Advisory U.S. Department of Transportation Federal Aviation Circular Administration Subject: Dynamic Gust Loads Date: 12/12/14 AC No: 25.341-1 Initiated By: ANM-115 1 PURPOSE.
This advisory circular (AC) describes acceptable means for showing compliance with the requirements of Title 14, Code of Federal Regulations (14 CFR) 25.341, Gust and turbulence loads. Section 25.341 specifies the discrete gust and continuous turbulence dynamic load conditions that apply to the airplane and engines.
2 APPLICABILITY.
2.1 T he guidance provided in this document is directed to airplane manufacturers, modifiers, foreign regulatory authorities, and Federal Aviation Administration (FAA) transport airplane type certification engineers and their designees.
2.2 The material in this AC is neither mandatory nor regulatory in nature and does not constitute a regulation. While these guidelines are not mandatory, they are derived from extensive FAA and industry experience in determining compliance with the relevant regulations. These means are issued, in the interest of standardization, for guidance purposes and to outline a method that has been found acceptable in showing compliance with the standards set forth in the rule. If, however, we become aware of circumstances that convince us that following this AC would not result in compliance with the applicable regulations, we will not be bound by the terms of this AC, and we may require additional substantiation or design changes as a basis for finding compliance.
2.3 The material in this AC does not change or create any additional regulatory requirements, nor does it authorize changes in, or permit deviations from, existing regulatory requirements.
3 RELATED REGULATIONS.
The following 14 CFR regulations are related to this AC. The full text of these regulations can be downloaded at the U.S. Government Printing Office e-CFR. You can order a paper copy by sending a request to the U.S. Superintendent of Documents,
U.S. Government Printing Office, Washington, D.C. 20402-0001; or by calling telephone number (202) 512-1800; or by sending a request by facsimile to
(202) 512-2250.
• Section 25.301, Loads.
• Section 25.303, Factor of safety.
• Section 25.305, Strength and deformation.
• Section 25.321, Flight Loads: General.
• Section 25.335, Design airspeeds.
• Section 25.343, Design fuel and oil loads.
• Section 25.345, High lift devices.
• Section 25.349, Rolling conditions.
• Section 25.371, Gyroscopic loads.
• Section 25.373, Speed control devices.
• Section 25.391, Control surface loads: General.
• Section 25.427, Unsymmetrical loads.
• Section 25 445, Auxiliary aerodynamic surfaces.
• Section 25.571, Damage-tolerance and fatigue evaluation of structure.
• Section 25.1517, Rough air speed VRA.
4 OVERVIEW.
4.1 T his AC addresses both discrete gust and continuous turbulence (or continuous gust) requirements of part 25. It provides some of the acceptable methods of modeling airplanes, airplane components, and configurations, and the validation of those modeling methods for the purpose of determining the response of the airplane to encounters with gusts.
4.2 How the various airplane modeling parameters are treated in the dynamic analysis can have a large influence on design load levels. The basic elements to be modeled in the analysis are the elastic, inertial, aerodynamic, and control system characteristics of the complete, coupled airplane. (See figure 1 of this AC.) The degree of sophistication and detail required in the modeling depends on the complexity of the airplane and its systems.
Figure 1. Basic Elements of the Gust Response Analysis Atmospheric Motion Dynamics and Structure Dynamic Loads Aerodynamic System Control System Limit Gust Loads Static Flight Loads Model Static 1g Flight Loads
4.3 Design loads for encounters with gusts are a combination of the steady, level 1g flight loads and the gust incremental loads including the dynamic response of the airplane.
The steady 1g flight loads can be realistically defined by the basic external parameters such as speed, altitude, weight, and fuel load. They can be determined using static aeroelastic methods.
4.4 The gust incremental loads result from the interaction of atmospheric turbulence and airplane rigid body and elastic motions. They may be calculated using linear analysis methods when the airplane and its flight control systems are reasonably or conservatively approximated by linear analysis models.
