A Survey of Unsteady Hypersonic Flow Problems

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plotted together only for convenience; strictly, the results of Young are not
comparable with those of Hanson since Young's measurements were made on a rnng
of aspect ratio 2.9 with pitching and plunging freedoms, whereas Hanson's
measurements were on a wing of aspect ratio 1-O with pitching and. flapping
freedoms, and parameters like frequency ratio and axis position were significantly
different for the two sets.
Runysn and Morgan58 Gve . experimental evidence of the inadequacy of
linear theory In results for the flutter of a double-wedge wing and a thin plate
wing with root flexibility. The results are given in Fig. 43. They show
clearly that three-dimensional linear theory, whxch takes account of tip effects,
is quite inadequate to predxt the experimental results.
All of these results show the destabilising effect of increaslng
thickness for particular conditions. Chawla's analysis suggested a general
relationship between flutter speed, Mach number, and thickness since the result
of his analysis using pxton theory showed that, If other parameters in the
problem were the same, the flutter speed depended dzrectly on the product M6.
ted experimentally for M > 2 by the results
~t~no~~~~~~~~5~nr;eG~~~pS.
The models in these tests were constructed so
that they mere identical 111 mass and mass distribution. and in axis position;
Vf
7
only the wedge thickness varies. In Fig. 44 the parameter - - is
bw 4 CrM
plotted against MS. Since Chawla has shown that Vf 13 prop%rtlonal to 43,
the effect of this variable should be eliminated from the flutter speed parameter
used. It can be seen that the results do collapse quite well on to a single
curve, confirming the slgnlficance of both parameters MS and $d.
(iii) Incidence
Chawla56 investigates theoretically the effect of the incidence
parameter Ma, on flutter of a double-wedge section. Sene results are given
in Fig. 45. Under the conditions given m the figure, Pnth M6 = O-25, an
Initial angle of attack giving Ma, = O-25 has a small stabxlxlng effect for
0 < wh/aa < I.0 and a small destabilising effect for &I& > 1.0. For a zero
thickness aerofoil, Chawla found that an initxal angle of attack reduces the
flutter speed by a constant amount: for Ma, = O-25 the multiplying factor
IS 0.982.
Zartarian and Hsu 26 investigate theoretxally the effect of initial
incidence at considerably greater values of Ma3 for a wing with 6 = O-05.
The result is shown in Fig. 46. Up to Mu, = O-25, the value of the flutter
velocity parameter is reduced by a factor of about O-99; for Ma, = O-50, whxh
represents only a moderate incdence even at M = 5, there is a reduction by a
factor of O-95.
These results receive confxmation from the experimental inVeStig*tion
of Young6' from which Fig. 47 is reproduced. Both theory and experiment show a
decrease i: the flutter speed parameter with lncdence and show agreement on
the amount. The results indicate some effect of thickness: for Ma9 = 0.10 and
M6 = 1.1, the theoretical reduction factor is about O-93; for Ma, = 0'10 and
M6 = l-5, the factor is O-95.
The good agreement on the effect of incidence on flutter Sped between
theory sd experiment in Ref. 61, is not repeated for the effect on flutter
frequency./