It's highly unlikely that installing a high flow filter will improve power in any road-going vehicle. That statement is based on dyno results from different sources and personal experiences in a number of vehicles including motorcycles. Factory filters are designed to allow air flow commensurate with the needs of an engine. Even removing filters completely does not result in more power. Those who report a power increase are only reacting to expectations which can fool anyone. If you believe strongly enough in a change you will feel it. In some cases there is the possibility of experiencing a little better throttle response which can be deceiving as far as greater power is concerned. The pressure drop due to filters alone is negligible. You need to look to other design factors to increase air flow and power.
High flow filters have the potential of allowing a greater flow but they filter poorly, and effective filtration is the reason for filters in the first place. Filtration shoud be the major concern for any road-going vehicle. Changes in fuel mileage will also be insignificant. To actually benefit from the potential greater flow you need to make other changes as well - like intake path, exhaust systems, valve timing, etc.
Oil impregnated gauze and foam filters have their uses but they are basically relegated to off road competition. I first used them several decades ago in motorcycles for off road competition. For that use they were indespensible since they didn't clog when wet, nor break apart, and they also continued to flow air even when covered with layers of dirt and mud. A paper filter would be disasterous. The situation is reversed for vehicles that travel on public roads, and particularly for those not engaged in competition.
K&N (the company) has done an terrific job in convincing car enthusiasts that their filters will provide benefits. Independent testing has proven otherwise, and indicated that they filter very poorly as well. They do have their uses as mentioned but not for vehicles such as smart cars.
The following references from a reputable source (bobistheoilguy) might be instructive -
Air Filter Flow Testing for Napa Gold, Amsoil two stage foam, Jackson Racing foam, Baldwin, Mazda and K&N
Filtration Testing for Amsoil, K&N, Napa, Jackson Racing, Baldwin, and Mazda air filters on a Miata
- and here is another report that might open a few eyes and minds -
ISO 5011 Duramax Air Filter Test Report
I've been through this issue on both other car and motorcycle forums over the past several decades. I don't know if anyone else has raised these points before, but it is sad to see that the smart car 'enthusiasts' are being lured into using these products as well. It's especially astonishing to read that people are wanting to do this thinking they'll get better fuel mileage to no avail and all at the expensive of increased engine wear.
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