A air box acts like a turbocharger. It takes air from outside the car, from a point on the bodywork where the airflow stagnates, and therefore has a high pressure. Ramming this high pressure air into the engine increases the power output because more oxygen and therefore fuel can be burnt inside the engine.
Boy-racers and the like may fit their cars with NACA ducts, basic scoops, and other simple designs in an effort to achieve similar effects. But for an F1 air box, design is much more complicated. Many factors must be accounted for during the design:
1. drag from the airbox, which slows the car down.
2. uniform air distribution into the cylinders, non-uniform distribution can starve cylinders of air which makes the car slower.
3. resonance effects between the engine and the air intake. In state-of-the-art CFD modelling, the CFD model of the air intake is combined with a 1D model of the engine to try to address this problem.
4. Preventing detached/recirculating flow inside the air box. immediately after entering the airbox, the flow turns a 90 degree bend into the engine. If the flow recirculates in this region it will case a higher pressure drop and non-uniform distribution of air into the cylinders.
5. In most modern formula one cars, the air box is segmented into multiple inlets, and supplies air for many other applications in addition to engine air supply. It may be used for cooling flow. It can be redirected over the rear wing, stalling the rear wing, which provides the driver with a means of controlling the cars down force.
6. you may also see air boxes which have a vertical ridge that seems to stick out after the duct:(http://www.racecar-engineering.com/wp-content/uploads/2010/05/mercbox.jpg). This may be another drag-reducing measure. similar modifications to crossflow over a cylinder serve to dampen the wake, reducing drag due to vortex shedding etc.
7. when the engine is not running at 100%, less air is going into the airbox, so more air must flow around the airbow. This can disturb the airflow over the car, affecting the rear wing, which can reduce downforce, for example, if the driver is slowing down to enter a corner - just when he/she would need the downforce !
The design of a modern F1 car's air intake has to take into account lots of factors and as a result the first (drag reduction) may be compromised to serve the others better. As I've been researching this, I was surprised to find there's actually isn't that much information available in open literature. This is probably because the various teams want details of their designs to stay secret to give them the competitive edge. This post serves a basic summary of what I've found in my short search.
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