U.S. Department

of Transportation

Federal Aviation

Administration

Advisory 

Circular

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 The 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, 
12/12/14 AC 25.341-1 

2 

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 This 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.
12/12/14 AC 25.341-1

3

Figure 1. Basic Elements of the Gust Response Analysis

Static Flight

Loads Model

Atmospheric 

Motion

Dynamics

and

Structure

Static 1g

Flight 

Loads

Dynamic

Loads

Limit 

Gust 

Loads

Aerodynamic

System

Control

System

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.
12/12/14 AC 25.341-1

4

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 Considerations for nonlinear airplane systems.

4.6.6 Analytical model validation techniques.

5 DESIGN CONDITIONS.

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.
12/12/14 AC 25.341-1

5

6 GUST MODEL CONSIDERATIONS.

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 
12/12/14 AC 25.341-1

6

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:

Udd = UrrrFg � H

350�

1

6�

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

0 100 200 300 400 500 600 700

Gust Penetration Distance, S (ft)

Gust Velocity, U (ft/s EAS)

Dust Dradient

5istance, H = 290 ft

H = 170 ft







 





 



 



 = − H

U S U ds π 1 cos

2

H = 50 ft

Uds

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.
12/12/14 AC 25.341-1

7

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:

PLL = P(1g) ± PI

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:

PLL = P(1g) ± PI

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 
12/12/14 AC 25.341-1

8

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-MinusCosine Gust Model, October 1999. Available at http://www.tc.faa.gov/its/worldpac/techrpt/ar99-62.pdf.
12/12/14 AC 25.341-1

9

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:

0.85LVV

��LVV

2 +LL2 �

and 0.85LL

��LVV

2 +LL2 �

, respectively.

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:

PI = 0.85�(LV

2 + LLL2 )

And the design limit load, PLi, corresponding to the maximum incremental 

load, PIi, for the given load quantity is then given by:

PLL = P(1g) ± PI

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:

0.85LVV

��LVV

2 +LL2 �

and 0.85LL

��LVV

2 +LL2 �

, respectively.

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:

PLL = P(1g) ± PI

Note: With significant nonlinearities, maximum positive incremental 

loads may differ from maximum negative incremental loads.
12/12/14 AC 25.341-1

10

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.

ΦI(Ω) = L

π

1 + 8

3� (1.339ΩL)2

[1 + (1.339ΩL)2]

11

6�

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

10-1

10-2

10-5 10-4 10-3 10-2 10-1 1

L = 2,500 ft

ΦI(Ω) (ft/rad)

Reduced Frequency, Ω (rad/ft)
12/12/14 AC 25.341-1

11

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:

Uσ = Uσ Fg

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:

A̅ = �� |h (Ω)|

2

∞

0

ΦI(Ω)dΩ�

1

2�

or

A̅ = �� ΦI(Ω)h (iΩ)h∗(iΩ)dΩ

∞

0

�

1

2�

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:
12/12/14 AC 25.341-1

12

PLL = P(1g) ± PI

= P(1g) ± UσA̅

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:

ρ = ∫ ΦI(Ω)rrrr 8

0 �h (iΩ)h∗(iΩ)�dΩ

A̅A̅

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:

PLL = P(1g) ± Uσρ A̅

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.
12/12/14 AC 25.341-1

13

Figure 4. Equal Probability Design Ellipse

Design Value 

of Shear

A

B C

D

E

G F

H

T

T

T

T

Design Value 

of Torsion

Equal Probability 

Design Ellipse

Torsion

1g Load

Shear

6.3.2.6 In figure 4 above, the points of tangency, T, correspond to the expressions 

for correlated load pairs given by the foregoing expressions. A practical 

additional set of equiprobable load pairs that should be considered to 

establish critical design stresses is given by the points of tangency to the 

ellipse by lines AB, CD, EF, and GH. These additional load pairs are 

given by the following expressions (where i = torsion and j = shear):

6.3.2.6.1 For tangents to lines AB and EF:

PLL = P(1g) ± A̅Uσ �

�1−ρ i�

2 �

1⁄2

and

PLL = P(1g) ∓ A̅Uσ �

�1−ρ i�

2 �

1⁄2

.
12/12/14 AC 25.341-1

14

6.3.2.6.2 For tangents to lines CD and GH:

PLL = P(1g) ± A̅Uσ �

�1+ρ i�

2 �

1⁄2

and

PLL = P(1g) ± A̅Uσ �

�1+ρ i�

2 �

1⁄2

.

