FORD qudratic equation.

[Joshua.Levin]

In imaginary terms..

Slope = LB MASS PER STROKE
Offset = PRESSURE AT WHICH ENGINE CANNOT INGEST AIR AT STANDARD ATMOSPHERE
IDGL = applied and weighted ideal gas law
Quadric Term=term*1.0-14
Q=(MAP-(BARO/29.95)*OFFSET)/SLOPE
R=(MAP-(BARO/29.95)*OFFSET)^2*QUADRATIC TERM
(Q+R)*IDGL=AIRMASS

SOLVED
Josh Levin

[jchambers]

You've got to abandon the linear interpretation. The quadratic equation is y = ax^2 + bx + c where y is the inferred mass per intake event and x is the inferred MAP. When solving for the inferred MAP, think back to the day of Algebra class where you're solving for the roots (note multiple) of the quadratic equation x = (-b +/- sqrt(4ac))/2a. You'll have two roots in most cases, only one of which is valid. You can also wind up with imaginary roots (where the sqrt function is of a negative number) which is not a valid solution for the inferred MAP. The Ford logic includes some IF/THEN logicals that lead to different solutions, including dropping back to the linear solution. This is why the speed density surface appears disjointed in the raw solution.

[Joshua.Levin]

You've got to abandon the linear interpretation. The quadratic equation is y = ax^2 + bx + c where y is the inferred mass per intake event and x is the inferred MAP. When solving for the inferred MAP, think back to the day of Algebra class where you're solving for the roots (note multiple) of the quadratic equation x = (-b +/- sqrt(4ac))/2a. You'll have two roots in most cases, only one of which is valid. You can also wind up with imaginary roots (where the sqrt function is of a negative number) which is not a valid solution for the inferred MAP. The Ford logic includes some IF/THEN logicals that lead to different solutions, including dropping back to the linear solution. This is why the speed density surface appears disjointed in the raw solution.

There must be something missing. I am working on a SD vehicle, not MAF with predicted airflow. Map is not inferred

[jchambers]

OK, so its essentially going to be the same except that the mass is being calculated directly from the MAP. The slope is the first derivative of the change in mass (df/ds) and the quadratic is the second derivative (df/ds^2). Algebraically, its the concavity of the function where slope is the rate of change of the function, offset is exactly that...the spatial offset of the singular solution of the function. As the function is extrapolated in the time-based domain (RPM), it forms the load/ve surface.

[Joshua.Levin]

osq.jpg

Answered

Map 30"

rpm 4300

Offset =0.83
Slope =19191
QT= -2283538*1.-14

Thank You.

[GapRider]

Answered

Map 30"

rpm 4300

Offset =0.83
Slope =19191
QT= -2283538*1.-14

Thank You.

Joshua, did you solve that with the linear or quadratic equation? Also, does "*1-14" mean "1 x 10 to the negative 14th"?

[reubone]

Please guys try to excuse my ignorance, but this info is going to be useful somehow I just feel it but ill be damned if its clicking yet. Help me understand where this applies please. Its amazing to me what I'm looking at here. Im sure I'll understand this eventually

[GapRider]

y=ax^2+bx+c
a = quad term
b = slope
c = offset
When I plot the graph in excel, using the quad term as is, I get a lot of excel errors, (I think when the [b^2-4ac] goes negative)
But, If I treat the quadratic term as an acceleration (inHg/lbm^2), like gravity in this equation s(t) = (a/2)t² + v₀t + s_0, and divide the quad term by 2 for each calculation, I get what looks like a clean graph, no excel math errors.
Is this the correct way to treat the quad term (parameter)?

[murfie]

Theres multiple steps and equations to it. MAP and Mass get plotted against each other as Y and X.

First you start with a given cylinder air charge in this equation.

m air x  ( k ) = m air cyl  ( k ) vol_eff  _cor  ( ACT , ECT ) * 30  [ in - Hg ] P exh  ( k ) is the equation in the patent.

scaled cylinder air charge (the theoretical maximum air charge that the cylinder can hold at a given pressure at intake valve closing) = cylinder air charge @(k) with applied ACT vs ECT table value to correct VE multiplied by the exhaust pressure(@k) over 30 inHg.

(k) is a sample interval. This would be a value like Lb/min. the Scaled air charge would form a straight line in the graph.

