By: Haitham Alhumsi
There are many factors that affect turbocharger sizing for peak performance. In this article I’ll try to cover as many of these topics as possible given all the research and findings that have gone into building our Turbo Calculator.
Some of the topics covered below are:
- Sizing your turbocharger for peak air flow
- Calculating required pressure ratio
- Turbocharger efficiency and Pressure Ratio (PR) vs. Density Ratio (DR).
- Sizing for peak flow vs Sizing for peak torque (flow vs spool)
- Factors affecting turbocharger spool times
- Intercooled vs non intercooled setups
- Intake Air Temps (IAT) vs. AIT (Auto Ignition Temps).
- Free Turbo Recommendation
Special Promo: tweet this article to download chapter one of The Tuner Mastermind (our best selling engine management tuning guide) for free!
[tweet2download file="TTM-Chapter1.pdf" tweet="Turbo Sizing Explained %%post-url%%" follow="@powercalculator" /]
Section 1: Sizing your turbocharger for peak air flow
The main equation typically used for sizing your turbocharger for your desired power level is as follows:
Peak Airflow (lbs/min) = Power Level (hp) * Air to fuel ratio (x:1) * BSFC /60
Where BSFC is brake specific fuel consumption which is a standardized measure of how much fuel is required or consumed to produce a unit of power.
If you break down this equation it basically sizes your turbocharger based on how much fuel you’re planning on using multiplied but ideal burn conditions for that fuel (how much air is required to properly consume all of that fuel)…
Multiply those two numbers together and you’ll get a good estimate of how much airflow you need , no matter what fuel is being used, so long as you know the BSFC (which is typically 0.55 for gasoline) and the target air to fuel ratio (which is typically 12:1 for gasoline as well).
The equation I use in my calculator is slightly different in that I’ve come up with an equation that:
- Calculates for Cubic Feet per Minute (CFM) of air vs lbs per minute (lbs/min) which helps in sizing other parts such as intake systems, carburetors, and cylinder head flow. This makes more sense for my application since our calculator is not just a turbo sizing calculator so it’s faster to go straight to CFM calculations to generate flow numbers that can be used in our other equations.
- I cancel out BSFC altogether and replace it with the Fuel’s Energy Density and mass density (which is well known and easy to find for any fuel) since Energy Density is a chemical property that you can find in any reference book for any desired fuel, where as BSFC is more of a laboratory derived constant that requires you to test each fuel independently to get the number to plug into the equation.
Calculating the required pressure ratio
Now that you know you’re target airflow level (in lbs/min, Kg/hr, or CFM) you’re ready to look into more details associated with answering the following questions:
- How much boost will it take to reach this power goal
- Is my compression ratio adequate for this boost level
- How much heat will I generate at this boost level
- How much charge cooling will I need to keep things safe
I don’t want to mention all the equations that are ‘typically’ used to answer these questions here because most of them are obscure engineering equations that most people end up using incorrectly, primarily because those equations force you to guess or estimate numbers that you’re not sure of to make the equations give you results. These results are typically flawed because the inputs were approximations and in the end , you get poor design results.
I also won’t give out all of my equations used in my calculator for a few reasons:
- Most of those equations are proprietary as I have derived them myself, to work with other equations in the calculator for best performance and fastest calculations
- Some of these equations are optimized for the software (a computer) to read them and are not typically pretty for human reading.
- Even if you wanted to read them and use them, they come as the 4th stage of the calculation after first calculating the engine VE, the stock air flow, and the boost subtracted power level of your engine if it is already turbocharged or supercharged
So listing them here is pointless as well…
Let’s forget about the typical ‘how to choose a turbocharger’ article that’s full of math, and focus on the main concepts that should affect your decision…
What I do want to get across though is this:
Boost pressure = (Forced Air Flow / Natural Airflow) + Effects of temperature rise
In an ideal world:
- An engine that makes about 100hp, consumes about 150 cfm of air naturally aspirated
- A 100% efficient turbocharger has no side effects due to temperature rise
- A pressure ratio of 2.0 (or 14.7 psi) is achieved when the turbo is flowing exactly double the airflow as the engine would on its own, which in this case is 300 cfm.
