Note:
1 cubic inch ( cu.in. ) = 16.387064 cubic centimeters

This will be important to know in a few minutes. Ever wanted to know how much an engine can theoretically flow at 100% volumetric efficiency (VE)? Ever wanted to know how to figure it out? Here’s how!

The first thing you need to know is your engine size in cubic inches. Then you need to know what rpm you are aiming for. You also need a couple of simple math formulas. First things first. We need to know how much theoretical airflow in cfm our engine can ingest at 100% volumetric efficency at our target rpm. From there we can always adjust the VE if your engine doesn’t hit 100% VE.

How large is a rotary engine? While you may think 80 cu in or 1.3 liters, this is really only half correct. Double it. 160 cu in or 2.6 liters is what you need to go off of. We need to figure out how much cfm our engine can theoretically flow at 100% VE at our target rpm. For that we need a formula.

(Displacement in cu in) X RPM) / 3456

I’m going to use 8500 for a peak power rpm for the Renesis.

(160cu in X 8500 rpm) / 3456 = 393.52 cfm at that rpm at 100% VE

How do I convert that to pounds of air? We keep hearing that the engine makes X amount of power per pound of air consumed. More math! We must first know how much air weighs. We also need to use a standard so we’ll base this on a 60*F dry day at sea level. 14 cu ft of air is 1 lb. That means we need to take our answer from above in cfm and divide it by 14.

That gives us:

393.52 / 14 = 28.11

That’s how many pounds of air we need to ingest per minute at that rpm to get 100% VE. Let’s take our actual power output at that rpm and divide it by 28.11. Let’s just say the engine does in fact do 238 hp. It's a good place to start. 238 / 28.11 = 8.47 lbs of air per horsepower. Again that assumes 100% VE at that rpm.

Speedsource Racing has gotten somewhere between 260-265 hp on their 2 rotor RX-8 engine. Let’s change some numbers around. I’m going to just base this off of 260 hp. I also don’t know exactly where their power peak is but let’s just say it is at 8700 rpm. This is a guess. That would mean they are right at 9 hp per pound of air ingested.

We keep hearing that the Renesis is less efficient than the average piston engine. Let’s see how that applies using math. Let’s also use a non-average piston engine. We’ll compare to both models of S2000 engine. Both the older 2 liter, and the current 2.2 liter. These engines are above average. We've been hearing that the rotary made about 8 hp per pound of air and based on above, it's pretty close. According to Richard it's actually right at 8.5 hp so we've pretty much hit it dead on! We also keep hearing that the average piston engine does about 10hp per pound of air ingested. Remember for this next comparison we are testing an above average piston engine so our number better top 10 if what we hear is accurate.

The 2.0L engine was rated at I believe 237hp (close enough!) at 8300 rpm. This engine had a CC displacement of 1997cc. This is where the first formula from the top comes in.

1997cc / 16.387064 = 121.86 cu in.

The 2.2L engine was also rated at the same power level so we’ll keep that at 238hp. This engine was slightly larger and displaced 2157cc.

2157cc / 16.387064 = 131.63 cu in.

Now we can plug in some numbers.

The 2.0L (121.86 cu in) engine had peak power at 8300 rpm. Therefore:

(121.86 X 8300) / 3456 = 292.66 cfm

The 2.2L (131.63 cu in) engine had peak power at 7800 rpm. Therefore:

(131.63 X 7800) / 3456 = 297.08 cfm

Plugging each number in as per above to figure out pounds per minute of airflow we get:

20.9 for the 2.0L engine and 21.22 for the 2.2L engine.

Divide the engine hp at the peak power rpm by this number and we see how efficient the engine is in terms of hp made per pound of air.

The 2.0L engine is 237hp / 20.90 = 11.34 hp per pound of air used.
The 2.2L engine is 237hp / 21.22 = 11.17 hp per pound of air used.

It’s true. A piston engine is more efficient than the rotary. At least the ones in this comparison are. You can duplicate this for any engine as long as you know it’s size, peak hp and at what rpm it makes it. Remember your numbers are based on the assumption that the engine is at 100% VE at this point. If it isn’t and you know what it is, adjust for it. With a Canscan or a Scanalyzer, you should be able to tell what VE is on an RX-8 at any rpm or load.

Pretty neat stuff huh! Go play around with some different numbers and engines now!

 

Couple of questions:

1) why's that?

2) where is the number 3456 from? Not sure what is represents or where you got it.

 

Yeppers. However, actual VE at your RPM is closer to 70%. Actual air consumed by the Renesis at 8500 is 275 CFM (20.1 lbs at SPT).
This is not a computed value but an actual water column measument on a flow bench.
It is interesting to note that at the 5500 RPM torque peak, a stock RX-8 is pulling 260 CFM (19 lbs), which is better than 100% efficiency.

 

The displacement of a piston engine is measured over the full swept volume of all of the chambers of the engine. This happens over 720 degrees of engine rotation. A rotary displacement is figured out over only 1 full rotation of the engine. We need to double it to get the piston equivalent. Although the rotary doesn't sweep each rotor face until 3 full rotations, for comparison sake we need to figure out how much it does over the same amount of time as a piston engine. Therefore we double it from 1.3 to 2.6

1728 is how many cubic inches of air are in a cubic foot. Since our equation involves 2 complete rotarions of the engine, we need to do this number twice which means 1728 X 2 = 3456. A 2 stroke engine would keep it as 1 X 1728 = 1728. It would be very easy to just figure our engine out as a 3.9 liter engine when you consider total displacement and then just change this figure to multiply times 3 to equal 5184. I just like the other way better though.

 

This is why I made it very clear it was based on 100% VE. Easy to adjust.

 

It's a good place to start. 238 / 28.11 = 8.47 lbs of air per horsepower. Again that assumes 100% VE at that rpm.

Edit: 8.47 hp per pound of air. =d
________
Medical marijuana ""alaska"" dispensary compassion club

 

I was just giving the real-world numbers as a comparison.

BTW - you can never be perfectly clear. Someone will always take those theoretical numbers and try to apply them in a practical way in the real world and wonder what went wrong.

 

so true ...

 

a more normal way of looking at efficiency of an engine is a brake specific fuel consumption curve since air is free and gasoline isn't...

 

Now you should go into how you would predict the power curve of a boosted RE based upon a given: stock RE power curve and VE, turbo compressor efficiency map, IC efficiency, adiabatic compression laws, and total intake pressure loss.

I play with numbers at work to pass the time.

 

your reasoning is on the right track but your math is wrong.

you realise it doesn't matter one little bit if you class it as a 1.3, 2.6 or 3.9L in you calculations above? first you double it, then you divide by the same multiple (applied to the cubic inches in a cubic foot). if you did it to 3.9L and triple the cubic inches in a cf then you get the same number. cubic inches in a cubic foot can't change.

the real reason is VE is calculated on total swept volume per revolution. a 4 stroke does it's full swept vol in 2 revolutions so it is divided by 2. a rotary dose it's full swept vol in 3 revolutions, like you pointed out. hence you divide 3.9L by 3 =1.3L

 

Whew! I have a headache now. Learn something new everyday.

 

I don't give a s**t - just give me MORE POWER !