# Setting of Wing Target Loads

Name | Affiliation | Phone Number | Email Address |
---|---|---|---|

Anthony Hutton | Airbus UK | Anthony.Hutton@airbus.com | |

Simon Coggon | Airbus UK |

Aeronautics

The aircraft design process proceeds through a series of maturity/decision gates. At the early stages of this process the design parameters are very fluid and uncertain and are progressively tightened and addressed in ever increasing detail as the design is converged by means of exploring various trades, options & interactions. Figure -1 summarises this process as deployed in AirbusAt maturity gate (MG)5 – ‘Freeze of Concept’ the global parameters of the design (i.e. shape & structural layout) are converged. The concept is now validated and frozen. At his stage the aircraft (a/c)’ target’ loads are set. Design loads are the limiting loads that an a/c (or a/c component) must be designed to withstand. A target for these are set at MG5. The objective is to anticipate the certification loads level, scale the calculated (reference) loads to match this anticipated level and issue this data as target loads. This provides a stable set of loads for use in the specific design process thus enabling a robust and compressed downstream programme whilst minimising the prospect of not meeting design requirements . Clearly it is important to limit the risk in setting these target loads. If the target loads are underestimated, as revealed following flight test, then expensive re-design is often required incurring the costs and penalties arising from programme delay. If the target loads are overestimated then the a/c will be heavier than need be at the risk of not meeting customer performance guarantees. A well-developed process for managing uncertainty in setting target loads is in place in Airbus, but the representation of uncertainty is fairly basic, relying largely on previous experience and knowledge, and statistical dependencies across uncertain parameters and functional dependencies within the process are not formally treated. The proposition explored in this use case is ‘Can formal UQ&M methods be deployed to improve and underpin confidence in setting target loads thus reducing conservatism and the weight of the a/c or component ? ‘ The analysis process by which the limit loads on and a/c or component are established is very complex and computationally demanding. A very large number of conditions across the loads envelope must be considered. For example, consider one such condition, symmetric discrete gust analysis. We need to analyse

- all relevant mass conditions (about 50)
- all relevant flight conditions (about 50)
- a range of gust gradient lengths (about 10)

This alone gives 25,000 possible load cases which could be critical at some point of the airframe, without considering up/down gust, airbrakes in / airbrakes out, high lift configurations, alternate control laws, failure etc. Add to this continuous turbulence analysis, manoeuvre analysis, longitudinal and lateral flight conditions, ground cases etc. and the number of conditions to be analysed grows very rapidly. The current use case has been designed to exercise most of the challenges of applying UQ&M to the setting of target loads whilst simplifying the range of conditions to be considered, i.e. it is not entirely realistic but is sufficiently testing. The focus is the setting of aircraft-in-flight target loads and the range of aerodynamic loading scenarios to be analysed is reduced by the following simplifications [1]:

- For longitudinal / symmetric manoeuvres consider static cases only – i.e. neglect dynamic cases, and also neglect high lift cases.
- For longitudinal / symmetric gusts ignore dynamic effects and treat the gusts as equivalent manoeuvres (with linearised aerodynamics) through use of the Pratt- Walker formula (ref: A revised gust-load formula and a re-evaluation of v-g data taken on civil transport airplanes from 1933 to 1950, Kermit G. Pratt, Walter G. Walker, naca-report-1206, 1954).
- Neglect lateral manoeuvres and gusts as discussed above.

When ranges in Mach number, altitude, payload and fuel mass are brought into play, the total number of loading conditions to be considered is ~10^4. For the application of UQ&M, this range of conditions covering the design load envelope, needs to be calculated for different combinations of the uncertain design data which incurs significant computational cost.The process underlying the use case is the Aero-Loads-Stress process. Each of the aerodynamic scenarios is analysed using a combination of low and high-fidelity CFD plus wind tunnel test results. The resulting loads for a specific design configuration are used to design the associated structure required to sustain the loads (in this case by varying the wing cover thickness. The internal structural layout is held fixed). This step alters the flexibility/stiffness of the wing and consequentially also the deformation of the wing under the applied forces (e.g. twist). For steady manoeuvres, the aeroelastic loop is iterated until it onverges and the a/c is in equilibrium under the converged forces (lift and moment) and given mass distribution (see Figure 2).This process must be performed in principle for all the loading conditions (although search algorithms may assist in converging rapidly onto the extreme region of loads space) and the limit loads identified. The cover thickness is then optimised (minimal thickness) to sustain this loading resulting in a wing weight. The challenge is can we formally introduce uncertainty and propagate this across the process yielding the limit loads and associated wing mass to specified levels of confidence.

