Data-informed lifting line theory

Abstract

We present a data-driven framework that extends the predictive capability of classical lifting-line theory (LLT) to a wider aerodynamic regime by incorporating higher-fidelity aerodynamic data from panel method simulations. A neural network architecture with a convolutional layer followed by fully connected layers is developed, comprising two parallel subnetworks to separately process spanwise collocation points and global geometric/aerodynamic inputs such as angle of attack, chord, twist, airfoil distribution, and sweep. Among several configurations tested, this architecture is most effective in learning corrections to LLT outputs. The trained model captures higher-order three-dimensional effects in spanwise lift and drag distributions in regimes where LLT is inaccurate, such as low aspect ratios and high sweep, and generalizes well to wing configurations outside both the LLT regime and the training data range. The method retains LLT's computational efficiency, enabling integration into aerodynamic optimization loops and early-stage aircraft design studies. This approach offers a practical path for embedding high-fidelity corrections into low-order methods and may be extended to other aerodynamic prediction tasks, such as propeller performance.

Figures (6)

• Figure 1: Neural network architecture: two parallel subnetworks (collocation; wing and flow) combine after optional convolution/dense layers to output spanwise lift, spanwise drag, and totals.
• Figure 2: Training (a,c) and validation (b,d) loss histories for four architectures under black-box and grey-box formulations with an initial learning rate of 0.001.
• Figure 3: Spanwise lift coefficient $c_l(y)$ distributions for different wing and flow configurations labeled on each panel.
• Figure 4: Spanwise induced-drag coefficient $c_d(y)$ distributions for different wing and flow configurations labeled on each panel.
• Figure 5: Lift-curve slope, normalized by AR$(1+\lambda)/2=b/c_{\text{root}}$=100, versus 1/AR with sweep, twist, and taper-ratio ($\lambda$) values within the training-data range. Gray shading marks OOD region (AR(1+$\lambda$)/2<4 or $b/c_{\text{root}}<4$).