Non-dimensional approach of aircraft crash equations and peak load force formula

Abstract

This paper is a development of the well-known Riera approach (1968, 1980) for the calculation of the loading force applied by an aircraft crashing on a rigid target. The purpose is to present a formula that provides the peak value of the loading force so that running time-response analysis is not any more necessary. For this purpose, we first develop a non-dimensional approach of Riera equations and we provide analytical solution of them. Then, we calculate the non-dimensional response of five different types of aircraft at different impact velocities. For every aircraft, we identify the non-dimensional peak force as a function of the non-dimensional velocity, and we translate it into $F_{\mathit{\text{peak}}}$ in the physical domain. In a next step, we derive an upper bound ${\widehat{F}}_{\mathit{\text{peak}}}^{\mathrm{ }}$ of $F_{\mathit{\text{peak}}},$ and we introduce $F_{\mathit{\text{peak}}}^{\text{*}},$ an approximate of $F_{\mathit{\text{peak}}}.$ The accuracy of $F_{\mathit{\text{peak}}}^{\text{*}}$ with respect to $F_{\mathit{\text{peak}}}$ is examined for the considered series of aircrafts and impact velocities. Eventually, we explain how the non-dimensional approach enables to derive the peak force generated by a given aircraft at a given velocity from the one of another aircraft at another velocity, provided that both aircrafts have some non-dimensional features in common.

Keywords:

• Aircraft crash
• impact velocity
• peak loading force
• non-dimensional analysis
• analytical resolution

Data availability statement

Data used in this paper are summarized in Table A1. All those data are provided in a supplemental on-line material.

Disclosure statement

No potential conflict of interest was reported by the author(s).