Rotary Math
 

I wanted to post a thread to which I could reference people for the required math for computing the performance of the Renesis, N/A or FI.
This is just going to be a list of required formulas with the required engine-specific and natural constants already in place.



For additional reference, here are two spreadsheets:




Ambient Air Temp (Ta) = 77°F (25°C)
Ambient Air Pressure (Pa) = 14.7 PSI (29.98 in/Hg)
Intake Temperature = Ambient
Intercooler Efficiency = 70%
Turbo Compressor Efficiency = 77%

{1 Cubic Inch (cid) = 16.39 Cubic Centimeters (cc)}
{1 Pound per Minute (lb/min) = 7.56 Grams per Second (g/sec)}

Renesis Displacement = 1308 cc (80 cid)
Renesis Volumetric Efficiency @ 8200 RPM (Ve) = 92%
Renesis Peak Horsepower RPM = 8200 RPM
Renesis Brake Specific Fuel Consumption (BSFC) = .60 lb/hp/hr (POUNDS per HORSEPOWER per HOUR)
Renesis Total Fuel Injected Volume = 2100 cc (3.33 lb/m)





ROTARY VOLUMETRIC FLOW RATE

VFR = ((DISPLACEMENT) x (RPM) ÷ 1728) x (VOLUMETRIC EFFICIENCY)
VFR = ((80cid) x (8200rpm) ÷ 1728) x (92%)
VFR = (380cfm) x (.90)
VFR = 360.65 cfm

ROTARY MASS FLOW RATE

MFR = (2.703) x (Pa) x (VFR) ÷ (Ta + 460)
MFR = (2.703) x (14.7) x (360.65) ÷ (77° + 460)
MFR = 26.85 POUNDS per MINUTE (lb/m)
MFR = 202.60 Grams per Second (g/sec)

POTENTIAL CRANKSHAFT HORSEPOWER ESTIMATE

HPo = (MFR) x (60) ÷ (AFR) x (BSFC)
HPo = (26.85) x (60) ÷ (13) x (.60)
HPo = 207 Hp


REQUIRED FUEL INJECTOR FLOW RATE

IFR = (MFR) ÷ (AFR)
IFR = (26.85 lb/m) ÷ (13)
IFR = 2.07 lb/m

For cc's, divide by 0.001586:

2.07 lb/m = 1305 cc

Here is how it would work out with 800cc P2 injectors:

Renesis Total Fuel Injected Volume = 2940 cc (4.66 lb/m)


SUPPORTED MASS FLOW RATE

MFRs = (IFR) x (AFR)
MFRs = (4.66) x (11)
MFRs = 51.26 lb/m

SUPPORTED VOLUMETRIC FLOW RATE

VFRs = (77° + 460) x (51.26 lb/m) ÷ (2.703) x (14.7)
VFRs = 688.56 cfm

DENSITY RATIO

Dr = (VFRs) ÷ (VFR)
Dr = (688.56) ÷ (360.65)
Dr = 1.91

PRESSURE RATIO

Dr = (Pr) ÷ ((Tin + 460) ÷ (Tout + 460))
1.64 = (Pr) ÷ ((77° + 460) ÷ (120° + 460))
Pr = 2.26

Boost = (Pa x Pr) - Pa
Boost = (14.7 x 1.54) - 14.7
Boost = 18.61 PSI

Been busy there I see.
I'll have to look at this for a while .

Yeah, this is the culmination of about a year of looking for solid ways to quantify everything I've been working on.

If you are interested in this, I will be updating this from the top (rather than adding responses), so you will want to check if the last "updated on" date-stamp is more current than your last visit.

Got that in a spreadsheet?

And that green is giving me a headache...

But is nice to know where I can go if I get serious. I printed this page to look at it a little harder.

Thanks Jeff!

Hope you dont mind me doing this but I am interested in understanding it all...

How is this figure achieved?

Also, can you explain the straight numbers in most of these equations, ie
What is 1728?

Thats all for now...keep up the good work.

Cheers

Andrew

Auzoom, not to jump into MM's action, but that is a cubic foot expressed in cubic inches.

