Am I Crazy: New but Quick Turbo/Supercharger Math?

[Kevin Shasteen]

For beginners, I dont hang out in other BBs so I dont know if what I am about to say is new or old hat.

 

BUTT, of all the magazine articles, and how to books I've read on turbo / supercharger engines I've not read anyone explain how they've come up w/the engine performance relative to the turbo/supercharger parameters utilized.

 

What I always try to do when I get a hold of a well written engine performance article is try to extrapolate their data to an equation or process of some kind; whereas if I had not had access to the engine dyno at the end of that article - I could still predict w/in close tolerance what said engine output would be.

 

Last night I think I had an interesting break thru regarding the turbo/supercharger engine potential that anyone can use to determine engine potential. This process isnt going to aid in turbo trim or supercharger selection as it only deals w/engine potential based on displacement, cylinder head CFM flow and Cam profile.

 

The process doesnt address peak engine rpm; but only addresses peak power potential. I would like someone to either tell me I'm on to something, its already been done, or whatever.

 

After I stumbled on to this process I went through all my magazine and how to book articles where turbo/supercharger write ups were done anywhere from 500hp engines up to 1200 hp engines and the process was w/in 10 hp each time; so here is the process - tell me what you think.

 

The first thing I always do whenever I'm looking at a new performance article is to work the HP to Cylinder Head formula which is:

 

CFM Cylinder Head Flow at Peak Valve Lift x # of Cyl's in Block x .257 = HP

 

As you know this formula only addresses a Normally Aspirated engine and doesnt take into fact the affect a positively charged intake would have on engine output. So, other than going by Corky Bell who says in his books that engine output w/a turbo or supercharger will amplify performance anywhere from .052 to .077; how would you know what affect your Boost PSI will have?

 

1) Take the Boost PSI you plan on using and multiply it by 14.7; the 14.7 will represent the atmospheric pressure in your area - so use whatever pressure your environment represents, but you have to use the atmospheric value not the Barametric value most turbo/supercharger calculators use. Anyway, if you are going to use 6 Boost PSI then multiply the 6 x 14.7. If you are going to use 10 psi then multiply the 10 x 14.7. Whatever Boost PSI you are going to utilise; it needs to be multiplied by 14.7

 

2) Now take the CFM your Cylinder Head flows at Peak Valve Lift -.100"; why .100" less than peak lift. Because the valve doesnt stay at peak lift long enough to really use that value. I've noticed that the HP/CFM formula works w/turbo and superchaged engines if you use .80 of full valve lift and .70 of full valve lift on normally aspirated engines. So, .80 of full valve lift works out to be .100" valve lift while .70 of full vavle lift usually works out to be about .150" less that full valve lift.

 

Anyway, HP/CFM value with the 14.7 x Boost PSI together and that will be your engine's peak HP potential w/in 10 hp. You can also work this process backwards. Say you wanted an engine w [x] hp and were going to use [x] Boost PSI. Simply deduct your desired peak hp from the Boost PSI x 14.7. Take this value and divide by the .257 x #of Cyl's in the HP/CFM formula which will give you the amount of CFM your cylinder head must flow at .100" valve lift less that peak valve lift.

 

Is this making sense? Or, has someone been pumping funny gas in my house?

 

Take a 350 V8 as an example, say it uses a .500 lift cam where at .400" valve lift the cylinder head flows 200 cfm, the HP formula would then look like:

 

200 x .257 x 8 = 411 hp

 

Now, if we were desired a 575 hp engine we could deduct the 411 hp from the 575 hp, like so:

 

575 - 411 = 164

 

Then take this number and divide it by 14.7 to get the required Boost PSI, like so:

 

164 / 14.7 = 11.15 Boost PSI

 

Is this process already known w/in the turbo/supercharger crowd or am I on to something.

 

Let us take this same 350 V8 and let us say we wanted 650hp from it and were going to ust AFR heads and a cam whose profile had a peak valve lift of .600" lift; and the .500" lift flow value was at 250 cfm.

 

250 x .257 x 8 = 514 hp normally aspirated

 

650 - 514 = 136

 

136 / 14.7 = 9.2 Boost PSI required

 

I would also assume this value is after the usual 2 psi lost due to port inefficiencies leading up to the throttle.

 

Again this doesnt address turbo trim, maps, temp rise, density ratio's ect. required for turbo selection or supercharger selection, as it only addresses engine potential based on what the cylinder head flows relative to cam profile: and assumes an 8.5:1 SCR.