[1] Exclusion of dynamic cases is a significant simplification. If a strong and successful collaboration emerges from the SIG, data and models could be made availablefor a successor use-case which includes gusts and lateral manoeuvres

The uncertainty in the process inputs arise principally from the aerodynamic data and the details of the structural layout and material properties (the latter reflect immaturity in the design).

__Aerodynamic Data__

- Errors and variation in wind tunnel data.
- Approximations and errors from CFD code.
- Compounding uncertainties from multiple sources. Approximations and errors from combining CFD and ‘wind tunnel’ (WTT) data, including from interpolation / extrapolation issues arising from limited WTT data along span, plus interpolation between alpha and Mach points

__Structural Data__

- Variation in material properties (e.g. use of novel materials), leading to stiffness uncertainties.
- Uncertainty in the structural stiffness and mass (e.g. wing) due to two separate effects
- Deterministic link of design loads to design stiffness and weight.
- Additional uncertainties in the structural definition due to design immaturity (i.e. all the really detailed aspects that affect structural design have not yet been fully considered such as manufacturing constraints, space allocations, fatigue design, maintenance analysis etc.).

- Uncertainty in layout such as fuel tank positions, engine integration etc.

In the main, the above uncertainties are difficult to quantify precisely due to lack of knowledge. Furthermore there are interdependencies between the aerodynamic data. For example, results from a specific CFD code tend to err in the same direction for different values of Mach number and alpha, and the various output quantities, e.g. lift and moment coefficients at locations along the span, at given a Mach number and angle of incidence are derived from the same pressure distribution. It becomes important to establish statistical covariances that capture such interdependencies.

Within Airbus it will not be acceptable to introduce intrusive methods, and thus the UQ&M capability must be able to wrap around existing processes. The computational scale of the problem is indeed very daunting. The process requires searches for the maximum loads in a very high dimensional space (Mach number, altitude, load factor, etc.) at many locations on the wing. Feasibility requires a sampling approach that is remarkably efficient, homing onto the most probable limiting loads within practical computational constraints. The Airbus frontline analysis tools are not fully integrated but, for this particular use case a simple loads analysis model (QHL) is made available ( this is not a ROM surrogate built on DoE, see below). QHL enables rapid estimation of the static aeroelastic analysis for steady manoeuvres and can be used for initial prototype studies. Clearly the aerodynamic and structural analysis steps are functionally interdependent as explained in section 1 above. Thus in principle the pdfs associated with the aero data and wing stiffness must be iterated. However, in order to limit complexity and render initial studies more tractable, the uncertainties arising from wing structure and layout can be removed from consideration if needs be [2].

[2] Again, this introduces a significant simplification. If a strong and successful collaboration emerges from the SIG, a successor use case could be made available that brings into consideration uncertainties arising from wing structure and layout.

The key benefit to flow from a demonstrable UQ&M capability is improved confidence levels in the target load setting decision gates, limiting the risk of penalties incurred by either over or under design. In order to present the decision maker with clear and enabling information, the visual functionality required by this use case is fairly modest. The essentials are exemplified in Figure 3.

Real-time and effort has been invested in addressing this use case. The approaches that have been explored and the success achieved can be discussed with interested parties who wish to engage and invest in this challenge. The simplified loads analysis model deployed, GT-QHL, is constructed within Mat Lab. It allows ‘plugin’ data and UQ&M methods. The reference aircraft model underlying the analysis is based upon the NASA developed Common Research Model (CRM), an open reference aircraft for CFD and wind tunnel validation studies. The outer mold line geometry of CRM has been used to create a vehicle model for GT-QHL, including internal layout, mass model, wing internal structure, and physics data.

A revised gust-load formula and a re-evaluation of v-g data taken on civil transport airplanes from 1933 to 1950’, Kermit G. Pratt, Walter G. Walker, naca-report-1206, 1954

J.C. Vassberg, M.A. DeHaan, S.M. Rivers, and R.A. Wahls,