Calculations of the flow over an inclined flat plate at free-stream Mach number 1 Page: 4 of 71

                                
NACA TN 3723

lower surface and the leading edge. In view of the known properties of
flows near the sonic flight speed (see refs. 5 and 6), the results should
be applicable for a range of free-stream Mach number either side of 1. This
is especially true of the flow in the immediate vicinity of the leading
edge. Because of the nature of the flow field, the findings for the lower
surface of the plate can be applied, within minor limitations, to the flow
on the underside of any sharp-nosed airfoil with a flat lower surface.
As in reference 3, the report is divided into two parts. Part I con-
tains an outline of the general problem and its solution and a discussion
of the final results. Part II supplies the mathematical details. A sum-
mary of the notation is given in an appendix at the end of the report.
The relaxation calculations for the lower surface of the plate were
performed with unusual skill and diligence by Mrs. Marjorie Sill. The
characteristics construction on the upper surface was programmed for the
electronic computer by Meyer M. Resnikoff, who contributed many valuable
ideas to this phase of the work.
I - GENERAL PROBLEM AND FINAL RESULTS
GENERAL PROBIEM
Description of Flow Field
The inviscid flow over an
inclined plate at free-stream                     0     Limiting
/     Lmiting
Mach number   has been described                        Machwave
by Guderley in reference 1. A                       /
qualitative picture of the flow                 * /          M>
is given in sketch (a), which                     /   /
is essentially a reproduction      M<1        * i    /
of figure 1 of Guderley's                          /   /
report.                                     ,                 Shock waves
As shown in the sketch,             .     le
there exists at angle of attack         D  C
a large region of subsonic flow
in front of and beneath the                   Separated  a
plate. This region is bounded                  region    "A
by the lower surface DB of the                                       "A
plate, by sonic lines DO and BO
springing from the leading and                       M<i
trailing edges, and by the free                                        \ M>
stream 0 at infinity. In this     -    -   Sonic line
region, as in incompressible               Expansion
flow, the fluid forward of the             Corson Mach wave         \
plate is deflected upward. As              Cp\
a result, a stagnation point
C  occurs on the lower surface                   Sketch (a)            0 0

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