 

Ya'll tell me what you think!

 

Kevin,

(Yea,Still an Inliner)

[MJLamberson]

dude you have way to much time on your hands, Ive always thought that you take the stock HP, then multiply that by what ever percent of atmospheric pressure your turbo is pumping out, 7psi aprox. 50%, 50% horsepower increase... or somthing

[X64v]

I don't see how any of that math is based in reality whatsoever, especially where you account for boost. According to your math, a certain boost level will add a certain amount of horsepower on any engine, always, which is obviously incorrect.

 

Let's just say, for the sake of argument, that your N/A HP calculations are correct (I have no clue if they are or not, but it doesn't matter, they don't factor into your boost calculations at all). So your engine is making 400 hp and you want 500 hp. You say to take the difference (in this case, 100 hp), and then come up with a boost number to make that horsepower. Let's take another example as a test. Say I'm making 5 horsepower on my engine. If I want 155 horsepower, according to your calculator I need 10.2 pounds of boost...

 

The problem is in multiplying atmospheric pressure by boost pressure and coming up with horsepower. Where did you come up with that one?

[Pop N Wood]

To first order it makes sense. If you double the boost, you double the amount of air/fuel charge being pumped into the cylinders.

 

I think the motor head term for what you are trying to measure is volumetric efficiency. You might do some reading on that.

 

But if you look at the ideal gas law equation temperature is as important as boost when it comes to determining how many molecules of air are being pumped into the engine. Then the unavoidable efficiencies that subtract from the ideal totals.

[Kevin Shasteen]

I'm well read on the Mechanical, Volumetric, and Thermal efficiencies of an engine. I wouldn't claim to be an expert but I would say I could listen and talk w/the experts and digest as well as add my .02c's worth.

 

Let me add this; I didnt mean to imply that the math is correct in that it is literally representing functions w/in an engine at any time. Nor did I intend for this idea to be an absolute.

 

What I meant to say is that I extrapolated a process, that worked on the few articles I have on hand, w/in the component parameters used in those articles. If this process plays out then it is more of an absolute than merely going by the .50% times boost psi process you hear everyone spouting.

 

I would like all those who eat, sleep, drink, walk, and talk turbo/superchargers to cut this idea to shreads or to prove it out.

 

I've only got 5 well written turbo/supercharger articles to view and that is why I'm running this by ya'll. Three of the articles were turbos and the other two were superchargers. If I remember correctly only two of the articles used intercoolers. The other articles ran the engine on an engine dyno.

 

I'ld like all who are interested to check their articles and crunch the numbers or check your own engines, their parameters, providing you also have a dyno to prove the numbers.

 

Assuming, yes I said assuming, that we all do the turbo trim calculations correctly, and we sized the supercharger selection correctly, then as far as my numbers for these articles have shown, will allow close proximation within 10 hp, of what that engine could produce.

 

I guess what I will do is go grab those articles and give ya'll the data on this thread so you too can see how the "extrapolated" equation does seem to play out.

 

Kevin,

(Yea,Still an Inliner)

[hughdogz]

 

1) Take the Boost PSI you plan on using and multiply it by 14.7; the 14.7 will represent the atmospheric pressure in your area - so use whatever pressure your environment represents, but you have to use the atmospheric value not the Barametric value most turbo/supercharger calculators use. Anyway, if you are going to use 6 Boost PSI then multiply the 6 x 14.7. If you are going to use 10 psi then multiply the 10 x 14.7. Whatever Boost PSI you are going to utilise; it needs to be multiplied by 14.7

 

This is where stopped reading last night. I don't understand the reasoning here. Are you confusing psi with bar? 1 bar = 1 atm =14.7 psi.

 

So if you run 6 psi of boost, you are increasing pressure (6+14.7)/14.7 = 1.41 times more than atmospheric. I think this is termed the "pressure ratio" in Corky's book.

[X64v]

To first order it makes sense. If you double the boost, you double the amount of air/fuel charge being pumped into the cylinders.

 

Yes, I agree that the ratio is right, but the number that is coming out of that still is not. Atmospheric pressure times boost pressure does not equal a set horsepower addition.

 

 

Kevin - I apologize for making my initial response so harsh. I don't mean to be at all, mathematics is a fun thing to play around with and I like testing out theories as well. Just simply saying that this will not work for all cases, it only seems to work in the narrow horsepower band (400-650) that you tested it out in.

