The preparation of a flight-by-flight load sequence is done in
five essential steps:
the representative life history mission ordering.
mission segment flight conditions.
the number of maneuver and gust load cycles at each load level in each mission
the maneuver and gust load cycles within each mission segment.
load cycles from other sources within each mission segment.
Giessler, et al. 
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, nz. 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
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  and VanDÿk .
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, nz. 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
These loads will be lower than B,
but higher than A. The exact magnitude of any one of the n1-n2 loads
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
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 Pxx
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
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
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
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
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 nz, 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
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.
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.
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.
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