The Wing weight function

The Wing weight function of Forrester et al. (2008) is a recurrent test case for modeling purpose and sensitivity analysis in aerospace context. This function is extracted and adapted from the Raymer handbook for aircraft design. It is representative of a Cessna C172 Skyhawk wing aircraft. It depends on the wing area, the weight of fuel in the wing, the aspect ratio, the quarter-chord sweep angle, the dynamic pressure at cruise, the taper ratio, the airfoil thickness to chord ratio, the ultimate load factor, the flight design gross weight and the paint weight.

use case geometry

The function is defined as follows:

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

with:

  • S_w \sim\mathcal{U}(150, 200), the wing area (ft^2)

  • W_{fw} \sim\mathcal{U}(220, 300), the weight of fuel in the wing (lb)

  • A : \sim\mathcal{U}(6, 10), the aspect ratio (-)

  • \Lambda : \sim\mathcal{U}(-10, 10), the quarter-chord sweep angle (deg)

  • q : \sim\mathcal{U}(16, 45), the dynamic pressure at cruise (lb/ft^2)

  • \ell : \sim\mathcal{U}(0.5, 1), the taper ratio (-)

  • t_c : \sim\mathcal{U}(0.08, 0.18), the airfoil thickness to chord ratio (-)

  • N_z : \sim\mathcal{U}(2.5, 6), the ultimate load factor (-)

  • W_{dg} : \sim\mathcal{U}(1700, 2500), the flight design gross weight (lb)

  • W_p : \sim\mathcal{U}(0.025, 0.08), the paint weight (lb/ft^2)

We assume that the input variables are independent.

References

  • Forrester, A., Sobester, A., & Keane, A. (2008). Engineering design via surrogate modelling: a practical guide. Wiley.

  • Moon, H., Dean, A. M., & Santner, T. J. (2012). Two-stage sensitivity-based group screening in computer experiments. Technometrics, 54(4), 376-387.

  • Raymer D.P. (2018). Aircraft Design: a conceptual approach. American Institute of Aeronautics and Astronautics.

API documentation

class WingWeightModel

Data class for the Wing weight model.

Attributes:
dimint

Dimension of the problem, dim = 10

SwUniform

Wing area (ft^2) distribution First marginal, ot.Uniform(150, 200)

WfwUniform

Weight of fuel in the wing (lb) distribution Second marginal, ot.Uniform(220, 300)

AUniform

Aspect ratio (-) distribution Third marginal, ot.Uniform(6, 10)

LambdaUniform

Quarter chord sweep (deg), distribution Fourth marginal, ot.Uniform(-10, 10)

qUniform

Dynamic pressure at cruise (lb/ft^2) distribution Fifth marginal, ot.Uniform(16, 45 )

lUniform

Taper ratio (-) distribution Sixth marginal, ot.Uniform(0.5, 1)

tcUniform

Airfoil thickness to chord ratio (-) distribution Seventh marginal, ot.Uniform(0.08, 0.18)

NzUniform

Ultimate load factor (-) distribution Eighth marginal, ot.Uniform(2.5, 6)

WdgUniform

Flight design gross weight (lb) distribution Nineth marginal, ot.Uniform(1700, 2500)

WpUniform

Paint weight (lb/ft^2) distribution Tenth marginal, ot.Uniform(0.025, 0.08)

inputDistributionJointDistribution

The joint distribution of the input parameters.

modelPythonFunction

The Wing weight model with Sw, Wfw, A, Lambda, q, l, tc, Nz, Wdg and Wp as variables.

Examples

>>> from openturns.usecases import wingweight_function
>>> # Load the Wing weight model
>>> ww = wingweight_function.WingWeightModel()

Examples based on this use case

Example of sensitivity analyses on the wing weight model

Example of sensitivity analyses on the wing weight model