The preparation of a flight-by-flight load sequence is done in five essential steps:

1.      Prepare the representative life history mission ordering.

2.      Define mission segment flight conditions.

3.      Determine the number of maneuver and gust load cycles at each load level in each mission segment.

4.      Order the maneuver and gust load cycles within each mission segment.

5.      Place load cycles from other sources within each mission segment.

Giessler, et al. [1981] presents detailed instructions to accomplish these steps; however, brief descriptions are presented here for completeness.

The establishment of the mission sequence for the life history of the aircraft is usually done in a deterministic manner and is based on past observations of similar type aircraft.  It is reasonable to assign missions in blocks as flying assignments usually follow specific groupings of missions as various flying skills are being stressed.  Missions occurring relatively few times are usually interspersed throughout the sequence either singly or in small numbers.  It is recommended that the severest missions be somewhat evenly spaced throughout the sequence.  It is common to treat the sequence as a repeating block.  Each block would contain all mission types and represent some proportion of the total flight history.  Blocks of five hundred or one thousand flight hours have been found to be convenient.  For example: for a 6,000 hour aircraft life, a 500 hour block would be repeated twelve times to obtain the total sequence.

Each mission is divided into segments for ease in defining the loading cycles.  This division is specified in the mission profile.  The same ordering of mission segments is used each time a mission occurs.  This division is useful in two ways: it facilitates the identification of load spectra and it provides for the definition of the flight condition parameters.  The flight condition parameters are the values of airspeed, altitude, gross weight, configuration, and time used for each mission segment.  These conditions are selected from the mission profile to give a set of representative loading conditions for each segment.  These are combined with the load level indicator to compute the loads.

The determination of the number and severity of loads assigned to each mission segment is based on a spectrum of a load level indicator.  For most applications this is the normal load factor, n_z.  This spectrum is obtained from analysis of previous usage of similar aircraft in the case of a design specification, or from current usage of the aircraft being analyzed in the case of an update to the design analysis.  Some of the concerns that need to be considered when applying this information will now be discussed.

The load information for an aircraft structure is usually in the form of an exceedance spectrum.  The spectrum is an interpretation of in-flight measurements of center-of-gravity accelerations or stresses at a particular location.  The interpretation consists of a counting procedure, which counts accelerations (or stresses) of a certain magnitude, or their variation (range).  Information on the various counting procedures can be found in Schijve [1963] and VanDÿk [1972].

Typical exceedance spectra are given in Figure 5.4.3 for a transport wing, bomber wing, and fighter wing.  The ordinate represents the normal load factor, n_z.  The abscissa represents the number of times a level on the vertical axis is exceeded.  For example, using the transport spectrum in Figure 5.4.3, level A is exceeded n₁ times and level B is exceeded n₂ times.  This means that there will be n₁-n₂ events of a load between levels A and B.  These loads will be lower than B, but higher than A.  The exact magnitude of any one of the n₁-n₂ loads remains undetermined.

Figure 5.4.3.  Exceedance Spectra for 1000 Hours

One can define an infinite number of load levels between A and B.  However, there are only n₁-n₂ occurrences, which means that while the number of load levels to be encountered is infinite; not every arbitrary load level will be experienced.  Strictly speaking each of the n₁-n₂ occurrences between A and B could be a different load level.  If one chose to divide the distance between A and B into n₁-n₂ equal parts, DA, each of these could occur once.  Mathematically, a level A+DA will be exceeded n₁-1 times.  Hence, there must be one occurrence between A and A+DA.  In practice, such small steps cannot be defined, nor is there a necessity for their definition.

If measurements were made again during an equal number of flight hours, the exceedance spectrum would be the same, but the actual load containment would be different.  This means that the conversion of a spectrum into a stress history for crack-growth analysis will have to be arbitrary because one can only select one case out of unlimited possibilities.

Going to the top of the spectrum in Figure 5.4.3, level C will be exceeded 10 times.  There must be a level above C that is exceeded 9 times, one that is exceeded 8 times, etc.  One could identify these levels, each of which would occur once.  In view of the foregoing discussion this becomes extremely unrealistic.  Imagine 10 levels above C at an equal spacing of DC, giving levels C, C+DC, C+2DC, etc.  If level C is exceeded 10 times, all of these exceedances may be of the level C+3DC for another aircraft.

As a consequence, it is unrealistic to apply only one load of a certain level, which would imply that all loads in the history would have a different magnitude.  Moreover, if high loads are beneficial for crack growth (retardation), it would be unconservative to apply once the level C+DC, once C+2DC, etc., if some aircraft would only see 10 times C.

Hence, the maximum load level for a fatigue analysis should be selected at a reasonable number of exceedances.  (This load level is called the clipping level).  From crack-growth experiments regarding the spectrum clipping level, it appears reasonable to select the highest level at 10 exceedances per 1,000 flights.  This will be discussed in more detail in later sections.  (Note that the maximum load used in the fatigue analysis has no relation whatsoever to the P_xx loads for residual strength analysis).

The same dilemma exists when lower load levels have to be selected.  Obviously, the n loads in 1,000 hours will not be at n different levels.  A number of discrete levels has to be selected.  This requires a stepwise approximation of the spectrum, as in Figure 5.4.4.  As shown in the following table, the number of occurrences of each level follows easily from subtracting exceedances.

 

Figure 5.4.4.  Stepped Approximation of Spectrum

Table 5.4.1.  Occurrences Calculated from the Exceedances of Figure 5.4.4

 

The more discrete load levels there are, the closer the stepwise approximation will approach the spectrum shape.  On the other hand, the foregoing discussion shows that too many levels are unrealistic.  The number of levels has to be chosen to give reliable crack-growth predictions.

