Physics Study Explains Inverse Velocity Force in Vehicle Engines and Electric Motors
A physics preprint posted to arXiv introduces the inverse velocity force F(v)=C/v as a foundational concept for understanding automotive acceleration and engine performance. The paper explains how this force arises from transmissions in internal combustion engines and from circuit controls in electric vehicles, and compares the torque-speed curves of both. The work argues this concept deserves greater attention in classical mechanics curricula despite its practical importance.
A preprint submitted to arXiv by Chris Lin (arXiv:2505.09631) presents a 19-page treatment of the inverse velocity force, defined as F(v)=C/v, as a central but underappreciated concept in automotive physics. The paper argues that this force represents the maximum deliverable force from a power-limited engine across a wide range of speeds, yet is rarely covered in standard classical mechanics courses. The authors detail how the force emerges mechanically through a transmission in gasoline-powered vehicles and more directly through electronic circuit controls in electric vehicles. The paper also addresses how the basic F(v)=C/v relationship must be modified and supplemented to accurately describe vehicle acceleration across the full speed range, including low-speed and high-speed regimes. A comparative analysis of gasoline and electric vehicle torque-speed curves is derived, highlighting fundamental differences in how each drivetrain delivers power. The paper has undergone four revisions since its initial submission in May 2025, with the most recent version substantially expanded to 519 KB. As a preprint, it has not yet undergone formal peer review.
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As a preprint, this work has not undergone formal peer review, so its pedagogical claims and derivations have not been independently validated by journal referees.
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- arXiv physicsCenter
The Inverse Velocity Force and Automotive Physics
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