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Related Experiment Videos

Optimal trajectory for the basketball free throw

G R Hamilton1, C Reinschmidt

  • 1Human Performance Laboratory, The University of Calgary, Alberta, Canada.

Journal of Sports Sciences
|January 10, 1998
PubMed
Summary

This study reveals the optimal basketball free throw trajectory involves a 60-degree angle and 7.3 m/s speed. High backspin is advantageous, with the ball aiming for the far rim for successful shots.

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Area of Science:

  • Sports Science
  • Biomechanics
  • Physics of Sports

Background:

  • The basketball free throw is a complex motor skill influenced by numerous physical variables.
  • Understanding the physics of a successful free throw can aid player development and coaching strategies.

Purpose of the Study:

  • To analytically determine the optimal angle, speed, and spin for a successful basketball free throw.
  • To investigate the influence of release parameters and ball-hoop interactions on shot success.
  • To provide evidence-based recommendations for free throw technique.

Main Methods:

  • A theoretical approach was employed to model the basketball free throw trajectory.
  • Calculations considered ball release angle, speed, and spin, including interactions with the backboard and hoop.
  • Standard deviations in shooter accuracy were incorporated to predict optimal trajectories from various release positions.

Main Results:

  • An optimal trajectory was identified with an initial release angle of approximately 60 degrees and a speed of 7.3 m/s.
  • A wide range of spins ( -2 to +2 m/s surface speed) were analyzed, with high backspin proving generally advantageous.
  • The study quantified the effects of air resistance and sagittal plane constraints on the optimal shot.

Conclusions:

  • Optimal free throw performance depends on shooter anthropometry and accuracy.
  • A trajectory directing the ball towards the far rim, combined with high backspin, is beneficial.
  • Recommendations are provided for free throw technique based on ball release height.

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