2 // Author: Phil Schubert
3 // Date started: 12/03/99
4 // Purpose: Models a Continental IO-520-M Engine
5 // Called by: FGSimExec
7 // Copyright (C) 1999 Philip L. Schubert (philings@ozemail.com.au)
9 // This program is free software; you can redistribute it and/or
10 // modify it under the terms of the GNU General Public License as
11 // published by the Free Software Foundation; either version 2 of the
12 // License, or (at your option) any later version.
14 // This program is distributed in the hope that it will be useful, but
15 // WITHOUT ANY WARRANTY; without even the implied warranty of
16 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
17 // General Public License for more details.
19 // You should have received a copy of the GNU General Public License
20 // along with this program; if not, write to the Free Software
21 // Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA
24 // Further information about the GNU General Public License can also
25 // be found on the world wide web at http://www.gnu.org.
27 // FUNCTIONAL DESCRIPTION
28 // ------------------------------------------------------------------------
29 // Models a Continental IO-520-M engine. This engine is used in Cessna
30 // 210, 310, Beechcraft Bonaza and Baron C55. The equations used below
31 // were determined by a first and second order curve fits using Excel.
32 // The data is from the Cessna Aircraft Corporations Engine and Flight
33 // Computer for C310. Part Number D3500-13
36 // ------------------------------------------------------------------------
40 // ------------------------------------------------------------------------
41 // 12/03/99 PLS Created
42 // 07/03/99 PLS Added Calculation of Density, and Prop_Torque
43 // 07/03/99 PLS Restructered Variables to allow easier implementation
45 // 15/03/99 PLS Added Oil Pressure, Oil Temperature and CH Temp
46 // ------------------------------------------------------------------------
48 // ------------------------------------------------------------------------
51 /////////////////////////////////////////////////////////////////////
53 // Modified by Dave Luff (david.luff@nottingham.ac.uk) September 2000
55 // Altered manifold pressure range to add a minimum value at idle to simulate the throttle stop / idle bypass valve,
56 // and to reduce the maximum value whilst the engine is running to slightly below ambient to account for CdA losses across the throttle
58 // Altered it a bit to model an IO360 from C172 - 360 cubic inches, 180 HP max, fixed pitch prop
59 // Added a simple fixed pitch prop model by Nev Harbor - this is not intended as a final model but simply a hack to get it running for now
60 // I used Phil's ManXRPM correlation for power rather than do a new one for the C172 for now, but altered it a bit to reduce power at the low end
62 // Added EGT model based on combustion efficiency and an energy balance with the exhaust gases
64 // Added a mixture - power correlation based on a curve in the IO360 operating manual
66 // I've tried to match the prop and engine model to give roughly 600 RPM idle and 180 HP at 2700 RPM
67 // but it is by no means currently at a completed stage - DCL 15/9/00
69 // DCL 28/09/00 - Added estimate of engine and prop inertia and changed engine speed calculation to be calculated from Angular acceleration = Torque / Inertia.
70 // Requires a timestep to be passed to FGNewEngine::init and currently assumes this timestep does not change.
71 // Could easily be altered to pass a variable timestep to FGNewEngine::update every step instead if required.
73 // DCL 27/10/00 - Added first stab at cylinder head temperature model
74 // See the comment block in the code for details
76 // DCL 02/11/00 - Modified EGT code to reduce values to those more representative of a sensor downstream
78 // DCL 02/02/01 - Changed the prop model to one based on efficiency and co-efficient of power curves from McCormick instead of the
79 // blade element method we were using previously. This works much better, and is similar to how Jon is doing it in JSBSim.
81 // DCL 08/02/01 - Overhauled fuel consumption rate support.
83 // DCL 22/03/01 - Added input of actual air pressure and temperature (and hence density) to the model. Hence the power correlation
84 // with pressure height and temperature is no longer required since the power is based on the actual manifold pressure.
