A Minimal Model for Conical Splash Cups Using Conformal Mapping

While most flowers use animals or wind to distribute seeds, splash-cup plants accelerate rain drops to ballistically fling their seeds through the air. Most splash cups have a conical shape---much like a cocktail glass---which, upon being hit by a rain drop, channels the water to send it out the other side at increased speeds. We present a minimal model to understand the effects of the conical geometry on the acceleration of the rain drop. We employ an Euler fluid with a conformal mapping to find the velocity field within the conical geometry. Our results imply that the primary effect of a steeper cup angle---outside of changing the launch angle---is to make the impact site effectively closer to the center of the cup.