Pressure ratio = 300 cfm / 150 cfm + 0 = 2.0
The problem with the traditional equations for calculating the pressure ratio (and why I’m not listing them here) is that they:
- Require you to know the volumetric efficiency (VE) of your engine, or guess at it
- Ignore the effects of temperature rise due to an inefficient compressor or guess at that as well
Our calculator calculates VE for you, so I know that number is for sure correct.
Our calculator also models temperature rise due to compressor efficiency, intercooler efficiency and water injection cooling so I also know that the results you get there are realistic as well.
Either way, let’s look back at the human readable equation rewritten in two different ways:
a. Boost pressure = (Forced Air Flow / Natural Airflow) + Effects of temperature rise
b. Forced Airflow = (Boost pressure – Effects of temperature rise) * Natural Airflow
From equation a we can understand:
- Always start with the best flowing engine you can before boosting it: The more power (flow) our naturally aspirated engine produces, the less boost it will take to reach our power goal because we are dividing by a larger number; inversely, the weaker our naturally aspirated engine is (small displacement, low redline, poor head flow, small valves, bad VE), the more boost it will take to reach the same power goal. This is why the same engine can produce different power levels, with the same turbocharger, at the same boost levels, with different supporting modifications. If the modifications affect how much the engine breathes on its own, it will affect how much resistance that engine poses to the turbocharger, and ultimately affect how much boost it takes to reach a power goal.
- Very high boost pressures don’t mean very high power levels: If the effects of temperature rise due to the turbocharger compression are significant (such as having a heat soaked intercooler, a turbocharger working out of its efficiency range, or really high intake temps into the turbocharger inlet) then most of that boost pressure will come from the air heating up and expanding in the charge piping, rather than coming from forced air flow. (more in this later where we compare pressure ratios with density ratios).
From equation b we can understand the following:
The amount of power produced by an engine is directly related to the amount of air molecules available to burn the fuel (which is the left side of the equation).
If we look at the right side of the equation we can see that there are 4 ways to make more power:
- Raise boost levels – while holding the other two factors numbers constant
- Reduce the effects of temperature rise – while holding the other two factors numbers constant
- Increase the amount of naturally aspirated engine airflow – while holding the other two factors numbers constant
- A combination of the above factors
The best way I know to manually calculate your required boost level or pressure ratio is to skip flow numbers altogether and jump into hp levels immediately:
Your engine makes 100hp now, you want it to make 200hp, and you’ll probably end up with a system that is 85% efficient.
Ideal pressure ratio = target power / stock power
In our example: ideal PR = 200/100 = 2.0
A pressure ratio of 2.0 is equivalent to 1.0 bar of pressure above atmospheric pressure and with each bar of pressure equation to around 15psi of boost pressure we get a target boost pressure of 15psi.
(this is where the rule of thumb about requiring 15psi of boost pressure to double your horsepower comes from).
Actual density ratio = target power / stock power * system efficiency
Actual density ratio = 200/100 * 0.85 = 1.7
Even though we are trying to force in twice as much air into our engine by doubling it’s pressure ratio, we are actually only achieving a 70% increase in air density and will end up with 170hp @ 15psi instead of the ideal 200hp @15psi with a system that is 85% thermally efficient.
This is the basic difference between pressure ratio and density ratio… if you look at certain cooling modifications such as intercoolers, water injection and ported turbo compressor houses, the aim of these modifications is to raise the overall system efficiency such that we can raise our density ratio (while keeping our pressure ratio constant)…
If for example you go from a stock intercooler with a 50% efficiency to an aftermarket unit with 75% efficiency, then you can gain about 20% overall system efficiency (depending on how efficient other parts of the system are) which can in our example result in a gain of 20hp at the same boost pressure level.
Doing all the exact numbers here, without an intercooler, even a pressure ratio of 2.4 (22psi of boost) is not enough to reach our power target.
Now going back to our original power goal of 200hp, we need to actually shoot for a density ratio higher than the ideal calculation of 2.0 and the exact boost pressure required will depend both on our compressor efficiency and our intercooler efficiency.
Redo the calculations and you end up with 200hp (300cfm) @ 20psi as your turbocharger requirement rather than 15psi, assuming that your overall system efficiency stays at 85% (with good compressor efficiency and charge cooling) when you raise boost pressure by those extra 5psi.