86 // DCL 22/03/01 - based on Riley's post on the list (25 rpm gain at 1000 rpm as lever is pulled out from full rich)
87 // I have reduced the sea level full rich mixture to thi = 1.3
88 //////////////////////////////////////////////////////////////////////
90 #include <simgear/compiler.h>
100 // Static utility functions
102 // Calculate Density Ratio
103 static float Density_Ratio ( float x )
106 y = ((3E-10 * x * x) - (3E-05 * x) + 0.9998);
111 // Calculate Air Density - Rho, using the ideal gas equation
112 // Takes and returns SI values
113 static float Density ( float temperature, float pressure )
119 float rho = pressure / (R * temperature);
124 // Calculate Speed in FPS given Knots CAS
125 static float IAS_to_FPS (float x)
132 // FGNewEngine member functions
134 float FGNewEngine::Lookup_Combustion_Efficiency(float thi_actual)
136 const int NUM_ELEMENTS = 11;
137 float thi[NUM_ELEMENTS] = {0.0, 0.9, 1.0, 1.05, 1.1, 1.15, 1.2, 1.3, 1.4, 1.5, 1.6}; //array of equivalence ratio values
138 float neta_comb[NUM_ELEMENTS] = {0.98, 0.98, 0.97, 0.95, 0.9, 0.85, 0.79, 0.7, 0.63, 0.57, 0.525}; //corresponding array of combustion efficiency values
139 //combustion efficiency values from Heywood, "Internal Combustion Engine Fundamentals", ISBN 0-07-100499-8
140 float neta_comb_actual;
144 int j = NUM_ELEMENTS; //This must be equal to the number of elements in the lookup table arrays
149 // Assume linear extrapolation of the slope between the last two points beyond the last point
150 float dydx = (neta_comb[i] - neta_comb[i-1]) / (thi[i] - thi[i-1]);
151 neta_comb_actual = neta_comb[i] + dydx * (thi_actual - thi[i]);
152 return neta_comb_actual;
154 if(thi_actual == thi[i]) {
155 neta_comb_actual = neta_comb[i];
156 return neta_comb_actual;
158 if((thi_actual > thi[i]) && (thi_actual < thi[i + 1])) {
159 //do linear interpolation between the two points
160 factor = (thi_actual - thi[i]) / (thi[i+1] - thi[i]);
161 neta_comb_actual = (factor * (neta_comb[i+1] - neta_comb[i])) + neta_comb[i];
162 return neta_comb_actual;
166 //if we get here something has gone badly wrong
167 cout << "ERROR: error in FGNewEngine::Lookup_Combustion_Efficiency\n";
168 return neta_comb_actual;
171 ////////////////////////////////////////////////////////////////////////////////////////////
172 // Return the percentage of best mixture power available at a given mixture strength
174 // Based on data from "Technical Considerations for Catalysts for the European Market"
175 // by H S Gandi, published 1988 by IMechE
177 // Note that currently no attempt is made to set a lean limit on stable combustion
178 ////////////////////////////////////////////////////////////////////////////////////////////
179 float FGNewEngine::Power_Mixture_Correlation(float thi_actual)
181 float AFR_actual = 14.7 / thi_actual;
182 // thi and thi_actual are equivalence ratio
183 const int NUM_ELEMENTS = 13;
184 // The lookup table is in AFR because the source data was. I added the two end elements to make sure we are almost always in it.
