In this section, methods to calculate mass flow rate and boost pressure required to meet a horsepower target are presented. This data will then be used to choose the appropriate compressor and turbocharger. Having a horsepower target in mind is a vital part of the process. In addition to being necessary for calculating mass flow and boost pressure, a horsepower target is required for choosing the right fuel injectors, fuel pump and regulator, and other engine components.

- Horsepower Target
- Engine displacement
- Maximum RPM
- Ambient conditions (temperature and barometric pressure. Barometric pressure is usually given as inches of mercury and can be converted to psi by dividing by 2)

- Engine Volumetric Efficiency. Typical numbers for peak Volumetric Efficiency (VE) range in the 95%-99% for modern 4-valve heads, to 88% - 95% for 2-valve designs. If you have a torque curve for your engine, you can use this to estimate VE at various engine speeds. On a well-tuned engine, the VE will peak at the torque peak, and this number can be used to scale the VE at other engine speeds. A 4-valve engine will typically have higher VE over more of its rev range than a two-valve engine.
- Intake Manifold Temperature. Compressors with higher efficiency give lower manifold temperatures. Manifold temperatures of intercooled setups are typically 100 - 130 degrees F, while non-intercooled values can reach from 175-300 degrees F.
- Brake Specific Fuel Consumption (BSFC). BSFC describes the fuel flow rate required to generate each horsepower. General values of BSFC for turbocharged gasoline engines range from 0.50 to 0.60 and higher. The units of BSFC are Lower BSFC means that the engine requires less fuel to generate a given horsepower. Race fuels and aggressive tuning are required to reach the low end of the BSFC range described above.

For the equations below, we will divide BSFC by 60 to convert from hours
to minutes.

To plot the compressor operating point, first calculate airflow:

Where:

- Wa = Airflow actual(lb/min)
- HP = Horsepower Target (flywheel)
- = Air/Fuel Ratio
- = Brake Specific Fuel Consumption ( ) ÷ 60 (to convert from hours to minutes)

Example

I have an engine that I would like to use to make 400Hp, I want to choose an air/fuel ratio of 12 and use a BSFC of 0.55. Plugging these numbers into the formula from above:

_{ of air}

Thus, a compressor map that has the capability of at least 44
pounds per minute of airflow capacity is a good starting point.

Note that nowhere in this calculation did we enter any engine
displacement or RPM numbers. This means that for any engine, in order to
make 400 Hp, it needs to flow about 44 lb/min (this assumes that BSFC
remains constant across all engine types).

Naturally, a smaller displacement engine will require more boost or
higher engine speed to meet this target than a larger engine will. So
how much boost pressure would be required?

Calculate required manifold pressure required to meet the horsepower, or flow target:

Where:

- MAP
_{req}= Manifold Absolute Pressure (psia) required to meet the horsepower target - Wa = Airflow actual(lb/min)
- R = Gas Constant = 639.6
- T
_{m}= Intake Manifold Temperature (degrees F) - VE = Volumetric Efficiency
- N = Engine speed (RPM)
- Vd = engine displacement (Cubic Inches, convert from liters to CI by multiplying by 61.02, ex. 2.0 liters * 61.02 = 122 CI)

To continue the example above, let’s consider a 2.0 liter engine with the following description:

- Wa = 44 lb/min as previously calculated
- T
_{m}= 130 degrees F - VE = 92% at peak power
- N = 7200 RPM
- Vd = 2.0 liters * 61.02 = 122 CI

= 41.1 psia (remember, this is absolute pressure. Subtract atmospheric pressure to get gauge pressure (aka boost):

41.1 psia – 14.7 psia (at sea level) = 26.4 psig boost

As a comparison let’s repeat the calculation for a larger displacement 5.0L (4942 cc/302 CI) engine.

Where:

- Wa = 44 lb/min as previously calculated
- T
_{m}= 130 degrees F - VE = 85% at peak power (it is a pushrod V-8)
- N = 6000 RPM
- Vd = 4.942*61.02= 302 CI
- P
_{2c}= Compressor Discharge Pressure (psia) - MAP = Manifold Absolute Pressure (psia)
- ΔP
_{loss}= Pressure Loss Between the Compressor and the Manifold (psi) - P
_{1c}= Compressor Inlet Pressure (psia) - P
_{amb}= Ambient Air pressure (psia) - ΔP
_{loss}= Pressure Loss due to Air Filter/Piping (psi) - Wa = Airflow
_{actual}(lb/min) - MAP = Manifold Absolute Pressure (psia) =41.1 psia
- R = Gas Constant = 639.6
- T
_{m}= Intake Manifold Temperature (degrees F) =130 - VE = Volumetric Efficiency = 0.98
- N = Engine speed (RPM) = 5000rpm
- Vd = engine displacement (Cubic Inches, convert from liters to CI by multiplying by 61, ex. 2.0 liters * 61 = 122 CI)

= 21.6 psia (or 6.9 psig boost)

This example illustrates in order to reach the horsepower target
of 400 hp, a larger engine requires lower manifold pressure *but
still needs 44lb/min of airflow*. This can have a very significant
effect on choosing the correct compressor.