4.5 Nonlinear solution methods are necessary for airplane and flight control systems that are not reasonably or conservatively represented by linear analysis models. Nonlinear features generally raise the level of complexity, particularly for the continuous turbulence analysis, because they often require that the solutions be carried out in the time domain.
4.6 The modeling parameters discussed in the following sections include:
4.6.1 Design conditions and associated steady, level 1g flight conditions.
4.6.2 The discrete and continuous gust models of atmospheric turbulence.
5 DESIGN CONDITIONS.
12/12/ 14 AC 25.341-1
4.6.3 Detailed representation of the airplane system including structural dynamics, aerodynamics, and control system modeling.
4.6.4 Solution of the equations of motion and the extraction of response loads.
4.6.5 C onsiderations for nonlinear airplane systems.
4.6.6 Analytical model validation techniques.
5.1 General.
Analyses should be conducted to determine gust response loads for the airplane throughout its design envelope, where the design envelope is taken to include, for example, all appropriate combinations of airplane configuration, weight, center of gravity, payload, fuel load, thrust, speed, and altitude.
5.2 Steady, Level 1g Flight Loads.
The total design load is made up of static and dynamic load components. In calculating the static component, the airplane is assumed to be in trimmed steady, level flight, either as the initial condition for the discrete gust evaluation or as the mean flight condition for the continuous turbulence evaluation. Static aeroelastic effects should be taken into account if significant. To ensure that the maximum total load on each part of the airplane is obtained, the associated steady-state conditions should be chosen in such a way as to reasonably envelope the range of possible steady-state conditions that could be achieved in that flight condition. Typically, this would include consideration of effects such as speed brakes, power settings between zero thrust and the maximum for the flight condition, etc.
5.3 Dynamic Response Loads.
The incremental loads from the dynamic gust solution are superimposed on the associated steady, level flight 1g loads. Load responses in both positive and negative senses should be assumed in calculating total gust response loads. Generally, the effects of speed brakes, flaps, or other drag or high lift devices, while they should be included in the steady-state condition, may be disregarded in the calculation of incremental loads.
5.4 Damage Tolerance Conditions.
Limit gust loads, treated as ultimate, need to be developed for the structural failure conditions considered under § 25.571(b). Generally, for redundant structures, significant changes in stiffness or geometry do not occur for the types of damage under consideration. As a result, the limit gust load values obtained for the undamaged airplane may be used and applied to the failed structure. However, when structural failures of the types considered under § 25.571(b) cause significant changes in stiffness or geometry, or both, these changes should be taken into account when calculating limit gust loads for the damaged structure.
GUST MODEL CONSIDERATIONS.
12/12/14 AC 25.341-1
6.1 General.
The gust criteria presented in § 25.341 consist of two models of atmospheric turbulence, a discrete model and a continuous turbulence model. This AC focuses on the application of those gust criteria to establish design limit loads. The discrete gust model is used to represent single discrete extreme turbulence events. The continuous turbulence model represents longer duration turbulence encounters that excite lightly damped modes.
Dynamic loads for both atmospheric models must be considered in the structural design of the airplane.
6.2 Discrete Gust Model.
6.2.1 Atmosphere.
The atmosphere is assumed to be one dimensional with the gust velocity acting normally (either vertically or laterally) to the direction of airplane travel. The one-dimensional assumption constrains the instantaneous vertical or lateral gust velocities to be the same at all points in planes normal to the direction of airplane travel.
Design level discrete gusts are assumed to have 1-cosine velocity profiles. The maximum velocity for a discrete gust is calculated using a reference gust velocity, Uref, a flight profile alleviation factor, Fg, and an expression that modifies the maximum velocity as a function of the gust gradient distance, H. These parameters are discussed further below.
6.2.1.1 Reference Gust Velocity, Uref.
Derived effective gust velocities representing gusts occurring once in 70,000 flight hours are the basis for design gust velocities. These reference velocities are specified as a function of altitude in § 25.341(a)(5) and are given in terms of feet per second equivalent airspeed for a gust gradient distance, H, of 350 feet.