185 float AFR[NUM_ELEMENTS] = {(14.7/1.6), 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, (14.7/0.6)}; //array of equivalence ratio values
186 float mixPerPow[NUM_ELEMENTS] = {78, 86, 93.5, 98, 100, 99, 96.4, 92.5, 88, 83, 78.5, 74, 58}; //corresponding array of combustion efficiency values
187 float mixPerPow_actual;
192 int j = NUM_ELEMENTS; //This must be equal to the number of elements in the lookup table arrays
197 // Assume linear extrapolation of the slope between the last two points beyond the last point
198 dydx = (mixPerPow[i] - mixPerPow[i-1]) / (AFR[i] - AFR[i-1]);
199 mixPerPow_actual = mixPerPow[i] + dydx * (AFR_actual - AFR[i]);
200 return mixPerPow_actual;
202 if((i == 0) && (AFR_actual < AFR[i])) {
203 // Assume linear extrapolation of the slope between the first two points for points before the first point
204 dydx = (mixPerPow[i] - mixPerPow[i-1]) / (AFR[i] - AFR[i-1]);
205 mixPerPow_actual = mixPerPow[i] + dydx * (AFR_actual - AFR[i]);
206 return mixPerPow_actual;
208 if(AFR_actual == AFR[i]) {
209 mixPerPow_actual = mixPerPow[i];
210 return mixPerPow_actual;
212 if((AFR_actual > AFR[i]) && (AFR_actual < AFR[i + 1])) {
213 //do linear interpolation between the two points
214 factor = (AFR_actual - AFR[i]) / (AFR[i+1] - AFR[i]);
215 mixPerPow_actual = (factor * (mixPerPow[i+1] - mixPerPow[i])) + mixPerPow[i];
216 return mixPerPow_actual;
220 //if we get here something has gone badly wrong
221 cout << "ERROR: error in FGNewEngine::Power_Mixture_Correlation\n";
222 return mixPerPow_actual;
227 // Calculate Manifold Pressure based on Throttle lever Position
228 float FGNewEngine::Calc_Manifold_Pressure ( float LeverPosn, float MaxMan, float MinMan)
235 //Note that setting the manifold pressure as a function of lever position only is not strictly accurate
236 //MAP is also a function of engine speed. (and ambient pressure if we are going for an actual MAP model)
237 Inches = MinMan + (LeverPosn * (MaxMan - MinMan) / 100);
239 //allow for idle bypass valve or slightly open throttle stop
249 // Calculate Oil Temperature
250 float FGNewEngine::Calc_Oil_Temp (float Fuel_Flow, float Mixture, float IAS)
257 // Calculate Oil Pressure
258 float FGNewEngine::Calc_Oil_Press (float Oil_Temp, float Engine_RPM)
260 float Oil_Pressure = 0; //PSI
261 float Oil_Press_Relief_Valve = 60; //PSI
262 float Oil_Press_RPM_Max = 1800;
263 float Design_Oil_Temp = 85; //Celsius
264 float Oil_Viscosity_Index = 0.25; // PSI/Deg C
265 float Temp_Deviation = 0; // Deg C
267 Oil_Pressure = (Oil_Press_Relief_Valve / Oil_Press_RPM_Max) * Engine_RPM;
269 // Pressure relief valve opens at Oil_Press_Relief_Valve PSI setting
270 if (Oil_Pressure >= Oil_Press_Relief_Valve)
272 Oil_Pressure = Oil_Press_Relief_Valve;
275 // Now adjust pressure according to Temp which affects the viscosity
277 Oil_Pressure += (Design_Oil_Temp - Oil_Temp) * Oil_Viscosity_Index;
282 //*************************************************************************************
283 // Initialise the engine model
284 void FGNewEngine::init(double dt) {
286 // These constants should probably be moved eventually
287 CONVERT_CUBIC_INCHES_TO_METERS_CUBED = 1.638706e-5;
288 CONVERT_HP_TO_WATTS = 745.6999;
290 // Properties of working fluids
291 Cp_air = 1005; // J/KgK
292 Cp_fuel = 1700; // J/KgK
293 calorific_value_fuel = 47.3e6; // W/Kg Note that this is only an approximate value
294 rho_fuel = 800; // kg/m^3 - an estimate for now
296 p_amb_sea_level = 101325;
298 // Control and environment inputs
300 Throttle_Lever_Pos = 75;
301 Propeller_Lever_Pos = 75;
302 Mixture_Lever_Pos = 100;
306 // Engine Specific Variables.
