Dougs951S

I have a question concerning the interplay between boost pressure/power output/displacement. We all know power is related to airflow, and that given some information about an engine's efficiency and it's target AFR, we can computer the required airflow to make a given amount of power. This relationship is given by AF (in lbs/min) = FWHP * (BSFC/60) * AFR.

What I am trying to understand further is the relationship between engine displacement, this required airflow, and the required boost pressure to achieve this flow.

MAP (boost pressure + atmospheric pressure) = (AF*R*Tm)/ (VE * (n/2) * d) where AF = airflow in lbs/min, R is the gas constant, Tm is the intake air temp in degrees farenheit, VE is the engine's VE at peak power, n is the rpm at peak power, and d is the displacement of motor in cubic inches.

This seems to imply that a given set of engine parameters, one needs a specific mathematically defined boost pressure to see a certain horsepower value.


Lets take a stock 951 engine as an example. We know the BSFC is ~.51 so it's easy to calculate required airflow for a given power goal. We know the AFR is hopefully ~11.8, and we'll assume peak power is at 6000 rpm. The VE is ~90% at that speed. R is a constant, d is the same for all stock displacement 944 engines, and Tm we could assume to be ambient, lets say it's the first pull on a still not 100% warmed up engine.


Following me still? That means that pretty much every variable in that equation is the same for all stock rotating assembly 951 engines. The only thing that differs is the airflow obtained perhaps from a bigger turbo. That equation then seems to imply there would be no benefit to a bigger turbo without running more boost, since to make more power, you need more air and more boost pressure is required to flow that air.

But that doesn't jive with what I know to be true, which is that bigger turbos flow air because they're bigger, and make more power and equal or even less boost pressure than a stock turbo. So, given those equations, how DOES one figure out how much boost is needed to achieve a certain power goal. In my eyes it can't be as simple as the above formulas. Can someone help clarify this?

Raceboy

With different turbos efficiency of the compressor also comes to play. That's why you get more (or less) power at given PR with different turbos. Also simple physics: better efficiency -> cooler charge -> more oxygen to engine -> more power.

raleighBahn

I believe Raceboy correct in that if a smaller turbo is out of its efficiency range, it is producing more heat than the larger turbo. If both are producing 11psi but the charge air is cooler with one vs the other, it should in principle be more efficient.

odonnell

Agreed. The error in the equation in post #1 is the assumption that Tm is truly atmospheric temp. To achieve that with a small compressor (with a lower efficiency in the range of interest) the intercooling needed to maintain Tm would need to be larger. But as you know there's an inherent pressure drop associated with that - due to pipe losses as well as temp drop (think Pv=zRT). Both can't be true: same temperature, and same pressure. This is why Raceboy's analysis is correct, IAT or boost pressure has to give, both cut into power.

Chris Prack

You would need to use torque IMO since HP is math and not measurable and changes wildly based on rpm.

V2Rocket

Displacement has a tendency to scale fairly linearly as long as the rest of the parts can keep up.

So if you took a 100% stock 951, removed the 2.5L lump and fitted a 3.0L lump and put all the stock parts back on "the outside" you could reasonably expect to make 20% more power/torque...if the K26 can keep up.

Easy example - Broadfoot advertises 3.0L NA engines at ~190hp with 10.something CR and a late 944 camshaft and has dynos to back it up.
A 1988 2.5 944 has 158hp...
(158/2.5)*(3.0)=190

It also has the effect of "moving down" a torque/power curve for a given cam/head setup. See the Ford Modular 2v engine...a 4.6 and 5.4L make the same peak HP (~260, the heads are very limiting and the cams very mild) but the 5.4 predictably makes more torque...4.6L ~300lbft, 5.4L 365lbft...365/300 = 1.20...5.4/4.6 = 1.17

IMO the 944 recipe is easy...if you don't want to dry sump it, you should make the most of the 1000-6000rpm range that you can, which maybe means to build the biggest engine you can afford...

Dougs951S

Going to address some of the points you guys have made.


Those formulas are just estimates based on a target flywheel horsepower used to plot points on a compressor map. Equations were taken from garrett's website.

I hear you guys about the bigger compressor running more efficiently and therefore having a lower compressor outlet temp. Lets say for the sake of a thought experiment that you have an extremely efficient intercooler, and that as long as the compressor outlet temps are below 350*, it is able to cool the temps down to 20* above ambient. Let's define Ti (inlet temp) as 100* then for all situations where To (compressor outlet temp) is below 350*.

Michael as you stated, basic thermo says that there will be a higher pressure drop the more you cool the air. So, lets say with turbo A, if To is 350* then the pressure drop in the interocooler is 4 psi. However, with bigger turbo B the drop is only 2 psi because To is say, 175*.

So, if your target pressure needed to make your target power is 16 psi measured in the manifold, then that means turbo A needs to spin faster to generate an extra 2 psi pre intercooler pressure vs turbo B.

So, that means turbo A is running less efficiently than turbo B and creating more heat....but we already said we have a great intercooler and as long as To is under 350*, than Ti will be 100*.

