Greek symbol

α _b

fuselage angle-of-attack in °

_θ

aircraft pitch angle in °

3.1 Conventional uniform Pratt model

In order to generate the distributed velocity field, a single time invariant signal is generated based on regulation specifications^{( 6 , 7 )}. The discrete gust is derived using

(1) $$U_{{{\rm dg}}} (x_{d} ){\equals}U_{{{\rm do}}} {\times}f_{x} (x_{d} ,H_{x} ){\equals}U_{{{\rm do}}} {\times}{1 \over 2}\left( {1{\minus}\cos {{\pi x_{d} } \over {H_{x} }}} \right)$$

where U _dg(xd) is the resulting disturbance velocity, U _do is the discrete gust reference or design velocity obtained using

(2) $$U_{{{\rm do}}} {\equals}U_{{{\rm ref}}} .F_{g} .\left( {{{H_{x} } \over {107}}} \right)^{{1/6}} $$

where U _do is the design gust velocity, U _ref is the reference gust velocity, specified as a function of altitude. F _g is the flight profile alleviation factor which serves as a correction to U _ref as a function of altitude. The expression for F _g is given in CS-25.341(a)(6)^{( 6 )}. H _x is the gust gradient, or half gust length, and x _d is the node position along the Earth longitudinal axis. A sufficient number of gust gradients ranging from 9 m to 107 m (30–350 ft)^{( 6 )} must be used. In the case of high mean geometric chord, specifications recommend to push the maximum gust gradient to an empirical 12.5 times the mean aerodynamic chord in order to capture the complete loads envelope. It is also recommended to push the range of gust gradients until maximum IQ values are reached and assess if these can be found within reasonable margins of the certification limiting gust lengths.

3.2 Multidimensional non-uniform model

In order to model a spanwise non-uniform loading, Eq. (1) was modified based on the principle of atmospheric isotropy⁽ Reference Houbolt ^{4 ,} Reference Hoblit ^{5 )}, which states that any assumptions made on gust chordwise definition are applicable to all spatial directions and independent of aircraft heading. This can be argued on larger scales, especially in the vertical direction as altitude plays a greater role in atmospheric property changes as latitude and longitude. Nonetheless, the lateral (spanwise) and longitudinal (chordwise) parameters are therefore treated equally. Therefore, a spanwise distribution function f _y mimicking f _x is coupled into the model such that Eq. (1) becomes

(3) $$U_{{{\rm dg}}} (x_{d} ,y_{d} ){\equals}U_{{{\rm do}}} .f_{x} (x_{d} ,H_{x} ).f_{y} (y_{d} ,H_{y} )$$

where x _d and y _d are now, respectively, the longitudinal and lateral co-ordinates of the aircraft in the earth reference frame, H _x and H _y are the gust gradient in both directions, assumed independent from one another and to follow the certification gust length recommendations ranging from 9 m to 107 m or 12.5 times the mean aerodynamic chord. Note that, like f _x , f _y is not a time dependant function: time dependency is introduced by the motion of the aircraft through the gust. Two different spanwise distribution functions f _y are illustrated in Fig. 3(a) and (b).

Figure 3 Illustrative f _y function examples of spanwise non-uniform gusts.

Different options can be used to scale the maximum gust intensity U _do: the conventional or single-gradient method, based only on the chordwise gust gradient H _x as given in Eq. (2), and an isotropic or multi-gradient method using the largest of H _x and H _y gradients, formulated in Eq. (4). Both will be investigated and compared in respective results section:

(4) $$U_{{{\rm do}}} {\equals}\left \{ {\matrix{ {\;\;U_{{{\rm ref}}} .F_{g} .\left( {{{H_{x} } \over {107}}} \right)^{{1\,/\,6}} } & {{\rm if}\;\;\;H_{x} \geq H_{y} } \hfill \cr {\;\;U_{{{\rm ref}}} .F_{g} .\left( {{{H_{y} } \over {107}}} \right)^{{1\,/\,6}} } & {{\rm if}\;\;\;107\geq H_{y} \geq H_{x} } \hfill \cr {\;\;U_{{{\rm ref}}} .F_{g} .\left( {{{107} \over {107}}} \right)^{{1\,/\,6}} } & {{\rm if}\;\;\;H_{y} \geq 107} \hfill \cr } } \right.$$

Additionally, it is possible to rotate the gust lateral and longitudinal axes around the vertical axes if an asymmetric penetration is desired. Independent offsets in both directions are also possible for gust placement relative to the aircraft by simply adding an additional phase term. Gust direction can be set to either vertical, lateral, longitudinal, a combination of any and normalised round-the-clock combinations. By selecting carefully the distribution functions f _x and f _y , total velocity direction can be set to vary locally if desired. In this study, only a head on vertical gust is investigated.