6.3.2.6.3 All correlated or equiprobable loads developed using correlation 

coefficients will provide balanced load distributions.

6.3.2.6.4 A more comprehensive approach for calculating critical design stresses 

that depend on a combination of external load quantities is to evaluate 

directly the transfer function for the stress quantity of interest from which 

can be calculated the gust response function, the value for RMS response, 

Ā, and the design stress values:

P(1g) ± UσA̅

7 AIRPLANE MODELING CONSIDERATIONS.

7.1 General.

The procedures presented in this section generally apply for airplanes having 

aerodynamic and structural properties and flight control systems that may be reasonably 

or conservatively approximated using linear analysis methods for calculating limit load.

Additional guidance material is presented in section 9 of this AC for airplanes having 

properties and/or systems not reasonably or conservatively approximated by linear 

analysis methods.

7.2 Structural Dynamic Model.

7.2.1 The model should include both rigid body and flexible airplane degrees of freedom. If a 

modal approach is used, the structural dynamic model should include a sufficient 

number of flexible airplane modes to ensure convergence of the modal superposition 

procedure, and to ensure responses from high frequency excitations are properly 

represented.

7.2.2 Most forms of structural modeling can be classified into two main categories:

7.2.2.1 The so-called “stick model” characterized by beams with lumped masses 

distributed along their lengths, and

7.2.2.2 Finite element models in which all major structural components (frames, 

ribs, stringers, skins) are represented with mass properties defined at grid 

points.

7.2.3 Regardless of the approach taken for the structural modeling, a minimum acceptable 

level of sophistication, consistent with configuration complexity, is necessary to 
12/12/14 AC 25.341-1

15

represent satisfactorily the critical modes of deformation of the primary structure and 

control surfaces. Results from the models should be compared to test data as outlined in

paragraph 10.2 of this AC in order to validate the accuracy of the model.

7.3 Structural Damping.

Structural dynamic models may include damping properties in addition to 

representations of mass and stiffness distributions. In the absence of better information,

it will normally be acceptable to assume 0.03 (i.e., 1.5 percent equivalent critical 

viscous damping) for all flexible modes. Structural damping may be increased over the 

0.03 value to be consistent with the high structural response levels caused by extreme 

gust intensity, provided justification is given.

7.4 Gust and Motion Response Aerodynamic Modeling.

Aerodynamic forces included in the analysis are produced by both the gust velocity 

directly and by the airplane response.

7.4.1 Aerodynamic modeling for dynamic gust response analyses requires the use of unsteady 

two-dimensional or three-dimensional panel theory methods for incompressible or 

compressible flow. The choice of the appropriate technique depends on the complexity 

of the aerodynamic configuration, the dynamic motion of the surfaces under 

investigation, and the flight speed envelope of the airplane. Generally, 

three-dimensional panel methods achieve better modeling of the aerodynamic 

interference between lifting surfaces. The model should have a sufficient number of 

aerodynamic degrees of freedom to properly represent the steady and unsteady 

aerodynamic distributions under consideration.

7.4.2 The buildup of unsteady aerodynamic forces should be represented. In two-dimensional 

unsteady analysis, this may be achieved in either the frequency domain or the time 

domain through the application of oscillatory or indicial lift functions, respectively.

Where three-dimensional panel aerodynamic theories are to be applied in the time 

domain (e.g., for nonlinear gust solutions), an approach such as the “rational function 

approximation” method may be employed to transform frequency domain aerodynamics 

into the time domain.

7.4.3 Oscillatory lift functions due to gust velocity or airplane response depend on the 

reduced frequency parameter, k. The maximum reduced frequency used in the 

generation of the unsteady aerodynamics should include the highest frequency of gust 

excitation and the highest structural frequency under consideration. Time lags 

representing the effect of the gradual penetration of the gust field by the airplane should 

also be accounted for in the buildup of lift due to gust velocity.