So, that means by the time the air gets to the intake manifold, both the temperature and pressure of the charge air is the same for turbo A as turbo B...But we all know turbo B is pushing a greater mass of air at any given pressure ratio. Since boost pressure is just a measure of restriction for the air getting into the cylinders, does that imply that for two engines operating with the same peak VE, air inlet temp, manifold pressure, ect that they are in fact ingesting the same mass of air per unit time IE making the same power?

I still don't see the inner workings, it has to be more complicated than that. In the scenario I just described, we have two identical motors that differ only by their turbos. Both are operating at the same intake air pressure and temperature. But one has a much larger turbo, so how can they make the same power?


If I drop a GT45 turbo onto my motor, it's going to make way more power (at the same boost level as say, a stock k26) when it finally spools up then is explainable by just saying that the turbo is more efficient so the charge air is cooler = more power. There is clearly more air mass being ingested by the motor, no? How does that work if boost pressure is just a measure of flow restriction? Does that mean its impossible given two identical engines to push more air without more pressure, or increasing the ability of the motor to flow? So, again assuming both motors have the same intake temp and pressure; that means they are ingesting the same amount of air even if the bigger turbo is "capable" of flowing much more?


Our 2 valve heads don't flow that well. That seems to imply; because of that flow restriction; that we will develop more boost pressure than we'd like (say, 20+ psi) at relatively low mass flows. Without making any internal changes to the motor, doesn't that mean the path to getting the best power and widest powerband cheaply is to go with the smallest, fastest spooling turbo that will still flow enough mass volume to "max out the head's ability to flow", and then slap on a really good intercooler to bring the intake temps down as low as possible?

Raceboy

Bigger turbo does not mean necessarily that it has better efficiency at low boost level, it all depends on the compressor impeller and housing. There are turbos that have higher efficiency islands at lower flow/high PR and vice versa. Usually very big turbos do not work best at very low boost levels. For example using Holset HX40 at 0.7-0.8 bars is a waste, it really shines at 1.3-1.4 and more.

V2Rocket

One thing to remember is that the head flows CFM...and a CF is a CF regardless of how dense it is.

So you want to make your CF's as dense (pressure) and cool (intercooler) as possible.

Head CFM x boost ratio does not make a higher CFM.
(200 cfm x 1.8 ratio ≠ 360 cfm)

Dougs951S

Right. So, imagine the world's most perfect 2.5 liter engine with the world's best flowing cylinder head, intake manifold, and exhaust. The whole engine flows so well, that it's hard to build pressure up in the intake because the required volumetric flow (CFM) to pressurize such a great flowing engine would be extremely high. It's hard to fill a tank that's draining water nearly as fast as you fill it.

So this theoretical motor maybe has 7 psi in the intake manifold. Air temps are the same 100* as we've been discussing because we have kickass intercoolers. The volume of the intake and the motor are the same as every other 944 engine.

Feeding this perfect motor is a huge turbo, a GT47 lets say. Next to it is another identical perfect motor, only difference is it's fed by a GT30 turbo.

Since the pressure in the intake is the same, the volume being pressurized is the same, and the temperature is the same; the density must also be the same and so these two engines must be taking in identical air masses, lbs/min.

So, the GT47 will make exactly the same power as the GT30 in this idealized setting?


Lets compare these perfect engines to a real life 951 engine. It's head and exhaust are restrictive, so the motor can take in less CFM at the same 7 psi and 100* temperature as the perfect engines. Since the CFM is lower, and we've already established that the pressure/temperature/density inside all three motors is the same; that means the factory engine flows less lb/min and makes less power...But how can that be, if the formulas say you need XX psi to make XXX horsepower?

V2Rocket

I guess the next question would be, how much power is each turbo taking to run?
They do take a LITTLE bit...but a turbo that isn't in its efficiency range will take more to spin than one that is happy...

raleighBahn

I get the thought experiment for sure - it is an exercise in building theoretical HP although it would certainly be the worst kind of dog on the street.

Your observation about personally seeing more power from a big turbo vs small at same PSI was based on the real world. And in that world, heat makes a big difference. Also - when there is too much heat, you have to richen things up to keep the engine from grenading. And that richening then throws off AFR and perhaps the BSFC.

However, I wish it were as easy as bigger turbo is better, but then you get so much boost lag you're getting eaten by Kia's from 0-60 and can only overtake them once 3 miles have passed under the car

rlm328

One of the big issues not being discussed in the compressor map and where its efficiencies are located and where your motor's variables fall on the map. The map is necessary to determine where the stall for your turbo will occur or if it does.

With the small compressor you will probably be more efficient at a lower rpms. With the bigger turbo you will not spool as quickly.

As far as VE (volumetric Efficiency) with a boosted engine this should be 1.

darek_u

Some good reading here and here

raleighBahn

I think the following thread is pertinent to what is being discussed- https://rennlist.com/forums/944-turb...y-point-3.html