Figure 5.4.5 shows results of crack-growth calculations in which the spectrum was approximated in different ways by selecting a different number of levels each time.  If the stepped approximation is made too coarse (small number of levels) the resulting crack-growth curve differs largely from those obtained with finer approximations.  However, if the number of levels is 8 or more, the crack-growth curves are identical for all practical purposes.  A further refinement of the stepped approximation only increases the complexity of the calculation; it does not lead to a different (or better) crack-growth prediction.  Crack-growth predictions contain many uncertainties anyway, which means that one would sacrifice efficiency to apparent sophistication by taking too many levels.  It turns out that 8 to 10 positive levels (above the in-flight stationary load) are sufficient.  The number of negative levels (below the in-flight stationary load) may be between 4 and 10.

 

Figure 5.4.5.  Fatigue-Crack Growth Behavior Under Various Spectra Approximations

Selection of the lowest positive level is also of importance, because it determines the total number of cycles in the crack-growth analysis.  This level is called the truncation level.  Within reasonable limits the lower truncation level has only a minor effect on the outcome of the crack-growth life.  Therefore, it is recommended that this lower truncation level be selected on the basis of exceedances rather than on stresses.  A number in the range of 10⁵ - 5 x 10⁵ exceedances per 1,000 flights seems reasonable.  This will be discussed in more detail in Section 5.5.

 

EXAMPLE 5.4.1         Constructing Occurrences from Exceedance Information

This example illustrates how a stepped approximation can be constructed.  Consider the positive load factor spectrum shown in Figure 5.4.4. 

First select the maximum level as the load which is exceeded 10 times in 1,000 flights.  This is done by constructing a line from the 10 exceedance level to the curve and then constructing the horizontal to intersect the vertical axis.  This gives L₁= 4.9 g.  Next construct a vertical from the 10⁵ exceedance value.  This line is extended until the area A₅ equals B₅.  The horizontal line defining the top of A₅ is extended to the vertical axis defining the level L₅.  In this case L₅ = 1.8g. 

Now the interval from L₅ to L₁ is divided into as many parts as desired.  They may be equal or not.  Current fighter aircraft practice uses 0.5 g intervals.  After the vertical divisions are selected, horizontal lines are extended at L₂, L₃, and L₄ such that the enclosed areas (A₂, B₂), (A₃, B₃) and (A₄, B₄) are approximately equal.  At that point the verticals are constructed to define n₂, n₃, and n₄.  This now gives the results:

 

 

This procedure is only used to construct the steps after the L₁ level.  The L₁ level is taken as the intersection with the curve.  It is seen that, as the exceedance plot tails off the high levels on n_z, to construct equal areas becomes difficult if not impossible.  In the present example, in order to keep the exceedance value of 10 for the high level, L₁ could not extend beyond 5.0 g and the lower limit of the range could not go below 4.75 g.  Now the range from 4.75 g to L₂ would need to be added to the number of levels.  This would add high level occurrences that may not be realistic.  It should be remembered that the exceedance plot is a curve faired through observed data and that the high level values are usually the result of very few observations. 

This method of approximating the spectrum associates the level L₅ with the occurrence represented by a range extending on either side of L₅ and similarly for L₁ which was discussed above.  An alternate procedure is to select the ranges first and then to associate the occurrences with the mid-point of the ranges.

 

 

After the levels and number of occurrences of the load indicator are determined for each mission segment, the actual loads are computed using the previously defined flight conditions and the specific load equations for the aircraft.  Cycles are formed by combining the positive loads with the mean or negative loads.  As there are more positive loads than negative loads, most cycles are formed with the mean, or 1.0g steady flight condition, as the minimum value of the cycle.  The assignment of the negative load cycles is usually on a random basis.

The sequencing of these load cycles is the next step.  In order to achieve a realistic effect on the crack-growth analysis, care must be taken in establishing this sequence.  Some guidelines are given below.

a)      Deterministic loads are placed directly in the sequence.  Obviously, the ground load of the ground-air-ground (G-A-G) cycle will occur at the beginning and at the end of each flight.  Similarly, maneuver loads associated with take-off will be at the beginning of the flight.

b)      Probabilistic loads due to gusts and maneuvers have to be arbitrarily assigned and sequenced.  The assignment of the loads in a particular mission segment is made on a random basis to all flights containing that mission segment.  This results in each flight of a particular mission having a different selection of loads.  If a repeating block approach is used, then each flight in the block would be different.  Sequencing of the assigned loads within a segment can be either random or deterministic.  A deterministic low-high-low sequence has been shown by Schijve [1970, 1972] to be very similar to random loading for a gust spectrum.  This sequence is also realistic for the combat maneuvering segments of fighter aircraft.  Thus, the low-high-low sequence is recommended if programmed sequencing is considered rather than random sequencing.

c)      After determination of all the mission stresses, simplifications are sometimes possible.  Usually the stresses will be given in tabular form.  They will show an apparent variability.  For example, if an acceleration, n₂, is exceeded 10,000 times, this will not result in the exceedance of 10,000 times of a certain stress level, since n₂ causes a different stress in different missions or mission segments.  However, if a stress exceedance spectrum is established for the various missions on the basis of the tabular stress history, it may turn out that two different missions may have nearly the same stress spectrum.  In that case, the missions can be made equal for the purpose of crack-growth predictions.

d)      Placement of non-probabilistic load sources which occur a specified number of times in a flight is made on a deterministic basis.  One such method is to place them after a certain number of occurrences of the probabilistic loads.  This is reasonable for a random sequencing, however, if the sequencing has been low-high-low, then following the same method and placing these miscellaneous cycles in the proper location is suggested.

While the above discussions were primarily directed toward development of wing loadings, similar methods are used to obtain the load sequencing for other parts of the aircraft.  Only the significant loading conditions will change.