Should a pop bottle rocket have a cone?

When designing a pop bottle rocket, your objectives are to minimize weight and drag.

Think of the pressure in the bottle as a fixed ammount of energy that will be turned into velocity of the rocket per Energy = 1/2 * Mass * Velocity^2. As your rocket flies up into the sky, two things will happen to that energy. First, the energy will change into potential energy per Energy = Height * Mass * Gravity. (Gravity = the rate of acceleration due to gravity = 9.8 meters / second^s.) Second, the energy will be lost to friction. As your rocket flies through the air, it will bump trillions of trillions of air molecules and give its kinetic energy to them.

To minimize this bumping, you want to make it easy for the rocket to push the air molecules out of the way. This would be best accomplished by a long, slowly tapering nose-cone. Keep in mind that the heavier your nose cone, the less velocity you get.