RPMs for Dummies

[RamblerRebel6]

Well, frankly, I'm a little intimidated by the depth of all-around technical knowledge in this forum, and I've felt somewhat diffident about even starting this thread. I'm only a student of automotive technology and don't have any hands-on experience, period, other than doing some routine maintenance on my old cars. However, I have picked up a few things along the way and formulated a few theories of my own based on my observations. And a lot of what I've learned has been picked up by way of intuition.

In order to understand four-stroke engines, I long ago began to focus on studying the camshaft and the intake system. Basically, I wanted a quick method to help me get a ballpark idea of what the potential RPMs might be. I think I've found such a method which is at least meets my satisfaction. I don't need pinpoint accuracy, just a general idea. Maybe there are others like me here who might find this of at least a little interest.

A few years ago, I was playing with a variation of the Helmoltz equation in one of my BASIC programs, and came up with a fairly simple formula which estimates engine RPMs based on a handful of criteria. I've tested it a number of times since and it seems to hold up okay.
(Note: This formula probably only applies to engines of the four-stroke Otto cycle. I haven't tested it with other types of engines.)

The basic formula calls for the cubic inch displacement (CID) and number of cylinders (CYLINDERS), the intake valve diameter (IVD), the intake valve lift (IVL), and the static compression ratio (CR). (And, of course, the number of intake valves per cylinder. If there are two, this means the IVD obviously gets multiplied by 2.) Of course, bore (BORE) and stroke (STROKE) could be used, but aren't necessary. (Also note: all measurements thus far are in inches.) It might also be helpful to know the lobe separation angle LSA and the intake centerline (ICL), but these values are optional.

One of the main constants of this formula is 67500, which is actually the speed of sound in feet per minute. (1125 x 60) I chose this particular value because it's nice and neat and easy to remember.

To proceed, we use a small value which I call V0. This is the cubic inch displacement expressed in cubic feet. So basically:

V0= CID / CYLINDERS / 1728

Of course, if we want to use bore and stroke, the calculation is slightly more complicated:

V0 = BORE * BORE * PI / 4 * STROKE / 1728

The next value we need is what I call IVA (intake valve area) which is simply the gross curtain area of the intake valve. This is, as expected:

IVA = IVD * PI * IVL * number of intake valves per cylinder

The final important value is the wildcard or fudge factor variable I call RUNLEN, which is expressed in feet. RUNLEN is theoretically the intake runner length--which it probably isn't, but the theory is at least good. Conventional wisdom states that the longer the runner length, the lower the revs. At any rate, I have assigned "lengths" to RUNLEN according to different applications. I know this part is mostly intuitive, but I think it does make some sense.

But first, the actual formula. I wrote it in two pieces to avoid clutter and confusion.


MAXRPM0 = 67500/(2*pi)*(IVA/144/(V0*RUNLEN))^0.5
MAXRPM = maxrpm0*((CR-1)/(CR+1))^.5

If I feel the need to fine-tune based on intake centerline/lobe separation considerations, I do this:

MAXRPM (new) = MAXRPM*ICL/LSA

This is based on the theory that advancing the cam x degrees will lower the rpms slightly, and retarding the cam increases them.

Now, back to the values I've come up with thus far for RUNLEN.

RUNLEN = 1.5' -- This is the shortest value I've used so far. (I applied this length to arrive at the value of 7000 rpm for the 426 Max Wedge "Short Ram" engine from the '60s. It's also what I employed to arrive at 6300 rpm for the 1962 Pontiac 421 Super Duty with its stingy valves. This value seems to be applicable to the top of the performance heap. I haven't needed it for high-performance street-driven vehicles.)

RUNLEN = 1.75' -- What I usually use to evaluate most racing engines. This "length" is what I use to estimate the maximum rpm for very high performance street applications, but almost never for hydraulic flat tappet valves. Where 1.5' might be used for the maximum RPM of a certain "well endowed" engine, 1.75' might be where I want to set the value for that engine's horsepower rpm.