This moves us nicely into the next topic I want to talk about which is compressor efficiency at different points on the compressor map.
If you look at any compressor map, you’ll see that the compressor has different efficiency islands at different flow and boost levels. The same compressor might have a 45% efficiency at 200cfm @ 15psi and 80% efficiency at 500cfm @ 24psi.
Question: Where do I want my compressor to be most efficient?
Answer: It depends on whether you are shooting for peak power or peak torque.
Let’s do a side by side calculated example to illustrate this point.
Let’s assume that:
- We have an engine that produces 100hp (150cfm) at 7000 rpms and 50hp (75cfm) at 3500 rpms.
- The engine has a camshaft that puts peak torque at 3500 rpms and that our turbo is also fully spooled by 3500 rpms so our peak torque rpm point is 3500.
- We are not using an intercooler and that the only side effects of temperature rise will come from differences in the compressor efficiency.
- That we are (as in our previous example) shooting for 20psi (or a pressure ratio of 2.35) because we aim to double our power level as discussed earlier.
|Parameter||Small Turbo||Big Turbo|
|Supported power levels||150 to 200hp||175 to 225hp|
|Efficiency @ 3500 rpm||75%||50%|
|Efficiency @ 7000 rpm||50%||75%|
|Density Ratio @ 3500 rpm||1.765||1.175|
|Density Ratio @ 7000 rpm||1.175||1.765|
|Peak Torque||132 ft-lbs||88 ft-lbs|
|Peak Power||118 hp||177 hp|
The small turbo in this (fictitious) example is designed for cars from 150 to 200hp. It hits its sweet spot at around the 150hp level and has peak efficiency of 75% in that flow level. Once you get closer to 200hp, the compressor is almost maxed out and its efficiency drops to 50% (which happens often on many stock sized turbochargers).
The large turbo in this example is designed for 175 to 225hp, and hits its sweet spot right as our engine approaches its 7000 rpm redline. Once you move much higher or much lower than this sweet spot you find that efficiency drops rapidly, but since we’re only going to 200hp we only see this adverse effect on our torque (one the lower end of the map)
Intercooled illustration of a large turbo with peak efficiency near redline vs a small turbo with peak efficiency at peak torque using the REAL equations. The high efficiency intercooler does reduce the difference between these two setups; setups with no or poor intercoolers or soaked intercoolers will have more dramatic variations between the two setups.
As you can see in (exaggerated for the purpose of illustration) how two different turbochargers operating at the same boost level produce drastically different cars with one car boasting 20% more torque than the other, with other producing a very mild torque increase over stock but with 20% more power than the smaller turbo and 50% more power than stock.
Our power calculator knows the effective rpm of our recommended camshafts (which is one of the two primary factors contributing to the torque peak) and in an upcoming version of the calculator we will plot both peak torque and peak power on our compressor maps such that you can compare turbo efficiencies at those two flow levels and choose the turbocharger that best suits your buildup (street car vs autox vs drag car vs time attack vs top speeder…etc)
In general though: Choosing a turbo with a higher peak efficiency will result in more peak power while choosing a turbo with wider efficiency islands (holding similar efficiency over a wider range of flow levels) will produce a more well rounded and versatile car.
Factors affecting spool time
For a turbocharger to spool it has to accelerate from idle to an rpm in the 50,000 rpm range. Typically turbochargers can peak at around 125,000 rpms, but for spool purposes the turbo has to accelerate to a point where it can outflow the motor’s naturally aspirated flow level and start to compress additional air into the cylinders.
Since we’re talking about acceleration here, all the factors that affect the turbocharger’s acceleration will affect your spool:
1- The weight of the center cartridge (including the compressor wheel, center shaft, and turbine wheel) – This is why lighter ceramic compressor wheels spool faster
2- The friction in the rotating bearings (this is why ball bearing turbos spool faster)
3- The amount of force acting on the turbine wheel to bring it up to speed:
- This is why lower Aspect Ratio (A/R) turbos spool faster (due to focusing the exhaust air into a tighter nozzle like thrust effect on the edge of the turbine wheel).