307 // Will be set in a parameter file to be read in to create
308 // and instance for each engine.
309 Max_Manifold_Pressure = 28.50; //Inches Hg. An approximation - should be able to find it in the engine performance data
310 Min_Manifold_Pressure = 6.5; //Inches Hg. This is a guess corresponding to approx 0.24 bar MAP (7 in Hg) - need to find some proper data for this
312 Min_RPM = 600; //Recommended idle from Continental data sheet
314 Mag_Derate_Percent = 5;
315 // MaxHP = 285; //Continental IO520-M
316 MaxHP = 180; //Lycoming IO360
317 // displacement = 520; //Continental IO520-M
318 displacement = 360; //Lycoming IO360
319 displacement_SI = displacement * CONVERT_CUBIC_INCHES_TO_METERS_CUBED;
320 engine_inertia = 0.2; //kgm^2 - value taken from a popular family saloon car engine - need to find an aeroengine value !!!!!
321 prop_inertia = 0.03; //kgm^2 - this value is a total guess - dcl
328 // Initialise Engine Variables used by this instance
329 Percentage_Power = 0;
330 Manifold_Pressure = 29.00; // Inches
332 Fuel_Flow_gals_hr = 0;
335 CHT = 298.0; //deg Kelvin
336 CHT_degF = (CHT * 1.8) - 459.67; //deg Fahrenheit
338 Oil_Pressure = 0; // PSI
339 Oil_Temp = 85; // Deg C
342 Torque_Imbalance = 0;
344 // Initialise Propellor Variables used by this instance
347 FGProp1_Blade_Angle = 13.5;
348 prop_diameter = 1.8; // meters
349 blade_angle = 23.0; // degrees
353 //*****************************************************************************
354 //*****************************************************************************
355 // update the engine model based on current control positions
356 void FGNewEngine::update() {
359 // Hack for testing - should output every 5 seconds
360 static int count1 = 0;
362 // cout << "P_atmos = " << p_amb << " T_atmos = " << T_amb << '\n';
363 // cout << "Manifold pressure = " << Manifold_Pressure << " True_Manifold_Pressure = " << True_Manifold_Pressure << '\n';
364 // cout << "p_amb_sea_level = " << p_amb_sea_level << '\n';
365 // cout << "equivalence_ratio = " << equivalence_ratio << '\n';
366 // cout << "combustion_efficiency = " << combustion_efficiency << '\n';
367 // cout << "AFR = " << 14.7 / equivalence_ratio << '\n';
368 // cout << "Mixture lever = " << Mixture_Lever_Pos << '\n';
369 // cout << "n = " << RPM << " rpm\n";
370 cout << "T_amb = " << T_amb << '\n';
381 // Set up the new variables
382 float PI = 3.1428571;
384 // Parameters that alter the operation of the engine.
385 int Fuel_Available = 1; // Yes = 1. Is there Fuel Available. Calculated elsewhere
386 int Alternate_Air_Pos =0; // Off = 0. Reduces power by 3 % for same throttle setting
387 int Magneto_Left = 1; // 1 = On. Reduces power by 5 % for same power lever settings
388 int Magneto_Right = 1; // 1 = On. Ditto, Both of the above though do not alter fuel flow
391 // Calculate Sea Level Manifold Pressure
392 Manifold_Pressure = Calc_Manifold_Pressure( Throttle_Lever_Pos, Max_Manifold_Pressure, Min_Manifold_Pressure );
393 // cout << "manifold pressure = " << Manifold_Pressure << endl;
395 //Then find the actual manifold pressure (the calculated one is the sea level pressure)
396 True_Manifold_Pressure = Manifold_Pressure * p_amb / p_amb_sea_level;
399 //DCL - next calculate m_dot_air and m_dot_fuel into engine
401 //DCL - calculate mass air flow into engine based on speed and load - separate this out into a function eventually
402 //t_amb is actual temperature calculated from altitude
403 //calculate density from ideal gas equation
404 rho_air = p_amb / ( R_air * T_amb );
405 rho_air_manifold = rho_air * Manifold_Pressure / 29.6; //This is a bit of a roundabout way of calculating this but it works !! If we put manifold pressure into SI units we could do it simpler.
