[ { "type": "text", "text": "provided that $M _ { 1 }$ sin $\\pmb \\theta$ is used instead of $M _ { 1 }$ and that the static temperature $\\pmb { T _ { i } }$ just upstream of the shock wave is the same for the oblique shock wave as for the normal shock wave.", "bbox": [ 75, 73, 526, 131 ], "page_idx": 0, "_demo": "equations", "_source": "NACA Report 1135, p.630 (1953 scan)" }, { "type": "text", "text": "PRANDTL-MEYER EXPANSION", "text_level": 2, "bbox": [ 186, 128, 416, 142 ], "page_idx": 0, "_demo": "equations", "_source": "NACA Report 1135, p.630 (1953 scan)" }, { "type": "text", "text": "The Prandtl-Meyer angle for the flow of an imperfect gas can be found by graphically integrating the equation (see ref. 8)", "bbox": [ 75, 147, 526, 193 ], "page_idx": 0, "_demo": "equations", "_source": "NACA Report 1135, p.630 (1953 scan)" }, { "type": "equation", "img_path": "images/ef7f0e858b992b83c8763826f3b3cd7d7652cf98f2de87bfd102425a630bffc0.jpg", "text": "$$\n\\scriptstyle \\mu = - \\int _ { p _ { * } } ^ { p } { \\frac { d p } { \\rho V ^ { 2 } { \\mathrm { ~ t a n ~ } } \\mu } } \\quad [ { \\mathrm { i s e n } } ]\\tag{199}\n$$", "text_format": "latex", "bbox": [ 195, 202, 404, 233 ], "page_idx": 0, "_demo": "equations", "_source": "NACA Report 1135, p.630 (1953 scan)" }, { "type": "text", "text": "The relations between ${ \\pmb { p } } , { \\pmb \\rho } , { \\pmb V } ,$ and $\\pmb { \\mu }$ can be found with the", "bbox": [ 75, 242, 524, 261 ], "page_idx": 0, "_demo": "equations", "_source": "NACA Report 1135, p.630 (1953 scan)" }, { "type": "text", "text": "aid of equations (5), (187), (183), and (185). For a thermally perfect gas this equation becomes (see, again, ref. 8)", "bbox": [ 544, 77, 993, 109 ], "page_idx": 0, "_demo": "equations", "_source": "NACA Report 1135, p.630 (1953 scan)" }, { "type": "equation", "img_path": "images/00608c0e2e4138acc5107f08cab4f6c4bb858d546ed7ace7a33baf7eb468a0e0.jpg", "text": "$$\n\\nu { = } { - } \\int _ { p _ { \\ast } } ^ { p } { \\frac { \\sin ~ 2 \\mu } { 2 \\gamma p } } ~ d p \\quad [ \\mathrm { i s e n , ~ t h e r m ~ p e r f } ]\\tag{200}\n$$", "text_format": "latex", "bbox": [ 622, 118, 914, 150 ], "page_idx": 0, "_demo": "equations", "_source": "NACA Report 1135, p.630 (1953 scan)" }, { "type": "text", "text": "The relations between ${ \\boldsymbol { \\gamma } } , { \\boldsymbol { p } } ,$ and $\\pmb { \\mu }$ can be found with the aid of equations (180), (189), and (186) using the temperature as a parameter. The graphical integration of equation (2o0) has been carried out, and the variations of $\\nu _ { \\mathrm { t h e r m ~ \\ p e r t } }$ and Vtherm per with Mach number for various values of total Vperf", "bbox": [ 542, 159, 993, 250 ], "page_idx": 0, "_demo": "equations", "_source": "NACA Report 1135, p.630 (1953 scan)" }, { "type": "page_number", "text": "630", "bbox": [ 78, 46, 114, 61 ], "page_idx": 0, "_demo": "equations", "_source": "NACA Report 1135, p.630 (1953 scan)" }, { "type": "header", "text": "REPORT 1135-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS", "bbox": [ 277, 51, 791, 68 ], "page_idx": 0, "_demo": "equations", "_source": "NACA Report 1135, p.630 (1953 scan)" }, { "type": "table", "img_path": "images/2a51000b4af3b805526f813f8ea27d22889039c4472cd02a415c6240af8f917f.jpg", "table_caption": [ "TABLE 2.—POST-STALL MAXIMUM DRAG COEFFICIENTS CALCULATED ACCORDING TO THREE MODELS AND COMPARED TO MEASURED COEFFICIENTS.", "[Test data sources: see Lindenburg 2000]" ], "table_footnote": [], "table_body": "