4.1 Aircraft model details

The aircraft that was selected for this specific study is the Cranfield University AX-1, which is effectively a close derivative from the Airbus eXperimental Research Forum model XRF-1 also found in other literature pieces⁽ Reference Timme, Badcock and Da Ronch ^{52 ,} Reference Kroll, Abu-Zurayk, Dimitrov, Franz, Führer, Gerhold, Görtz, Heinrich, Ilic, Jepsen, Jägersküpper, Kruse, Krumbein, Langer, Liu, Liepelt, Reimer, Ritter, Schwöppe, Scherer, Spiering, Thormann, Togiti, Vollmer and Wendisch ^{53 )}. Generic details of the aircraft geometry can be found in Fig. 4. Additionally, Fig. 5 illustrates the aircraft’s beam model, with specific mass, structural node and aerodynamic station distribution. Stiffness parameters of the wing structure are also slightly different so as to emphasise the aeroservoelastic effects within the framework. With a wingspan of 29 m, the aircraft wingtip elastic deformation in cruise flight and gust encounter are approximately 2.4 m and 3.1 m above the aircraft jig shape. This effectively keeps deflection below the 10% of wingspan mark in cruise and slightly over during gust events, which is generally accepted as the limit of linear structural behaviour.

Figure 4 Cranfield University AX-1 large long range aircraft.

Figure 5 Discretised model.

4.2 Test conditions

Open-loop simulations, as prescribed by certification requirements, will be presented here for a single aircraft configuration at two specific mass cases given in Table 1. In the first case, the aircraft is loaded to near maximum take-off weight (MTOW) in a heavy take off configuration where the CoG position lies within the static margin (SM) of the aircraft at 22% of the mean aerodynamic chord. The second case considers the aircraft loaded near the maximum zero fuel weight (MZFW) with a similar static margin (19%) so as to model a heavily loaded landing scenario. This ensures that both scenarios are realistic and that the aircraft naturally converges back to a stable state after the gust encounter in the open loop simulations. In other words, the pilot or flight control system is assumed not to compensate for any attitude or motion changes, which could lead to drastically different results in structural loading. Multiple flight conditions (FCs) were selected. Details are given in Fig. 6 and Table 2. Flight points are all located along the design cruise speed envelope for the lower altitude spectrum where dynamic pressures are higher. It also suits the aerodynamic limitations of the framework linked to the modified strip theory and the lack of transonic aerodynamic modelling⁽ Reference Andrews ^{44 ,} Reference Lone ^{50 )}. Selected FCs and aircraft loading are also aimed at reproducing isolated worst case gust encounters at normal operating conditions during the ascent and descent phases.

Figure 6 AX-1 Operating flight envelope and selected flight conditions.

Table 1 Aircraft loading details

Table 2 Flight conditions details for the selected conditions

Lastly, the spanwise distribution function selected for this study follows Eq. (5). Gust total velocity is given by Eq. (6) as a function of both lateral and longitudinal co-ordinates of the interest point. This specific distribution allows for a symmetric loading regardless of the gust gradient. Furthermore, it leads to opposite velocity directions between wingtip and root (see Fig. 7(b)) for the lower end of the H _y spectrum. The higher end of the H _y spectrum converges to a shape similar to that of the uniform 1-cos conventional model (Fig. 7(a)–(d)), justifying a comparison between the two models. Furthermore, the angle-of-attack due to the gust at the fuselage is kept similar regardless of the spanwise gust gradient. On the other hand, changes in gust distribution and subsequent aircraft responses lead to differences in vertical acceleration, pitch and plunging motions during and after the encounter

(5) $$f_{y} (y_{d} ,H_{y} ){\equals}\cos \left( {{{\pi .y_{d} } \over {H_{y} }}} \right)$$

(6) $$U_{{{\rm dg}}} (x_{d} ,y_{d} ){\equals}U_{{{\rm do}}} .f_{x} (x_{d} ,H_{x} ).f_{y} (y_{d} ,H_{y} )$$

(7) $${\equals}U_{{{\rm do}}} .{1 \over 2}.\left( {1{\minus}\cos {{\pi .x_{d} } \over {H_{x} }}} \right).\cos \left( {{{\pi .y_{d} } \over {H_{y} }}} \right)$$

Figure 7 Effect of H _y on the discrete gust shape for a given f _y distribution.