- Why massive diameter exhausts help spool on turbo cars because they maximize the pressure differential between the pre-turbine and post-turbine zones (thus maximizing the applied force on the turbine as a result of those pressure differences and the exhaust gas velocity)
- Short and insulated exhaust manifold runners that retain more of the exhaust gas energy to deliver it to the turbine (rather than radiating that energy as heat into the engine compartment).
- The exact amount of timing advance and how that affects peak cylinder pressure and peak exhaust gas energies
All of these factors combined lead to the typical small turbo vs large turbo dilemma.
- Smaller, lighter turbochargers that are ‘undersized’ compared to the engine size will accelerate to spool fairly quickly. The downside here is that the smaller compressor will have a lower peak flow and lower efficiencies at high flow levels and the turbine wheel itself will further worsen this by choking the engine’s flow capacity on the exhaust side.
- Larger, heavier, and more ‘oversized’ turbochargers compared to the engine size will take longer to accelerate and spool. But, these larger turbos will have better intake and exhaust flow at higher demand points.
So typically there is a trade off of spool for peak flow unless you use some interesting tricks:
- For smaller displacement engines shooting for very high specific output (such as a 2.0 litre being built up for 800hp) it is common to use a hybrid turbocharger such as a T3/T4 or a GT25/37 with a smaller turbine wheel combined with a larger compressor wheel.
- The spool time can further be enhanced by using a small aspect ratio on the smaller turbine wheel which ultimately will limit exhaust side flow, but counteract this problem with using an oversized wastegate. When the wastegate is shut all the energy goes through the small turbine with a low aspect ratio trying to maximize spool. When the wastegate opens the flow is diverted away from the turbine wheel and it is no longer such a flow restriction.
- In applications where oversized wastegates or standalone wastegates are not possible (due to size and packaging limitations) then adjustable ‘vanes’ in the turbine can be used to direct exhaust gasses to focus them on the outer tips of the turbine wheel to simulate the effects of a lower aspect ratio (A/R) … once the turbo is spooled, the vanes move outwards allowing the gasses to evenly distribute among the entire area of the turbine wheel maximizing flow through the exhaust side of the turbo cartridge …
- Innovative compressor and turbine wheel designs with complex shaped blades that are aerodynamically designed for a best balance of flow and block off pressure, combined with 5-axis CNC machining to realize these complex curved blades into reality allow for a new class of high efficiency , high flow, lightweight, exotic material’d fast spooling turbochargers that seem to break the conventional rules of small turbo vs large turbo vs small twins.
Choosing the right wastegate size and aspect ratio
With variable area turbine nozzle (VATN) turbochargers being more expensive and rare than conventional turbochargers, most enthusiasts are limited to using conventional methods for maximizing the balance between flow and spool.
- Choosing the right aspect ratio A/R
It’s very hard to give a mathematical approach to calculating the right aspect ratio to maximize engine performance.
In general, if your turbo is properly matched to your engine then an aspect ratio of around 0.60 (or 60% inlet area to turbine radius ratio) is going to be a good balance between flow and spool.
If you know that you’ve fitted an oversized turbo (that your setup will eventually ‘grow into’ with more upgrades then you’ll want to step down to an A/R that is less than 0.6 to help spool (and possibly upsize your wastegate port for peak flow).
If you’re boosting significantly higher than the 2.0 pressure ratio, or working with a high flow engine that shifts most of its power-band towards redline such as motorcycle engines then opt for an aspect ratio higher than 0.6 to allow higher flow through the turbine for best high rpm power
The problem with all of these rules of thumb is that they get thrown out of the window when your turbo is poorly matched for your engine demand.
- Choosing the right wastegate size
Wastegate size is directly related to how many CFM you need the wastegate to flow. This is inversely related to turbosize which is counter intuitive:
If you have an 800hp turbo fitted to a 400hp engine, then your wastegate needs to dissipate about 40% of the exhaust gas energy and keep it away from the turbine wheel. That is to say, if the turbo were allowed to run at 100% of its capacity it will deliver 800hp to the motor instead of the desired 400. To prevent the turbo from spooling up that high you have to dump 50% of the exhaust gas away from the turbine. In this situation you can imagine that having a 3″ exhaust and a 0.5″ (14mm) wastegate is not going to work… with only 0.5″ of wastegate flow, most of the exhaust air will be forced through the turbine, and the boost will spike and you will not be able to properly regulate boost at your target boost level.