 

An example of how numbers can seem to work out, but not actually mean anything at all: Take your waste size in inches and multiply by your height in feet. For me, that makes 168. Could that be my weight in pounds? Sure, and it might work for a few cases, but by no means does one calculate weight that way.

[MrFancypants]

This is where stopped reading last night. I don't understand the reasoning here. Are you confusing psi with bar? 1 bar = 1 atm =14.7 psi.

 

Actually 1 bar and 1 atm are not the same.

 

1 bar = 14.5 psi

1 atm = 14.7 psi

 

Pretty close, but the difference adds up at high pressures.

 

Kevin, Im wondering what the point of this is. Are you trying to come up with a universal formula to estimate HP or are you just looking for some kind of "bullsh!t check"? I typically just compare NA crank HP to claimed boosted HP and use the ratio described earlier. That gets you somewhat close but there are just too many variables to really estimate this accurately. Even a dyno isnt really "accurate" per se.

 

 

 

- Greg -

[Kevin Shasteen]

x64v, you dont have to apologize - that is the scruitinay I am looking for.

 

I know this is nothing more than an anomaly; it is definately an interesting one - but nothing more than an anomaly yet it is one I would like to see played out or put to rest.

 

After looking at the few articles I have on hand, I would agree they are in the 450 to 650hp range; with the exception of one. The one exception was a 1030hp superchaged engine planned for the salt flats at 22psi boost with a 150 shot of nitrous.

 

When I have a little more time I will get all those numbers and put them up here for everyone's scruitiny.

 

It appears to me, the real variable is VE%. One article I have where David Vizard built an 8-71 Blown BBC 509 ran at 1.09 VE; and that caused this quirky anomaly of mine to be 4psi off. The article did admit they used a combination of high octane fuel w/pump gas.., dont know what effect that had.

 

With that in mind, the other 4 or 5 articles I have fall right in line.

 

Here is one example built by Corky Bell himself when he was promoting his TT SBF Cobra Kit. The article was written in the April 2006 Hot Rod magazine.

 

The engine was a 385 using Canfield Heads. The article didnt say which cc head they used but I would venture a guess that it was their 192's. SCR was 8.5:1 and the tt set up only utilized 7.5 boost. Unfortunately, the article did not give the actual cam specs.

 

Corky was quoted at stating the RWHP was 505.

 

With those figures in mind we can take the RWHP and assume, yes I said assume again, a 15% hp loss between Flywheel and the rear wheels which would put the assumed FWHP at 594. That's 1.54 hp per cu.in.

 

Following this anomaly's process presented in this thread we can then deduct the boost psi x 14.7 from the total HP,

 

594 - (14.7 x 7.5) = [x]

594 - 110.25 = [x]

483.75

 

Now take this 483.75 hp anomaly value...for the lack of a better word, and put it in the hp equation to obtain the required cfm that must flow through the cylinder heads.

 

.257 x 8 x [x] = 483.75

 

Since our engine is a V8 we can simply divide the .257 x 8, which is 2.056 into the 483.75 for our cfm requirement.

 

483.75 / 2.056 = 235 cfm

 

Interesting isnt it? The 192 Canfield heads flow 242 at .400" lift. Because this engine is only utilizing 7.5 boost; it is a pretty good assumption, again I am assuming, that the cam is also a mild cam probably in the .500" to 550" lift range with a 114 to 116 LSA and probably using a 260 to 270 duration.

 

Oh, and this is one of the articles where an intercooler was used.

 

I'll offer the other examples when I get a little more time.

 

Kevin,

(Yea,Still an Inliner)

[Kevin Shasteen]

Greg,

 

Yes, to answer your question about it being a check point.

 

This anomaly amounts to nothing more than a shoot from the hip check point.

 

It is the same as using the hp formula: Valve Lift CFM x .257 x #cyl's = HP by itself and not taking into consideration SCR, DCR, Cam Profile, or Peak RPMs, and peak hp intensity. If you dont include all the variables available to us, a not yet built engine could care less about the hp formula...yet we all still use the formula anyway. So, using the hp formula w/out actually having an engine on hand does not mean we cant build that engine - it just a tool to help in choosing a cylinder head. When comparing this hp formula to the other needs in an engine we can then gain value from the hp formula.

 

As I said in the post after you posted; it is nothing more than an anomaly. It is an iteresting anomaly - but does not represent the other real world variables that goes into a performance engine.

 

Therefore, in order to acurately ustilise this anomaly, you really need to understand the remaining engine variables that make up performance.