6.2.1.2 Flight Profile Alleviation Factor, Fg.
The reference gust velocity, Uref, is a measure of turbulence intensity as a function of altitude. In defining the value of Uref at each altitude, it is assumed that the airplane is flown 100 percent of the time at that altitude.
The factor Fg is then applied to account for the expected service experience in terms of the probability of the airplane flying at any given altitude within its certification altitude range. Fg is a minimum value at sea level, linearly increasing to 1.0 at the certified maximum altitude. The expression for Fg is given in § 25.341(a)(6).
6.2.1.3 Gust Gradient Distance, H.
The gust gradient distance is that distance over which the gust velocity increases to a maximum value. Its value is specified as ranging from 30 to 350 feet. If 12.5 times the mean geometric chord of the airplane’s wing 5
exceeds 350 feet, consideration should be given to covering increased maximum gust gradient distances.
6.2.1.4 Design Gust Velocity, Uds.
Maximum velocities for design gusts are proportional to the sixth root of the gust gradient distance, H. The maximum gust velocity for a given gust is then defined as:
𝑈𝑈𝑑𝑑𝑑𝑑 = 𝑈𝑈𝑟𝑟𝑟𝑟𝑟𝑟𝐹𝐹𝑔𝑔 ൬ 𝐻𝐻 1ൗ6 350൰
6.2.1.5 The maximum design gust velocity envelope, Uds, and example design gust velocity profiles are illustrated in figure 2 of this AC.
Figure 2. Typical (1-Cosine) Design Gust Velocity Profiles Gust Velocity, U (ft/s EAS) Gust Gradient Distance, H = 290 ft H = 170 ft − = H SUU ds π cos 1 2 H = 50 ft Uds 0 100 200 300 400 500 600 700 Gust Penetration Distance, S (ft)
6.2.2 Discrete Gust Response.
6.2.2.1 The solution for discrete gust response time histories can be achieved by a number of techniques. These include the explicit integration of the airplane equations of motion in the time domain and frequency domain solutions using Fourier transform techniques. These are discussed further in section 8 of this AC.
6.2.2.2 Maximum incremental loads, PIi, are identified by the peak values selected from time histories arising from a series of separate, 1-cosine shaped gusts having gradient distances ranging from 30 to 350 feet. Input gust profiles should cover this gradient distance range in sufficiently small increments to determine peak loads and responses. Historically, 10 to 20 gradient distances have been found to be acceptable. Both positive and negative gust velocities should be assumed in calculating total gust response loads.
In some cases, the peak incremental loads can occur well after the prescribed gust velocity has returned to zero. In such cases, the gust response calculation should be run for sufficient additional time to ensure that the critical incremental loads are achieved.
6.2.2.3 The design limit load, PLi, corresponding to the maximum incremental load, PIi for a given load quantity, i, is then defined as:
𝑃𝑃𝐿𝐿𝐿𝐿 = 𝑃𝑃(1g)𝐿𝐿 ± 𝑃𝑃𝐼𝐼𝐿𝐿 where P(1g)i is the 1g steady load for the load quantity under consideration.
The set of time-correlated design loads, PLj, corresponding to the peak value of the load quantity, PLi, are calculated for the same instant in time using the expression:
𝑃𝑃𝐿𝐿𝐿𝐿 = 𝑃𝑃(1g)𝐿𝐿 ± 𝑃𝑃𝐼𝐼𝐿𝐿 Note: With significant nonlinearities, maximum positive incremental loads may differ from maximum negative incremental loads.
6.2.2.4 When calculating stresses that depend on a combination of external loads, it may be necessary to consider time-correlated load sets at time instants other than those that result in peaks for individual external load quantities.
6.2.3 Round-the-Clock Gust.
6.2.3.1 When the effect of combined vertical and lateral gusts on airplane components is significant, then “round-the-clock” analysis should be conducted on these components and supporting structures. The vertical and lateral components of the gust are assumed to have the same gust gradient distance, H, and to start at the same time. Components that should be considered include horizontal tail surfaces having appreciable dihedral or anhedral (i.e., greater than 10º), or components supported by other lifting surfaces, for example, T-tails, outboard fins, and winglets. While the round-the-clock load assessment may be limited to just the components under consideration, the loads themselves should be calculated from a whole airplane dynamic analysis.