To convert the engine capacity to cf from ci.

1 cf = 1728 ci

Good question though. Google came through again.

Conversion from Cubic Inches to Cubic Feet.

Nice work.

How about this:
[[SEE LINKS IN TOP POST]]

BTW - I am assuming that I have made some mistakes along the way, so feel free to interject corrections - as long as you can support them with math, not "well, my buddy got more power out of his RX-7 with that much boost...".

Cheers guys but what about the rest:

2.703 and 460

60

9

Yes I will go and look them up but thought that it would be nice to have them in one spot so people dont have to to and fro with google every time they view this.

Cheers

Andrew

Wow Jeff, I was just being a pain about the spreadsheet. Impressive work!

I didn't think I was going to have to define how many minutes there are in an hour, but I did point out the difference in BSFC at the beginning (and end, with a footnote) of the post.http://www.mazdamaniac.com/portal/sm...n_rolleyes.gif

You may want to get a handle on the basics before you tackle any of this.

That is a bit off the cuff by doing a bell curve (and then a statistical average) with 100% at the torque peak.
This is typical of a modern motor.

forget it!

And in addition to your additional information I will add that a simple "Lets save that for another thread" or even "I didnt want this thread to turn into a basics lesson" would have sufficed. I did prefix my first post with the "bail out clause.

Did you not read the VERY FIRST LINE of my first post?

Certainly did, and the fact you were trying to help people I thought I might try and understand it a bit better, hence my questions. Like I said, forget it. Next time I wont ask.

:Peace: Happy New year :beerchug:

how much of this would be the same for a 4 port?
considering that there 2 less injectors and intake ports. I would venture to say the fuel and air.

thank you for the info sharing Jeff.

BUMP

Updated first post with Excel spreadsheets for the formulas in this thread and an injector matrix. The latter is still a "beta", so it may have some flaws.

Just to second that...I'm by no means an expert, just slowly learning this math myself over the past few months...but below is what was confirmed for me by Cobb Racing:

On the dyno we see right around 200 g/sec @ Redline which works out to be 26.5 lbs/min if my math is correct.

Or in other words, MM's calcs are pretty much dead on.

Thumpitybump.

Just uploaded a greatly improved Injector Math spreadsheet that computes target values based on the OEM model, the "optimized" e-Manage model and the Interceptor-X model.

The sheet allows for different injector setups and even has the ability to compute 3-rotor setups.

This version also has 3D graphs of each resulting injector MAP.

What does cfm stand for?

turbonetic T3/T4 turbo kit
anyone heard of it? they claimed they give u 450HP with a kit.

CFM does not equal VFR!

You have turned the math upside down.
Those formulas compute the flow of the engine, not the power adder. They just point out the requirements for the power adder.

At what Pr does that fan move 130CFM? Probably 1.0 (which is Pa)! As soon as you raise the pressure ratio for the fan, its flow will drop to almost zero.
Do you have a flow map for the fan? I doubt it.

Turbonetics is a decent company, but I was unaware that they made a kit for the RX-8.
I had one of their T3/T4 hybrids on my '8 for a while and it was perfect.

Really...looked to me like their A/Rs matched with the outlets may be too small for the Renesis on the top end. I saw some of them can flow up to 60lbs/min, though, but was thinking the inlet T3 side would be too small, also.

I've been looking at the 60-1 hifi ceramic bearing, but have yet to get my requests for the compressor maps from a few vendors.

The model I have has an .82 A/R on the turbine and a .76 on the compressor.

I think most people are aiming way too high on their flow assessments. You end up with a laggy turbo that way.
This is a street-driven car. Maximum flow is mostly useless.

Was about to edit my above post, but you'd already responded...

Well, using rough calcs: @ 12psi I'm looking at flowing ~46lbs/min...but more realistically the car will be running between 7-10psi daily.

http://www.treadstoneperformance.com...im+stage+3+.63

One of the ones I was looking at, previously. Looking through the Turbonetics catalogue I didn't see your A/R options, but admittedly I hadn't yet considered it fully explored...or got down into the P trim, O trim, etc...