International Journal of Aerospace Engineering

Volume 2018 (2018), Article ID 2105682, 14 pages

https://doi.org/10.1155/2018/2105682

## Analysis of Global Sensitivity of Landing Variables on Landing Loads and Extreme Values of the Loads in Carrier-Based Aircrafts

College of Aerospace Engineering, Nanjing University of Aeronautics & Astronautics, Nanjing, China

Correspondence should be addressed to Mingbo Tong; nc.ude.aaun@wgnot

Received 12 June 2017; Revised 26 October 2017; Accepted 9 November 2017; Published 14 January 2018

Academic Editor: Kenneth M. Sobel

Copyright © 2018 Jin Zhou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

When a carrier-based aircraft is in arrested landing on deck, the impact loads on landing gears and airframe are closely related to landing states. The distribution and extreme values of the landing loads obtained during life-cycle analysis provide an important basis for buffering parameter design and fatigue design. In this paper, the effect of the multivariate distribution was studied based on military standards and guides. By establishment of a virtual prototype, the extended Fourier amplitude sensitivity test (EFAST) method is applied on sensitivity analysis of landing variables. The results show that sinking speed and rolling angle are the main influencing factors on the landing gear’s course load and vertical load; sinking speed, rolling angle, and yawing angle are the main influencing factors on the landing gear’s lateral load; and sinking speed is the main influencing factor on the barycenter overload. The extreme values of loads show that the typical condition design in the structural strength analysis is safe. The maximum difference value of the vertical load of the main landing gear is 12.0%. This research may provide some reference for structure design of landing gears and compilation of load spectrum for carrier-based aircrafts.

#### 1. Introduction

Carrier-based aircraft is the most important method for aircraft carrier strike group to control sea supremacy, and it is also an indispensable power for modern navies. Due to limited area in deck landing zone and the demand for bolting and go-around, carrier-based aircraft usually lands on deck via impact method under high sinking speed and high engaging speed along a fixed glide path angle [1]. The impact load, braking load of arresting cable [2, 3], and other loads at the moment when the aircraft touches deck put forward higher requirements for design and analysis of landing gears and airframe structure, especially for the structures closely related to landing [4].

At the primary design stage of an aircraft landing gear, the landing loads and the most severe landing conditions of the landing gear under different landing conditions should be determined according to design outline, which will be adopted in the parameter design of landing gear buffers and structural strength analysis. At the detailed design stage, optimization design will be carried out to balance performance and structure of the landing gear according to the relation between landing conditions and landing loads. Finally, the maneuvering envelope will be determined and the design of service load spectrum will be compiled for the assessment of fatigue life [5, 6].

At present, the research literatures and reports on definition of arrested deck landing conditions are mainly military standards and guides [7, 8]. MIL-A-8863C (AS) provides the landing variables, their distribution form, and empirical formula of mean value and standard deviation that should be considered in deck landing. Micklos [9] provided a measurement report on the landing variables of all kinds of carrier-based aircrafts landed on the Enterprise Aircraft Carrier in both day and night. The measurement of landing variables and loads is a costly and tedious task, thus a large amount of researches have been carried out on the simulation and analysis of landing dynamics to analyze different landing conditions and loads in recent years. Zhang [10] introduced deck motion into a dynamics model through the wheel-deck coordinate system and simulated three landing situations to verify the model. Mikhaluk [11] and Lihua et al. [12] used finite element model to analyze forces on cables under different initial velocities and masses. Sati et al. [13] built a detailed aircraft arresting system using bond graph approach and studied the landing performance at different engagement speeds and masses.