406 //calculate ideal engine volume inducted per second
407 swept_volume = (displacement_SI * (RPM / 60)) / 2; //This equation is only valid for a four stroke engine
408 //calculate volumetric efficiency - for now we will just use 0.8, but actually it is a function of engine speed and the exhaust to manifold pressure ratio
409 //Note that this is cylinder vol eff - the throttle drop is already accounted for in the MAP calculation
410 volumetric_efficiency = 0.8;
411 //Now use volumetric efficiency to calculate actual air volume inducted per second
412 v_dot_air = swept_volume * volumetric_efficiency;
413 //Now calculate mass flow rate of air into engine
414 m_dot_air = v_dot_air * rho_air_manifold;
418 //DCL - now calculate fuel flow into engine based on air flow and mixture lever position
419 //assume lever runs from no flow at fully out to thi = 1.3 at fully in at sea level
420 //also assume that the injector linkage is ideal - hence the set mixture is maintained at a given altitude throughout the speed and load range
421 thi_sea_level = 1.3 * ( Mixture_Lever_Pos / 100.0 );
422 equivalence_ratio = thi_sea_level * p_amb_sea_level / p_amb; //ie as we go higher the mixture gets richer for a given lever position
423 m_dot_fuel = m_dot_air / 14.7 * equivalence_ratio;
424 Fuel_Flow_gals_hr = (m_dot_fuel / rho_fuel) * 264.172 * 3600.0; // Note this assumes US gallons
426 //***********************************************************************
427 //Engine power and torque calculations
429 // For a given Manifold Pressure and RPM calculate the % Power
430 // Multiply Manifold Pressure by RPM
431 ManXRPM = True_Manifold_Pressure * RPM;
432 // ManXRPM = Manifold_Pressure * RPM;
437 // Phil's %power correlation
439 Percentage_Power = (+ 7E-09 * ManXRPM * ManXRPM) + ( + 7E-04 * ManXRPM) - 0.1218;
440 // cout << Percentage_Power << "%" << "\t";
443 // DCL %power correlation - basically Phil's correlation modified to give slighty less power at the low end
444 // might need some adjustment as the prop model is adjusted
445 // My aim is to match the prop model and engine model at the low end to give the manufacturer's recommended idle speed with the throttle closed - 600rpm for the Continental IO520
446 // Calculate % Power for Nev's prop model
447 //Percentage_Power = (+ 6E-09 * ManXRPM * ManXRPM) + ( + 8E-04 * ManXRPM) - 1.8524;
449 // Calculate %power for DCL prop model
450 Percentage_Power = (7e-9 * ManXRPM * ManXRPM) + (7e-4 * ManXRPM) - 1.0;
452 // Power de-rating for altitude has been removed now that we are basing the power
453 // on the actual manifold pressure, which takes air pressure into account. However - this fails to
454 // take the temperature into account - this is TODO.