Airfoil designationThicknessratio,t/cAspect ratio,ARMeas. post-stallmax drag coef.,CD2maxModel calculations of post-stall max drag coef.,CD2max
AERODASmodelStC modelFlat-platemodel
NACA 00120.12Inf.2.0902.0531.9021.980
NACA 00120.12Inf.2.0902.0531.9021.980
NACA 00150.15Inf.1.7002.0071.8781.980
NACA 44090.09Inf.2.1002.1001.9851.980
NACA 44120.12Inf.2.0602.0531.9591.980
NACA 44150.15Inf.2.0682.0071.9331.980
NACA 44180.18Inf.2.0601.9641.9061.980
NACA 00120.12Inf.2.0502.0531.9021.980
NACA 230120.12Inf.2.0822.0531.9481.980
NACA 230170.17Inf.2.0781.9781.9021.980
FX-84-W-1270.13Inf.2.0002.0421.9641.980
FX-84-W-2180.22Inf.2.0401.9111.9391.980
LS-421 Mod0.21Inf.2.0201.9222.0101.980
NACA 230240.24Inf.1.9701.8811.7981.980
NACA 63-2150.15Inf.1.9802.0071.9591.980
GA(W)-10.17Inf.1.8301.9782.0321.980
GA(W)-1 Inverted0.17Inf.1.7201.9781.7941.980
NACA 44090.09121.7501.6981.3701.322
NACA 44120.12121.6901.6591.3561.322
NACA 44180.18121.6801.5871.3271.322
NACA 44090.0991.5901.5931.2961.256
NACA 44120.1291.6401.5571.2821.256
NACA 44180.1891.4801.4901.2541.256
Clark-Y0.1881.4701.4421.2511.235
NACA 44090.0961.4501.4301.2201.197
NACA 44120.1261.4501.3981.2061.197
NACA 44180.1861.3201.3371.1771.197
Clark-Y0.1861.3601.3331.2041.197
Infinite length airfoilsMean deviation of model from test data:Standard deviation:0.0060.1200.0720.139-0.0160.123
Finite-length airfoils:Mean deviation of model from test data:Standard deviation:0.0320.0470.2670.2780.2840.299
All airfoils:Mean deviation of model from test data:Standard deviation:0.0090.0980.1490.205-0.1210.210
", "bbox": [ 107, 180, 890, 806 ], "page_idx": 0, "_demo": "table", "_source": "NASA/CR-2008-215434, Table 2 (born-digital)" }, { "type": "footer", "text": "NASA/CR—2008-215434", "bbox": [ 112, 939, 292, 953 ], "page_idx": 0, "_demo": "table", "_source": "NASA/CR-2008-215434, Table 2 (born-digital)" }, { "type": "page_number", "text": "8", "bbox": [ 493, 940, 504, 953 ], "page_idx": 0, "_demo": "table", "_source": "NASA/CR-2008-215434, Table 2 (born-digital)" }, { "type": "image", "img_path": "images/2faf199423ae68050074d181a5dfbccc31370690b6ef89d696a4d066779fea45.jpg", "image_caption": [ "(\"hakr ti.--Variation of surface pressure coefficient with cone semivertex angle for various upstream Mach numbers. Perfect gas, γ= 1.405." ], "image_footnote": [], "bbox": [ 108, 77, 883, 915 ], "page_idx": 0, "_demo": "figure", "_source": "NACA Report 1135, Chart 13 (1953 scan)" }, { "type": "page_number", "text": "66i2", "bbox": [ 24, 55, 67, 71 ], "page_idx": 0, "_demo": "figure", "_source": "NACA Report 1135, Chart 13 (1953 scan)" }, { "type": "header", "text": "REPORT JB5 -NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS", "bbox": [ 224, 53, 762, 69 ], "page_idx": 0, "_demo": "figure", "_source": "NACA Report 1135, Chart 13 (1953 scan)" } ]