# Benchmark case - Wing weight function **URL:** \ **Category:** Benchmarks\ **Created:** [July 3, 2024, 3:04pm UTC](https://uqworld.org/t/benchmark-case-wing-weight-function/3728 "2024-07-03T15:04:58Z")\ **Posts on this page:** 1\ **Page:** 1
**Author:** ![Adela](https://uqworld.org/user_avatar/uqworld.org/adela/32/2301_2.png) [@Adela](https://uqworld.org/u/Adela)\ **Post date:** [July 3, 2024, 3:04pm UTC](https://uqworld.org/t/benchmark-case-wing-weight-function/3728/1 "2024-07-03T15:04:58Z")
# 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](https://uqworld.org/uploads/short-url/mcuxnYqe2vCoHu3spqZfVVNKJET.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](https://doi.org/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](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](https://doi.org/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](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](https://doi.org/10.1137/20M1315774)