Machine learning for propeller design and analysis
What if you could get CFD‑level accuracy at the speed of a simple blade element model? That is the promise of combining physical propeller theories with machine learning.
Traditional low‑fidelity methods like BEMT are fast but can introduce errors greater than 10%. High‑fidelity CFD is accurate but too slow for early design stages. The solution lies in a multi‑fidelity approach: a model that learns to correct BEMT errors using just a handful of strategically chosen CFD simulations. With Gaussian processes and active learning, this metamodel delivers both speed and accuracy.
Training such models requires solid data, mathematical foundations, and experimental validation. Propeller theories—momentum, blade element, and lifting line—provide the physical backbone, though they come with limitations like convergence issues and idealized flow assumptions.
The practical impact is significant. Systematic errors often lead to a 20–30% overestimation of flight range. If your requirement is 40 km, a conventional calculation might show a comfortable margin, but real reliability could drop below 60%. To achieve 90% confidence, you would need to target 55 km from the start. Machine learning helps reduce unnecessary safety margins, saving 12–15% in power plant mass.
With tools like NeuralFoiland recent advances in physics‑informed neural networks, ML is becoming a practical partner in propeller design—not a black box, but a smart correction mechanism that engineers can trust.
Traditional low‑fidelity methods like BEMT are fast but can introduce errors greater than 10%. High‑fidelity CFD is accurate but too slow for early design stages. The solution lies in a multi‑fidelity approach: a model that learns to correct BEMT errors using just a handful of strategically chosen CFD simulations. With Gaussian processes and active learning, this metamodel delivers both speed and accuracy.
Training such models requires solid data, mathematical foundations, and experimental validation. Propeller theories—momentum, blade element, and lifting line—provide the physical backbone, though they come with limitations like convergence issues and idealized flow assumptions.
The practical impact is significant. Systematic errors often lead to a 20–30% overestimation of flight range. If your requirement is 40 km, a conventional calculation might show a comfortable margin, but real reliability could drop below 60%. To achieve 90% confidence, you would need to target 55 km from the start. Machine learning helps reduce unnecessary safety margins, saving 12–15% in power plant mass.
With tools like NeuralFoiland recent advances in physics‑informed neural networks, ML is becoming a practical partner in propeller design—not a black box, but a smart correction mechanism that engineers can trust.
First architecture of the propeller metamodel method
The core idea is surprisingly simple: instead of replacing the traditional blade element momentum theory (BEMT) with a machine learning model, we let the model learn how to correct BEMT's mistakes. The low‑fidelity BEMT calculation runs quickly across the entire design space, covering two thousand operating points. Then, we perform just fifty high‑fidelity CFD simulations at strategically chosen points. A Gaussian process learns the difference between the two, effectively building a correction map. With active learning, the model identifies where adding another high‑fidelity point would reduce uncertainty the most. The final prediction combines the fast BEMT result with the learned correction, delivering CFD‑like accuracy at BEMT speed. This hybrid approach gives you both speed and trust.
Our Blade-Element-Momentum theory code as the low-fidelity analysis method
Our BEMT implementation combines momentum theory and blade element theory in an iterative scheme. The momentum part, originally proposed by Rankine and Froude, treats the propeller as an actuator disk. The blade element part, first described by Drzewiecki, divides each blade into radial sections and treats each as a 2D airfoil.
The iteration seeks convergence between the thrust predicted by momentum theory (via induced velocities) and the thrust integrated from blade element forces. This gives me both physical rigor and geometric detail.
The features of the code are:
1) ML model Neuralfoil for aerodynamic analysis of airfoils (GitHub - peterdsharpe/NeuralFoil: NeuralFoil is a practical airfoil aerodynamics analysis tool using physics-informed machine learning, exposed to end-users in pure Python/NumPy. · GitHub)
2) Correction for the Coriolis force (stabilizing the boundary layer)
The iteration seeks convergence between the thrust predicted by momentum theory (via induced velocities) and the thrust integrated from blade element forces. This gives me both physical rigor and geometric detail.
The features of the code are:
1) ML model Neuralfoil for aerodynamic analysis of airfoils (GitHub - peterdsharpe/NeuralFoil: NeuralFoil is a practical airfoil aerodynamics analysis tool using physics-informed machine learning, exposed to end-users in pure Python/NumPy. · GitHub)
2) Correction for the Coriolis force (stabilizing the boundary layer)
he greatest source of error seems to be Neuralfoil, especially at lower Re.
BEMT Validation
I tested the code against three APC propellers (16x8, 11x7, and 20x10).
The error tends to grow with increasing pitch and reducing diameter of the prop; for thrust coefficient, power coefficient and efficiency the average errors for the three props are 15.2, 19.1, and 18.6%, respectively.
The error tends to grow with increasing pitch and reducing diameter of the prop; for thrust coefficient, power coefficient and efficiency the average errors for the three props are 15.2, 19.1, and 18.6%, respectively.
The J‑ref method for static conditions and its validation
My BEMT implementation did not work properly for zero forward speed (V = 0). To overcome this limitation, I developed what I call the J‑ref method. This approach extrapolates BEMT results to static conditions starting from a converged advance ratio (J) value, with an additional correction.
Strictly speaking, the method is theoretically unsound. Yet, surprisingly, it turned out to be remarkably accurate.
Strictly speaking, the method is theoretically unsound. Yet, surprisingly, it turned out to be remarkably accurate.
Neuralfoil validation at low Re
For airfoil aerodynamic calculations in my propeller code, I used NeuralFoil, a neural network model trained on tens of millions of XFoil simulations. The model works entirely in Python/NumPy and runs about 30 times faster than XFoil for a single point and up to 1000 times faster for batch calculations thanks to vectorization. Results typically stay within a few percent of XFoil, even for airfoils not seen during training. NeuralFoil also provides eight accuracy levels and estimates prediction reliability based on XFoil convergence probability.
One particularly valuable feature is its stability across an extremely wide range of Reynolds numbers (from 5e+03 to 2e+05) and angles of attack from 0° to 360°. This makes it ideal for small propellers, whose blade sections operate at very low Reynolds numbers and wide angle ranges.
Since NeuralFoil was originally validated only against XFoil rather than experiments, I conducted my own validation using wind tunnel data for the SD7037 airfoil from a published report. At Reynolds number 60,000, the average error for drag coefficient was 13%, with a maximum above 40% at negative angles of attack. For positive angles, the average dropped to 10%. The lift coefficient results showed a 9% average error at positive angles but increased to 136% at negative angles.
This validation revealed that NeuralFoil performs well in the positive lift region where propellers typically operate, but users should be cautious at negative angles of attack.
One particularly valuable feature is its stability across an extremely wide range of Reynolds numbers (from 5e+03 to 2e+05) and angles of attack from 0° to 360°. This makes it ideal for small propellers, whose blade sections operate at very low Reynolds numbers and wide angle ranges.
Since NeuralFoil was originally validated only against XFoil rather than experiments, I conducted my own validation using wind tunnel data for the SD7037 airfoil from a published report. At Reynolds number 60,000, the average error for drag coefficient was 13%, with a maximum above 40% at negative angles of attack. For positive angles, the average dropped to 10%. The lift coefficient results showed a 9% average error at positive angles but increased to 136% at negative angles.
This validation revealed that NeuralFoil performs well in the positive lift region where propellers typically operate, but users should be cautious at negative angles of attack.
