AIRDEN Equation

[rscubelek]

In the "How Megasquirt Works" section of http://www.megasquirt.info, the given AIRDEN equation is as follows:

AIRDEN(MAP, temp) = (0.0391568* (MAP*10-31.0)) / ((temp+459.7) * 1728)

and below the equation is the explanation of the equation, where it states:

459.7 is used to convert from Fahrenheit to absolute temperature


Degrees fahrenheit do NOT have a linear relationship with degrees Kelvin, so where does that 459.7 come from? The proper equation to convert degrees fahrenheit to degrees kelvin is as follows:

K = 5/9 (Degrees fahrenheit - 32) + 273

Is this an error in the Megasquirt literature, or is there some kind of justification for using the number 459.7? Because 459.7 K is like 368 F.

If anyone knows, please help me out.


EDIT: Also, what is the constant 0.0391568 used for?

[Matt Cramer]

Because absolute zero is -459.7 degrees Fahrenheit, to the nearest degree. The equation is not working in degrees Kelvin at this point, but degrees Rankine.

http://en.wikipedia.org/wiki/Rankine_scale

[rscubelek]

Ah, alright. The page said nothing about degrees Rankine, I actually have never heard of it until I looked at that wikipedia page.

When I plug in the same information, in its respective units, into both the standard version and the metric version of this AIRDEN equation, should I not get the same number from either equation?

Also, what is that constant 0.0391568 used for?

[msiddalingaiah]

When I plug in the same information, in its respective units, into both the standard version and the metric version of this AIRDEN equation, should I not get the same number from either equation?

The quantity will be the same, but the numbers will be different since the units are not the same.

Also, what is that constant 0.0391568 used for?

It looks like it is the universal gas constant multiplied by a factor to make the units work:

http://en.wikipedia.org/wiki/Gas_constant

As far as I can tell, the AIRDEN equation is the ideal gas law rearranged with different units:

http://en.wikipedia.org/wiki/Ideal_gas_law

[rscubelek]

Ah, alright, thank you guys for your help.

[rscubelek]

I was wondering, does anyone have the derivations of the equations used in Megasquirt, such as the AIRDEN equation and the REQ_FUEL equation? I would be very interested in knowing more about these equations. Thanks in advance.

[msiddalingaiah]

I was wondering, does anyone have the derivations of the equations used in Megasquirt, such as the AIRDEN equation and the REQ_FUEL equation? I would be very interested in knowing more about these equations. Thanks in advance.

I went through it once using MKS units. For whatever reason, I think MS does it English units, which gives me a headache.
The outline is spelled out in the Megamanual. For speed-density, it goes something like this:

Given the ideal gas law:

PV = nRT

You need air mass per engine stroke, which is

m_air = n * molar_mass_air

P is the manifold pressure (MAP), V is the engine displacement (DISP), R is the gas constant, T is air temperature. Rearranging, you get:

m_air = MAP * DISP * molar_mass_air / (R * T)

From thisou you calculate fuel mass, which is

m_fuel = m_air / AFR

Given fuel per engine stroke, pulse width per stroke is

t = m_fuel / inj_flow_rate

This is multiplied by the appropriate entry in the VE table, corrections for warm up, accel/decel enrichment, injector open time are added, and there you have it.