Theoretical Maximum Power

[Ron Earp]

Is there a formula that will provide the theoretical maximum power for an engine of a given configuration if one provides some basic information about the engine?

I would think there would be since we have an air pump of a known compression ratio and gasoline of a certain energy content and so forth. I'm sure the camshaft of course plays a big role in this, but I'm looking for an estimation that can provide a theoretical maximum with a certain % error.

If an piston engine is X size, has Y compression ratio, burns gasoline, is not forced induction, will only run to Z RPM can one calculate a fairly accurate amount of power one could possibly obtain from the engine?

Thanks,
Ron

[Gary Gibbs]

Obviously this is complicated and depends on a lot of calculations. Basically the engine is an air pump and the heads and cam make the power. This assumes that the crank/rods can take the required RPM to get the power out of the heads/engine. Assuming you can get 100% volumetric eff. out of the intake and cam the max power is

~~~~= 0.257*(number of cyl.)*(intake cfm at cam max lift) {from AFR site}

Example: Theoretical max for AFR 225 heads with 0.600" lift cam.
P=0.257*8*307 CFM = 631 HP

My 427 with a hyd roller cam (not the maximum that could be used) made 615 HP. Any restriction that keeps you from 100% vol. eff. will proportionally reduce HP.

The RPM at peak HP will depend on displacement. Have not seen a formula estimate for this. From my dyno sheet the peak HP was at 5600 RPM (427 CI displacement). Same heads on a 302 would make the same HP at (427/302*5600 = ) 7900 RPM. Thus a 302 at 7900 RPM is pumping the same air and fuel as the 427 at 5600 RPM. Hope this short description makes sense.
Gary

[John Fitzpatrick]

Ron
The power of an internal combustion engine is directly dependent on it’s efficiency of energy conversion. Here is an abstract from a paper titled "Air Standard" Internal Combustion Engine Cycles and their Efficiencies published in the proceedings of the Physical Society of London Dec, 1917. The solutions to the question you asked are non-trivial.
Abstract. It is well known that the efficiency of an air standard internal combustion engine working through a cycle bounded by two adiabaties, and either two isothermals, two constant volume lines or two constant pressure lines is given by 1 -(1/r)γ-1 where r is the compression ratio and γ is the ratio of the two specific heats of air.
In the present Paper it is shown that the efficiency is given by the same expression if the cycle is composed of two adiabaties and two curves pωα = A, pωα=a, where a has any positive or negative value and A and a are constants. Since a may be chosen so that any explosion curve may be followed as closely as desired by short lengths of a curves, a cycle can be drawn with the above efficiency and any prescribed explosion curve. The ratio of the efficiency of a cycle with prescribed explosion and exhaust curves to that of the cycle so drawn is shown to be the ratio of the two areas on the indicator diagram. The thermal efficiency of a cycle with prescribed explosion and exhaust curves is therefore readily found.

Unfortunately, there are so many independent variables involved in describing the modern internal combustion engine that an accurate solution to your question will necessarily be applicable to a very specific configuration. An answer which has the sort of general applicability that you asked for is, by necessity, going to be a “rule of thumb” and, I think, not a lot more useful than simply relying on your experience.

[Colin Artus]

I think it is fair to say that the absolute maximum power a particular engine can produce is constrained by its ability to flow air. At its simplest this ability can be expressed as the maximum cfm the heads will flow and the (AFR) formula above does give an idea of a theoretical maximum ( although a well matched intake/exhaust system can achieve well over 100% VE). Computer dyno programs can give quite accurate predictions of theoretical power - reality unfortunately usually takes a slice off the top, a bit like the phenomenon where engines automatically lose 100bhp when they cross the
Atlantic from America to Europe.

[John Fitzpatrick]

Ron-
I went back to my books last night after thinking over your inquiry and couldn’t locate anything that would really answer your question directly. Gary’s formula from the AFR seems like a pretty workable solution for what you asked for. However, for and old Physics guy like me, the theoretical maximum power that can be got from a thermal engine is pretty interesting, although not of much help in real-world applications.

Assuming standard temp and pressure, etc, etc, the only factors involved are the heat content of the fuel, and how fast it is burned. Given the BTU/gal of gasoline is 115,400 (net) and the conversion factor of 0.000,393 hp-hr per BTU, a 100% efficient engine would produce 2,721 hp if it burned one gal/minute.

I’m not an automotive engineer, but I would think everything from head design to induction manifold configuration is done with an eye to delivering the largest possible volume of oxygen into the cylinder per induction stroke-which in turn permits the most fuel to be burned during the power stroke. Thermal efficiency and mechanical efficiency play an important part from a practical standpoint, but how much fuel you burn, and how fast, are the ultimate limiting factors.

[Sandy]

Ron -

Do you have any of the desk top dyno software? I don't but always wanted to play with it to see how things affect hp/tq. Ron also look at some of the engine shoot outs, Kaase and some others make loads of power with the imposed limitations.

You might look at it this way, how much power do I want, and work back from that

Sandy

[Ron Earp]

Well, what I'm thinking of is my JH 4 pot 2L motor.

I know I need a target hp, at the wheels, of around 150 or so for the car to be in the hunt in the ITS class. Right now we are pretty far below that number, over 25hp below. Now I know 2L 4 pots can manage that, modern designs can, but I was trying to figure out at what compression ratio one needed to have, and what airflow one needed to have to make a target number. So, I was planning on working backward a bit from whatever formula etc. was thrown out there.

Oh, no, I don't have an Dyno software. I used to have a copy in about 1999 or 2000, but that is long gone...

R

[Lynn]

Ron,

Adam Christian had access to software at OS that would do this, but I don't know if that is still true or not.

Here are some charts he ran for me with AFR 205s, the Jack Roush intake and a couple of different cams for a 347 w/3.25 stroke & 4.125 bore:

[Hammer]

Yea, I love my dyno program....I've been playing around w/ it alot...it's fun to go find cam specs for actual cams and load them on, and head flow numbers. I found a website that has a dyno, you just fill in the boxes and it runs it. http://www.edyno.com/Eng_spec.html

I've been changing cam specs on my own like the valve events by the degree or 2 and been working on fine tuning a cam that works w/ my head flow, and my valve sizes, and static CR. I've got my 445 FE build going now, and been playing around w/ everything, and w/ a real low rpm motor for the street, I'm getting 613 ft. lbs of torque @ 2,500....can't wait to get that into something!