Cone vs. Flat air filter/intake

[vtraudt]

Looking at modifying my intake (2.7T), ghetto style.
The "Darin" intake mod has a lot of followers. So got the drill, jigsaw, dremel out and cut the whole.
Next is getting a 3" pipe bent 30 degree and a cone filter.
Looked at the K&N cones.

Thought to apply some physics and math to the issue at hand:
How much more filter area do I get from the cone?

Word is that my Allroad can take a RX-4990 cone (airbox longer than S4 box)
http://www.knfilters.com/search/prod...x?Prod=RX-4990
It tapers from 6 to 5 inch, 5.5 inches long. Thats 95 sq inch.
Granted: this version (XStream) has a few square inches in the front)
The flat filter is: 11x9 or 99 sq inch.

Assuming the flat and cone filter (say both from K&N) use the same material and giving the 'XStream' an extra 5 inch2 for the front:
There is NO reduction in pressure drop over the filter between the 2.
Or in car speak: they will flow the same amount of air.
In short: Physics dictate that there is no power gain!

To get say 10% more filter area, the cone has to be 6 inches long (tapering from 6 to 5 inch, including counting the full 5" diameter front area as filter).
The RX-4730 has that potential.
http://www.knfilters.com/search/prod...x?Prod=RX-4730

Save conclusion: going from an 11x9 flat filter to a 6"/5" x 5.5" long cone (same material) does NOT result in a reduction of filter losses!

Question is:
a) does a 6.5" long cone fit into the Allroad air box (likely not into the S4 box)
b) does 10% increase in area (=10% loss reduction) equate to 10% more airflow on a turbo charged engine (likely not?)

[Nateness]

Question is:
b) does 10% increase in area (=10% loss reduction) equate to 10% more airflow on a turbo charged engine (likely not?)

The short answer to your question is no, however there will likely be an increase in airflow (just not 10%).

Pressure drop ("loss") is a function of air velocity squared. In short, reducing the velocity can have a reduction in pressure drop that is non-linear.

Below is a link to a graph that shows the concept:
http://medicaldesign.com/contract-ma...drop-chart.jpg

The characteristic of the curve will depend on the media and to some degree, the geometry (aspect ratio on cone filters will come into play here).

More area is going to generally be better, but there is definitely a point where you will reach diminishing returns.

Take a look at the fan curve below (similar enough to be a useful comparison to turbochargers):
http://www.greenheck.com/images/articles/pag_fig7.gif

Note that for a fixed fan speed (rpm) that airflow (x-axis) can be increased by a reduction in external pressure drop (y-axis). Airflow for a fixed fan RPM will follow the curve that is characteristic to that particular fan.