Why a Belly Flop is the Worst Way to Land in a Pool

Looking outside to a landscape of snow and ice, it is a good time to reminisce on warmer days in the summer. More specifically, I spent part of my summer on the beach or in a pool. A key part of every pool is the diving board, and I distinctly remember how different each way of diving into the pool can be. 

So why is a belly flop the most painful when compared to other ways of diving?

First, we have to assume that all dives are from a peak height that is 3m above the surface of the water, and you are 2m tall with a mass of 70kg. The velocity at the time of landing in the water, assuming there are no non-conservative forces acting on you during the jump, is the same no matter if you dive in with a cannonball, pencil dive or the dreaded belly flop. 

PEi=KEf

mgh=1/2mv^2

(70kg)(9.8m/s^2)(3m)=1/2(70kg)(v^2)

v=7.67m/s

Now, a way to demonstrate the difference between the jumps is by looking at the change in momentum during the jump in order to find the applied force from the collision with the water using the equation F = ∆p/∆t. The ∆t in the impulse equation represents the time of the collision itself, and the time it takes to reach zero velocity from the velocity before the collision. 

F=∆p/∆t

F=(m∆v)/∆t

F=(70kg)(-7.67m/s)/∆t

The time that it takes to reach zero velocity depends on how you jump. For a belly flop, this time is approximately 0.4 seconds. For a pencil dive, this is closer to 2 seconds, likely higher. 

As we can see below, the collision time is incredibly low when landing on a hard surface such as ice, which explains the visible pain the diver experiences. 

That being said, using the impulse equation, the force felt from the collision breaking the surface tension of water will be significantly greater from a bellyflop than other methods of diving

Another way to look at a bellyflop is by the amount of water displaced during the dive. With a much higher surface area breaking this surface tension, a bellyflop displaces a high amount of water. These factors can result in a greater resistance force being applied across the body, and ultimately a more painful jump.