Unlocking the Science of Perfect Belly Flops: A Dive into Hydroelastic Forces

We have all experienced the less-than-graceful impact of a belly flop, and scientists are delving into the physics behind these slamming forces during water entry. The research article titled “Slamming forces during water entry of a simple harmonic oscillator” (J.T. Antolik, J.L. Belden, N.B. Speirs and D.M. Harris) sheds light on understanding hydroelastic factors and how you may use them to do less painful belly flops.

What is In a Splash?

When a blunt body hits the air-water interface, it creates substantial hydrodynamic forces, a phenomenon familiar to those who’ve attempted a graceful dive only to end up with a belly flop. While it’s amusing when it happens at the pool, these slamming forces pose serious challenges for the design of structures like ships and seaplanes.

Dive Into the Study!

The research team systematically investigated the water entry of a simple harmonic oscillator, perhaps the simplest scenario for studying these forces. Contrary to common intuition, they found that making the point of impact (impactor) “softer” doesn’t always reduce peak impact force. The transition from force reduction to force amplification is determined by a critical ‘hydroelastic’ factor that relates hydrodynamic and elastic time scales.

The Key Player: Hydroelastic Factor

The hydroelastic factor, becomes the linchpin of the study. It’s a ratio of the time scale of hydrodynamic loading to the free fundamental oscillation period of the elastic structure. This factor dictates whether the impact force increases or decreases. If the elastic mode starts oscillating before the hydrodynamic force decays, the impactor experiences an increased force. In layman’s terms this implies that you should flex your abdominal muscles before impact and keep them flexed for sometimes after the impact to reduce the movement of your stomach, which in this case is the elastic oscillator.

Perfect Belly Flop Form?

So, what does this mean for creating the perfect art of belly flopping? Well, it turns out that the ideal form might depend on finding the sweet spot between impactor stiffness, speed, and nose geometry. Impactor stiffness in this case would be the “stiffness” of ones belly, it turns out we are quite mushy and you should aim for the hardest abs possible. Speed on the other hand simply correlates to height you jumped from. As for nose geometry, this part reveals that belly flops are in fact not the most optimal way to land in water (shocking, we know). Nose geometry refers to area of the surface hitting the water, the requirement of having a high impactor stiffness and low nose geometry almost immediately rule out the belly flop in favour of feet first, which generally meet this requirement way better and almost seem optimised for landing in water. This is because you need very low fat to reach close to the stiffness described in the article which would imply you have a very flat stomach but a more rounded stomach will have the advantage in nose geometry creating a sort of belly flop paradox where improving one factor will weaken the other. The study highlights that force reduction or amplification is highly sensitive to these factors, giving divers and engineers alike some food for thought.

Beyond the Belly Flop: Engineering Implications

While belly flops provided a quirky context for the study, the implications go far beyond belly flopping antics. Understanding hydroelastic forces is crucial for designing structures in naval and aerospace engineering. By considering these factors, engineers can optimize the impact resilience of structures such as ships and airplanes, making them safer to use.


In conclusion, next time you find yourself mid-belly flop, remember: it’s not just a flop but a delicate interplay of hydrodynamic and elastic forces, as revealed by the great scientific belly flop research!


Sources used:

Antolik, J. T., Belden, J. L., Speirs, N. B., & Harris, D. M. (2023, November 6). Slamming forces during water entry of a simple harmonic oscillator: Journal of Fluid Mechanics. Cambridge Core. https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/slamming-forces-during-water-entry-of-a-simple-harmonic-oscillator/4E80C056B7CF95B96714AB11BDF938DF

Written by Elia Tallqvist

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