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.

Examples

>>> from openturns.usecases import wingweight_function
>>> # Load the Wing weight model
>>> ww = wingweight_function.WingWeightModel()
Attributes:
dimThe dimension of the problem

dim = 10

SwWing area (ft^2), Uniform distribution

First marginal, ot.Uniform(150, 200)

WfwWeight of fuel in the wing (lb), Uniform distribution

Second marginal, ot.Uniform(220, 300)

AAspect ratio (-), Uniform distribution

Third marginal, ot.Uniform(6, 10)

LambdaQuarter chord sweep (deg), Uniform distribution

Fourth marginal, ot.Uniform(-10, 10)

qDynamic pressure at cruise (lb/ft^2), Uniform distribution

Fifth marginal, ot.Uniform(16, 45 )

lTaper ratio (-), Uniform distribution

Sixth marginal, ot.Uniform(0.5, 1)

tcAirfoil thickness to chord ratio (-), Uniform distribution

Seventh marginal, ot.Uniform(0.08, 0.18)

NzUltimate load factor (-), Uniform distribution

Eighth marginal, ot.Uniform(2.5, 6)

WdgFlight design gross weight (lb), Uniform distribution

Nineth marginal, ot.Uniform(1700, 2500)

WpPaint weight (lb/ft^2), Uniform distribution

Tenth marginal, ot.Uniform(0.025, 0.08)

distributionXJointDistribution

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 based on this use case

Example of sensitivity analyses on the wing weight model

Example of sensitivity analyses on the wing weight model