6.2.3.2 The round-the-clock gust model assumes that discrete gusts may act at any angle normal to the flight path of the airplane. Lateral and vertical gust components are correlated since the round-the-clock gust is a single discrete event. For a linear airplane system, the loads due to a gust applied 7
from a direction intermediate to the vertical and lateral directions—the round-the-clock gust loads—can be obtained using a linear combination of the load time histories induced from pure vertical and pure lateral gusts.
The resultant incremental design value for a particular load of interest is obtained by determining the round-the-clock gust angle and gust length giving the largest (tuned) response value for that load. The design limit load is then obtained using the expression for PL given in paragraph 6.2.2 of this AC.
6.2.4 Supplementary Gust Conditions for Wing-Mounted Engines.
6.2.4.1 Atmosphere.
6.2.4.1.1 For airplanes equipped with wing-mounted engines, § 25.341(c) requires that engine mounts, pylons, and wing supporting structure be designed to meet a round-the-clock discrete gust requirement and a multi-axis discrete gust requirement.
6.2.4.1.2 The model of the atmosphere and the method for calculating response loads for the round-the-clock gust requirement is the same as that described in paragraph 6.2.3 of this AC.
6.2.4.1.3 For the multi-axis gust requirement, the model of the atmosphere consists of two independent discrete gust components, one vertical and one lateral, having amplitudes such that the overall probability of the combined gust pair is the same as that of a single discrete gust as defined by § 25.341(a) and described in paragraph 6.2.1 of this AC. To achieve this equal-probability condition, in addition to the reductions in gust amplitudes that would be applicable if the input were a multi-axis Gaussian process, a further factor of 0.85 is incorporated into the gust amplitudes to account for non-Gaussian properties of severe discrete gusts.
This factor was derived from severe gust data obtained by a research airplane specially instrumented to measure vertical and lateral gust components. This information is contained in FAA report number DOT/FAA/AR-99/621.
6.2.4.2 Multi-Axis Gust Response.
6.2.4.2.1 For a particular airplane flight condition, the calculation of a specific response load requires that the amplitudes, and the time phasing, of the two gust components be chosen, subject to the condition on overall probability specified in paragraph 6.2.4.1.3 of this AC, such that the 1 DOT/FAA/AR-99/62, Studies of Time-Phased Vertical and Lateral Gusts: Development of Multiaxis One-Minus- Cosine Gust Model, October 1999. Available at http://www.tc.faa.gov/its/worldpac/techrpt/ar99-62.pdf.
resulting combined load is maximized. For loads calculated using a linear airplane model, the response load may be based on the separately tuned vertical and lateral discrete gust responses for that load, each calculated as described in paragraph 6.2.2 of this AC. In general, the vertical and lateral tuned gust lengths and the times to maximum response (measured from the onset of each gust) will not be the same.
6.2.4.2.2 Denote the independently tuned vertical and lateral incremental responses for a particular airplane flight condition and load quantity i by LVi and LLi, respectively. The associated multi-axis gust input is obtained by multiplying the amplitudes of the independently-tuned vertical and lateral discrete gusts, obtained as described in the previous paragraph, by:
0.85𝐿𝐿𝑉𝑉𝑉𝑉 0.85𝐿𝐿𝐿𝐿𝑉𝑉and , respectively.
ට൫𝐿𝐿2𝑉𝑉𝑉𝑉+𝐿𝐿2𝐿𝐿𝑉𝑉൯ ට൫𝐿𝐿2𝑉𝑉𝑉𝑉+𝐿𝐿2𝐿𝐿𝑉𝑉൯ The time-phasing of the two scaled gust components is such that their associated peak loads occur at the same instant.
