#include "Atmosphere.hpp" #include "Math.hpp" #include "PistonEngine.hpp" namespace yasim { const static float HP2W = 745.7f; const static float CIN2CM = 1.6387064e-5f; const static float RPM2RADPS = 0.1047198f; PistonEngine::PistonEngine(float power, float speed) { _boost = 1; _running = false; _fuel = true; // Presume a BSFC (in lb/hour per HP) of 0.45. In SI that becomes // (2.2 lb/kg, 745.7 W/hp, 3600 sec/hour) 7.62e-08 kg/Ws. _f0 = power * 7.62e-08f; _power0 = power; _omega0 = speed; // We must be at sea level under standard conditions _rho0 = Atmosphere::getStdDensity(0); // Further presume that takeoff is (duh) full throttle and // peak-power, that means that by our efficiency function, we are // at 11/8 of "ideal" fuel flow. float realFlow = _f0 * (11.0f/8.0f); _mixCoeff = realFlow * 1.1f / _omega0; _turbo = 1; _maxMP = 1e6; // No waste gate on non-turbo engines. // Guess at reasonable values for these guys. Displacements run // at about 2 cubic inches per horsepower or so, at least for // non-turbocharged engines. _compression = 8; _displacement = power * (2*CIN2CM/HP2W); } void PistonEngine::setTurboParams(float turbo, float maxMP) { _turbo = turbo; _maxMP = maxMP; // This changes the "sea level" manifold air density float P0 = Atmosphere::getStdPressure(0); float P = P0 * (1 + _boost * (_turbo - 1)); if(P > _maxMP) P = _maxMP; float T = Atmosphere::getStdTemperature(0) * Math::pow(P/P0, 2./7.); _rho0 = P / (287.1f * T); } void PistonEngine::setDisplacement(float d) { _displacement = d; } void PistonEngine::setCompression(float c) { _compression = c; } float PistonEngine::getMaxPower() { return _power0; } bool PistonEngine::isCranking() { return _starter; } float PistonEngine::getTorque() { return _torque; } float PistonEngine::getFuelFlow() { return _fuelFlow; } float PistonEngine::getMP() { return _mp; } float PistonEngine::getEGT() { return _egt; } void PistonEngine::calc(float pressure, float temp, float speed) { if(_magnetos == 0 || speed < 60*RPM2RADPS) _running = false; else if(_fuel == false) _running = false; else _running = true; // Calculate manifold pressure as ambient pressure modified for // turbocharging and reduced by the throttle setting. According // to Dave Luff, minimum throttle at sea level corresponds to 6" // manifold pressure. Assume that this means that minimum MP is // always 20% of ambient pressure. (But that's too much idle // power, so use 10% instead!) But we need to produce _zero_ // thrust at that setting, so hold onto the "output" value // separately. Ick. _mp = pressure * (1 + _boost*(_turbo-1)); // turbocharger float mp = _mp * (0.1f + 0.9f * _throttle); // throttle _mp *= _throttle; if(mp > _maxMP) mp = _maxMP; // wastegate // Air entering the manifold does so rapidly, and thus the // pressure change can be assumed to be adiabatic. Calculate a // temperature change, and use that to get the density. float T = temp * Math::pow(mp/pressure, 2.0/7.0); float rho = mp / (287.1f * T); // The actual fuel flow is determined only by engine RPM and the // mixture setting. Not all of this will burn with the same // efficiency. _fuelFlow = _mixture * speed * _mixCoeff; if(_fuel == false) _fuelFlow = 0; // How much fuel could be burned with ideal (i.e. uncorrected!) // combustion. float burnable = _f0 * (rho/_rho0) * (speed/_omega0); // Calculate the fuel that actually burns to produce work. The // idea is that less than 5/8 of ideal, we get complete // combustion. We use up all the oxygen at 1 3/8 of ideal (that // is, you need to waste fuel to use all your O2). In between, // interpolate. This vaguely matches a curve I copied out of a // book for a single engine. Shrug. float burned; float r = _fuelFlow/burnable; if (burnable == 0) burned = 0; else if(r < .625) burned = _fuelFlow; else if(r > 1.375) burned = burnable; else burned = _fuelFlow + (burnable-_fuelFlow)*(r-0.625f)*(4.0f/3.0f); // Correct for engine control state if(!_running) burned = 0; if(_magnetos < 3) burned *= 0.9f; // And finally the power is just the reference power scaled by the // amount of fuel burned, and torque is that divided by RPM. float power = _power0 * burned/_f0; _torque = power/speed; // Figure that the starter motor produces 15% of the engine's // cruise torque. Assuming 60RPM starter speed vs. 1800RPM cruise // speed on a 160HP engine, that comes out to about 160*.15/30 == // 0.8 HP starter motor. Which sounds about right to me. I think // I've finally got this tuned. :) if(_starter && !_running) _torque += 0.15f * _power0/_omega0; // Also, add a negative torque of 8% of cruise, to represent // internal friction. Propeller aerodynamic friction is too low // at low RPMs to provide a good deceleration. Interpolate it // away as we approach cruise RPMs (full at 50%, zero at 100%), // though, to prevent interaction with the power computations. // Ugly. if(speed > 0 && speed < _omega0) { float interp = 2 - 2*speed/_omega0; interp = (interp > 1) ? 1 : interp; _torque -= 0.08f * (_power0/_omega0) * interp; } // Now EGT. This one gets a little goofy. We can calculate the // work done by an isentropically expanding exhaust gas as the // mass of the gas times the specific heat times the change in // temperature. The mass is just the engine displacement times // the manifold density, plus the mass of the fuel, which we know. // The change in temperature can be calculated adiabatically as a // function of the exhaust gas temperature and the compression // ratio (which we know). So just rearrange the equation to get // EGT as a function of engine power. Cool. I'm using a value of // 1300 J/(kg*K) for the exhaust gas specific heat. I found this // on a web page somewhere; no idea if it's accurate. Also, // remember that four stroke engines do one combustion cycle every // TWO revolutions, so the displacement per revolution is half of // what we'd expect. And diddle the work done by the gas a bit to // account for non-thermodynamic losses like internal friction; // 10% should do it. float massFlow = _fuelFlow + (rho * 0.5f * _displacement * speed); float specHeat = 1300; float corr = 1.0f/(Math::pow(_compression, 0.4f) - 1.0f); _egt = corr * (power * 1.1f) / (massFlow * specHeat); if(_egt < temp) _egt = temp; } }; // namespace yasim