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](../_images/wingweight.png)
The function is defined as follows:
with:
, the wing area (ft^2)
, the weight of fuel in the wing (lb)
, the aspect ratio (-)
, the quarter-chord sweep angle (deg)
, the dynamic pressure at cruise (lb/ft^2)
, the taper ratio (-)
, the airfoil thickness to chord ratio (-)
, the ultimate load factor (-)
, the flight design gross weight (lb)
, 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)
- distributionX
JointDistribution
The joint distribution of the input parameters.
- model
PythonFunction
The Wing weight model with Sw, Wfw, A, Lambda, q, l, tc, Nz, Wdg and Wp as variables.
Examples based on this use case¶
![](../_images/sphx_glr_plot_sensitivity_wingweight_thumb.png)
Example of sensitivity analyses on the wing weight model