6.2.4.2.3 The combined incremental response load is given by:
2 2 )𝑃𝑃𝐼𝐼𝐿𝐿 = 0.85ට(𝐿𝐿𝑉𝑉𝐿𝐿 + 𝐿𝐿𝐿𝐿𝐿𝐿 And the design limit load, PLi, corresponding to the maximum incremental load, PIi, for the given load quantity is then given by:
𝑃𝑃𝐿𝐿𝐿𝐿 = 𝑃𝑃(1g)𝐿𝐿 ± 𝑃𝑃𝐼𝐼𝐿𝐿 where P(1g)i is the 1g steady load for the load quantity under consideration.
6.2.4.2.4 The incremental, time-correlated loads corresponding to the specific flight condition under consideration are obtained from the independently-tuned vertical and lateral gust inputs for load quantity i. The vertical and lateral gust amplitudes are factored by:
0.85𝐿𝐿𝑉𝑉𝑉𝑉 0.85𝐿𝐿𝐿𝐿𝑉𝑉and , respectively.
2 ൯ 2 ൯ට൫𝐿𝐿2𝑉𝑉𝑉𝑉+𝐿𝐿𝐿𝐿𝑉𝑉 ට൫𝐿𝐿2𝑉𝑉𝑉𝑉+𝐿𝐿𝐿𝐿𝑉𝑉 Loads LVj and LLj resulting from these reduced vertical and lateral gust inputs, at the time when the amplitude of load quantity i is at a maximum value, are added to yield the multi-axis incremental time-correlated value PIj for load quantity j.
6.2.4.2.5 The set of time-correlated design loads, PLj, corresponding to the peak value of the load quantity, PLi, are obtained using the expression:
𝑃𝑃𝐿𝐿𝐿𝐿 = 𝑃𝑃(1g)𝐿𝐿 ± 𝑃𝑃𝐼𝐼𝐿𝐿 Note: With significant nonlinearities, maximum positive incremental loads may differ from maximum negative incremental loads.
6.3 Continuous Turbulence Model.
6.3.1 Atmosphere.
6.3.1.1 The atmosphere for the determination of continuous gust responses is assumed to be one dimensional with the gust velocity acting normal (either vertically or laterally) to the direction of airplane travel. The one-dimensional assumption constrains the instantaneous vertical or lateral gust velocities to be the same at all points in planes normal to the direction of airplane travel.
6.3.1.2 The random atmosphere is assumed to have a Gaussian distribution of gust velocity intensities and a von Kármán power spectral density with a scale of turbulence, L, equal to 2500 feet. The expression for the von Kármán spectrum for unit root-mean-square (RMS) gust intensity, ΦI(Ω), is given below. In this expression, Ω = ω/V, where ω is the circular frequency in radians per second, and V is the airplane velocity in feet per second true airspeed.
𝐿𝐿 1 + 8ൗ3 (1.339Ω𝐿𝐿)2 Φ𝐼𝐼 (Ω) = 𝜋𝜋 [1 + (1.339Ω𝐿𝐿)2]11ൗ6
6.3.1.3 The von Kármán power spectrum for unit RMS gust intensity is illustrated in figure 3 below.
Figure 3. The von Kármán Power Spectral Density Function, ΦI(Ω) 103 102 101 1
L = 2,500 ft
10-1 10-2
10-5 10-4 Reduced Frequency, Ω (rad/ft) ΦI (Ω) (ft/rad) 10-3 10-2 10-1 1 10
6.3.1.4 The design gust velocity, Uσ, applied in the analysis is given by the product of the reference gust velocity, Uσref, and the profile alleviation factor, Fg, as follows:
𝑈𝑈𝜎𝜎 = 𝑈𝑈𝜎𝜎𝑟𝑟𝑟𝑟𝑟𝑟 𝐹𝐹𝑔𝑔 where values for Uσref are specified in § 25.341(b)(3) in feet per second true airspeed, and Fg is defined in § 25.341(a)(6). The value of Fg is based on airplane design parameters and is a minimum value at sea level, linearly increasing to 1.0 at the certified maximum design altitude. It is identical to that used in the discrete gust analysis.
