# Speed Density Mathematical Model

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edit: This thread is now super seeded by the speed density tuning guide found in the link below. However if you would like to understand the full mathematical model behind the calculation then continue reading this thread.

Speed Density is the name of the air flow model that the Falcon platform uses. Speed density works by calculating the airmass at any given point in time, the PCM can then easily infer how much fuel is required for a given commanded lambda.

Now to calculate the airmass at any point in time you need a lot of information. The following will all influence the volumetric efficiency and hence total airmass.

• RPM,
• Intake Cam Angle
• Exhaust Cam Angle
• Overlap between intake and exhaust cam
• Air pressure (MAP)
• Air temperature
• Humidity
• Exhaust gas recirculation

The PCM takes all of the above into consideration and then uses this to determine airmass. This takes on the form of the following two equations (approximately)

slope_mod = 1 / auF16454 fg, auF16632 bf tuning correction (rpm, load) * (auF0059 fg , auF0061 bf slope of map (n, cam_angle) + auF2928 fg,auF0064 bf slope overlap adder (rpm,overlap_angle) )

offset_mod = (auF0055 bf, auF0056 fg map at zero (rpm, cam_angle) + auF16657 fg, auF0066 bf exhaust cam angle offset adder  (rpm, overlap_angle)) * slope

auF16454,auF16632 is a fudge factor map to account for non linearities at low rpm.

auF0059,auF0061 is the main "slope" factor

auF2928,auF0064 is an adder to the slope for exhaust camshaft overlap to account for air that is lost out the exhaust

volumetric_correction = various tables used to correct for intake temp and coolant temp. You should never need to touch these.

The Final air mass equation is as follows.

Cylinder_Air_Mass = volumetric_correction * (MAP * slope_mod - offset_mod)

This can be approximated by:

Cylinder_Air_Mass = MAP * Slope_mod - offset_mod

To further approximate it:

Cylinder_Air_Mass = (MAP - auF0055 bf, auF0056 fg map at zero) / auF0059 fg, auF0061 bf slope of map

Now that we know how the airmass is calculated we can re-tune the various tables for different camshafts. If you have large camshafts ensure they are installed so that you have 0 overlap (this will be mean installing them differently to the manufacturer), then command the required overlap so the PCM knows how much overlap there is. If you don't do the above you will need to recalculate the base offset and slope tables instead.

Eg increased overlap (big cams) with the stock VCT system installed and a large commanded overlap can be tuned by modifying the various overlap adders depending on where you have issues. If you have issues at low load/map you should modify the offset auF16657 fg/ auF0066 bf

If you have issues when on load you should modify the slope auF2928 fg/auF0064 bf

If you have installed the camshafts with overlap (how most tuners install them) and are not commanding any overlap then you should modify the following tables

If you have issues at low load/map pressures modify the offset auF0055 bf /auF0056 fg

If you have issues on load then modify the slope auF0059 fg / auF0061 bf

Note. The PCM also uses a second airmass model to calculate transient filtered airflow for tip in and other events, the transient equation is approximately as follows:

exhaust_gas_recirc_factor = modelled based on how much exhaust gas will recirculate into the intake at certain times

air_previous = various fudge factors based on manifold filling and the previous air mass last cycle

Transient_air_mass = volumetric_correction * (air_previous  + exhaust_gas_recirc_factor * (slope + offset / map))

This can be approximated by

Transient_air_mass = air_previous + map * (slope + offset / map)

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