Industry: Aerospace
Product: ModelRisk
Application: Aerodynamic Testing

ModelRisk Revolutionizes Aerodynamic Testing by Quantifying Uncertainty in Wind Tunnel Experiments

A single cruise drag number hid a ±8% spread

A leading aerospace manufacturer developing a next-generation commercial jet had been reporting cruise drag as a single number: a drag coefficient \(C_D\) of about 0.0245. That number drove the fuel-burn guarantee, the range calculation, and the wing sign-off. But wind tunnel measurements and CFD predictions both carry uncertainty — measurement error, Reynolds scaling, environmental drift, turbulence-model choice — and a point estimate quietly discards all of it.

When the engineering team rebuilt the same cruise condition as a Monte Carlo model in Vose Software's ModelRisk and ran 20,000 trials, the mean cruise \(C_D\) came in at 0.0246, but the 90% credible interval spanned [0.0226, 0.0266] — roughly an ±8% band the single number had hidden entirely. The chart below is the result the program had been flying blind to.

For the cruise condition shown above, the mean cruise drag coefficient is 0.0246 with a 90% credible interval of [0.0226, 0.0266] — roughly the ±8% spread that traditional point estimates would have hidden.

Quantifying Uncertainty in Wind Tunnel Testing

Wind tunnel testing is a cornerstone of aerodynamic analysis, providing critical data on lift, drag, and moment coefficients under controlled conditions. However, the results are influenced by several sources of uncertainty, including:

1. Measurement errors. Instrumentation used to measure forces and pressures in the wind tunnel has inherent inaccuracies — load cells and pressure transducers each have calibration tolerances that propagate into the data.
2. Reynolds number effects. Wind tunnel tests are typically run at lower Reynolds numbers than full-scale flight, so scaling corrections must be applied — and those corrections are themselves uncertain.
3. Environmental variability. Temperature, humidity, and air density drift during a test campaign and bias the measured coefficients.

The team used ModelRisk to build a probabilistic model of the wind tunnel testing process. Key aerodynamic parameters, such as the lift coefficient \(C_L\) and drag coefficient \(C_D\), were modeled as random variables with probability distributions:

• Measurement errors were modeled using Normal distributions with standard deviations derived from instrument calibration data.
• Reynolds number scaling was captured using Triangular distributions based on historical correction factors.
• Environmental variability was modeled using Uniform distributions for temperature and air density within the expected range of test conditions.

The probabilistic model was then used to simulate 20,000 wind tunnel runs, generating the full distribution of possible outcomes for \(C_L\) and \(C_D\) shown above, instead of a single point estimate.

Integrating CFD Simulations with Experimental Data

While wind tunnel testing provides anchor measurements, CFD simulations are needed to explore a wider range of flight conditions and design configurations than any tunnel campaign can cover. CFD models are themselves approximate — they rely on numerical schemes and turbulence closures that carry their own uncertainty.

The team used ModelRisk to fuse CFD results with wind tunnel data, creating a hybrid model that accounted for the uncertainties in both methods:

1. Uncertainty in CFD inputs. Boundary conditions, turbulence parameters, and mesh resolution were treated as random variables. Turbulence intensity, for example, was modeled using a LogNormal distribution fitted to empirical data.
2. Discrepancy modeling. The difference between CFD predictions and wind tunnel measurements was treated as its own random variable, capturing systematic CFD bias as well as residual scatter.
3. Bayesian updating. ModelRisk's Bayesian updating combined the probabilistic CFD prior with the wind tunnel likelihood to produce a posterior distribution that reflects both information sources.

In the example above, CFD alone predicted \(C_L \approx 0.520 \pm 0.012\); the wind tunnel measured \(0.508 \pm 0.006\). The Bayesian posterior tightens to \(\mu = 0.510, \sigma = 0.005\) — narrower than either source on its own, and shifted toward the higher-precision tunnel data exactly as Bayes' rule dictates.

Sensitivity Analysis and Design Optimization

One of the key benefits of using ModelRisk was the ability to perform sensitivity analysis, identifying the factors that had the greatest impact on aerodynamic performance.

The tornado chart immediately makes the priorities visible: drag load-cell calibration dominates the \(C_D\) uncertainty budget, followed by turbulence-intensity assumptions in CFD. Reynolds scaling — the focus of much classical attention — only ranks third. This insight redirected investment toward recalibrating force balances and refining the turbulence closure, where each dollar bought the most uncertainty reduction.

The probabilistic aerodynamic model was then used to optimize the wing design. The team simulated three candidate wings — a baseline, a higher-aspect-ratio variant, and a raked-tip variant — and used ModelRisk to evaluate the probability of meeting the cruise lift-to-drag target \(L/D \geq 18.5\).

The deterministic comparison would have ranked Wing B (higher AR) on top because of its higher mean L/D. The probabilistic view tells a more nuanced story: Wing B has the highest mean, but Wing C (raked tip) has the highest probability of meeting the target because its predicted L/D is much tighter. For a certification-driven program where the relevant question is "what is the probability that the airplane meets spec?", Wing C is the better bet.

Communicating Results to Stakeholders

A critical aspect of the project was communicating the results of the probabilistic analysis to non-technical stakeholders, including executives and regulatory authorities. ModelRisk's visualization tools played a key role:

• Histograms and cumulative distribution functions (CDFs) showed the range of possible values for \(C_L\) and \(C_D\).
• Tornado charts highlighted the factors that contributed most to uncertainty, helping stakeholders understand the key drivers of risk.
• Scenario analysis explored the impact of different design choices and testing conditions on aerodynamic performance.

These visualizations helped build confidence in the probabilistic approach and facilitated more informed decision-making.

Impact and Lessons Learned

The adoption of ModelRisk transformed the company's approach to aerodynamic testing:

1. Better decisions. Quantifying uncertainty reduced overengineering and ensured performance targets were met with a stated confidence.
2. Cost savings. Sensitivity analysis directed test and modeling spend toward the few inputs that actually moved the needle.
3. Better collaboration. A common probabilistic framework gave experimentalists and CFD engineers a single language for combining their results.
4. Regulatory compliance. The probabilistic model provided a rigorous basis for demonstrating compliance with stability and safety requirements across the full operating envelope.

Key lessons:

• High-quality calibration data is essential to define the input distributions accurately.
• Sensitivity analysis is what turns Monte Carlo from a "nice picture" into actionable engineering decisions.
• Clear, visual communication is what gets probabilistic results trusted and adopted.

ModelRisk Functionality Used

• Monte Carlo simulation to propagate uncertainty through wind tunnel testing and CFD predictions.
• Distribution fitting for measurement errors, Reynolds number effects, and CFD inputs.
• Bayesian updating to combine experimental and computational data.
• Sensitivity analysis to identify key drivers of aerodynamic uncertainty.
• Scenario analysis to evaluate the impact of design choices and testing conditions.
• Visualization tools to communicate results effectively to stakeholders.

By leveraging ModelRisk, the aerospace manufacturer revolutionized its aerodynamic testing process, delivering a next-generation aircraft that met performance targets with confidence while minimizing development costs and risk.