RUNLEN = 2' Used to get redline for many high performance street engines with mechanical lifters (not very often for hydraulic lifters, either roller or flat tappet.) Possibly HP RPM's for those with a redline derived from RUNLEN=1.75

RUNLEN= 2.25' A rarely used value. I sometimes apply it to give HP RPMs of high performance street vehicles with what I consider to be a suitable intake system.

RUNLEN = 2.5' The most common value to give redline RPM for hydraulic lifters, both flat-tappet and roller. Fairly often for horsepower RPM for engines evaluated with max RPMS with a RUNLEN value of 2, especially older high performance solid-lifter engines.

RUNLEN=2.75' Another rarely used value. Could be applicable for certain hi-po hydraulic-lifter engines.

RUNLEN = 3' The common max value for HP RPM of lower performance street vehicles, mainly with smaller carburetors. The value I usually use for 2bbl carb engines & less to get maximum RPM

I haven't used a RUNLEN value of 3.25', but the highest value I use is 3.5. You probably get the point of what this "intake runner length" covers.

Here is one worked example to illustrate:

350 4 barrel "300 horsepower" of 1967-1970-- Bore: 4", Stroke: 3.48"; Valve diameters (int/exh): 1.94 / 1.50. Valve lifts (int/exh): 0.390 / 0.410. LSA: 112, ICL: 108. Compression ratio: 10.25:1

V0=350 / 8 / 1728 = 0.0253 cu.ft.
IVA= 1.94 * pi * 0.390 = 2.3770 sq. in.

To proceed, I need to establish the value for RUNLEN. I choose 2.5' because this is a hydraulic valve engine.

So plugging it all in:

RPM0 = 67500 / (2*pi) * (2.3770/144/(0.0253*2.5))^.5 = 5488 rpms
And finally:
RPM (final): RPM0 * (9.25/11.25)^.5 = 5488 * .9068 = 4977 rpms (I usually round to the nearest 50 in my BASIC program, so finally 4950-5000)
If I use the intake centerline/lobe separation, I get 4977 * ICL/LSA = 4799 rpm, or 4800 rounded.

For the RPM of horsepower, I might use 3 feet as my "runner length", so I get:

RPM0= 67500 / (2*pi) * (2.3770/144/(.0253*3))^.5 = 5010
And then:
RPM = 5010 * .9068 = 4543 or 4550
Fine tuning with ICL/LSA:
RPM (final) = 4543 * ICL/LSA = 4381 or approx. 4400 RPMs.


So I thought I'd throw this on out there, if just for your amusement. Like a friend of mine observed about me, I'm the type of guy who sometimes throws things against the wall to see what sticks. This is probably one of those times.

[n2xlr8n]

Welcome to the forum.

One small observation- careful with your thread titles.

Of the folks that post meaningful things here, most are highly skilled engineers, fabricators, airflow specialists, and racers. I'll dare say none are dummies.

You likely will not be catching "new fish" or disproving general relativity on this forum.

Relax and enjoy the reading.

[Fastvette94]

You might want to check out Design and Simulation of Four Stroke Engines by Gordon Blair. He has a chapter on determining starting lengths for intake track, exhaust, collector, etc using simple equations derived from his simulation output.

[user-23911]

If you're a student, you need to get into the 21st century and forget about feet and inches.

They're obsolete.

As are horses.


Engines don't use Helmholtz either, they use organ pipe theory.

[maxracesoftware]

Here is one worked example to illustrate:

350 4 barrel "300 horsepower" of 1967-1970-- Bore: 4", Stroke: 3.48"; Valve diameters (int/exh): 1.94 / 1.50. Valve lifts (int/exh): 0.390 / 0.410. LSA: 112, ICL: 108. Compression ratio: 10.25:1

V0=350 / 8 / 1728 = 0.0253 cu.ft.
IVA= 1.94 * pi * 0.390 = 2.3770 sq. in.

To proceed, I need to establish the value for RUNLEN. I choose 2.5' because this is a hydraulic valve engine.

