U.S. Department

of Transportation

Federal Aviation

Administration

Advisory 

Circular

Subject: Dynamic Gust Loads Date: D R A F T

Initiated By: ANM-115

AC No: 25.341-X

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.

2.4 Except in the explanations of what the regulations require, the term “must” is used in 

this AC only in the sense of ensuring applicability of this particular method of 

compliance when the acceptable method of compliance described in this AC is used.
XX/XX/XX D R A F T AC 25.341-X

2

3. RELATED 14 CFR REGULATIONS.

 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 (figure 1). The degree of sophistication and detail required 

in the modeling depends on the complexity of the airplane and its systems.
XX/XX/XX D R A F T AC 25.341-X

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 1-g flight 

loads and the gust incremental loads including the dynamic response of the airplane. 

The steady 1-g 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 1-g flight conditions.

4.6.2 The discrete and continuous gust models of atmospheric turbulence.
XX/XX/XX D R A F T AC 25.341-X

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 1-g 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 1-g 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.
XX/XX/XX D R A F T AC 25.341-X

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 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:

( /350)

(1 6)

Uds Uref Fg H




XX/XX/XX D R A F T AC 25.341-X

6

6.2.1.5 The maximum design gust velocity envelope, Uds, and example design gust velocity 

profiles are illustrated in figure 2.

Figure 2. Typical (1-Cosine) Design Gust Velocity Profiles

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 paragraph 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:

U

U SH

ds  























 2

1 cos 

0 100 200 300 400 500 600 700 Gust Penetration Distance, S ~ Feet Gust Velocity, U ~ Ft/Sec EAS 

Gust Gradient

 Distance, H = 290 Ft

H = 50 Ft H = 170 Ft

Uds
XX/XX/XX D R A F T AC 25.341-X

7

PLi P g i PIi

  (1 )

where P(1-g)i is the 1-g 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:

PLj P g j PIj

  (1 )

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 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 aircraft 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.
XX/XX/XX D R A F T AC 25.341-X

8

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) as 

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 

Stirling Dynamics Limited Report No. SDL-571-TR-2, dated May 1999.

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 of this AC, such that the resulting combined 

load is maximized. For loads calculated using a linear airplane model, the 

response load may be based upon 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 

0.85*LVi/(LVi

2

+LLi

2

) and 0.85*LLi/(LVi

2

+LLi

2

) 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:

P L L  Ii Vi Li

2 2

 0.85 

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

load, PIi, for the given load quantity is then given by:
XX/XX/XX D R A F T AC 25.341-X

9

PLi P g i PIi

  (1 )

where P(1-g)i is the 1-g 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 0.85*LVi/(LVi

2

+LLi

2

) and 

0.85*LLi/(LVi

2

+LLi

2

) 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:

PLj P g j PIj

  (1 )

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(), is given below. In this expression  = Φ/V where, ω is 

the circular frequency in radians per second, and V is the airplane velocity in feet per 

second true airspeed.

 

 

   

6

1 1 2

2

I

1 1.339 L

1.339 L

3

8

1

L

 

 

  



6.3.1.3 The von Kármán power spectrum for unit RMS gust intensity is illustrated in figure 3.
XX/XX/XX D R A F T AC 25.341-X

10

Figure 3. The von Kármán Power Spectral Density Function, ΦI(Ω)

1.E -2

1.E -1

1.E +0

1.E +1

1.E +2

1.E +3

1.0E -5 1.0E -4 1.0E -3 1.0E -2 1.0E -1 1.0E +0

R educed Frequency,  ~ R ad/Ft

() ~ (F t/S ec)

2/(R ad/F t)

L = 2500 Feet

Reduced Frequency, Ω ~ Rad/Ft

Φ1(Ω) – Ft/Rad 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:

U Uref 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 
XX/XX/XX D R A F T AC 25.341-X

11

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:

2

1

0

2

i A ( ) ( ) 











   



hiId

or

2

1

0

*

i A ( ) ( ) ( ) 











    



Ihii hii d

6.3.2.2 In the above expression, ΦI() is the input von Kármán power spectrum of the 

turbulence and is defined in paragraph 6.3.1 of this AC; hi(i)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:

PLi P g i PIi

  (1 )

Ai P(1 g)i U

  

where U is defined in paragraph 6.3 of this AC, and P(1-g)i is the 1-g 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:

 





ij

I i

j

i j

real h i h i d

A A







( ) ( ) ( )

*    

0

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:
XX/XX/XX D R A F T AC 25.341-X

12 P P U ij Aj Lj



(1g) j



 

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.

Figure 4. Equal Probability Design Ellipse

6.3.2.6 In figure 4, 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 are 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):

T

T

T

T

B

A

C

E

D

F

H

G

One-g Load

Torsion

Shear

Equal Probability

Design Ellipse

Design Value

of Shear

Design Value

of Torsion
XX/XX/XX D R A F T AC 25.341-X

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6.3.2.6.1 For tangents to lines AB and EF:

  

1/ 2

(1 )

/ 1 ij / 2

i PLi P g i AU  

    

and

  

1/ 2

(1 )

/ 1 ij / 2

j PLj P g j AU  

    

6.3.2.6.2 For tangents to lines CD and GH:

  

1/ 2

(1 )

1 ij / 2

i PLi P g i AU  

   

and

  

1/ 2

(1 )

1 ij / 2

j PLj P g j AU  

   

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(1-g)  U Ā.

7. AIRPLANE MODELING CONSIDERATIONS.

7.1 General. The procedures presented in this paragraph 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 paragraph 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 both convergence of the modal 

superposition procedure, and that 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.
XX/XX/XX D R A F T AC 25.341-X

14

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 

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 
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aerodynamic forces should also ensure that the rigid body motion of the airplane is 

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 (rpm). 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 paragraph 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 
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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 

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 If 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.

7.7.2.2 Dynamic stability of the unaugmented airplane.

7.7.2.3 The static aeroelastic effectiveness of all control surfaces utilized 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.

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.

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

discrete gust analysis:
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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 

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 
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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.

 Hinge moment performance and saturation of aerodynamic control actuators.
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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 1-g 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 upon 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 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 figure 5. 

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.
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Figure 5. Establishing Limit Load for a Nonlinear Airplane

Nonlinear Model Linear Model

Nonlinear Design Load Limit Load L

Exceedence Level oad Exceedences

Incremental Load U AL

Log(Ny) 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 AC 25.629-1A or later approved 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 
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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 have 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 25.629-1A, or later approved 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. Response of the system to artificial stimuli can 

be measured to verify the following:

10.5.3.1 The transfer functions of the sensors and any pre-control system anti-aliasing or other 

filtering.

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

10.5.3.3 The behavior of the control law itself.
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10.5.3.4 Any control system output delay and filter transfer function.

10.5.3.5 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.

10.5.4 If this 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.

10.5.5 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. If this testing is performed, input stimuli should be selected such that 

they exercise the features of the control system and the interaction with the airplane that 

are significant in the use of the mathematical model for gust load analysis. These might 

include:

10.5.5.1 Airplane response to pitching and yawing maneuver demands.

10.5.5.2 Control system and airplane response to sudden artificially introduced demands such as 

pulses and steps.

10.5.5.3 Gain and phase margins determined using data acquired within the flutter test program. 

These gain and phase margins can be generated by passing known signals through the 

open loop system during flight test.

END