If on the other hand you have a 400hp turbo, fitted to an 800hp engine… then you have no need what so ever for a wastegate. Since you never reach your target boost setting or power level, even if you dump ALL your exhaust energy into the turbine, you still will not reach your target 800hp level, you will not build enough boost, and the wastegate will never open.
So let’s summarize again: Wastegate size is directly related to how mismatched your turbo is for your target power level. Undersized wastegates will have spike and creep issues and have problems regulating boost. Oversized wastegates will regulate boost pressure properly but once you reach that point of control, going even larger will have no impact on performance.
Your goal here is to get a waste-gate that is large enough to regulate boost without undersizing.
Just as with aspect ratio sizing, our calculator recommends turbochargers that are properly sized for you target power goals, and doing so we are able to recommend reasonably accruate A/R and wastegate options.
If you choose to go off on a tangent by choosing a smaller turbo to fatten up your midrange power (while sacrificing top end) or a monster turbo (with room to grow) then you should adjust your A/R (up for smaller and down for larger) and your waste-gate (down for smaller, and up for larger) accordingly…
By now in the design and selection process we have:
- Figured out our target power level
- Found an approximate Pressure Ratio required to reach that power level
- Looked into approximately how much our density ratio lags our pressure ratio
- Figured out a higher pressure ratio required to reach our power goals.
- Chosen a turbo that is properly sized for our targets with the highest average compressor efficiency over the power band that we want to use it in
- And chosen the correct aspect ratio and wastegate size accordingly to maximize our spool and peak flow to maximize the usage of this turbo.
Now that we’ve done all that and chosen our turbo, let’s move on to two things:
- Maximizing the power delivery of our setup through the use of proper intercooling
- Maximizing the reliability of our setup by understanding how close we are to preignition and what is required to keep us safe at this pressure ratio of 2.4 (around 22psi) on gasoline.
This is probably a good time to talk about the range of these figures….turbo efficiencies typically vary between 45% and 76% depending on where you are in the compressor map. Intercooler efficiencies vary but peak at around 75% or as a rule of thumb within 15 degrees of ambient intake air temps.
So our illustration above presents the upper limit (green) and lower limit (yellow) of what kind of power boost you can expect out of your car at a certain boost level. I was using 100hp as my example because it’s a good unit where you can multiply the numbers you read off this chart, by your stock horsepower, divide by 100 and you’ll get an easy estimate of what your car will do with your setup.
- Starting with a 400hp mustang
- Adding a typical 75% efficient Vortech bolt on supercharger kit geared for 8psi
- Ignoring supercharger belt drag
- and using the basic kit without an intercooler
Our expected power at 8psi (or a pressure ratio of (1+8psi/14.7psi)= 1.54) we can expect:
- 400 * 130 / 100 = 520 horsepower un-intercooled
- 400 * 150 / 100 = 680 horsepower with an intercooler upgrade
With intercooler prices ranging from $100 to $400 and kits ranging from $300 to $1000, intercooler upgrades can deliver a huge amount of horsepower per dollar (assuming you have enough fuel on hand in your supply system to match the increased air density resultant from the cooler air).
Intercoolers are not only a power adder as we’ve seen in the previous section, they are also a great peace of mind. They cool the intake air temps down, they reduce the amount of boost required for us to reach a power goal, the can help us reduce the overall boost level of our system which reduces stress on intake parts, gaskets and seals, and they reduce the overal intake temps which can extend the life of intake sensors, under hood wiring …etc
Besides all of those benefits, intercoolers help directly at fighting off preignition which is the #1 cause of catastrophic engine failure in forced induction engines at high boost levels:
|Why do we hate pre-igntion?
Here is a piston showing classic signs of pre-ignition. Pre-ignition occurs when the optimum ignition conditions occur prior to the spark event (the spark plug firing) and the combustion process occurs as a result of these conditions without any input or control from the ignition timing circuit.
Unlike excessive timing advance, pre-ignition is more catastrophic because it usually initiates the combustion process much earlier in the engine rotation (possibly even 100* prior to the spark event). The result of this very early combustion is that the piston is abused with a long duration of exposure to heat and high pressure from battling the downward moving flame front on its upwards journey during the compression stroke.
