Steam engine: superheat temperature in F

[Wesley Johnson]

File: MSTSSteamLocomotive.cs

However ORTS has some degree F around, It keeps the superheat temperature in degree F,
and this one calculation seems to multiply by degree F,
without converting to degree K. I cannot see how this could be valid.

In ORTS code:

// Calculate superheat steam reference temperature based upon heating area of superheater
// SuperTemp = (SuperHeatArea x HeatTransmissionCoeff * (MeanGasTemp - MeanSteamTemp)) / (SteamQuantity * MeanSpecificSteamHeat)
// Formula has been simplified as follows: SuperTemp = (SuperHeatArea x FlueTempK x SFactor) / SteamQuantity
// SFactor is a "loose reprentation" = (HeatTransmissionCoeff / MeanSpecificSteamHeat) - Av figure calculate by comparing a number of "known" units for superheat.
SuperheatRefTempF = (Me2.ToFt2(SuperheatAreaM2) * C.ToF(C.FromK(MaxFlueTempK)) * SuperheatKFactor) / pS.TopH(TheoreticalMaxSteamOutputLBpS);
SuperheatTempRatio = SuperheatRefTempF / SuperheatTempLbpHtoDegF[pS.TopH(TheoreticalMaxSteamOutputLBpS)]; // calculate a ratio figure for known value against reference curve.

In my code (which is easier to follow and has the comments):
I have changed my superheat temperatures to entirely degree K.

// SuperheatKFactor = (HeatTransmissionCoeff / MeanSpecificSteamHeat) - Av figure calculate by comparing a number of "known" units for superheat.
#ifdef KELVIN_SUPERHEAT
  // flue_temp = 775K = 492C = 917F
  // boiler_temp = 110C = 383K = 230F
  float superheat_K_kelvin; // Factor used to calculate superheat temperature - guesstimate
#else
  float SuperheatKFactor; // Factor used to calculate superheat temperature - guesstimate
#endif
  float superheater_MSTS_factor = 1.0f; // MSTS parameter
      // Currently 2 values respected: 0.0 for no superheat (default), > 1.0 for typical superheat
      // SuperheaterFactor

void verify_and_correct()
{
  if( num_cylinders == 0 )
      num_cylinders = 2;

  // SuperheatKFactor = (HeatTransmissionCoeff / MeanSpecificSteamHeat) - Av figure calculate by comparing a number of "known" units for superheat.
#ifdef KELVIN_SUPERHEAT
  // flue_temp = 775K = 492C = 917F
  // boiler_temp = 110C = 383K = 230F
  superheat_K_kelvin = 27.3f; // degree K based
#else
  SuperheatKFactor = 11.7f; // ORTS
#endif

    safety_valve_high_trip = boiler_pressure_max + safety_valve_high_margin;
    safety_valve_low_reset = boiler_pressure_max - safety_valve_low_margin;

.....
}

// Calculate superheat steam reference temperature based upon heating area of superheater
/ SuperTemp = (SuperHeatArea x HeatTransmissionCoeff * (MeanGasTemp - MeanSteamTemp)) / (SteamQuantity * MeanSpecificSteamHeat)
// Formula has been simplified as follows: SuperTemp = (SuperHeatArea x flue_temperature x SFactor) / SteamQuantity
// SFactor is a "loose representation" = (HeatTransmissionCoeff / MeanSpecificSteamHeat) - Av figure calculate by comparing a number of "known" units for superheat.

#ifdef KELVIN_SUPERHEAT
  // FIXME: use better formula, * (flue_temperature_max - steam_temp),
  // Assume steam_temp approx 110 degree C. or so, depending on boiler pressure
  superheat_ref_temperature = superheat_area * (flue_temperature_max - C_to_K(110)) * superheat_K_kelvin / pS.TopH(boiler_steam_output_max);
#else
  // ORTS: Has multiply by degree F, this is not normal.
  // This is after translations to degree K, kg, joule, meter.
  // flue_temperture_max is now in degree K.
  // ORTS equation:
  // model->superheat_ref_temperature = ((superheat_area * K_to_F(flue_temperature_max) * SuperheatKFactor) / pS.TopH((model->boiler_steam_output_max))); // ORTS
  // Fixed: Multiply by degree K.
  superheat_ref_temperature = superheat_area * flue_temperature_max * SuperheatKFactor / boiler_steam_output_max;
#endif
// calculate a ratio figure for known value against reference curve.
superheat_temperature_ratio = superheat_ref_temperature / SuperheatTemp(boiler_steam_output_max);

[Wesley Johnson (trackcreworts)]

Offending line:
SuperheatRefTempF = (Me2.ToFt2(SuperheatAreaM2) * C.ToF(C.FromK(MaxFlueTempK)) * SuperheatKFactor) / pS.TopH(TheoreticalMaxSteamOutputLBpS);

It may be that ORTS code should be (moving two paren):
SuperheatRefTempF = (Me2.ToFt2(SuperheatAreaM2) * C.ToF(C.FromK( MaxFlueTempK * SuperheatKFactor )) ) / pS.TopH(TheoreticalMaxSteamOutputLBpS);

If I could figure out what that SuperheatKFactor had for units, it would help.
But it still leaves you with the rest of the equation being a ratio upon a temp in degree F, which cannot be valid. You need degree K to multiply ratios like that.
That conversion to degree F involves adding some constants, so it does not act like a const multiply.

So my best guess is that it should be (moving conversion to F around entire result):
SuperheatRefTempF = C.ToF(C.FromK( (Me2.ToFt2(SuperheatAreaM2) * MaxFlueTempK * SuperheatKFactor) / pS.TopH(TheoreticalMaxSteamOutputLBpS) ));