456 // Adjust power for temperature - this is temporary until the power is done as a function of mass flow rate induced
457 // Adjust for Temperature - Temperature above Standard decrease
458 // power by 7/120 % per degree F increase, and incease power for
459 // temps below at the same ratio
460 float T_amb_degF = (T_amb * 1.8) - 459.67;
461 float T_amb_sea_lev_degF = (288 * 1.8) - 459.67;
462 Percentage_Power = Percentage_Power + ((T_amb_sea_lev_degF - T_amb_degF) * 7 /120);
464 //DCL - now adjust power to compensate for mixture
465 Percentage_of_best_power_mixture_power = Power_Mixture_Correlation(equivalence_ratio);
466 Percentage_Power = Percentage_Power * Percentage_of_best_power_mixture_power / 100.0;
468 // Now Derate engine for the effects of Bad/Switched off magnetos
469 if (Magneto_Left == 0 && Magneto_Right == 0) {
470 // cout << "Both OFF\n";
471 Percentage_Power = 0;
472 } else if (Magneto_Left && Magneto_Right) {
473 // cout << "Both On ";
474 } else if (Magneto_Left == 0 || Magneto_Right== 0) {
475 // cout << "1 Magneto Failed ";
476 Percentage_Power = Percentage_Power * ((100.0 - Mag_Derate_Percent)/100.0);
477 // cout << FGEng1_Percentage_Power << "%" << "\t";
480 HP = Percentage_Power * MaxHP / 100.0;
482 Power_SI = HP * CONVERT_HP_TO_WATTS;
484 // Calculate Engine Torque. Check for div by zero since percentage power correlation does not guarantee zero power at zero rpm.
489 Torque_SI = (Power_SI * 60.0) / (2.0 * PI * RPM); //Torque = power / angular velocity
490 // cout << Torque << " Nm\n";
493 //**********************************************************************
494 //Calculate Exhaust gas temperature
496 // cout << "Thi = " << equivalence_ratio << '\n';
498 combustion_efficiency = Lookup_Combustion_Efficiency(equivalence_ratio); //The combustion efficiency basically tells us what proportion of the fuels calorific value is released
500 // cout << "Combustion efficiency = " << combustion_efficiency << '\n';
502 //now calculate energy release to exhaust
503 //We will assume a three way split of fuel energy between useful work, the coolant system and the exhaust system
504 //This is a reasonable first suck of the thumb estimate for a water cooled automotive engine - whether it holds for an air cooled aero engine is probably open to question
505 //Regardless - it won't affect the variation of EGT with mixture, and we can always put a multiplier on EGT to get a reasonable peak value.
506 enthalpy_exhaust = m_dot_fuel * calorific_value_fuel * combustion_efficiency * 0.33;
507 heat_capacity_exhaust = (Cp_air * m_dot_air) + (Cp_fuel * m_dot_fuel);
508 delta_T_exhaust = enthalpy_exhaust / heat_capacity_exhaust;
509 // delta_T_exhaust = Calculate_Delta_T_Exhaust();
511 // cout << "T_amb " << T_amb;
512 // cout << " dT exhaust = " << delta_T_exhaust;
514 EGT = T_amb + delta_T_exhaust;
516 //The above gives the exhaust temperature immediately prior to leaving the combustion chamber
517 //Now derate to give a more realistic figure as measured downstream
518 //For now we will aim for a peak of around 400 degC (750 degF)
520 EGT *= 0.444 + ((0.544 - 0.444) * Percentage_Power / 100.0);
522 EGT_degF = (EGT * 1.8) - 459.67;
524 //cout << " EGT = " << EGT << " degK " << EGT_degF << " degF";// << '\n';
526 //***************************************************************************************
527 // Calculate Cylinder Head Temperature
531 This is a somewhat rough first attempt at modelling cylinder head temperature. The cylinder head
532 is assumed to be at uniform temperature. Obviously this is incorrect, but it simplifies things a
533 lot, and we're just looking for the behaviour of CHT to be correct. Energy transfer to the cylinder
534 head is assumed to be one third of the energy released by combustion at all conditions. This is a
535 reasonable estimate, although obviously in real life it varies with different conditions and possibly
536 with CHT itself. I've split energy transfer from the cylinder head into 2 terms - free convection -
537 ie convection to stationary air, and forced convection, ie convection into flowing air. The basic
538 free convection equation is: dqdt = -hAdT Since we don't know A and are going to set h quite arbitarily
539 anyway I've knocked A out and just wrapped it up in h - the only real significance is that the units
540 of h will be different but that dosn't really matter to us anyway. In addition, we have the problem
541 that the prop model I'm currently using dosn't model the backwash from the prop which will add to the
542 velocity of the cooling air when the prop is turning, so I've added an extra term to try and cope
545 In real life, forced convection equations are genarally empirically derived, and are quite complicated
546 and generally contain such things as the Reynolds and Nusselt numbers to various powers. The best
547 course of action would probably to find an empirical correlation from the literature for a similar
548 situation and try and get it to fit well. However, for now I am using my own made up very simple
549 correlation for the energy transfer from the cylinder head:
551 dqdt = -(h1.dT) -(h2.m_dot.dT) -(h3.rpm.dT)
553 where dT is the temperature different between the cylinder head and the surrounding air, m_dot is the
554 mass flow rate of cooling air through an arbitary volume, rpm is the engine speed in rpm (this is the
555 backwash term), and h1, h2, h3 are co-efficients which we can play with to attempt to get the CHT
556 behaviour to match real life.
