Saturday, January 30, 2016

By the Numbers, Part One

I am not a "numbers guy" the way some are. I don't find joy in numbers just for the sake of numbers. One reason might be that I generally don't remember them especially well, though there are a few exceptions; mainly those numbers burned into my brain from repetition, repetition, repetition. For instance I have not yet, and may never forget my social security number since that dark night on the bus taking a load of new recruits from the airport in San Antonio to Lackland Air Force Base for Basic Training. A very intimidating uniformed fellow informed us in no uncertain terms that "YOU WILL HAVE YOUR SOCIAL SECURITY NUMBER MEMORIZED BY THE TIME YOU GET TO THE BASE!" Possible consequences for failure were left to our imaginations, but for an 18 year old fresh off the farm ..., well let's just say I didn't spend much of that ride gazing out the window.

Some of the other numbers that seem to be forever stuck in my brain are strictly due to much use. Its been many years since I have had to look up the center to center rod length for a pre Twin Cam big twin. 7.43875" for the late and 7.46875" for the early. I'm pretty sure that comes from balancing well over 100 sets of flywheels (last time I counted) over the last 35 years.

But other than that, numbers don't hold any special favor in my consciousness. What numbers can do for me, on the other hand ..., that I can get excited about. That's why I just had to share a couple of formulas that I recently ran across while searching some of my reference material. The particular reference book I was perusing was "Engine Airflow" by Harold Bettes. He's a smart guy, so I've read through the book more than once. By the way, I titled this post before noticing Mr. Bettes has a like named chapter in his book, but I didn't get it from him - I would assume that I inadvertently stole it from somewhere else.

One of the first formulas that caught my attention on this particular day concerns determining curtain area of a valve. If you're not familiar with the term, picture a valve lifted off its seat, with a "curtain" hanging around the perimeter of the valve  to the seat. Okay, maybe it will help if you begin by picturing this on a Flathead motor where the valve head faces up so that you don't have to concern yourself with how a curtain could defeat gravity and "hang" from a valve "up" to its seat. Are you picturing it now? Good. The area of that "curtain" has a good bit to do with flow potential. The simplified formula for computing this is the following:

Before we get into applying this formula, let's consider something else. Cross Sectional Area (or CSA). When dealing with heads, the CSA we often are concerned with is the Minimum Cross Sectional Area. Now, it is self evident that there is limit to the volume of air that can pass through a given size hole at a given pressure. There is one place in every intake tract that is smaller that the rest of the system, and the point with the smallest cross sectional area can be the limiting factor in air flow (in the real world it will take a well ported head for this to be true). That smallest point in the intake tract, or minimum cross sectional area is only easy to measure where the intake tract is round, but for my purposes right now, that is okay because the Harley ports are round (or at least they were meant to be) at the port opening. Another point where the intake tract is round and thus easy to measure, is the "choke" or "venturi" just under the valve seat.

So, if we were to take, say for example an 80" Evo... Why an 80" Evo, you ask? Well, it is clearly the direct forerunner of the Twin Cam. The ports are quite similar, and in fact they share the same port opening diameter and even the same intake valve (at least to 2004). That port opening diameter is 1.625".

Happily the choke I.D. (under the valve) also is 1.625". I say happily because that is the one place in the intake tract that you absolutely must have a "choke" point so it is the obvious place for the minimum CSA. If you are wondering why Harley left a second minimum CSA at the port opening, they didn't, but we'll get back to that in a moment. First lets convert that diameter to Cross Sectional Area. The formula is this:

That gives us a CSA of 2.074 square inches for a 1.625 diameter opening. In other words the CSA for the port opening is 2.074". But not quite for the "choke" under the seat, because that also happens to have a valve stem protruding through the center of it. Once we calculate the CSA of that stem (which generally measures .310" diameter) and subtract it, we see that our choke just under the seat of 1.999 square inches is indeed the minimum CSA.

Now back to that curtain area formula. One of the cool things about algebra is that it allows you to turn formulas around to suit your needs. In this case, computing the curtain area for your intake valve at full lift might be handy, but wouldn't it be even more interesting to see what lift it would take so we can be sure the valve curtain area is not the limiting factor. In other words, what valve lift would it require to equal the minimum CSA of the port. Turning that curtain area formula around would look like this:

If we take our previously calculated minimum CSA of 1.999 (which is our desired curtain area) and divide it by the product of pi (3.1416) multiplied by the valve diameter (1.843), we come up with .345" valve lift. So, you can see that the Harley engineers did their homework in providing a stock cam with more than enough lift (.472") to provide a curtain area theoretically large enough that it does not become a limiting factor. If one were to take things a step further, Bettes' book also includes a formula for computing the minimum CSA required for a given Cubic Feet per Minute (CFM) of air flow measured at a 28" test pressure. That formula is:

Or, once again to turn that formula around for my own purposes:

If we were to plug our minimum CSA into that formula we would find that theoretically, our stock Evo (or Twin Cam) heads with stock valves and valve seats, together with a stock cam, should have the potential to flow nearly 292 CFM (1.999 x 146) @ 28" test pressure. Wow.

But back in the real world... That theoretical flow potential of 146 CFM per square inch of Cross Sectional Area is a figure that has been calculated and confirmed by a number of people way smarter than me over the years, and while correct, it admittedly does not take into account any friction losses, and perhaps most importantly it does not account for loss of flow due to expansion which must happen when the air flows out of the port and into the cylinder. According to Patrick Hale's "Engine Pro- The Book" this figure when adjusted to take these other factors into account, along with "benchmark" results (as of 2004) reduces the target to a more reasonable 133 CFM per square inch. Still, that leaves your OEM head with a potential of 265 CFM (1.999 x 133).

But if we were taking a trip back to the real world when we reduced the flow potential to 133 CFM per square inch, then its time to get our heads out of the clouds, because even if the clouds are in the real world, most of us don't ride our Harleys there. So keep in mind that it will take a very good porting job to take full advantage of the potential flow through that minimum Cross Sectional Area.

On the next installment of this multi-post series, I'll try to take a look at a few things such as why the minimum cross section we just spent our time calculating may not be where the actual minimum CSA is located, what happens when we add porting and bigger valves, and eventually on to how much air flow your engine really wants.