As a result of this superheating of the piston (and as you can see in the image to the right), the hottest part on the crown of the piston begins to deform, melt and then blows through leaving a hole in the crown (with the rest of the crown looking like it had been at one point melted or welded and then refrozen).
At the same time, due to the heating, the piston expands in the bore until contacts the inner cylinder walls. This is clear by the scuff and scrape marks on the side of the skirt where the pisons and cylinder walls made contact. In some cases the engine will also seize due to this contact.
Gasoline has an high auto-ignition probability when the compressed air and fuel mixture in the cylinder exceeds 240*C. Below is a comparison of different compressor and intercooler combinations running at the same pressure ratio of 2.4 (which in our 100hp engine example theoretically produces 240 crank horsepower).
|(Degrees Celcius)||Intercooler Efficiency|
A little bit of practical advice at the end of all of this theory. With performance parts, you usually get what you pay for. Go cheap on your turbo, get one with poor flow properties or poor efficiency and you’ll be leaving power on the table. Go cheap on your intercooler, get a poorly designed or undersized core, and you’ll have a higher than needed pressure drop and a poor density ratio.
The image below is to illustrate 3 different setups:
- A great turbo with an average intercooler (yellow) vs.
- A great intercooler fitted to an average turbo (red) vs.
- A great turbo coupled with a great intercooler (green)
As you can see… you are only as strong as your weakest link. Invest in an awesome turbo, and couple it with a budget intercooler and you have completely undermined your turbocharger. Invest in the best intercooler system possible on top of some undersized stock turbochargers and you yes you will make more power, but the best intercooler in the world can only do so much when it’s faced with with really hot air coming from a stressed turbocharger struggling to compress and creating gobs of heat, and as you can see on the graph, turbo efficiency (yellow) trumps intercooler efficiency (red) with the good turbo + bad intercooler combo outdoing the bad turbo + good intercooler combination.
Match a high efficiency turbo with a high efficiency intercooler, and watch your car walk way from everyone that has cut a corner on either their turbo or their intercooler …. a mistake that they may have under estimated the effects of, and one that they will only realize when they see your tail lights in the horizon.
Thank you for reading this far into this article.
Even though this is a long article describing a very long and complex calculation process, our power calculator can do all of this complicated work for you, in under 5 minutes.
Here is our process:
Load your platform from our saved platform database or input the specifications of your current engine. Choose ‘Turbocharged’ as your power adder of choice and click next to go to the advanced inputs screen.
On the advanced inputs screen, choose your desired setup be it single or twin turbo and click next to advance to the octane center
On the octane center, input your target fuel for this platform, or leave it blank (to default to gasoline) and click next to advance. Notice that each fuel, and your resultant mixture has a different auto-ignition-probability threshold temperature with Gasoline at 280*C
Now you see our results page… notice:
- We calculate a ‘boost subtracted’ volumetric efficiency for your engine so you don’t need to guess at that.
- We calculate the ideal pressure ratio for your power goal (we don’t know yet which turbo you’re going to use so we can’t calculate the density ratio or the exact pressure ratio yet).
- We also calculate the target Aspect Ratio (A/R) for your turbine housing and your wastegate size assuming you stick to one of our recommended turbochargers.
Clicking next once again now takes you to the chargers screen. Here are the 10 most relevant turbochargers for your target power level (for this boost and flow level, for this fuel). By clicking on the + sign at the end of the row, you can also see the compressor map for this charger (we don’t yet plot demand lines on the maps… but that is planned for a future update of the software).
Click next once again and you’ll be taken to our preignition and density ratio model. On this screen you can set your exact intercooler and turbocharger efficiencies, your exact final pressure ratio, and your static compression ratio and click the calculate button. The simulation calculates:
- Your actual density ratio and your actual power level at this pressure and density ratio
- Your final in cylinder compressed air temperature and compares it to your fuels auto-ignition threshold temperature
- Your probability of running into pre-ignition
- And through a process of iteration, the exact final pressure ratio you need to run to have a high enough density ratio to reach your original desired power goal.
Special Promo: tweet this article to download chapter one of The Tuner Mastermind (our best selling engine management tuning guide) for free!
[tweet2download file="TTM-Chapter1.pdf" tweet="Turbo Sizing Explained %%post-url%%" follow="@powercalculator" /]