Only vertical velocity gust encounters are discussed in this paper. Both longitudinal (chordwise) and lateral (spanwise) vertical gust gradients, H _x and H _y respectively, are varied between identical limits ranging from 9 m to 180 m. The range of gust gradients was increased from 107 m in an attempt to reach an eventual IQ maxima with gust gradient. In the case of the uniform model, the model neglects the H _y value and applies a spanwise uniform loading. Both upward and downward gust cases are compared so as to capture the vertical worst case scenario. In order to capture spanwise variation effects whist keeping a relatively low number of simulations, a non-linear distribution of 16 H _y values was selected. Smaller intervals at the lower end of the H _y gust gradients were used so as to capture the effect of local vertical velocity direction changes. A linear distribution of 15 H _x values is used, similar to conventional recommendations.

4.3 Loads simulation process

A loads loop process was set-up following the logical diagram given in Fig. 8. The use of a spanwise distribution with different gust gradients adds an extra loop to the process, increasing the required amount of simulations proportionally to the number of gust gradients H _y , spanwise distribution function and possible local gust direction combinations. With a set of 16 H _y gradients (as shown in Fig. 8), process computational time rises by an order of magnitude, regardless of eventual simulation parallelisation when compared with the conventional uniform approach.

Figure 8 Gust loads loop process diagram.

At the end of each simulation, IQ data are saved. The worst case maximum and minimum loading of specific IQs of each simulation is identified and stored for a batch comparison of results.

5.1 Impact of H _y on aircraft maximum loading

Ultimately, the metrics used to size the structural limits of the aircraft are the maximum loading quantities encountered during the various gust cases throughout the flight envelope. To efficiently compare the entire simulation batch (which usually involves millions of test cases in industry), the maximum or minimum wing root (WR) load P _^WR is identified in each of the open loop simulation case, regardless of the time at which it occurs. Additionally, the following normalisation metric is defined:

(8) $$\Delta P^{{{\rm WR}}} (H_{x} ,H_{y} ){\equals}{{\left( {P_{{{\rm ori}}}^{{{\rm WR}}} (H_{x} ){\minus}P_{{{\rm nu}}}^{{{\rm WR}}} (H_{x} ,H_{y} )} \right)} \over {P_{{{\rm ori}}}^{{{\rm WR}}} (H_{x} )}}$$

where $$P^{{{\rm WR}}} (H_{x} ,H_{y} )$$ is the maximum wing root IQ obtained at gust gradients H _x and H _y . $$P_{{{\rm ori}}}^{{{\rm WR}}} $$ refers to results obtained using the conventional model, whereas $$P_{{{\rm nu}}}^{{{\rm WR}}} $$ refers to results obtained with the non-uniform model. $$\Delta P^{{{\rm WR}}} (H_{x} ,H_{y} )$$ is, therefore, the normalised difference between both methods against the original local maximal load value $$P_{{{\rm ori}}}^{{{\rm WR}}} $$ . Values should, therefore, range between 1 at maximum difference and 0 when both models are equivalent. The value falls below 0 when the non-uniform model leads to a more extreme local loading. Similarly, the normalised difference against the global maximal load value can be defined as

(9) $$\Delta \tilde{P}^{{{\rm WR}}} (H_{x} ,H_{y} ){\equals}{{\left( {P_{{{\rm ori}}}^{{{\rm WR}}} (H_{x} ){\minus}P_{{{\rm nu}}}^{{{\rm WR}}} (H_{x} ,H_{y} )} \right)} \over {{\rm max}(P_{{{\rm ori}}}^{{{\rm WR}}} (H_{x} ))}}$$

where $${\rm max}(P_{{{\rm ori}}}^{{{\rm WR}}} (H_{x} ))$$ is the overall maximum load obtained from the original model for the entire spectrum of chordwise gradients. Therefore, $$\Delta \tilde{P}^{{{\rm WR}}} (H_{x} ,H_{y} )$$ is the normalised difference between any data point of the non-uniform model and the overall maximum loading obtained with the conventional model. Both of the above metrics can be used for different objectives: the first indicates which model leads to higher loads for a given set of gradients whilst the latter compares against the global maximum for the entire set of gradients used in the process. Hence, $$\Delta \tilde{P}^{{{\rm WR}}} (H_{x} ,H_{y} )$$ can be used for the critical gust load case identification and comparison whilst $$\Delta P^{{{\rm WR}}} (H_{x} ,H_{y} )$$ will be used in the direct comparison of models, fatigue and life cycle analysis.