7.4.4 The aerodynamic modeling should be supported by tests or previous experience as 

indicated in paragraph 10.4 of this AC. Primary lifting and control surface distributed 

aerodynamic data are commonly adjusted by weighting factors in the dynamic gust 

response analyses. The weighting factors for steady flow (k = 0) may be obtained by 

comparing wind tunnel test results with theoretical data. The correction of the 

aerodynamic forces should also ensure that the rigid body motion of the airplane is 
12/12/14 AC 25.341-1

16

accurately represented in order to provide satisfactory short period and Dutch roll 

frequencies and damping ratios. Corrections to primary surface aerodynamic loading 

due to control surface deflection should be considered. Special attention should also be 

given to control surface hinge moments and to fuselage and nacelle aerodynamics 

because viscous and other effects may require more extensive adjustments to the 

theoretical coefficients. Aerodynamic gust forces should reflect weighting factor 

adjustments performed on the steady or unsteady motion response aerodynamics.

7.5 Gyroscopic Loads.

7.5.1 As specified in § 25.371, the structure supporting the engines and the auxiliary power 

units should be designed for the gyroscopic loads induced by both discrete gusts and 

continuous turbulence. The gyroscopic loads for turbopropellers and turbofans may be 

calculated as an integral part of the solution process by including the gyroscopic terms 

in the equations of motion, or the gyroscopic loads can be superimposed after the 

solution of the equations of motion. Propeller and fan gyroscopic coupling forces (due 

to rotational direction) between symmetric and antisymmetric modes need not be taken 

into account if the coupling forces are shown to be negligible.

7.5.2 The gyroscopic loads used in this analysis should be determined with the engine or 

auxiliary power units at maximum continuous revolutions per minute. The mass polar 

moment of inertia used in calculating gyroscopic inertia terms should include the mass 

polar moments of inertia of all significant rotating parts, taking into account their 

respective rotational gearing ratios and directions of rotation.

7.6 Control Systems.

7.6.1 Gust analyses of the basic configuration should include simulation of any control 

system for which interaction may exist with the rigid body response, structural dynamic 

response, or external loads. If possible, these control systems should be uncoupled such 

that the systems that affect “symmetric flight” are included in the vertical gust analysis,

and those that affect “antisymmetric flight” are included in the lateral gust analysis.

7.6.2 The control systems considered should include all relevant modes of operation.

7.6.3 The control systems included in the gust analysis may be assumed to be linear if the 

impact of the nonlinearity is negligible, or if it can be shown by analysis on a similar 

airplane/control system that a linear control law representation is conservative. If the 

control system is significantly nonlinear, and a conservative linear approximation to the 

control system cannot be developed, then the effect of the control system on the 

airplane responses should be evaluated in accordance with section 9 of this AC.

7.7 Stability.

7.7.1 Solutions of the equations of motion for either discrete gusts or continuous turbulence 

require the dynamic model be stable. This applies for all modes, except possibly for 

very low frequency modes that do not affect load responses, such as the phugoid mode.

The short period and Dutch roll modes do affect load responses. A stability check 
12/12/14 AC 25.341-1

17

should be performed for the dynamic model using conventional stability criteria 

appropriate for the linear or nonlinear system in question, and adjustments should be 

made to the dynamic model, as required, to achieve appropriate frequency and damping 

characteristics.

7.7.2 When control system models are to be included in the gust analysis, it is advisable to 

check that the following characteristics are acceptable and are representative of the 

airplane:

7.7.2.1 Static margin of the unaugmented airplane. “Unaugmented airplane” 

means the natural airplane without any feedback control system.

7.7.2.2 Dynamic stability of the unaugmented airplane.

7.7.2.3 The static aeroelastic effectiveness of all control surfaces used by any 

feedback control system.

7.7.2.4 Gain and phase margins of any feedback control system coupled with the 

airplane rigid body and flexible modes (aeroservoelastic stability 

margins).

7.7.2.5 The aeroelastic flutter and divergence margins of the unaugmented 

airplane and also for any feedback control system coupled with the 

airplane.

8 DYNAMIC LOADS.

8.1 General.

This section describes methods for formulating and solving the airplane equations of 

motion and extracting dynamic loads from the airplane response. The airplane equations 

of motion are solved in either physical or modal coordinates and include all terms 

important in the loads calculation including stiffness, damping, mass, and aerodynamic 

forces due to both airplane motions and gust excitation. Generally, the airplane 

equations are solved in modal coordinates. For the purposes of describing the solution 

of these equations in the remainder of this AC, modal coordinates will be assumed. A 

sufficient number of modal coordinates should be included to ensure that the loads 

extracted provide converged values.

