Gravity Tunnel Drag

TL;DR

This paper investigates the effects of air resistance and side friction on objects traveling through a tunnel across the Earth, comparing different Earth density models to more realistic scenarios.

Contribution

It relaxes the assumptions of zero friction and air resistance in gravity tunnel models, analyzing their impact using various Earth density profiles including PREM.

Findings

Constant gravitational acceleration model fits tunnel motion better than PREM.

Uniform density model performs worse in realistic tunnel simulations.

Air resistance and side friction significantly affect transit time and dynamics.

Abstract

The time it takes to fall down a tunnel through the center of the Earth to the other side takes approximately 42 minutes, but only when given several simplifying assumptions: a uniform density Earth; a gravitational field that varies linearly with radial position; a non-rotating Earth; a tunnel evacuated of air; and zero friction along the sides of the tunnel. Though several papers have singularly relaxed the first three assumptions, in this paper we relax the final two assumptions and analyze the motion of a body experiencing these types of drag forces in the tunnel. Under such drag forces, we calculate the motion of a transport vehicle through a tunnel of the Earth under uniform density, under constant gravitational acceleration, and finally under the more realistic Preliminary Reference Earth Model (PREM) density data. We find the density profile corresponding to a constant gravitational acceleration better models the motion through the tunnel compared to the PREM density profile, and the uniform density model fares worse.