6.3.1.5 As for the discrete gust analysis, the reference continuous turbulence gust intensity, Uσref, defines the design value of the associated gust field at each altitude. In defining the value of Uσref at each altitude, it is assumed that the airplane is flown 100 percent of the time at that altitude. The factor Fg is then applied to account for the probability of the airplane flying at any given altitude during its service lifetime.
6.3.1.6 It should be noted that the reference gust velocity is comprised of two components, an RMS gust intensity and a peak-to-RMS ratio. The separation of these components is not defined and is not required for the linear airplane analysis. Guidance is provided in paragraph 9.4 of this AC for generating an RMS gust intensity for a nonlinear simulation.
6.3.2 Continuous Turbulence Response.
6.3.2.1 For linear airplane systems, the solution for the response to continuous turbulence may be performed entirely in the frequency domain, using the RMS response. Ā is defined in § 25.341(b)(2) and is repeated here in modified notation for load quantity i, where:
∞ 1ൗ2 𝐴𝐴̅𝐿𝐿 = ቈන |ℎ𝐿𝐿(Ω)|2 Φ𝐼𝐼(Ω)𝑑𝑑Ω 0 or ∞ 1ൗ2 𝐴𝐴̅𝐿𝐿 = ቈන Φ𝐼𝐼(Ω)ℎ𝐿𝐿(𝑖𝑖Ω)ℎ𝐿𝐿∗(𝑖𝑖Ω)𝑑𝑑Ω 0
6.3.2.2 In the above expressions, ΦI(Ω) is the input von Kármán power spectrum of the turbulence and is defined in paragraph 6.3.1 of this AC; hi(iΩ) is the transfer function relating the output load quantity, i, to a unit, harmonically oscillating, one-dimensional gust field; and the asterisk superscript denotes the complex conjugate. When evaluating Āi, the integration should be continued until a converged value is achieved since, realistically, the integration to infinity may be impractical. The design limit load, PLi, is then defined as:
𝑃𝑃𝐿𝐿𝐿𝐿 = 𝑃𝑃(1g)𝐿𝐿 ± 𝑃𝑃𝐼𝐼𝐿𝐿 = 𝑃𝑃(1g)𝐿𝐿 ± 𝑈𝑈𝜎𝜎𝐴𝐴̅𝐿𝐿 where Uσ is defined in paragraph 6.3.1 of this AC, and P(1g)i is the 1g steady-state value for the load quantity, i, under consideration. As indicated by the formula, both positive and negative load responses should be considered when calculating limit loads.
6.3.2.3 Correlated (or equiprobable) loads can be developed using cross-correlation coefficients, ρij, computed as follows:
∫ 8 Φ𝐼𝐼(Ω)𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 ൣℎ𝐿𝐿(𝑖𝑖Ω)ℎ𝐿𝐿∗(𝑖𝑖Ω)൧𝑑𝑑Ω =𝜌𝜌𝐿𝐿𝐿𝐿 0 𝐴𝐴̅𝐿𝐿𝐴𝐴̅𝐿𝐿 where, ‘real[...]’ denotes the real part of the complex function contained within the brackets. In this equation, the lowercase subscripts i and j denote the responses being correlated. A set of design loads, PLj, correlated to the design limit load PLi, are then calculated as follows:
𝑃𝑃𝐿𝐿𝐿𝐿 = 𝑃𝑃(1g)𝐿𝐿 ± 𝑈𝑈𝜎𝜎𝜌𝜌𝐿𝐿𝐿𝐿𝐴𝐴̅𝐿𝐿
6.3.2.4 The correlated load sets calculated in the foregoing manner provide balanced load distributions corresponding to the maximum value of the response for each external load quantity, i, calculated.
6.3.2.5 When calculating stresses, the foregoing load distributions may not yield critical design values because critical stress values may depend on a combination of external loads. In these cases, a more general application of the correlation coefficient method is required. For example, when the value of stress depends on two externally applied loads, such as torsion and shear, the equiprobable relationship between the two parameters forms an ellipse as illustrated in figure 4 of this AC.