558 In order to change the values of CHT that the engine settles down at at various conditions,
559 have a play with h1, h2 and h3. In order to change the rate of heating/cooling without affecting
560 equilibrium values alter the cylinder head mass, which is really quite arbitary. Bear in mind that
561 altering h1, h2 and h3 will also alter the rate of heating or cooling as well as equilibrium values,
562 but altering the cylinder head mass will only alter the rate. It would I suppose be better to read
563 the values from file to avoid the necessity for re-compilation every time I change them.
566 //CHT = Calc_CHT( Fuel_Flow, Mixture, IAS);
567 // cout << "Cylinder Head Temp (F) = " << CHT << endl;
568 float h1 = -95.0; //co-efficient for free convection
569 float h2 = -3.95; //co-efficient for forced convection
570 float h3 = -0.05; //co-efficient for forced convection due to prop backwash
571 float v_apparent; //air velocity over cylinder head in m/s
572 float v_dot_cooling_air;
573 float m_dot_cooling_air;
574 float temperature_difference;
575 float arbitary_area = 1.0;
576 float dqdt_from_combustion;
577 float dqdt_forced; //Rate of energy transfer to/from cylinder head due to forced convection (Joules) (sign convention: to cylinder head is +ve)
578 float dqdt_free; //Rate of energy transfer to/from cylinder head due to free convection (Joules) (sign convention: to cylinder head is +ve)
579 float dqdt_cylinder_head; //Overall energy change in cylinder head
580 float CpCylinderHead = 800.0; //FIXME - this is a guess - I need to look up the correct value
581 float MassCylinderHead = 8.0; //Kg - this is a guess - it dosn't have to be absolutely accurate but can be varied to alter the warm-up rate
582 float HeatCapacityCylinderHead;
585 temperature_difference = CHT - T_amb;
587 v_apparent = IAS * 0.5144444; //convert from knots to m/s
588 v_dot_cooling_air = arbitary_area * v_apparent;
589 m_dot_cooling_air = v_dot_cooling_air * rho_air;
591 //Calculate rate of energy transfer to cylinder head from combustion
592 dqdt_from_combustion = m_dot_fuel * calorific_value_fuel * combustion_efficiency * 0.33;
594 //Calculate rate of energy transfer from cylinder head due to cooling NOTE is calculated as rate to but negative
595 dqdt_forced = (h2 * m_dot_cooling_air * temperature_difference) + (h3 * RPM * temperature_difference);
596 dqdt_free = h1 * temperature_difference;
598 //Calculate net rate of energy transfer to or from cylinder head
599 dqdt_cylinder_head = dqdt_from_combustion + dqdt_forced + dqdt_free;
601 HeatCapacityCylinderHead = CpCylinderHead * MassCylinderHead;
603 dCHTdt = dqdt_cylinder_head / HeatCapacityCylinderHead;
605 CHT += (dCHTdt * time_step);
607 CHT_degF = (CHT * 1.8) - 459.67;
609 //cout << " CHT = " << CHT_degF << " degF\n";
612 // End calculate Cylinder Head Temperature
615 //***************************************************************************************
616 // Oil pressure calculation
618 // Calculate Oil Pressure
619 Oil_Pressure = Calc_Oil_Press( Oil_Temp, RPM );
620 // cout << "Oil Pressure (PSI) = " << Oil_Pressure << endl;
622 //**************************************************************************************