From here it goes in to and IF else statement. If scaled cylinder air charge is greater than the critical point at which blow through occurs then infer MAP with one equation else infer with another equation.

The second line would be formed by a least-squares or other regression from actual engine data. Excel 2010 scatter plot layout 3 is good for this. Where these two lines intersect is your critical point. So as you can see where actual exceeds therotical is where blow through occurs.

This would be your blow through area equation
P inf  ( k ) =  P exh  ( k ) 30  [ in - Hg ]  max  { 1 c norm * m c  ( k ) , [ 1 c norm * m c  ( k ) + slp * ( m air x  ( k ) - m c  ( k ) ] }

1 c norm is the theoretical MAP value on the scaled line. m c is the critical mass point. slp is the slope of the regression line.

This would be your non blow through area equation
P inf  ( k ) =  P exh  ( k ) 30  [ in - Hg ]  ( air_offset + air_slope ? m air x  ( k ) + air_quad ? m air x  ( k ) 2 )

I wouldn't divide it by 2 but multiply it by the LBm^2. sample interval of (m air x)^2. Lb per min divided by revolution per min gives you Lb per revolution. divided that by 4 because its a four stroke engine. This gives you the LBm per cylinder intake event to plot against MAP.

The most important thing to do when correcting your SD is to get MAP data vs intake event mass data and regress a curve and equation from this. The MAP max vs airmass table gives you the Theoretical scaled line. Compare the two and apply the appropriate equation to the appropriate data.

FIG 2 is a good visual.
Fig 2.PNG

[GapRider]

thanks for the detailed reply murfie, you're about 3 degrees ahead of me in math but I'm not ready to give up yet : )
As a matter of fact, I thought I was getting closer but now it seems like my presupposition that the speed density has done a simple evolution in this generation of Fords from the linear y=mx+b to the curve y=ax^2+bx+c is not all at all the way to look at this? And I've been letting x=mass and y=MAP where that seems backwards to posts above.

Anyway, I've got the new math hitting me simultaneously with the "new" idea making it tougher also.
I will go back to that patent but can't help asking this:
Conceptually, I derive the curved line and the straight, sloped line both from parameters available? cyl mass will follow the curved speed density line until it reaches a blow through max and then it will follow that straight, sloped max?

[GapRider]

OK I went back and looked at the links for the patents that we've referenced here and in the "Ford Speed Density tuning" thread but I don't see the diagram you posted above. Do you have a link to that patent?

[murfie]

https://www.google.com/patents/US20130111900

The solid line is a standard non blow through regression curve. The dotted line that follows the data points is a regression curve with blow through.

[GapRider]

That patent is for turbo cars right, where you have boost available to put cyl mass over the blow though threshold? Does the coyote use that strategy?

[murfie]

That patent covers both concepts for cars with and with out blow through. The coyote uses this strategy, the blow through tables are just full of 0's.


"The parameters air_offset, air_slope, and air_quad represent the conventional non-blow-through curve 204 and can be calibrated by a least squares fit of the engine data."

How to do regression using least squares in excel
http://www.westmont.edu/~phunter/ma5...egression.html

[ghostofnyc]

great info

[GapRider]

That patent covers both concepts for cars with and with out blow through. The coyote uses this strategy, the blow through tables are just full of 0's.


"The parameters air_offset, air_slope, and air_quad represent the conventional non-blow-through curve 204 and can be calibrated by a least squares fit of the engine data."

How to do regression using least squares in excel
http://www.westmont.edu/~phunter/ma5...egression.html

you good man murfie

[4wheelinls1]

Do you know if the SD data impacts the Mustang given its a MAF car? If we did forced induction we should correct the blow through tables that are currently 0's. Could this be what is contributing to the difficulty tuning these cars with forced induction regarding transition stability and surge?

[caniggia]

Not tested coyote in this case, but there is another topic i created sometime ago for 4.6 which i tried to run without MAF. No matter what changes i made in speed density tables, fuel trims did not changed. Are you going to tune mixture without MAF?

[4wheelinls1]

Not tested coyote in this case, but there is another topic i created sometime ago for 4.6 which i tried to run without MAF. No matter what changes i made in speed density tables, fuel trims did not changed. Are you going to tune mixture without MAF?

I have tried this too with the same resut but was wondereing if influences the torque or the cars ability to run with a failled MAF or for cross checking.