 

Besides that point, I would still like to obtain more supercharger/turbocharger articles that include all variables including a dyno to further prove or disprove this anomaly.

 

Kevin,

(Yea,Still an Inliner)

[Kevin Shasteen]

So if you run 6 psi of boost, you are increasing pressure (6+14.7)/14.7 = 1.41 times more than atmospheric. I think this is termed the "pressure ratio" in Corky's book.

 

I believe you are correct regarding what you have listed is the Pressure Ratio. That value is then used to calculate temperature rise prior to the intercooler having its affect.

 

I'm not putting forth this anomaly to aid turbo trim or intercooler affect.., I'm not sure what its function could be other than it is there for us to build up or shoot down.

 

Kevin,

(Yea,Still an Inliner)

[MJLamberson]

I figured it out, a perfect way to figure out HP... a dyno

[Top Secret]

I figured it out, a perfect way to figure out HP... a dyno

 

lol

 

 

 

 

 

I stopped reading when I read that you were multiplying things by atmospheric pressure to figure out boost. A turbo putting out 1 lb of boost is effectively upping atmospheric pressure by 1 lb, not going "2 x 14.7" more like "1 + 14.7"

[Kevin Shasteen]

Forgive me for implying the 14.7 represents atmospheric pressure; maybe it does or maybe it doesnt.

 

I am not saying that any of this makes sense. I am saying if you do the math you will see that the anomaly is there: what it means, I dont know as I came upon it by accident.

 

I dont know if the 14.7 actually represents atmospheric pressure; I do know this constant multiplied by the amount of boost plus the amount of hp created by whatever the cylinder head valve lift cfm; equals the peak hp of that engine.

 

Another example is from "Power & Performance" magazine's winter 2005 issue. It swapped cams in a Ford 4.6 DOHC engine and then installed a Kenne Bell supercharger running at 15psi. The engine produced 670hp at 6500rpms. The cams were 262 Duration, w/.425" lift and 112 LSA. That amounts to 38 degrees overlap.

 

Putting these numbers thru this anomaly process we get:

 

670 - (15 x 14.7) = Normally Aspirated HP

670 - 220.5 = NA HP

449.5 = NA HP

 

Take the NA HP and put it in the hp formula to obtain the required cfm flow at valve lift and you get:

 

cfm x 2.056 = 449.5

cfm = 218.63

 

My problem on this one is I can only find a cfm flow chart for a Stage III 4.6 DOHC engine. I dont know what these heads flow from in stock form. The Stage III head flowed 300cfm at .400" lift and 255 at .300 lift. I dont think a 35 cfm increase from a stock head to a Stage III head is out of the question. So once again this anomaly plays out.

 

Kevin,

(Yea,Still an Inliner)

[getZ]

The math is all fine and great but they are only to get you to a reasonable starting point. There are way to many variables and unforeseen items to get perfect calculations for everything, weight of vehicle, gearing, type of driving, homogeneous chamber burn/swirl, adiabatic efficiency, and the list goes on and on.

 

You can nail everything on a dyno and still not be happy how the car, boat or whatever performs because the load on the engine has now changed. That's where experience of the tuner/crew chief comes into play and why winning race teams have good crew chief along with solid engineering.

[Z-8]

I like the idea of the possibility of a new math equation. I say keep trying it out until it is proven true or false. All the different variables that could effect it, also effect every other equation used to guess HP, or whatever, even a dyno. I understand that one would use this for an engine that's not built, or is in the process of building(i.e. trying to pick the right parts). So if one cylinder has 14.7 pounds of A.P. in it, then a turbo with 1 psi of boost would then douple the A.P. in the cylinder? The question seems to be, is that a reliable way to estimate HP gain, A.P.(14.7) x psi? That might be common knowledge that I don't know(very possible:redface:), or is this the "anamoly" that your trying to see if it plays out? If you want, I have a couple engine building mags, I can flip through them and see if they have any builds with the numbers you need for this. Just let me know if your down for that.

[SHO-Z]

I am lazy http://www.superchargeronline.com/hp_calculator.asp

[Kevin Shasteen]

I have a couple engine building mags, I can flip through them and see if they have any builds with the numbers you need for this. Just let me know if your down for that.

 

Thank you Z8, that is exactly what I am looking for.

