# parse-docs · MinerU 解析输出 / parsed output ## 1. 扫描论文页的公式 / Equations from a scanned page *Source: NACA Report 1135, p.630 (1953 scan) — parsed with `mineru -b pipeline -m ocr`* 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. ## PRANDTL-MEYER EXPANSION The Prandtl-Meyer angle for the flow of an imperfect gas can be found by graphically integrating the equation (see ref. 8) $$ \scriptstyle \mu = - \int _ { p _ { * } } ^ { p } { \frac { d p } { \rho V ^ { 2 } { \mathrm { ~ t a n ~ } } \mu } } \quad [ { \mathrm { i s e n } } ]\tag{199} $$ The relations between ${ \pmb { p } } , { \pmb \rho } , { \pmb V } ,$ and $\pmb { \mu }$ can be found with the aid of equations (5), (187), (183), and (185). For a thermally perfect gas this equation becomes (see, again, ref. 8) $$ \nu { = } { - } \int _ { p _ { \ast } } ^ { p } { \frac { \sin ~ 2 \mu } { 2 \gamma p } } ~ d p \quad [ \mathrm { i s e n , ~ t h e r m ~ p e r f } ]\tag{200} $$ 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 ## 2. 数据表还原 / Reconstructed data table *Source: NASA/CR-2008-215434, Table 2 (born-digital) — parsed with `mineru`* TABLE 2.—POST-STALL MAXIMUM DRAG COEFFICIENTS CALCULATED ACCORDING TO THREE MODELS AND COMPARED TO MEASURED COEFFICIENTS. [Test data sources: see Lindenburg 2000]

Airfoil designation	Thicknessratio,t/c	Aspect ratio,AR	Meas. post-stallmax drag coef.,CD2max	Model calculations of post-stall max drag coef.,CD2max
				AERODASmodel	StC model	Flat-platemodel
NACA 0012	0.12	Inf.	2.090	2.053	1.902	1.980
NACA 0012	0.12	Inf.	2.090	2.053	1.902	1.980
NACA 0015	0.15	Inf.	1.700	2.007	1.878	1.980
NACA 4409	0.09	Inf.	2.100	2.100	1.985	1.980
NACA 4412	0.12	Inf.	2.060	2.053	1.959	1.980
NACA 4415	0.15	Inf.	2.068	2.007	1.933	1.980
NACA 4418	0.18	Inf.	2.060	1.964	1.906	1.980
NACA 0012	0.12	Inf.	2.050	2.053	1.902	1.980
NACA 23012	0.12	Inf.	2.082	2.053	1.948	1.980
NACA 23017	0.17	Inf.	2.078	1.978	1.902	1.980
FX-84-W-127	0.13	Inf.	2.000	2.042	1.964	1.980
FX-84-W-218	0.22	Inf.	2.040	1.911	1.939	1.980
LS-421 Mod	0.21	Inf.	2.020	1.922	2.010	1.980
NACA 23024	0.24	Inf.	1.970	1.881	1.798	1.980
NACA 63-215	0.15	Inf.	1.980	2.007	1.959	1.980
GA(W)-1	0.17	Inf.	1.830	1.978	2.032	1.980
GA(W)-1 Inverted	0.17	Inf.	1.720	1.978	1.794	1.980
NACA 4409	0.09	12	1.750	1.698	1.370	1.322
NACA 4412	0.12	12	1.690	1.659	1.356	1.322
NACA 4418	0.18	12	1.680	1.587	1.327	1.322
NACA 4409	0.09	9	1.590	1.593	1.296	1.256
NACA 4412	0.12	9	1.640	1.557	1.282	1.256
NACA 4418	0.18	9	1.480	1.490	1.254	1.256
Clark-Y	0.18	8	1.470	1.442	1.251	1.235
NACA 4409	0.09	6	1.450	1.430	1.220	1.197
NACA 4412	0.12	6	1.450	1.398	1.206	1.197
NACA 4418	0.18	6	1.320	1.337	1.177	1.197
Clark-Y	0.18	6	1.360	1.333	1.204	1.197
Infinite length airfoilsMean deviation of model from test data:Standard deviation:				0.0060.120	0.0720.139	-0.0160.123
Finite-length airfoils:Mean deviation of model from test data:Standard deviation:				0.0320.047	0.2670.278	0.2840.299
All airfoils:Mean deviation of model from test data:Standard deviation:				0.0090.098	0.1490.205	-0.1210.210

## 3. 图表抽取 / Extracted figure *Source: NACA Report 1135, Chart 13 (1953 scan)*  ("hakr ti.--Variation of surface pressure coefficient with cone semivertex angle for various upstream Mach numbers. Perfect gas, γ= 1.405.