8.2 Solution of the Equations of Motion.

8.2.1 Solution of the equations of motion can be achieved through a number of techniques.

For the continuous turbulence analysis, the equations of motion are generally solved in 

the frequency domain. Transfer functions that relate the output response quantity to an 

input harmonically oscillating gust field are generated, and these transfer functions are 

used (in paragraph 6.3 of this AC) to generate the RMS value of the output response 

quantity.
12/12/14 AC 25.341-1

18

8.2.2 There are two primary approaches used to generate the output time histories for the 

discrete gust analysis:

8.2.2.1 By explicit integration of the airplane equations of motion in the time 

domain, and

8.2.2.2 By frequency domain solutions that can use Fourier transform techniques.

8.3 Extraction of Loads and Responses.

8.3.1 The output quantities that may be extracted from a gust response analysis include 

displacements, velocities, and accelerations at structural locations; load quantities such 

as shears, bending moments, and torques on structural components; and stresses and 

shear flows in structural components. The calculation of the physical responses is given 

by a modal superposition of the displacements, velocities, and accelerations of the rigid 

and elastic modes of vibration of the airplane structure. The number of modes carried in 

the summation should be sufficient to ensure converged results.

8.3.2 A variety of methods may be used to obtain physical structural loads from a solution of 

the modal equations of motion governing gust response. These include the Mode 

Displacement method, the Mode Acceleration method, and the Force Summation 

method. All three methods are capable of providing a balanced set of airplane loads. If 

an infinite number of modes can be considered in the analysis, the three will lead to 

essentially identical results.

8.3.3 The Mode Displacement method is the simplest. In this method, total dynamic loads are 

calculated from the structural deformations produced by the gust using modal 

superposition. Specifically, the contribution of a given mode is equal to the product of 

the load associated with the normalized deformed shape of that mode and the value of 

the displacement response given by the associated modal coordinate. For converged 

results, the Mode Displacement method may need a significantly larger number of 

modal coordinates than the other two methods.

8.3.4 In the Mode Acceleration method, the dynamic load response is composed of a static 

part and a dynamic part. The static part is determined by conventional static analysis 

(including rigid body “inertia relief”), with the externally applied gust loads treated as 

static loads. The dynamic part is computed by the superposition of appropriate modal 

quantities and is a function of the number of modes carried in the solution. The 

quantities to be superimposed involve both motion response forces and acceleration 

responses (thus giving this method its name). Since the static part is determined 

completely and independently of the number of normal modes carried, adequate 

accuracy may be achieved with fewer modes than would be needed in the Mode 

Displacement method.

8.3.5 The Force Summation method is the most laborious and the most intuitive. In this 

method, physical displacements, velocities, and accelerations are first computed by 

superposition of the modal responses. These are then used to determine the physical 
12/12/14 AC 25.341-1

19

inertia forces and other motion dependent forces. Finally, these forces are added to the 

externally applied forces to give the total dynamic loads acting on the structure.

8.3.6 If balanced airplane load distributions are needed from the discrete gust analysis, they 

may be determined using time-correlated solution results. Similarly, as explained in 

paragraph 6.3 of this AC, if balanced airplane load distributions are needed from the 

continuous turbulence analysis, they may be determined from equiprobable solution 

results obtained using cross-correlation coefficients.

9 NONLINEAR CONSIDERATIONS.

9.1 General.

9.1.1 Any structural, aerodynamic, or automatic control system characteristic that may cause 

airplane response to discrete gusts or continuous turbulence to become nonlinear with 

respect to intensity or shape should be represented realistically or conservatively in the 

calculation of loads. While many minor nonlinearities are amenable to a conservative 

linear solution, the effect of major nonlinearities cannot usually be quantified without 

explicit calculation.

9.1.2 The effect of nonlinearities should be investigated above limit conditions to assure that 

the system presents no anomaly compared to behavior below limit conditions.

9.2 Structural and Aerodynamic Nonlinearity.

A linear elastic structural model and a linear (unstalled) aerodynamic model are 

normally recommended as conservative and acceptable for the unaugmented airplane 

elements of a loads calculation. Aerodynamic models may be refined to take account of 

minor nonlinear variation of aerodynamic distributions due to local separation, etc., 

through simple linear piecewise solution. Local or complete stall of a lifting surface 

would constitute a major nonlinearity and should not be represented without account 

being taken of the influence of rate of change of incidence, i.e., the so-called “dynamic 

stall” in which the range of linear incremental aerodynamics may extend significantly 

beyond the static stall incidence.