Wing root loading IQ and normalised differences can be presented in the form of surface plots, as illustrated in Fig. 9(a) and (b). Minimum and maximum wing root bending moment are displayed for both models as a function of both gust gradients in Fig. 9(a). Structural loads are given in offset percentage relative to trim values. Results are given for the bidirectional gust loads batch for a given flight condition and loading. The non-uniform model leads to lower wing root bending moment and, therefore, lies below the boundaries defined by the conventional model (transparent grid). $$1{\minus}\Delta P_{{{\rm local}}}^{{{\rm WR}}} $$ quantities are given in Fig. 9(b). Both the normalised difference and wing root bending map clearly show that the non-uniform model leads to lower loads prediction. This is true for all aircraft loading and flight conditions included in this study. With increasing H _y gradients, the non-uniform model converges to the conventional uniform model, as expected from gust velocity trends with gradients presented in Section 3. Furthermore, as H _x increases, maximum or minimum loading shifts to the aircraft recovery phase (pitch and heave motion), and no longer takes place during the gust encounter. Despite increasing H _x past the recommended 107 m limit, no maximum loading peak with H _x was found. Higher loading was achieved during low-altitude gust encounters. Overall, the critical scenario was identified at the sea-level flight with the less fuel, the remaining of which being stored in the fuselage (FC 1 LC 2 set-up).

Figure 9 Gust loads envelope for WR BM and model normalised difference (FC 5 LC 1 set-up).

As the normalised difference illustrated in Fig. 9(b) lies well between 0 and 1 for the entire spectrum of gust gradients, it could be concluded that the addition of the spanwise variation function has not introduced disruptive modifications to structural loading maximum or minimum values when compared to the conventional model. In fact, in the region of lower gust gradients in the (H _x ,H _y ) plane, the difference between the two models is significant, which could highlight potential over-engineering or conservative practices. But as only gust induced fuselage angle-of-attack were kept identical between conventional and non-uniform model for similar gust gradients (not vertical acceleration), it can be argued that both models do not effectively lead to an equivalent worst case gust. As models were in part historically derived from vertical acceleration measurements, it would be more relevant to compare structural loads induced by gusts of similar load factors n _g .

By examining the contours of both vertical acceleration n _g and any structural wing root IQ, a number of equivalent conventional gusts can be found for any non-uniform gust encounter. The example of wing root bending moment is given in Fig. 10, where both maximum of wing root bending moment and n _g values reached during the bidirectional loads process are given for a specific flight case. With the conventional model equivalent to the higher H _y gradients given in the far right of the contour plot, an infinite number of equivalent non-uniform gusts can be found to reach similar wing root loading when following the maximum WR BM contour (Fig. 10).

Figure 10 Wing root BM and fuselage n _g maximum contours for various gust gradients (FC 5 LC 1 set-up).

On the other hand, these do not lead to equivalent vertical load n _g for the entire path. Therefore, comparable gust measurements based on n _g do not lead to similar loadings with the non-uniform gusts. By overlaying both metrics, specific (H _x ,H _y ) couples can be found where equivalent wing root loading is obtained for similar maximum n _g as shown in the plot (orange dot). It is also possible to find equivalent points between the conventional model and the non-uniform model (red dot). Hence, it is possible to induce similar maximum wing root loading and n _g with different gust velocity fields (but the same maximum angle-of-attack due to gust at the fuselage) when investigating a single structural IQ such as bending moment in this example. Furthermore, the effect of H _y on wing root loading for a constant n _g varies with the specified value of n _g and considered chordwise gradient. In the (H _x ,H _y ) plane area where $$H_{x} \leq 100$$ and $$H_{y} \leq 100$$ and for a given n _g , reducing H _y leads to an initial reduction in structural load before increasing back as H _x increases to following the iso n _g line. In other parts of the (H _x ,H _y ) plane, including the H _y gradient to match vertical load can lead to higher wing root loading maximum, specifically for high H _x gradients (above certification recommendations of 107 m). Similar trends were identified for all flight and loading cases. The impact of aircraft loading on the airframe bending moment loading and vertical accelerations are given in Fig. 11(a) and (b). A significant loading difference is noticed in the LC 2 (as expected for a heavy landing configuration) for all gust gradient co-ordinates. Smaller changes to the load factor n _g are also registered. Otherwise, the overall trend of the contour is very similar, leading to similar conclusions in all loading and flight conditions.