So plugging it all in:

RPM0 = 67500 / (2*pi) * (2.3770/144/(0.0253*2.5))^.5 = 5488 rpms
And finally:
RPM (final): RPM0 * (9.25/11.25)^.5 = 5488 * .9068 = 4977 rpms (I usually round to the nearest 50 in my BASIC program, so finally 4950-5000)
If I use the intake centerline/lobe separation, I get 4977 * ICL/LSA = 4799 rpm, or 4800 rounded.

its predicting the 1st Harmonic Length

and i tested 4 other Combos :
its actually very close for NHRA ProStock
pretty far off for Sonny's 1006cid
not too bad for SS/IA Chevy 350
way off for Briggs Raptor 1 Cylinder 6HP , but if you divide by 2 = its just about spot on

[statsystems]

If you're a student, you need to get into the 21st century and forget about feet and inches.

They're obsolete.

As are horses.


Engines don't use Helmholtz either, they use organ pipe theory.

The metric system is no better than anything else. Geez.

[user-23911]

There's only 2 counties in the whole world not using the metric system.
One of them is in Africa.
Even the original inventors of the imperial system don't use it anymore.
America uses their own version which is "wrong" due to taxation.

Even "new" american engines are now designed in metric.

[Circlotron]

No metric unit could ever replace this one -> https://en.m.wikipedia.org/wiki/Ship_load

[statsystems]

There's only 2 counties in the whole world not using the metric system.
One of them is in Africa.
Even the original inventors of the imperial system don't use it anymore.
America uses their own version which is "wrong" due to taxation.

Even "new" american engines are now designed in metric.

Yep, just like the rest of the world. WGAFF what the world does? Ridiculous.

The fact is, if you can't use the fractional system you'd be better off doing something else. Damn

[user-23911]

For me, I can use either because I went through school using the proper imperial system which changed in about 1971.

I know which is easier and at the same time less confusing, which leads to less mistakes.


I'm sure that I read somewhere that NASA missed the moon altogether in one of the earlier missions, blamed it on wrong conversion, metric/ imperial.
But then again, maybe it was all one big fraud.

http://edition.cnn.com/TECH/space/9909/ ... metric.02/

[David Redszus]

Engines don't use Helmholtz either, they use organ pipe theory.

Some engines do.

Most of the resonant tuned engines I've worked with use pipe organ theory, Hemholz resonance and Coldbox effects.
Each can be designed to stack torque performance at some engine speed or to spread the torque values if desired.

[RamblerRebel6]

Well, thanks for taking time to read and comment and even test for yourselves, in some cases.

[statsystems]

For me, I can use either because I went through school using the proper imperial system which changed in about 1971.

I know which is easier and at the same time less confusing, which leads to less mistakes.


I'm sure that I read somewhere that NASA missed the moon altogether in one of the earlier missions, blamed it on wrong conversion, metric/ imperial.
But then again, maybe it was all one big fraud.

http://edition.cnn.com/TECH/space/9909/ ... metric.02/

I was in school when it changed and I can use both. The metric system is a dumbed down deal so any retarded third grader can add and divide by ten.

Show me a kid today who can make change for a dollar. If they can give it to you in dimes you might get lucky. It's the same principal.

And, for the record, the Hubbel telescope was done using fractional math and IIRC they went 10 places to the right of the decimal point.

[maxracesoftware]

Well, thanks for taking time to read and comment and even test for yourselves, in some cases.

don't get discouraged , great first try

Results :
100.0 % = your engine ( 350 4 barrel "300 horsepower" of 1967-1970)
100.0 % = ProStock
81.0 % = Sonny 1006cid
96.0 % = SS/IA 1995
50.0 % = Briggs 6HP

thats just 5 simulations

[RamblerRebel6]

Well, thanks for taking time to read and comment and even test for yourselves, in some cases.

don't get discouraged , great first try

Results :
100.0 % = your engine ( 350 4 barrel "300 horsepower" of 1967-1970)
100.0 % = ProStock
81.0 % = Sonny 1006cid
96.0 % = SS/IA 1995
50.0 % = Briggs 6HP

thats just 5 simulations

No, I've never said anything about being discouraged. I've been through much of the following online camshaft catalogues with that little model: Competition, Crane, Edelbrock, Howard, Lunati, etc. I just posted one for brevity's sake. I've had some flops, sure. And I don't know beans about the Briggs 6HP engine, so I'm at a disadvantage there because I have no specs to go by.