9.3 Automatic Control System Nonlinearity.

9.3.1 Automatic flight control systems, autopilots, stability control systems, and load 

alleviation systems often constitute the primary source of nonlinear response. For 

example:

• Non-proportional feedback gains.

• Rate and amplitude limiters.

• Changes in the control laws or control law switching.

• Hysteresis.

• Use of one-sided aerodynamic controls such as spoilers.
12/12/14 AC 25.341-1

20

• Hinge moment performance and saturation of aerodynamic control actuators.

9.3.2 The resulting influences on response will be airplane design dependent, and the manner 

in which they are to be considered will normally have to be assessed for each design.

9.3.3 Minor influences such as occasional clipping of response due to rate or amplitude 

limitations, where it is symmetric about the stabilized 1g condition, can often be 

represented through quasi-linear modeling techniques such as describing functions or 

use of a linear equivalent gain.

9.3.4 Major and unsymmetrical influences, such as application of spoilers for load alleviation, 

normally require explicit simulation and, therefore, adoption of an appropriate solution 

based in the time domain.

9.3.5 The influence of nonlinearities on one load quantity often runs contrary to the influence 

on other load quantities. For example, an aileron used for load alleviation may 

simultaneously relieve wing bending moment while increasing wing torsion. Since it 

may not be possible to represent such features conservatively with a single airplane 

model, it may be conservatively acceptable to consider loads computed for two 

(possibly linear) representations that bound the realistic condition. Another example of 

this approach would be separate representation of continuous turbulence response for 

the two control law states to cover a situation where the airplane may occasionally 

switch from one state to another.

9.4 Nonlinear Solution Methodology.

9.4.1 Where explicit simulation of nonlinearities is required, the loads response may be 

calculated through time domain integration of the equations of motion.

9.4.2 For the tuned discrete gust conditions of § 25.341(a), limit loads should be identified by 

peak values in the nonlinear time domain simulation response of the airplane model 

excited by the discrete gust model described in paragraph 6.2 of this AC.

9.4.3 For time domain solution of the continuous turbulence conditions of § 25.341(b), a 

variety of approaches may be taken for the specification of the turbulence input time 

history and the mechanism for identifying limit loads from the resulting responses.

9.4.4 It will normally be necessary to justify that the selected approach provides an equivalent 

level of safety as a conventional linear analysis and is appropriate to handle the types of 

nonlinearity on the airplane. This should include verification that the approach provides 

adequate statistical significance in the loads results.

9.4.5 A methodology based on stochastic simulation has been found to be acceptable for load 

alleviation and flight control system nonlinearities. In this simulation, the input is a 

long, Gaussian, pseudo-random turbulence stream conforming to a von Kármán 

spectrum with an RMS amplitude of 0.4 times Uσ (defined in paragraph 6.3.1 of this 

AC). The value of limit load is that load with the same probability of exceedance as 

ĀUσ of the same load quantity in a linear model. This is illustrated graphically in 
12/12/14 AC 25.341-1

21

figure 5 of this AC. When using an analysis of this type, exceedance curves should be 

constructed using incremental load values up to, or just beyond, the limit load value.

Figure 5. Establishing Limit Load for a Nonlinear Airplane

Nonlinear Model Linear Model

Nonlinear 

Design 

Load

Limit Load 

Exceedance Level

Lo

Md Exceedences 

Log(Ny)

IncrementMl LoMd

D σ Ā L

9.4.6 The nonlinear simulation may also be performed in the frequency domain if the 

frequency domain method is shown to produce conservative results. Frequency domain 

methods include, but are not limited to, Matched Filter Theory and Equivalent 

Linearization.

10 ANALYTICAL MODEL VALIDATION.

10.1 General.

The intent of analytical model validation is to establish that the analytical model is 

adequate for the prediction of gust response loads. The following paragraphs discuss 

acceptable, but not the only methods, of validating the analytical model. In general, it is 

not intended that specific testing be required to validate the dynamic gust loads model.