Figure 11 Fuselage n _g and WR BM maximum contours comparison for two loading cases (FC 5 set-up).

This could mean that conventional loads practices lead to lower maximum critical loads by assuming uniform models, as a non-uniform model leads to worse loads in specific gust specifications. The extension of the uniform model with spanwise variation introduced new worst case scenarios for wing root bending moment for gusts with matching maximum load factor n _g measurements. Despite being minor overshoot when confined to the 107 m certification gradient limitation, this could potentially lead to uniform models becoming unsuitable for worst case loading identification and loads alleviation investigations. This has also only been verified for the aircraft configuration presented herein and could potentially be different for a design employing HARW or any other disruptive design.

5.2 Impact of H _y on aircraft time-correlated gust loads

Extreme loading is not the only concern when investigating structural loads and flight dynamics as a result of discrete gust encounters. Given the scope of this study, it is also relevant to investigate the effect of the additional gradient H _y on loads time histories throughout the entire gust encounter and recovery scenario. Therefore, time histories were used to compare all different H _y gust gradient results for given H _x , direction and FC sets. An illustrative comparison of H _y gradients impact on loads for a given H _x =82 m upward vertical gust (purple line in Fig. 10) is used in this section. Wing root bending moment (Fig. 12(a)), torsion moment (Fig. 12(b)), vertical load factor n _g (Fig. 12(d)) and pitch angle θ (Fig. 12(c)) are monitored throughout the entire simulation.

Figure 12 Effect of H _y for H _x =82 m on wing root and fuselage IQs (FC 5 LC 1 upward gust set-up).

Gust-induced loading (initial peak) as well as the loading due to aircraft’s inherent restoring motion (secondary peak and onward) is clearly visible in the loading history given in Fig. 12. In this example, the pitch-induced loading (secondary peak) clearly defines the minimum loading for torsion, bending moment and shear force. In the symmetric downward gust scenario, it defines the maximum loading values. With increasing values of H _x , the amplitude of pitch and heave induced loading overtakes the initial peak. Therefore, when analysing both upward and downward gusts together at a given flight condition, extreme loads can occur during the aircraft pitch and heave oscillation after and not during the gust encounter for the higher end of H _x . This is confirmed by the break in surface gradient in Fig. 9(a). The value of H _x at which pitch induced loading overtakes the gust induced loading differs among IQs, flight and loading cases. In these conditions, the limit has been identified at $$H_{x} {\gtrsim}90\,{\rm m}$$ for root bending and $$H_{x} {\gtrsim}80\,{\rm m}$$ for root torsion moment. This does not apply to the lower H _y spectrum, where despite pitch and vertical accelerations peaks, structural loads do not follow the conventional oscillation trend, and is clearly visible in the above-mentioned envelope plots (Fig. 9(a) and (b)).

Note that H _y gradients below wing semi-span lead to gust induced loading of opposite direction as velocity direction flips along the wingspan. This means that a conventional uniform gust with matching initial acceleration maxima would be of opposite direction, despite both models matching fuselage gust angle-of-attack values in the present settings. Hence, structural loading time histories, similar to maximum loading, differ drastically with changing H _y . Furthermore, oscillations for both root torsion and bending moments appear at approximately 2.4 Hz after the gust encounter. This frequency matches that of the second wing bending mode of the aircraft which is not as severely excited by the uniform model.

