From Geometry to Code
A mathematical model of the conventional deadlift with an Android implementation.
The conventional deadlift is one of the fundamental compound exercises in strength training. In this exercise, the athlete approaches a barbell resting on the floor, bends down to grip it with straight arms, and lifts it until standing upright.
One of the most common mistakes made by novice athletes is adopting an incorrect starting position with excessive forward trunk inclination. Such a position increases the risk of lower‑back injury.
Recently, I was approached by a representative of a fitness startup with the idea of developing a mobile application capable of determining whether the conventional deadlift is performed correctly from a photograph or video. This immediately raised a natural question: what body position at the start of the lift should be considered the reference? While there are well-known technical recommendations — such as keeping the shoulders directly above the barbell at lift-off and maintaining straight arms — an athlete's anthropometric characteristics also play a significant role.
To address this question, I was provided with photographs of athletes performing the exercise correctly. The coach identified the key technical requirements satisfied in each case. However, when we measured the initial back angle, we found that every athlete had a different value.
This led me to develop a geometric model of the starting position that satisfies the coach's recommendations while clearly demonstrating how the initial back angle (α) depends on the athlete's anthropometric parameters: foot length (p), shank length (s), femur length (f), torso length (t), and arm length (a). It did not take long to derive the following formula—a formula impressive enough to frighten schoolchildren while simultaneously demonstrating the practical value of trigonometry.
Recently, I was approached by a representative of a fitness startup with the idea of developing a mobile application capable of determining whether the conventional deadlift is performed correctly from a photograph or video. This immediately raised a natural question: what body position at the start of the lift should be considered the reference? While there are well-known technical recommendations — such as keeping the shoulders directly above the barbell at lift-off and maintaining straight arms — an athlete's anthropometric characteristics also play a significant role.
To address this question, I was provided with photographs of athletes performing the exercise correctly. The coach identified the key technical requirements satisfied in each case. However, when we measured the initial back angle, we found that every athlete had a different value.
This led me to develop a geometric model of the starting position that satisfies the coach's recommendations while clearly demonstrating how the initial back angle (α) depends on the athlete's anthropometric parameters: foot length (p), shank length (s), femur length (f), torso length (t), and arm length (a). It did not take long to derive the following formula—a formula impressive enough to frighten schoolchildren while simultaneously demonstrating the practical value of trigonometry.
The practical value of this formula is difficult to overstate. It allows every athlete to determine a simple personalized target value for the initial back angle, making it possible to perform the exercise with proper technique.
The complete mathematical derivation is presented in my scientific paper on Figshare. Here, however, our focus is the Android application, whose development could now begin on a solid mathematical foundation.
The first version of the application was developed by me. With the client's permission, I am sharing a download link here. The application asks the athlete to enter their anthropometric measurements and immediately calculates the personalized optimal back angle. It also generates a schematic figure with the same body proportions as the athlete, illustrating the correct starting position specifically for that individual.
The complete mathematical derivation is presented in my scientific paper on Figshare. Here, however, our focus is the Android application, whose development could now begin on a solid mathematical foundation.
The first version of the application was developed by me. With the client's permission, I am sharing a download link here. The application asks the athlete to enter their anthropometric measurements and immediately calculates the personalized optimal back angle. It also generates a schematic figure with the same body proportions as the athlete, illustrating the correct starting position specifically for that individual.
For now, this is where the story ends — I would rather not reveal the client's future plans for the application just yet.
In the meantime, feel free to explore my collaboration plans and get in touch to discuss how mathematics and computational modeling can help solve your own challenge.
In the meantime, feel free to explore my collaboration plans and get in touch to discuss how mathematics and computational modeling can help solve your own challenge.
