# Wing weight function

The wing weight analytical function provides an estimate of the weight of a light aircraft wing, with input values derived from estimates for a Cessna C172 Skyhawk aircraft. The chosen ranges for each variable were selected to introduce probabilistic input into the analytical model in Forrester et al., 2008.

## Description

The wing weight function is defined as:

f(\mathbf{x}) = 0.036 S_w^{0.758} W_{fw}^{0.0035} \left( \frac{A}{\cos^2{(\Lambda)}}\right)^{0.6} q^{0.006} \lambda^{0.04} \left(\frac{100t_c}{\cos{(\Lambda)}}\right)^{-0.3} (N_z W_{dg})^{0.49} + S_w W_p,

where \mathbf{x} = \{S_w, W_{fw}, A, \Lambda, q, \lambda, t_c, N_z, W_{dg}, W_p \} are independent uniform input variables.

## Inputs

For computer experiment purposes, the inputs S_w, W_{fw}, A, \Lambda, q, \lambda, t_c, N_z, W_{dg}, W_p are modeled as ten independent uniformly distributed random variables.

No Variable Description Distribution Range
1 S_w Wing area (ft²) Uniform [150, 200]
2 W_{fw} Weight of fuel in the wing (lb) Uniform [220, 300]
3 A Aspect ratio Uniform [6, 10]
4 \Lambda Quarter-chord sweep (degrees) Uniform [-10, 10]
5 q Dynamic pressure at cruise (lb/ft²) Uniform [16, 45]
6 \lambda Taper ratio Uniform [0.5, 1]
7 t_c Aerofoil thickness to chord ratio Uniform [0.08, 0.18]
8 N_z Ultimate load factor Uniform [2.5, 6]
9 W_{dg} Flight design gross weight (lb) Uniform [1{,}700, 2{,}500]
10 W_p Paint weight (lb/ft²) Uniform [0.025, 0.08]

## Resources

The vectorized implementation of the wing weight function in MATLAB, as well as the script file with the model and probabilistic inputs definitions for the function in UQLab, can be downloaded below:

uq_wingweight.zip (2.3 KB)

The contents of the file are:

Filename Description
uq_wingweight.m vectorized implementation of the Wing weight function in MATLAB
uq_Example_wingweight.m definitions for the model and probabilistic inputs in UQLab
LICENSE license for the function (BSD 3-Clause)

## Open-access repository

The dataset used in this benchmark study is titled “Benchmark case datasets - Wing weight function” and is authored by Adéla Hlobilová, Stefano Marelli, and Bruno Sudret. It was published in 2024 and is available on Zenodo. The dataset can be accessed directly via the following DOI link: 10.5281/zenodo.12687230.

The experimental designs include datasets with 100, 200, 300, 400, and 500 samples, each generated using optimized Latin Hypercube Sampling (LHS) with 1000 iterations to improve the maximin criterion. Each dataset is replicated 20 times. The validation set contains 100,000 samples generated by Monte Carlo. Each dataset contains samples and the responses of the computational model.

For citation purposes, please use the following format:
Hlobilová, A., Marelli, S., and Sudret, B. (2024). Benchmark case datasets - Wing weight function. Zenodo. https://doi.org/10.5281/zenodo.12687230.

This project was supported by the Open Research Data Program of the ETH Board under Grant number EPFL SCR0902285.

## References

• Forrester, A., Sobester, A., Keane, A. “Engineering design via surrogate modelling: a practical guide,” Wiley, 2008. DOI:10.1002/9780470770801
• Surjanovic, S., Bingham, D. “Wing weight function,” Virtual Library of Simulation Experiments: Test Functions and Datasets. Retrieved July 3, 2024, from https://www.sfu.ca/~ssurjano/wingweight.html.
• Lüthen, N., Marelli, S., Sudret, B. “Sparse Polynomial Chaos Expansions: Literature Survey and Benchmark,” SIAM/ASA Journal on Uncertainty Quantification, vol. 9, issue 2, pp. 593–649, 2021. DOI:10.1137/20M1315774