# Mathematical model of non-deformed cargo parachute landing system with dampers on rigid plane in case of stationary wind field

DOI: 10.34759/trd-2023-131-01

### Аuthors

Averyanov I. O.

Moscow design industrial complex "MKPK "Universal", 79A, Altufevskoe shosse, Moscow, 127410, Russia

e-mail: i.averyanov@mail.ru

### Abstract

This article describes the mathematical model (MM) that extends MM of cargo parachute vertical landing system with dampers process on rigid plane developed in [1] to the case of its landing with horizontal velocity. The aim of the research is to update the model of statistical modelling of cargo landing process [2] to the case of its parachute landing. Wind effect is the main reason of parachute-cargo system (PCS) horizontal velocity. In this article the stationary wind field is considered.

The overturning moment is applied to the cargo in case of its parachute landing with horizontal velocity. One part of the moment comes to the cargo from its lower part due to frictional effects when it contacts to the plane. This effect considered in [1] and [3] and is taken into account in this MM. The second one – comes from the parachute system and passes through the suspension system to the cargo structure. Therefore, to get the overturning moment correctly the following changes are added to the MM [1]: multiple canopy parachute system (MCPS) instead of the equivalent canopy, suspension system and the parachute unlocking system (PUS).

MCPS is commonly used for heavy cargos parachute landing, that’s why the MM of MCPS is developed. It consists of separate inertial canopies with elastic slings. The canopies can receive the aerodynamics loads and have elastic contacts to each other. The MM of suspension system consists of elastic links joined through the point inertial elements. PUS is modelled with the special condition to the correspondence suspension system link. The wind field is modelled by aerodynamics loads applied to the canopies of MCPS and the cargo.

The task of parachute horizontal landing of cargo with dampers is considered to demonstrate the influence of parachute system to the landing process. Analysis of the results makes it possible to conclude that the developed model shows the plausible characteristics of the landing process and can be used in [2].

### Keywords:

parachute landing, multiple canopy parachute system, air damper, soft landing system, statistical modelling, landing process, parachute-cargo system

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