For values similar to aircraft semi-span (27.4 m in this example), the wing root bending and torsion moments are only slightly modified during the gust encounter (seen in Fig. 12(a) and (b)) despite having significant n _g and pitch motion induced by the gust (seen in Fig. 12(c) and (d)). As H _y increases to the higher end of the spectrum, all quantities converge to the conventional trend. Maximum loading and worst case gusts occur with the conventional model for all H _x gradients, gust directions, aircraft loading and flight conditions included in this simulation set. This is verified for the given f _y intensity distribution and was expected because the overall gust velocity integral during the encounter is lower in the non-uniform model.

With the apparition of lags and time delays with H _y in both wing root bending and torsion moments, it must be verified that the non-uniform model does not introduce radically different torsion/bending paths to the conventional model. In other words, no radical phase delay is introduced. An example of the widely used bending/torsion correlated plot, or Convex Hull plot is given in Fig. 13. Once again, the effect of H _y on maximal loads amplitude is clear, where loads due to larger H _y gradients clearly exceed those obtained with the lower end of the spectrum. The high collinearity of the linear structural model is highlighted in the diagram, torsion and bending values being highly linked in the gust encounter scenario due to the aircraft structural model properties. Despite being negligible on the overall maximum loading, a small deviation from the quasi-linear correlation is induced for H _y between 15 m and 27 m during the first seconds of the encounter, highlighting the impact of the difference in second wing bending moment excitation. When comparing all gust gradient combinations, gust directions, flight conditions and aircraft loading cases, H _y does not lead to any other significant changes in coupled bending/torsion envelopes, and, therefore, does not introduce more major phase delays between the two quantities.

Figure 13 Effect of H _y for H _x =82 m on correlated bending/torsion moment path (FC 5 LC 1 upward gust set-up).

Overall, the addition of the spanwise variation function has introduced major trend modifications to structural loading time histories for low H _y values. Small phase shifts as well as oscillations linked to wing flexibility have been encountered in specific cases. Lower gust gradients have also led to inverted peak magnitudes. But maximum loading amplitude is clearly still defined by the uniform model for all loading and flight dynamic IQs. Maximum bending and torsion moment path contour have also seen very little modifications. Therefore, when comparing similar H _x gust gradients, the uniform model still appears as the most critical. Despite this, it would be relevant to compare the time histories of matching n _g similar to what was done before and investigate the implications of the non-uniform loading on the time histories, and is included in further development plans of the process.

5.3 Non-uniform discrete models and loads alleviation

Active loads alleviation systems ideally require predictive actuation for best efficiency. Ideally, predictive local angle-of-attack measurements would greatly improve loads alleviation strategies. Actuation systems require predictive measurements to be efficient, as actuation is not instantaneous.

But currently, loads alleviation relies on angle-of-attack measured at the nose of the aircraft as well as the load factor n _g measured from the fuselage and conventional systems such as spoilers or ailerons are distributed along the wings to ensure efficient off-load. The wing lag in penetrating the gust compared to the nose helps in pre-emptive surface actuation. If wing-tip systems or outboard ailerons are used, their physical positioning implies that the effective disturbance could be drastically different to that measured at the nose of the aircraft. This is particularly true for low H _y gradients. Outer wing gust velocities being of opposite signs to that of the fuselage for the lower H _y gradients system deployment could potentially be detrimental or dangerous if loads alleviation is achieved by effective angle-of-attack modifications such as ailerons.

In this section, the authors have investigated a possibility to consider both n _g and α _b as a correlated pair, to differentiate gusts of various H _y , which would in turn require different off-load control strategies. This could ideally be possible once a better understanding of the relation between α _b and n _g for a uniform and non-uniform model is achieved (through the analysis of a sufficiently large database of spanwise distribution functions). Corrected loads alleviation strategies could then be developed to account for non-uniform gusts.

Hence, the effect of H _y on the coupled metrics is analysed. A coupled α _b (n _g ) path, or phase plot, is given Fig. 14(a), next to the WR BM(n _g ) path given in Fig. 14(b). α _b accounts for pitch and gust-induced modifications, corresponding to on-board instrument measurements. Changes in H _y clearly leads to variations in the α _b (n _g ) path, shifting n _g to the opposite sign as H _y decreases. The amplitude and trend of α _b is also modified with pitching and vertical heave motion transferred to the aircraft. Therefore, a difference in gust shape can be identified solely based on coupled measurements of α _b and n _g quite quickly into the encounter (within the first 1/10th of a second). Symmetric behaviour is obtained for a downward gust. During build up to the initial α _b peak (which occurs roughly at the same time for all H _y gradients), the value of n _g values can be used to assess the dominant motion of the aircraft and therefore correct for the alleviation strategy.

