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Formula sheet for Aerodynamics Y3...

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Formulae and Diagrams for Section A For planar oblique shock waves, with γ = 1.4:

tan ( ξ−δ ) =tan ξ 2

[(

1 5 1+ 2 2 6 M 1 sin ξ

)]

2

p2 2 . 8 M 1 sin ξ−0 . 4 = p1 2.4 2 2 ρ2 2 . 4 M 1 sin ξ = ρ 1 0 . 4 M 2 sin2 ξ +2 1

V 22

[(

1 5 =cos ξ+ sin ξ 1+ 2 2 2 6 V1 M 1 sin ξ M 22

2

)]

2

( )( )( )

= 2

M1

2

V 22

V 21

ρ2 ρ1

p1 p2

For Simple-wave Flows Θ degrees 0 1 2 3 4 5 6 7 8 9 10 12

M 1.000 1.082 1.133 1.177 1.218 1.257 1.294 1.330 1.366 1.401 1.435 1.503

Θ degrees 14 16 18 20 25 30 35 40 45 50 55 60

M 1.571 1.639 1.707 1.775 1.950 2.134 2.329 2.538 2.765 3.013 3.287 3.594

Θ degrees 65 70 75 80 85 90 100 110 120 130 130.45

M 3.941 4.339 4.801 5.348 6.006 7.751 9.210 13.875 27.34 630.25 ∞

For high-speed flows: T0 =1+0. 2 M 2 T1

p0 3. 5 = (1+0 . 2 M 2 ) p For infinite swept wings, the critical Mach number, M c, is related to wing sweep, Λ, by the equation:

[(

C ¿pi 2 D

1+0. 2 M2c cos 2 Λ 2 = 1.2 cos Λ 1 . 4 M c2 cos2 Λ

)

3. 5

]

−1 √ 1−M 2c cos2 Λ

where Cp*i2D, refers to the minimum Cp for the streamwise aerofoil profile in low-speed flow.

For plane wings in supersonic flows, linearised theory gives for zero taper ratio: (USAF DATCOM publications)

Here,

C Nα≈

dC L dα

C L≈ C N α

for small incidences, and

α

β= √ M 2−1 For supersonic leading-edges,

and for subsonic leading-edges,

C 2L C Di = CN

α

C 2L β C Di= 1+ tan Λ LE 2 CN α

(

)...