With Mass Flow and Manifold Pressure, we are nearly ready to plot the data on the compressor map. The next step is to determine how much pressure loss exists between the compressor and the manifold. The best way to do this is to measure the pressure drop with a data acquisition system, but many times that is not practical.

Depending upon flow rate, charge air cooler characteristics, piping size, number/quality of the bends, throttle body restriction, etc., the plumbing pressure drop can be estimated. This can be 1 psi or less for a very well designed system. On certain restrictive OEM setups, especially those that have now higher-than-stock airflow levels, the pressure drop can be 4 psi or greater.

For our examples we will assume that there is a 2 psi loss. So
to determine the Compressor Discharge Pressure (P_{2c}), 2 psi will be added to the
manifold pressure calculated above.

Where:

For the 2.0 L engine:

= 43.1 psia

For the 5.0 L engine:

= 23.6 psia

Remember our discussion on inlet depression in the Pressure Ratio discussion earlier, we said that a typical value might be 1 psi, so that is what will be used in this calculation. For this example, assume that we are at sea level, so ambient pressure is 14.7 psia.

We will need to subtract the 1 psi pressure loss from the
ambient pressure to determine the Compressor Inlet Pressure (P_{1}).

Where:

P_{1c} = 14.7 - 1

= 13.7 psia

With this, we can calculate Pressure Ratio () using the equation.

For the 2.0 L engine:

= 3.14

For the 5.0 L engine:

= 1.72

We now have enough information to plot these operating points on the compressor map. First we will try a GT2860RS. This turbo has a 60mm, 60 trim compressor wheel.

Clearly this compressor is too small, as both points are positioned far to the right and beyond the compressor’s choke line.

Another potential candidate might be the GT3076R. This turbo has a 76mm, 56 trim compressor wheel:

This is much better; at least both points are on the map! Let’s look at each point in more detail.

For the 2.0L engine this point is in a very efficient area of the map, but since it is in the center of the map, there would be a concern that at a lower engine speeds that it would be near or over the surge line. This might be ok for a high-rpm-biased powerband that might be used on a racing application, but a street application would be better served by a different compressor.

For the 5.0L engine, this looks like a very good street-biased powerband, with the lower engine speeds passing through the highest efficiency zone on the map, and plenty of margin to stay clear of surge. One area of concern would be turbo overspeed when revving the engine past peak power. A larger compressor would place the operating point nearer to the center of the map and would give some additional benefit to a high-rpm-biased powerband. We’ll look at a larger compressor for the 5.0L after we figure out a good street match for the 2.0L engine.

So now lets look at a GT3071R, which uses a 71mm, 56 trim compressor wheel.

For the 2.0L engine, this is a much more mid-range-oriented compressor. The operating point is shifted a bit towards the choke side of the map and this provides additional surge margin. The lower engine speeds will now pass through the higher efficiency zones and give excellent performance and response.

For the 5.0L engine, the compressor is clearly too small and would not be considered.

Now that we have arrived at an acceptable compressor for the 2.0L engine, lets calculate a lower rpm point to put on the map to better get a feel for what the engine operating line will look like. We can calculate this using the following formula:

We’ll choose the engine speed at which we would expect to see peak torque, based on experience or an educated guess. In this case we’ll choose 5000rpm.

Where:

= 32.5 lb/min

Plotting this on the GT3071R compressor map gives the following operating points.

This gives a good representation of the operating line at that boost level, which is well suited to this map. At engine speeds lower than 5000rpm the boost pressure will be lower, and the pressure ratio would be lower, to keep the compressor out of surge.

Back to the 5.0 L engine. Let’s look at a larger compressor’s map. This time we will try a GT3582R with an 82mm, 56 trim compressor.

Here , compared to the GT3076R, we can see that this point is not quite so deep into choke and will give better high-rpm performance than the 76mm wheel. A further increase in wheel size would give even better high-rpm performance, but at the cost of low- and mid-range response and drivability.

Hopefully this has given a basic idea of what a compressor map displays and how to choose a compressor. As you can see, a few simple estimations and calculations can provide a good basis for compressor selection. If real data is available to be substituted in place of estimation, more accurate results can be generated.