So I have been going through my notes lately and found some good information on Turbos, wheel efficiency,wheel matching, and other stuff like how to calculate the compressor and turbine wheel trim, how figure your pressure ratios for choosing a turbo, and how to read compressor maps. The images for this post were taken from

https://www.turbobygarrett.com/turbobygarrett/ if you would like to read more on your own.

Yes. I am bored. I don't have my heads back from Champion yet, so I can't really do anything other than keep on reading and learning, so hopefully some of this stuff helps you guys that want to get a little more "how-to" info on turbos that what we commonly see..

In order to get into some of the explanations here, I need to establish a few definitions for us. This is just some basic notes that you should be familiar with if you choose to get into the more complicated areas of determining what compressor or turbine wheels to choose.

**#1 First Law of Thermodynamics, aka the "Ideal Gas Law" **= states that the relationship between volume (v), pressure (p), and temperature (t) can be expressed as the following:

PV / T = Constant

Where ;

P = Pressure of the gas

V = Volume it occupies

T = Temperature of the gas

**Variation A) **If the Volume (v) is a constant, and increase in temperature (t) results in a proportional increase in pressure (p)

**Variation B)** If Pressure (p) is constant, an increase in temperature (t) results in a proportional increase in volume (v) .

**Variation C) **Inversely, if volume (v) is decreased, and pressure (p) remains constant, temperature (t) must decrease.

**Note: **Pressure (p) and volume (v) are directly proportional to temperature (t), and inversely proportional to each other.

With all that established, first we will look at

**Compressor Wheel Efficiency**
1) When the compressor wheel is operating at the max efficiency within its' flow range, that efficiency is expressed as a percentage of how close it comes to compressing the gas to meet the mathematical requirements of the

*Ideal Gas Law*.

2) A compressor wheel that is 100% efficient is called

**adiabatic, which means "occurring without gain or loss of heat".** If this is transpiring, you could essentially calculate the compressor's discharge air temp just by knowing the inlet temperature and discharge pressure.

3) When a compressor is said to have efficiency of 76% that means it has the capability to compress air with a 76%

**adiabatic** level of efficiency.

**1) Determining the Required Mass Air Flow and Boost Pressures to Reach a Target Horsepower:**
In order to take our best shot at this, some things will have to be estimated. We need to know the following:

*Horsepower Target =** 1,000**

*Engine Displacement **=273**

*Max RPM ** = 6750**

*Ambient Conditions

We will have to estimate the following:

*Engine Volumetric Efficiency **(80-95% for a 2-valve engine)**

*Intake Manifold Pressure

*BSFC (Brake Specific Fuel Consumption) **.85**

**2)** Now that we know what we are going to be looking for, we need to start off by calculating the airflow required to generate the horsepower we are aiming for.

The formula for this is;

Airflow = Wa = HP * A/F * BSFC/60

Where:
*Wa = Airflow (lb/min)

*HP = Horsepower Target (flywheel)

*A/F = Air/Fuel Ratio

*BSFC/60 = Brake Specific Fuel Consumption .85 / 60

**So:**

Step 1: Wa = (1,000 * 8) * (.85/60)

**Step 2: **Wa = 8,000 * 0.0141

**Step 3:** Wa = 113.33 lb/min of air

***This means that in order for my engine to make 1,000hp, it will need to flow 113.33 lb/min of air.**

**3) **Now that we know how much air we need to move through our engine, we now need to calculate the required manifold pressure needed to meet our horsepower, aka airflow target.
To do so, we use the following equation:

**MAPreq = Wa * R * (460 + Tm) / VE * N/2 * Vd**

Where:

Wa = Airflow in lb/min - 113.33 lb/hr

R = Fuel Constant 639.6 (We're gonna use gasoline for this)

Tm = Intake Manifold Temperature (degrees in Fahrenheit) 140degree

VE = Volumetric Efficiency - .85

N = Engine Speed (RPM) - 6,750

Vd = Engine Displacement in cubic inches (convert Liters to C.I. by X 61.02 ) - 273ci

So now we begin to fill in our equation:

**Step 1: **MAPreq = (113.33 * 639.6) * (460 + 140) / .85 * 6750/2 * 273

**Step 2:** MAPreq = 72,485.87 * 600 / .85 * 3,375 * 273

**Step 3:** MAPreq = 43,491,522 / 2,868.75 * 273

**Step 4:** MAPreq = 43,491,522 / 783,168.75

**Step 5:** MAPreq = **55.53psia**

The 55.53psi is absolute pressure so we need to subtract the atmospheric pressure (14.7psi) from the 55.53psi, in order to get what we call "gauge" pressure. = 55.53psi - 14.7psi = **40.8psi manifold pressure required, or 2.72 Bar. **
Now, remember that I am using a Volumetric Efficiency of only 85%, an inlet air temp of 140 degrees, and a max rpm of 6,750. If I were to increase the VE of the engine or lower the rpms it would have a significant effect on the manifold pressure required.
**4) **Now we know that we need 113.33 lb/min of airflow, and a manifold pressure of 40.8psi, so we can begin looking through compressor maps to see if we can find a wheel with those requirements.

Here is a basic compressor map:

On the left side of the map, going vertically, you can see the measurements in units of "Bar", or atmospheric pressure. 1 Bar = 14.7psi. So 2 Bar = 14.7 x 2 = 29.4psi.

On the bottom of the map you can see numbers that denote the airflow in lbs/min for that wheel.

Knowing that we need 2.72 Bar with 113.33lbs/min airflow, we will now look for a compressor wheel that can flow 113.33lb/min at 2.72 Bar and still be inside one of the "efficiency islands" on the map (these are the various circles on the map that relate to the efficiency percentage of the wheel when it is operating at that pressure and airflow.

So just to make it easy, I found this turbo with a wheel that works perfectly for our needs: https://www.turbobygarrett.com/turbobygarrett/turbochargers/gtx4508r

Hopefully this writeup has shown you a much more precise way to calculate just exactly how much airflow you will need from your turbo, and at what manifold pressure as well.

Oh, Just in case any of you are curious, here is an equation to figure an engine's potential cfm flow...

How To Calculate Your Engine's Potential CFM flow:
1) Density Ratio = For any given compressor efficiency line there will be a resulting increase in air density as a given pressure....as the compressor is operated progressively more and more towards the more efficient ranges of the wheel, the wheel does not heat up the air as much as it would at the less-efficient areas of operation, and thus the air is increasingly more dense since it is not operating at a higher temperature (due to it being at a more more efficient operating level).

2) In order to know how much turbo cfm we need, we first need to calculate the potential airflow of the engine.

If our engine displacement is rated in CC's, we take our displacement in CC's and divide it by 16.387 which gives us our cubic inch displacement. EX: A 4.5L motor is 4,500cc's. 4,500 / 16.387 = 274 cubic inches.

If we already have the cubic inches of our engine, we can move on to the cfm equation.

Equation: CFM = ( cid (cubic inch displacement) X Max RPM of engine ) / 3,456, and then multiply that number by the VE (volumetric efficiency), and that will give you the potential cfm flow of the engine.

Step 1: EX: ( 274 X 6750 ) / 3,456

Step 2: EX: (274 x 6750) = 1,849,500

Step 3: EX: 1,849,500 / 3,456 = 535cfm

Step 4: EX: 535cfm X .85% =454.75cfm is the potential CFM flow of my engine.