Page 283 - Aircraft Stuctures for Engineering Student
P. 283
264 Airworthiness and airframe loads
Fatigue damage is also caused by gusts encountered in flight, particularly during the
climb and descent. Suppose that a gust of velocity u, causes a stress S, about a mean
stress corresponding to level flight, and suppose also that the number of stress cycles
of this magnitude required to cause failure is N(S,); the damage caused by one cycle is
then l/N(S,). Thus, from the Palmgren-Miner hypothesis, when sufficient gusts of
this and all other magnitudes together with the effects of all other load cycles produce
a cumulative damage of 1.0, fatigue failure will occur. It is therefore necessary to
know the number and magnitude of gusts likely to be encountered in flight.
Gust data have been accumulated over a number of years from accelerometer
records from aircraft flying over different routes and terrains, at different heights
and at different seasons. The ESDU data sheets7 present the data in two forms, as
we have previously noted. First Zlo against altitude curves show the distance which
must be flown at a given altitude in order that a gust (positive or negative) having
a velocity 2 3.05m/s be encountered. It follows that l/Zlo is the number of gusts
encountered in unit distance (1 km) at a particular height. Secondly, gust frequency
distribution curves, r(ue) against u,, give the number of gusts of velocity u, for
every 1000 gusts of velocity 3.05 m/s.
From these two curves the gust exceedance E(ue) is obtained; E(u,) is the number
of times a gust of a given magnitude (u,) will be equalled or exceeded in 1 km of flight.
Thus, from the above
number of gusts 2 3.05m/s per km = l/Zlo
number of gusts equal to u, per 1000 gusts equal to 3.05m/s = r(ue)
Hence
number of gusts equal to ue per single gust equal to 3.05m/s = r(u,)/1000
It follows that the gust exceedance E(u,) is given by
(8.50)
in which llo is dependent on height. A good approximation for the curve of r(ue)
against u, in the region u, = 3.05 m/s is
= 3.23 105~i5.26 (8.51)
Consider now the typical gust exceedance curve shown in Fig. 8.18. In 1 km of flight
there are likely to be E(u,) gusts exceeding u, m/s and E(ue) - SE(u,) gusts exceeding
ue + Sue m/s. Thus, there will be SE(u,)fewer gusts exceeding u, + Sue m/s than ue m/s
and the increment in gust speed Sue corresponds to a number -SE(u,) of gusts at a
gust speed close to u,. Half of these gusts will be positive (upgusts) and half negative
(downgusts) so that if it is assumed that each upgust is followed by a downgust of
equal magnitude the number of complete gust cycles will be -SE(u,)/2. Suppose
that each cycle produces a stress S(ue) and that the number of these cycles required
to produce failure is N(S,:,). The damage caused by one cycle is then l/N(Su,e)
and over the gust velocity interval Sue the total damage SD is given by
(8.52)