Airboxes help the engine get undisturbed air and also produce a power enhancing ram-effect.
Airboxes started appearing in 1970 and quickly grew to ridiculous sizes until they were banned in 1976.
Airboxes have four benefits:
1. Their height gives the engine access to undisturbed cool air, which enhances its output and reduces wear.
2. Because of the airbox's shape and size, more air is pushed in than the engine than consume. This cause a ram or compression effect. The airbox thus functions like a mini supercharger compressing the air and thus raising engine performance
3. Airboxes provide extra space for sponsorship
4. Airboxes can, through their teardrop shape, provide a better air supply to the rear wing or not. I don't have any measurements on this aspect, but I suspect that airboxes tend to be beneficial to the rear wing.
By 1976 air boxes had reached massive sizes and were thus banned.
Air boxes started re-appearing on non-turbocharged cars from 1987 onwards. Their job was to gain a little bit of power through this ram effect.
Turbo cars never used them, as the ram-effect contribution is minimal compared to the turbochargers' contribution. Only Williams used a pair of mini airboxes on their FW11B in 1987.
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