac{U_B}{R} \cdot \left(1 - e^{-\frac{R}{L} \cdot t} \right)

E_{\text{spark}} =\frac{1}{2} \cdot L_{\text{primary}} \cdot I_{\text{peak}}^2\approx 45\text{ mJ}

\text{Estimated Brake Horsepower (BHP)}\approx \frac{\text{Peak Mass Airflow (g/s)}}{0.80}