10.2 Structural Dynamic Model Validation.

The methods and test data used to validate the flutter analysis model should also be 

applied to validate the gust analysis model. These procedures are addressed in 
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22

AC 25.629-1B, Aeroelastic Stability Substantiation of Transport Category Airplanes, 

dated October 27, 2014, or later revision.

10.3 Damping Model Validation.

In the absence of better information, it will normally be acceptable to assume 0.03 

(i.e., 1.5 percent equivalent critical viscous damping) for all flexible modes. Structural 

damping may be increased over the 0.03 value to be consistent with the high structural 

response levels caused by extreme gust intensity, provided justification is given.

10.4 Aerodynamic Model Validation.

10.4.1 Aerodynamic modeling parameters fall into two categories:

• Steady or quasi-steady aerodynamics governing static aeroelastic and flight dynamic 

airload distributions.

• Unsteady aerodynamics that interact with the flexible modes of the airplane.

10.4.2 Flight stability aerodynamic distributions and derivatives may be validated by wind 

tunnel tests, detailed aerodynamic modeling methods (such as computational fluid 

dynamics), or flight test data. If detailed analysis or testing reveals that flight dynamic 

characteristics of the airplane differ significantly from those to which the gust response 

model has been matched, then the implications on gust loads should be investigated.

10.4.3 The analytical and experimental methods for flutter analyses presented in 

AC 25.629-1B, or later revision, provide acceptable means for establishing reliable 

unsteady aerodynamic characteristics both for motion response and gust excitation 

aerodynamic force distributions. The aeroelastic implications on airplane flight dynamic 

stability should also be assessed.

10.5 Control System Validation.

10.5.1 If the airplane mathematical model used for gust analysis contains a representation of 

any feedback control system, then this segment of the model should be validated. The 

level of validation that should be performed depends on the complexity of the system 

and the particular airplane response parameter being controlled. Systems that control 

elastic modes of the airplane may require more validation than those that control the 

airplane rigid body response. Validation of elements of the control system (sensors, 

actuators, anti-aliasing filters, control laws, etc.) that have a minimal effect on the 

output load and response quantities under consideration can be disregarded.

10.5.2 It will normally be more convenient to substantiate elements of the control system 

independently, i.e., open loop, before undertaking the validation of the closed loop 

system.

10.5.3 System Rig or Airplane Ground Testing.

10.5.3.1 Response of the system to artificial stimuli can be measured to verify the 

following:
12/12/ 14 	 AC 25.341-1 


• 	 The transfer functions of the sensors and any pre-control system 

anti-aliasing or other filtering. 

• 	 The sampling delays of acquiring data into the control system. 

• 	 The behavior of the control law itself. 

• 	 Any control system output delay and filter transfer function. 

• 	 The transfer functions of the actuators, and any features of actuation 

system performance characteristics that may influence the actuator 

response to the maximum demands that might arise in turbulence, e.g., 

maximum rate of deployment, actuator hinge moment capability, etc. 

10.5.3.2 	 If this ground testing is performed, it is recommended that following any 

adaptation of the model to reflect this information, the complete feedback 

path be validated (open loop) against measurements taken from the rig or 

ground tests. 

1 0.5.4 	 Flight Testing. 

The functionality and performance of any feedback control system can also be validated 

by direct comparison of the analytical model and measurement for input stimuli. When 

this testing is performed, input stimuli should be selected such that they exercise the 

features ofthe control system and the interaction with the airplane that are significant in 

the use ofthe mathematical model for gust load analysis. These might include: 

1 0.5.4.1 	 Airplane response to pitching and yawing maneuver demands. 

1 0.5.4.2 	 Control system and airplane response to sudden artificially introduced 

demands such as pulses and steps. 

10.5.4.3 	 Gain and phase margins determined using data acquired during the flight 

flutter test program or flight controls validation program. These gain and 

phase margins can be generated by passing known signals through the 

open loop system during flight test. 

If you have any suggestions for improving this AC, you may use the Advisory Circular Feedback 

form at the end of this AC. 

f}'-ff7C:(l_, 

Jeffrey E. Duven 

Manager, Transport Airplane Directorate 

Aircraft Certification Service 

23 

Advisory Circular Feedback

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new items/subjects to be added, you may let us know by (1) emailing this form to 9-AWA-AVSAIR500-Coord@faa.gov or (2) faxing it to the attention of the Aircraft Certification Service 

Directives Management Officer at (202) 267-3983. 

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