# Scaling laws for the oblique impact cratering on an inclined granular surface

## TL;DR

This study develops new scaling laws for impact craters on inclined granular surfaces by systematically varying impact and target angles, providing insights into natural crater formation and impact conditions.

## Contribution

It introduces a comprehensive experimental approach varying both impact and inclination angles to derive scaling laws for crater dimensions on inclined surfaces.

## Key findings

- Crater dimensions scale with impact and target angles using sine and cosine functions.
- The derived laws relate crater size to impact velocity, projectile size, and surface inclination.
- Application potential for estimating impact conditions from natural craters.

## Abstract

Although a large number of astronomical craters are actually produced by the oblique impacts onto inclined surfaces, most of the laboratory experiments mimicking the impact cratering have been performed by the vertical impact onto a horizontal target surface. In previous studies on the effects of oblique impact and inclined terrain, only one of the impact angle $\varphi$ or target inclination angle $\theta$ has been varied in the experiments. Therefore, we perform impact-cratering experiments by systematically varying both $\varphi$ and $\theta$. A solid projectile of diameter $D_{\rm i}=6$~mm is impacted onto a sand surface with the range of impact velocity $v_{\rm i}=7$--$97$~m~s$^{-1}$. From the experimental result, we develop scaling laws for the crater dimensions on the basis of $\Pi$-group scaling. As a result, the crater dimensions such as cavity volume, diameter, aspect ratio, and depth-diameter ratio can be scaled by the factors $\sin \varphi$ and $\cos \theta$ as well as the usual impact parameters ($v_{\rm i}$, $D_{\rm i}$, density of projectile, and surface gravity). Finally, we consider the possible application of the obtained scaling laws to the estimate of impact conditions (e.g., impact speed and impact angle) in natural crater records.