Rep Power: 194

This is based on many mathematical formulas that I have read in books, found online, and have been taught in various classes. If I have posted something incorrect, please pm me or comment below and I will either change it or prove you wrong.

Lets start at the base. The D17 has a bore of 75mm (7.5 cm & 2.9528 in) and a stroke of 94.4mm (9.44 cm & 3.7165 in). The formula for displacement is bore^2(squared) * stroke * 0.7853982(constant) * number of cylinders.

(0.7853982 is a constant value derived from pi/4)

Lets use centimeters so that our displacement will calculate to cubic centimeters instead of cubic millimeters. Applied to the D17 this is 7.5cm^2 * 9.44cm * 0.7853982 * 4 cylinders = 1,668.185777 cubic centimeters.
To convert this to cubic inches divide it by 16.387.
1,668.185777cc / 16.387 = 101.7993 cubic inches

To calculate how much air the stock D17 flows in pounds per minute follow the formula.

(Boost pressure (psi) + Ambient pressure (psi)) / (53.35(constant from the ideal gas law)* 12 (to preserve inch units) * (460+Air Intake Temp. in degrees Fahrenheit)

(0 psi + 14.7 psi (Pressure @ Sea-Level)) / (53.35 * 12 * (460+85 (Average Temp. w/Cold Air Intake)) = 0.000042131 lbs/inch
This is the Air Density in lbs/inch

To figure out the mass air flow of the engine in pounds per minute follow the formula below.

Mass Air Flow (lbs/min) = Air Density (lbs/inch) * Displacement (ci) * (RPM/2) * Volumetric Efficiency (%)

0.000042131 lbs/inch * 101.7993 ci * (6,100 rpm/2) (This is where peak horsepower is made) * 0.85 (85%) = 11.1190 lbs/min stock

This is where it gets complicated. Lets throw on a turbo running 10 lbs of boost with a compressor efficiency of 72% (Compressor efficiencies usually are between 65% and 78%, anything below 65% you shouldn’t even consider)

The first step is calculating the compressor outlet temperature.

Intake Temp. (degrees Fahrenheit) * (-1+(Total Pressure (psi) / Ambient Pressure (psi)))^0.263

Divide this by the compressor efficiency (72% = 0.72)

Then add the Intake Temp. to the final number
Let’s run our D17 on 10 lbs of boost.

85 * (-1+(24.7 / 14.7))^0.263 = 76.8094
76.8094 / 0.72 = 106.6797
106.6797 + 85 = 191.6797 Degrees F

This is how hot the air is coming out of the compressor.

Lets Plug that into the Air Density formula I explained before.

(10 psi + 14.7 psi) / (53.35 * 12 * (460 + 191.6797)) = 0.000059203 lbs/inch

0.000059203 lbs/inch * 101.7993 ci * (6,750 rpm (Redline) / 2) * 0.85 = 17.2896 lbs/min

This is assuming the pressure is at 14.7 psi inside the intake. There’s actually a slight vacuum and Garret Turbochargers made a Corrected Mass Air Flow formula. Simply divide the Mass Air Flow by (Atmospheric Pressure / Corrected Compressor Inlet Pressure)

17.2896 lbs/min / (14.7 / 13.95) = 16.4075 lbs/min @ 6,750 RPM

If we want full boost to be at 4,000 RPM this figures out to be 9.7229 lbs/min @ 4,000 RPM

If you plug in 13.95 instead of 14.7 for all the equations you get 16.7266 lbs/min @ 6,750 RPM. Not really sure why, but the two numbers are so close it probably won’t matter.

The pressure ratio is the (Boost Pressure + Atmospheric Pressure) / Atmospheric Pressure
Let’s use 13.95 to get a more accurate reading.

(10 psi + 13.95 psi) / (13.95 psi) = 1.7168 Pressure Ratio

Now we can actually see what turbocharger would be best for the D17
If you look at the Garrett compressor maps provided, hey all work pretty well for the D17.

 
Rep Power: 285

The math looks correct and I am very impressed, which is not an easy task. Well done!


+ rep

 
Rep Power: 352

all i see is blah blah blah blah blah lol