[Christ]

Mandrel bends are used where exhaust routing cannot be made straight. There are space constraints to working with mass production and existing chassis designs. Those are still the only reason for using bends at all.

I've said it once already, a bend slows down flow, no ifs, ands, or buts about it. There is no optimal bend in an exhaust system that cannot be countered by tuning the cross sectional area of the exhaust tube.

Bends in the header are solely there to facilitate equal length tubes to the collector, and, again, space constraints. If the headers could be made straighter, they would.

In all of motorsports history, the ultimate aspiration in dealing with exhausts has been to make them as straight as possible, regardless of the tuning characteristics desired.

It is generally accepted that bends restrict flow, and are not desirable.

You fail to mention exactly (using science) how a bend can be beneficial to anything except space constraints and scavenging (scavenging can still be had in other ways, so even this is not a 100% downfall to straight pipes.)