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re: untightened sparkplugs vs. Poiseuille's Law

Back-of-the-envelope time. How much leakage past a loose sparkplug is not
enough to notice the effects--or is too much to endure? Can a plug be
pretty damn loose, yet offer considerable resistance to leakage?

Thinking about my recently posted concern about engine performance
vis-a-vis untorqued sparkplugs, I recalled something called Poiseuille's
Law. This bit of physics permits one to estimate the volumetric flow or
"leak" rate (U) for any fluid with viscosity (n) passing though a capillary
tube of radius (r) and length (L) while under uniform pressure (P).

Air qualifies as a fluid, as has been discussed in many posts of some
months ago. I approximated the path offered by loose sparkplug threads as
being equivalent to a capillary tube (hey, remember this is the Qlist, not
the Society of Automotive Engineers). So, according to Monsieur Poiseuille,

		U= ()(P)(r^4)/(8)(n)(L).

At the end of the compression stroke, the 3B engine develops approx. 11
atmospheres of pressure in each cylinder. A leakage path of cylinder gases
is assumed to be along the "loose" sparkplug threads, and I approximate
that path as having a radius of, oh say from about 0.01 to 0.03 cm--really
a wild guess. The pathlength L around the threads is fairly close to 50 cm.
The viscosity of compressed air at 400 degrees K is about 225 x 10^-6 dyne
sec/cm^2. The pressure of 11 atmospheres is expressed as 1.114 x 10^7

Plugging all this into Poiseuille's equation (for several guessed values of
the capillary radius) gives the following results:

radius., r 	0.01 cm			0.02 cm			0.03 cm

leak rate	3.9 cc/sec		62 cc/sec		314 cc/sec

compress. loss
@3000 rpm	0.1%			1.6%			7.5%

@1000 rpm	0.3%			4.8%			22%

Note that there is a very large (4th power) dependence of the leak rate on
the diameter of the capillary ("open" thread path).

To arrive at the 3rd and 4th rows of results, there are two _additional_
factors to consider:

(1) Cylinder volume-->2300 cc divided by 5 and then divided again by
compression  of 11-fold yields a compressed cylinder volume of about 40 cc.
So compression loss (%) can be calculated based on this number.

(2) At 3000 rpm, there is one engine rev every 0.02 seconds. This gives the
entire compression stroke about a 0.01 second duration (10 milliseconds).
Hence, I estimate for the _worst_ case (the huge 0.03 cm capillary
radius--or over 1/2 millimeter) that the total volume of cylinder gases
lost by the plug is (0.01 x 314) about 3 cc, making about 7% loss of
compression. Heck, this is within compression specs, isn't it?  But at 1000
rpm it's a pretty big loss (22%).

Clearly, the narrower leak paths reduce the leakage (and compression loss)
to pretty negligible values (in my inexpert opinion). I don't know of an
untorqued sparkplug would offer a pathway equivalent to a 0.3 mm radius; it
seems big, but maybe possible. Does someone have tables of tapped thread
dimensions that would be applicable for Audi engines?

While a few percent loss may not be significant for compression, _any_
leakage translates directly to a loss of fuel, which surely becomes
measurable at the level of a few percent.  Since the absolute amount of
plug leakage will be inversely proportional to engine speed, owing to the
increased  duration per stroke, I suspect that increased fuel consumption
at very low rpm (e.g., idle speed) may turn out to be the main problem from
moderately loose plugs.

Obviously, having plugs with lots of fine threads helps to retard these
losses. But nothing beats remembering to tighten them correctly. There
could be important secondary effects on leak rate from heating/expansion
that can't easily be calculated.

Now, back to driving.


Phil Rose		Rochester, NY
'89 100
'91 200q		pjrose@servtech.com