I've been going through this equation and am not clear on how it was derived.
1. The multiplier for fuel rate in the previous equation is (0.132276). This is saying that there are 7.56 pounds of gasoline per gallon. That number is way too high. 6.4 pounds is about right.
2. The previous equation below provided a correction for volumetric changes in gasoline using what appears to be Boyle's Law. Moreover, it appears to have been inverted - yielding incorrect results anyway. In other words when the temperature of the fuel increased, it increased its density and by large amounts.
REGARDLESS, BOYLE'S ONLY APPLIES TO GASES. IT DOES NOT APPLY TO LIQUIDS AT ALL. In addition, the temperatures are converted from relative temperatures to absolute temperatures by adding 273.15 degrees. But this number is used for the Celsius scale - and the temperatures are being provided in Fahrenheit. Assuming ECT is 200 F and IAT is 100 F, this part of the equation would alter the fuel density by 41%! Even for a temperature swing of 200 F I doubt you would see a 4% variation in the density of gasoline. To account for density changes in gasoline you would have to use an Equation of State like Peng-Robinson. Hardly worthwhile since a center value gets you within 2% of actual mileage.
If we were working with a gas and using the Fahrenheit scale, conversion to the Rankine scale would have been appropriate (adding about 460 degrees to go to absolute temperature).
Nonetheless, if people here are really interested, I will take the time to derive a correlation that will account for temperature changes. Keep in mind however that injectors are rated in mass per time and not volume per time. This is due to inertial effects within the injector. The primary delivery effects are due to pressure differentials and not density variations. In other words, when the gasoline is lighter (because it is less dense) the pressure difference across the injector orifice is able to throw more gasoline out, negating the effects of minor density variations. In essence, there is no need for correction or a very small need.
I recalculated the equation and hopefully didn't make any mistakes as it is easy to do so.
We have:
- speed - Miles / Hour
- Injector flow rate - lb/ hour (per injector)
- number of injectors - dimensionless
- % duty - dimensionless
We are interested in getting miles per gallon.
The Injector value returns the flow in pounds for one injector (about 27 pounds per hour) assuming it is on continuously.
The value returned by [PID.6210] is about 3.5 (clearly in grams per second - which converts to about 27.5 lb/hr)
If we have 8 injectors that number would then be multiplied by 8
There are approximately 6.4 pounds of gasoline in a gallon.
So the total fuel (if the injectors were on all the time) would be (in gallons):
Flow Rate (conversion factor to pounds per hour) * number of injectors / 6.4 pounds per gallon.
(g/s) * (3600 s/1hr) * (1lb/453.69 g) = fuel rate * 7.9367 lb / hr
For an 8 cylinder engine, this is:
Fuel Rate * 7.9367 * 8 / 6.4 = 9.92 * Fuel Rate (now in gallons per hour):
Since the injectors aren't on all time, we need to determine what part of the total time they are on. This is referred to as the DUTY.
In this case, the injector duty divided by the length of time between injector pulses will yield the duty:
The length of a cycle can be calculated from the engine speed variable which is given in rotations per minute.
The injectors are fired for each cylinder ever two engine rotations. The length of time is thus:
(Rotations / minute) * (60 seconds / rotation) * 2
This gives us the number of rotations in 1 seconds. To get the number of seconds in a rotations, we simply take the reciprocal.
Our formula for the total time is then:
120/RPM
We will also need the injector pulse time to be in seconds.
(#ms) * (1s / 1000 ms)
The DUTY is the ratio of ON TIME over TOTAL TIME yielding a dimensionless number.
Injector Pulse Width / 1000 / (120 / RPM) = Injector Pulse Width * RPM / 120000
Bringing all of this together, we simply get (8 cylinder):
12096 * speed / flow / PW / RPM (no parenthesis to enter)
This equation is markedly different from the equation prior and yields dramatically different results.
In addition to being inherently different, there are other problems with the equation derived earlier.
The final formula to enter for an 8 cylinder engine in the PID is then:
12096 * [SENS.20] / [PID.6210] / [SENS.112] / [SENS.70]
For a 6 cylinder engine the equation is:
9072 * [SENS.20] / [PID.6210] / [SENS.112] / [SENS.70]
The ability for the above equations to yield accurate results is dependent on numerous factors, not the least of which is that we are always getting data from the computer. In essence, we are performing an integration of a function (Miles per gallon) in an attempt to get average MPG.
If the above data does not yield the correct MPG for a vehicle, it can be easily corrected by a correction factor.
For example if your averaging function reported that you got 34 MPG but you actually got 24, you would simply multiply the 12096 number by (24/34) which would yield 8538. From that point on, your data would accurate for your car and more importantly, the instantaneous MPG numbers would be accurate and helpful in tuning.
Sam Michael
Chemical Engineer.
Reply With Quote
Originally Posted by samgm2
. I will have to move my WBO2 to the Blazer but that won't be too hard.