Figure 14 Effect of H _y on wing root and fuselage IQ correlated paths (FC 5 LC 1 upward gust set-up).

Therefore, if perfected to recognise non-uniform loading, the loads alleviation system could respond according to best applicable strategy (loads alleviation, passenger comfort, etc.). In Fig. 14(a), one can easily see the phase shift between the angle-of-attack, reaching nearly identical maximum values, and the simultaneous load factor, for various H _y . A gradient H _y of 36 m is highlighted in cyan as an example. Using Fig. 14(a) and previous times histories and plots, it can be seen that for that gradient, wing root loading reaches $$\,\pm30\,\%\,$$ offset relative to trim, corresponding to a uniform model vertical load factor (seen from Fig. 10 of approximately 0.2 g). In the non-uniform case, the maximum vertical load factor is much higher, at 0.9 g during the first $$n_{g} $$ peak. This corresponds to a 45% BM loading in the conventional model, which could in turn lead to an excess load alleviation strategy, applied at the wrong time. If parametrised, the phase difference between the two metrics, specifically during the gust encounter, could ideally be used to improve load alleviation strategies specifically during the gust encounter with only fuselage angle-of-attack and load factor measurements. This analysis can be made in all test cases. Hence, for any given H _x gradient, gust direction, FC and LC of the tested aircraft and f _y distribution function, load alleviation during gust loads application to the aircraft could lead to drastically different performances and results depending on H _y values, specifically for the lower end of the spectrum, below wing semi-span.

All points of the aircraft, despite lags and offsets due to flexibility that can be accounted for, share common flight dynamics during manoeuvre. This can easily be seen through all time history plots, and phase plots presented above, as all metrics converge to similar trends and values with time during the restoring pitch and heave motion. Therefore, when loads are generated by aircraft pitching and flight dynamics in the gust recovery phase, centralised measurements can be used to apply spanwise distributed loads alleviation strategies similar to what is conventionally done in manoeuvre loads alleviation.

5.4 Intensity tuning method comparison

As described in the framework set-up, a new intensity tuning or scaling method was derived based on an isotropic model assumption. Both gradients are now used to define the maximum gust intensity. This naturally had some drastic effects on the gust loads. Similar to what was introduced earlier, Fig. 15(a) and (b) represents the new loading envelope encountered during the gust.

Figure 15 Gust loads envelope for WR BM and model normalised difference with multidimensional intensity scaling (FC 5 LC 1 set-up).

This new scaling approach clearly leads to more intense loading in some regions of the (H _x ,H _y ) plane, more specifically where $$H_{y} \,\gg\,H_{x} $$ . This corresponds to regions where the spanwise gust gradient is used to scale the gust intensity. It is clear from the surface plots that the non-uniform model now exceeds the uniform model for specific gust gradients. Nevertheless, a comparison based on the global normalised difference shows that maximum loading is still achieved with the uniform model when comparing all gust gradient couples.

Once again, a comparison for matching vertical load factor n _g must be made. Similar to what was obtained with the previous model, it is possible to find equivalent gusts in terms of n _g that lead to higher bending moment or torsion moment at the aircraft wing root. Furthermore, the trend of all metrics envelope has significantly changed, as shown in the contours of Fig. 16(a) and (b) which compare results of similar flight conditions and loading for the two intensity scaling methods. By overlaying both metrics, a similar analysis to that which was made in Section 5.1 can be made: greater loading can be achieved with the non-uniform model for a given n _g . In terms of time history trends (time-correlated), results are very similar between the scaling methods. Only the maximal amplitudes vary significantly.

Figure 16 Fuselage n _g and WR BM maximum contours comparison for two tuning methods (FC 5 LC 2 set-up).

It can be seen from this brief comparison of gust intensity scaling methods that an even greater difference has been introduced over a significant area of the gust gradient plane. The worst case gust scenario, in the case of a large conventional aircraft, is reached in the non-uniform model for a non-negligible area of the (H _x ,H _y ) plane when the multi-gradient tuning method is used.

Results have focused exclusively on wing root quantities in this paper. But distributed loading is also influenced by H _y . Further investigations focusing on the distributed loads along the wing, and not exclusively wing root, could also lead to interesting conclusions regarding H _y impact on design loads.