Modern aviation engineering constantly seeks ways to make flight more efficient, safer, and more sustainable. The multi engine propeller aircraft remains a cornerstone of regional, utility, and training aviation — combining reliability with efficiency. This article explores a multidisciplinary possibilistic approach to the design and optimization of such aircraft, focusing particularly on tail (empennage) sizing and uncertainty modeling in the conceptual stage.

Introduction: Challenges in Multi Engine Propeller Aircraft Design

Traditional civil aircraft design has focused on meeting performance goals while minimizing operating costs. Earlier engineers relied on sequential strategies — trial, error, and iterative assumptions. Without the benefit of computational tools, aircraft such as early multi engine propeller aircraft were designed through experience and semi-empirical estimations.

As aviation evolved, market demands for affordable, safe, and fuel-efficient airplanes increased. Designers began integrating numerous disciplines: aerodynamics, propulsion, structures, stability and control, avionics, and environmental performance.
Yet the early design stages still pose challenges. Simplified assumptions can cause errors in predicting aerodynamic loads or control authority — particularly critical for multi engine aircraft, where asymmetric thrust and propeller slipstream effects must be considered.

Multidisciplinary Design Optimization (MDO) in Aircraft Engineering

The Multidisciplinary Design Optimization (MDO) framework was introduced to handle complex engineering systems like multi engine propeller aircraft. Instead of optimizing each discipline separately, MDO evaluates their interactions simultaneously — improving both performance and reliability.

Classic methods such as MDF (Multidisciplinary Feasible), IDF (Individual Discipline Feasible), and AAO (All-at-Once) balance aerodynamics, stability, weight, and propulsion. However, many traditional MDO frameworks assume deterministic (fixed) data, overlooking modeling uncertainty and empirical variability.

Possibilistic Design Optimization: Handling Uncertainty

In the conceptual design stage, detailed probabilistic data is often unavailable. Instead, engineers apply possibilistic optimization — an approach based on fuzzy logic, interval modeling, and possibility theory.
This method treats uncertain parameters as intervals or fuzzy sets, defining possible but not precisely known values. For example, the lift coefficient of a tailplane in a multi engine propeller aircraft may vary due to propwash, Reynolds effects, or engine-out asymmetry. By representing these variables as ranges instead of fixed numbers, designers can guarantee stable solutions even in worst-case conditions.

When compared to Reliability-Based Design Optimization (RBDO), the Possibility-Based Design Optimization (PBDO) approach excels in situations with limited or incomplete data. It ensures feasible, robust designs while minimizing the computational cost of repeated simulations.

Methodology: Empennage Sizing for Multi Engine Propeller Aircraft

The empennage — the horizontal and vertical tail — plays a key role in stability and control. For multi engine propeller-driven aircraft, it must ensure proper trim, yaw control, and stability under one-engine-inoperative (OEI) scenarios.

The proposed framework combines aerodynamics, stability and control, propulsion effects, and weight and balance. Each discipline interacts within a coupled optimization loop. Using Sequential Quadratic Programming (SQP) integrated with a Performance Measure Approach (PMA), the algorithm evaluates design feasibility under uncertainty and adjusts constraints accordingly.

Core Design Variables

• Horizontal and vertical tail areas

• Tail moment arms (distance from CG)

• Engine placement on the wings

• Sweep angles and taper ratios of tail surfaces

Key Constraints

• Static and dynamic stability (Cmα, Cnβ, Clβ within certified ranges)

• Adequate rudder authority under asymmetric thrust

• Airworthiness standards (CS-23, MIL-F-8785C compliance)

Results: Performance of the Optimized Multi Engine Propeller Aircraft

After several iterations, the optimized empennage geometry showed excellent agreement between two optimization goals — mass minimization and drag reduction. The final design met all aerodynamic and stability criteria while remaining lightweight and robust under uncertainty.

The aerodynamic coefficients (Cmα, Cnβ, Clβ) stayed within acceptable ranges. Flight dynamic analysis confirmed stable phugoid, short-period, Dutch roll, and spiral modes. The design complied with international airworthiness standards, proving that the possibilistic multidisciplinary optimization method delivers reliable, real-world results for multi engine propeller aircraft.

Conclusion

This multidisciplinary possibilistic approach demonstrates that it is possible to size the empennage of multi engine propeller-driven light aircraft in a robust and efficient way. By explicitly modeling uncertainties from low-fidelity approximations and coupling multiple disciplines — aerodynamics, stability and control, propulsion, weight and balance — the method generates designs that are both optimized and reliable.

In the evolution of aviation, methods like this help shorten design cycles, reduce costly redesigns, and accelerate innovation in multi engine aircraft engineering. As computational power increases and uncertainty modeling improves, future aircraft can be optimized reliably even at the concept stage — minimizing risk while maximizing performance.

If you’d like to understand more about how multi-engine piston aircraft behave in general, check out:
What Is a Multi-Engine Piston Airplane?