The studies mentioned above give a simple trend of the relationship between landing variables and loads under a few landing conditions. However, the conditions empirically selected are unrepresentative. During the compilation of design service load spectrum, representative values of typical landing conditions can be obtained by discretizing the interval of landing parameters through sensitivity analysis. Incorrect structural load analysis may lead to excessive design, which would induce large weight and high cost at the primary stage of structure design. A further determination of the relationship between landing variables as well as the extreme value of the loads is required. Sebastian [14] analyzed the condition of free flight engagement (FFE), and the results show that the most severe loading condition of the landing gear takes place under the condition of free flight engagement at small sinking speed. Chester [15] researched the response of the main and nose gears via simulation of landing impact considering pitching and heaving degrees of freedom of the aircraft motion. The simulation indicates that the maximum vertical loads of main gears are almost linearly dependent on the sinking speed, while the response of nose gear is very sensitive to the initial values of pitch angle and pitching inertia. Yunwen et al. [16] explored the effect of different landing variables on sinking velocity based on the landing data measured from an E-2C. The results show that aircraft path angle and deck pitch angle are highly correlated with sinking velocity. Although they have studied part of the relevance between landing variables and loads, there is no direct conclusion on method accurate enough for determination of the representative values that can reflect typical landing conditions. Therefore, sensitivity and extreme value analysis need to be studied and it provides an important basis for the parameter design of landing gear buffer, structural optimization design [17], and fatigue analysis. However, theoretical basis and analysis method still need to be further investigated.

The extended Fourier amplitude sensitive test (EFAST) analysis method [18] is adopted in this paper to study the coupling and sensitivity between landing variables and landing loads. The method has been well applied in the field of hydrology [19], physical model [20], and so on. Based on military standards and guides, the effects of the multivariate distribution on the probability density function of single landing variable were analyzed and the distribution of single landing variable was fitted. By using the simplified landing virtual prototype and analysis of a large amount of landing conditions with the multicondition automatic simulation technology, the first-order and global sensitivity coefficients of landing variables on landing loads were calculated quantitatively, and the extreme value conditions and the frequency curves of the landing load were obtained.

#### 2. Studies on Landing Variables in Military Standards

Many factors would affect the carrier-based aircrafts during the arrested deck landing. The landing variables and their relationships are mainly stipulated by related military standards and specifications.

##### 2.1. Landing Variables and Multivariate Distribution

The military standard MIL-A-8863C (AS) stipulates the landing variables and their distributions. The condition of the landing variables needs to satisfy the demands of the multivariate distributions. The joint probability of the eight landing variables *P*_{T} is calculated by
where is the approaching speed, is the engaging speed, is the sinking speed, is the aircraft pitching angle, is the aircraft rolling angle, is the aircraft rolling rate, is the aircraft yawing angle, and is the off-center arresting distance. The subscript denotes the initial value of each landing variable. The symbol is chosen to be either or according to the initial value of the variable. When the initial value of any landing variable is greater than the average one, the symbol is chosen and it represents that the cumulative probability of that landing variable is greater than the initial value. Conversely, when the symbol is chosen, it represents that the cumulative probability of that landing variable is less than the initial value.

The evaluation of the landing variables is determined by the extreme value of the cumulative probability , namely, where and are the maximum and minimum value of the variables. In this paper, only the touch-and-go and arrested landing conditions are considered and the landing variables follow a normal distribution. The cumulative probability and the multivariate joint probability

##### 2.2. The Effects of the Multivariate Distribution on the Landing Variables

The relationships among landing variables are according to the multivariate distribution. The product of the joint probability of the landing variables does not reflect the effects on the distribution of the single landing variable directly. Therefore, the distribution of landing variables is investigated according to the multivariate distribution.

Take the approaching speed as an example. There exists a relationship: where is the average of the carrier engaging speeds. Take and as an example. The extreme value of the joint probability of any two landing variables is given by inserting (3) into (1).

The distribution of the landing variable is mapped to a standard normal distribution in order to unify the range of the variables. The mutual effects among the value ranges of the landing variables are determined by the multivariate distribution [21]. In Figure 1, there are six equiprobable design envelopes of any two landing variables. The probability of each equiprobable envelope is shown in the figure.