Designing a convertible car is not as simple as just cutting off the roof and installing a folding cloth top. There are other issues to consider.
Structure
The roof of a conventional car is essential to the stiffness of the chassis. The roof helps keep the car from twisting and bending. Building a car without a roof is a bit like building a suspension bridge without the cables. As such, the bottom part of the structure of a convertible has to be stiffened considerably. Heavy reinforcing brackets have to be added to the body of the car. This is why convertibles often weigh more than their fixed-roof counterparts.
If you were to cut the roof off of your car, you'd find that the body would twist a lot, especially if you were to do something like, say, drive diagonally over speed bumps. Eventually, the car would develop all sorts of squeaks and rattles and exhibit some poor handling characteristics. It's important for convertibles to have an especially sound structure to make up for the lack of a roof.
Aerodynamics
Usually, convertibles with their top down are much less aerodynamic than similar cars with permanent roofs. A long, flowing roof smoothes the airflow over the car, resulting in less drag. However, careful attention to detail can result in a convertible that is almost as aerodynamic with the top down as with it up.
One of these details is the small, glass shield located behind the headrests. Have you ever seen people driving a convertible with their hair blowing forward? This happens because the fast-moving air coming off the top of the windshield encounters the slow-moving air inside the cabin. Some of the fast-moving air is decelerated by the slow-moving air. As it slows down, it becomes turbulent, and vortexes form. These vortexes of turbulent air are like little horizontal tornadoes. They spin in such a way as to blow air forward into the cockpit. This can be uncomfortable for the occupants, and can increase the aerodynamic drag. The glass shield behind the headrests blocks this air, making the cabin quieter and more comfortable, as well as improving the aerodynamics.
The Lexus SC430 is almost as aerodynamic with the top down as it is with the top up. We'll take a closer look at this car later. First, let's see how a conventional cloth-top convertible works.