The front lateral cross-sectional shapes of cars,what are they fns of?

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The front lateral cross-sectional shapes of cars are influenced by several key factors, including engine size and layout, drivetrain configuration, and aerodynamics. The design must accommodate air intake and cooling requirements, while also considering airflow dynamics that affect understeer and downforce. Safety regulations play a role in determining bumper height and crash performance, impacting the overall shape. Aesthetic considerations and brand styling contribute significantly to the final design, often starting from a clean slate by stylists. Ultimately, the interplay of these elements shapes the distinctive profiles seen in modern vehicles.
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BMW has a kidney shaped grill for the air intake but the front looks weird from the side.Looking at a M3 inline-6 from the side,the front seems so long.This brings me to my question,how do engineers arrive at the front lateral cross sectional shapes of cars?

I assume that the front lateral cross-sectional shape would be functions of:
1.Engine size
2.Air-intake/cooling(naturally asp OR charged)
3.Amount of air going under the car that might cause understeer

I have not included 'aerodynamic drag force' because the aerodynamic drag force is a function of the frontal cross-sectional area(as viewed from the front OR by shining a beam of light from the back and looking at its shadow).

Nor have I included beauty/aesthetic sense.
 
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Obviously, your course work has omitted the functions of car stylists in laying out the shape of car bodies and their appurtenances. Sure, as a car model moves toward production, the engineers provide their input (especially on the aerodynamics of cars), but the stylists usually start with a clean sheet of paper in laying out their ideas in graphic form. Certain elements, like BMWs kidney bean radiator grille, are carried over in new models to provide visual continuity between older models and newer designs. Other elements are purely stylistic and do not originate from any functional purpose.
 
The largest impacts will be:

Engine dimensions
Drivetrain layout (FWD cars often mount the engine transversely, while RWD cars mount it longitudinally, which makes a large difference in the required dimensions)
Aerodynamics (which, unlike your statement above would imply, definitely depends on the profile of the car and not just its cross sectional area)
Styling - you say you are neglecting this, but it's definitely a large part of what drives the shape of most cars on the market today
Safety - bumper height is at least partially determined based on safety requirements, both based on hitting other cars, and based on hitting pedestrians.

Looking at your example of the BMW M3 with an inline 6 engine, it has a very long hood for a couple of reasons. It's a rear wheel drive car, so it has a longitudinally mounted engine. This places the engine's longest dimension in the front-back direction in the car. To further compound this factor, the inline-6 is a very long engine compared to the majority of engines out there. In a V configuration, the cylinders are staggered, so the length of the engine is much shorter, so as a result, even a V-8 tends to be shorter than an inline 6 with similar cylinder dimensions. Finally, the M3 is a fairly small car, so the cabin dimensions are not very large. These factors combine to give it a proportionally very long hood compared to the overall size of the car, as you noticed.
 
Yes,I forgot to factor in drivetrain layout and art styling. Also noticed how the F1 cars changed their front ends to provide for better crash performance.So,crash performance would also figure.Ofcourse,aerodynamics as a function of laminar flow over the entire car length seems very unclear to me still.Nonce of the books feature more than a line in this respect.

The updated list stands like this:

I assume that the front lateral cross-sectional shape would be functions of:

1.Engine size+Engine layout(long.,transv.)+drivetrain layout
2.Air-intake/cooling(naturally asp OR charged)
3.Amount of air going under the car that might cause understeer(Aerodynamics force under the car)
4.Air flow to create down-force at rear(Aerodynamics over upper car body)
5.Crash performance(pedestrian AND vehicle)
6.Art/styling+Brand styling/visual continuity
 
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