623 // Now do the Propeller Calculations
626 FGProp1_RPS = RPM * Gear_Ratio / 60.0; // Borrow this variable from Phils model for now !!
627 angular_velocity_SI = 2.0 * PI * RPM / 60.0;
628 forward_velocity = IAS * 0.514444444444; // Convert to m/s
630 //cout << "Gear_Ratio = " << Gear_Ratio << '\n';
631 //cout << "IAS = " << IAS << '\n';
632 //cout << "forward_velocity = " << forward_velocity << '\n';
633 //cout << "FGProp1_RPS = " << FGProp1_RPS << '\n';
634 //cout << "prop_diameter = " << prop_diameter << '\n';
638 J = forward_velocity / (FGProp1_RPS * prop_diameter);
639 //cout << "advance_ratio = " << J << '\n';
641 //Cp correlations based on data from McCormick
642 Cp_20 = 0.0342*J*J*J*J - 0.1102*J*J*J + 0.0365*J*J - 0.0133*J + 0.064;
643 Cp_25 = 0.0119*J*J*J*J - 0.0652*J*J*J + 0.018*J*J - 0.0077*J + 0.0921;
645 //cout << "Cp_20 = " << Cp_20 << '\n';
646 //cout << "Cp_25 = " << Cp_25 << '\n';
648 //Assume that the blade angle is between 20 and 25 deg - reasonable for fixed pitch prop but won't hold for variable one !!!
649 Cp = Cp_20 + ( (Cp_25 - Cp_20) * ((blade_angle - 20)/(25 - 20)) );
650 //cout << "Cp = " << Cp << '\n';
651 //cout << "RPM = " << RPM << '\n';
652 //cout << "angular_velocity_SI = " << angular_velocity_SI << '\n';
654 prop_power_consumed_SI = Cp * rho_air * pow(FGProp1_RPS,3.0) * pow(prop_diameter,5.0);
655 //cout << "prop HP consumed = " << prop_power_consumed_SI / 745.699 << '\n';
656 if(angular_velocity_SI == 0)
659 prop_torque = prop_power_consumed_SI / angular_velocity_SI;
661 // calculate neta_prop here
662 neta_prop_20 = 0.1328*J*J*J*J - 1.3073*J*J*J + 0.3525*J*J + 1.5591*J + 0.0007;
663 neta_prop_25 = -0.3121*J*J*J*J + 0.4234*J*J*J - 0.7686*J*J + 1.5237*J - 0.0004;
664 neta_prop = neta_prop_20 + ( (neta_prop_25 - neta_prop_20) * ((blade_angle - 20)/(25 - 20)) );
666 //FIXME - need to check for zero forward velocity to avoid divide by zero
667 if(forward_velocity < 0.0001)
670 prop_thrust = neta_prop * prop_power_consumed_SI / forward_velocity; //TODO - rename forward_velocity to IAS_SI
671 //cout << "prop_thrust = " << prop_thrust << '\n';
673 //******************************************************************************
674 // Now do the engine - prop torque balance to calculate final RPM
676 //Calculate new RPM from torque balance and inertia.
677 Torque_Imbalance = Torque_SI - prop_torque; //This gives a +ve value when the engine torque exeeds the prop torque
679 angular_acceleration = Torque_Imbalance / (engine_inertia + prop_inertia);
680 angular_velocity_SI += (angular_acceleration * time_step);
681 RPM = (angular_velocity_SI * 60) / (2.0 * PI);
683 //DCL - stall the engine if RPM drops below 500 - this is possible if mixture lever is pulled right out