 

What we need from your articles are:

 

1) Engine Displacement (Bore x Stroke if offered)

2) Cylinder Heads (and their Intake Port cc's if offered)

3) Cam Profile (Lift, LSA, and Advertised Duration and the @ .050" if given

4) Also, I would like to know on the cam profile if it was a flat/roller, hydrualic/mechanical camshaft

5) The peak psi the Supercharged or Turbocharged engine created at peak hp rpm. Also, please note if the peak psi was pipe psi or carb/throttle body enclosure psi.

6) If the article gives a CFM flow chart of the cylinder heads being used, we will need that data as well

 

Here is another example from this month's "Engine Masters" winter 2007 issue. The add on the front of the mag says 720hp but their dyno indicates 712hp. It is a modern 712hp 5.7 Hemi using a Paxton centrifugal supercharger at 10.4 psi at peak hp at 7000 rpms. The cam was a Comp Cam XFI 273 hyd.roller with 224/228 duration at .050" lift using a .547/.550" lift.

 

This engine utilized new performance cylinder heads from Chrysler's own Mopar Performance Parts dept. They gave a CFM flow chart for these heads after the porting was completed. The chart is as follows:

 

Lift"......Intake...Exhaust*

.100.......64.........47

.200......134.......109

.300......210.......152

.400......266.......187

.500......300.......215

.600......320.......227

.700......321.......231

 

*Exh test w/a 1 7/8 inch flow tube

 

With this in mind we can put the numbers into this process.

 

712hp - (10.4 x 14.7) = NA HP

712hp - 152.88 = NA HP

559.12 = NA HP

 

CFM x .257 x 8 = 559.12

CFM x 2.057 = 559.12

CFM = 559.12 / 2.057

CFM = 271.9

 

So, if we have a cam whose lift is .550"; we can now deduct the usual .100" less lift, which according to the CFM airflow chart puts us at .450" lift flowing somewhere in the 270cfm to 280cfm.

 

One more time this anomaly plays out.

 

Kevin,

(Yea,Still an Inliner)

[zguy36]

Kevin,

 

Great attempt at coming up with an equation, but you just don't have enough tools to get this done. Looking through your equations, I can see that you had your inputs and your results and tried really hard to fudge the numbers in between.

 

What you need to do, in order to continue building your equations, is manipulate your variables. Each variable plays a role in the equation and should vary your answer accordingly. Pick one variable and change it keeping all others the same, then look at your result and see if it changed how you thought it should. Using this method, your equation has quite a few holes in it.

 

To run this equation for turbocharged engines, you are going to have to add a lot more variables into the equation, which is exactly why you don't see catch all equations floating around. There are too many factors to deal with and it gets too tough to find the math to cover it.

 

For example, take two identical engines running 15psi of boost. Lets put small turbo on one and a large turbo on the other. Even though they are running the same boost pressure, the larger turbo will most likely make more power at the same boost level. The turbocharger has a huge effect on the actual horsepower output of an engine, but is very very difficult to model as a whole system with an engine.

[Kevin Shasteen]

Zguy,

 

That is a good point about turbo sizing.

 

My issue w/this anomaly isn't that it is to be an end all to any turbo/supercharger engine. It, the anomaly, is nothing more than an anomaly.

 

How I see this anomaly is how I see any auto math equation, if said equation is by itself and not added to the entire picture then any auto math equation is by itself worthless.

 

This anomaly, as I see it makes no promises other than..., it is there. It is a fact that it is there and I cant duck it; and so far no one else has given any real input other than:

 

"There are too many variables to take this process for real" comments.

 

I liken this anomaly to the same point as, let us say someone began bragging about the SCR of their engine they were going to build - but couldnt give any other details because they didnt know how to qualify those details. Any real engine analyst worth their salt knows that SCR by itself means nothing; so big deal.

 

I understand that w/out further variables being added to the after thought of any paper engine's initial beginnings; it, by itself, means nothing.

 

I am not trying to say to anyone that this anomaly replaces actual sound conclusions obtained thru facts. All, I am saying is "Here is an anomaly" and I find it interesting.

 

I guess, that would be one quailification of this anomaly.

 

1) All other components being properly sized/selected..., then, and only then this anomaly (w/out any other input at this time) appears to have some interesting merit.

 

I like your idea about manipulating one variable to confirm the equation; my only problem is I dont have access to a turbo/supercharged engine, additional components for swapping, and an engine dyno to prove it out.

 

BTW; what numbers do you think were fudged, as I approached each example the same way?

 

I like your post and it appears thought out, keep your insight and your ideas coming, please!

 

Kevin,

(Yea,Still an Inliner)