Volumetric Efficiency 101
by Brian Barnhill
The basis of any good engine map starts with an accurate Volumetric Efficiency table. This is a critical component of most OEM and Aftermarket speed-density based fuel calculations. While the concept in relatively simple, there are many misconceptions amount new tuners and mistakes made when first tackling this concept.
This can actually be a quite tricky subject, mostly due to confusion and differing opinions among many people. In the simplest form:
Volumetric efficiency (VE) is typically defined as "the actual amount of air being pumped by the engine as compared to its theoretical maximum."
Basically, VE is a measure of how "full" the cylinders are. As most of us will know from basic science, gas will expand to fill its container. Seemingly, that would suggest that the cylinder is always full. And, in the pure volumetric sense, that is correct. A 0.5 Liter cylinder will always have 0.5 liters of air in it. The measure we are looking for here is air density. A cylinder with 500 grams of air in it is said to me "more full" than one with 400 grams. In the end the “fuller” cylinder will have a greater mass of oxygen molecules present.
Why does this matter?
Despite all its many complexities, moving parts and that a great chemical and thermal event is what generates the power we’re after – the engine is essentially just a large air pump. Its job is to move air in and out of the cylinders. Everything we do is in an effort to maximize this mass of air. Volumetric efficiency is the root of this concept and measurement, and understanding how it is calculate and used is a key part of understanding your Engine Management system.
Where is this air density measured?
VE is a measure of how much air makes it into the cylinder vs how much is in available at the manifold – it does not care about ambient pressure (outside of its impact on air density, which is part of the speed density calculation.) This is a common misconception when it comes to VE and how it is used in your fueling calculations. If you use this method, you would also artificially inflate VE on forced induction cars - these engines are NOT 1000 times more efficient just because there is more air! (That said, a higher pressure differential from boost can increase efficiency - but that's another topic!)
How is it calculated?
As we discussed – an engine is essentially just a large air pump. As such it’s major behavior is governed by simple physics and fluid mechanics (that stuff you learned in basic High school physics)
If you recall the ideal gas law:
- P = Pressure (think MAP) Pressure will be absolute – so 14.6 psi = atmospheric
- V = Volume (displacement)
- T = Temperate (IAT) Temperature must be in absolute – Rankine or Kelvin
- n = molar mass/# of mols
- R = Gas Constant
N and R are constants (based on molecular mass and Avogadro’s number if you want to get nerdy about it) In this case, this can be broken down much simpler, as we can combine our constants (n and R) to a constant value and rearrange the formula to calculate Air Mass in lb/min. This equation is:
MAF (lb/min) =[ (Displacement *RPM/2)/123] * 2.7 (P/T)
Displacement = engine size in cubic inches
RPM = Engine Speed (the division by 2 is because an engine cycle takes 2 rpms)
- Division by 123 if for units, as displacement is in cubic inches
P = MAP in PSI absolute
T = IAT in temperature Rankine
So, given any parameters, we can calculate theoretical MAF! Now, we know an engine isn’t going to consume all of this, so our air mass calculation for the ECU actually is:
MAF(engine) = MAF (Calculated) * VE
When we fill in the VE table on a tuning program, we are letting the ecu know to use in this calculation for final air mass. This is why Speed-Density systems utilize an IAT and MAP sensor.
From here, calculating fuel is trivial. We know the mass of the air, we have a table with desired Air/Fuel ratio, and can therefore calculate the desired mass of fuel required based on the injector size (this is why getting your injectors characterized properly in your tune is important!) Skipping this math for now to simplify things, we can also calculate VE based on this data (or based on error in air fuel ratio)
VE Error (%) = AFR actual/AFR Commanded - 1
For example – If you are asking the engine to run at a lambda of 0.85 (or 12.5:1 gas AFR scale) and have told the engine your ve is 100%, but the engine is instead running at a lambda of 0.75 (11.03:1), we have an error of -11.2% so our correct VE would be 100 – 11.2 = 88.8%
Now - Put it to use!
The only way to know VE is to use very complex simulation programs, or to measure it empirically, i.e. to through tuning an engine - Which in the end, is simply just comparing theoretical 100% efficiency, to actual. If we have a running engine, we know this, as we know how much fuel is being injected as well. If you want to estimate VE, a good place to start would be the torque curve. Maximum VE will occur mostly around peak torque, and follow the curve closely (i.e. if the engine is make 50% of the torque at one point, you can estimate base VE to be 50% of the peak value).
Volumetric Efficiency plays a large role in how your engine operates. By understanding this parameter one can begin to grasp the details required to properly tune any engine and properly calibrate your engine management system.
Using the basics outlined here you should be able to get a rough VE table and start tuning!