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! _γ ₋₁ ¹

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lo

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2 )

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•

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•

•

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• a 0 = 0.0, 2.0, 4.0, ...20.0 ◦

• p 0 = 1.0

• ρ 0 = 1.0

• γ = 1 . 4

• l = 2.0

h = 0.2

• θ = arctan 2 l h

•

[ − 2 , − 3] × [4 , 3]

•

( − 1; 0) , (1; 0) , (0; 0.2)

c = r

γ p ρ

M = V c

p

ρ = R · T

ρ 1 = ρ 0

1 + γ − 2 1 M 0 2

1 + γ − 2 1 M 1 2

! γ −1 1

p 1 = p 0

1 + γ − 2 1 M 0 2

1 + γ − 2 1 M 1 2

! γ−1 γ

tan( σ 1 − ϑ )

tan(σ 1 ) = 2 γ + 1

1

M 0 2 sin 2 ( σ 1 ) + γ − 1 γ + 1

ρ 1 = ρ 0

tan(σ 1 ) tan(σ 1 − ϑ)

M 0 n 1 = M 0 sin(σ 1 )

p 1 = p 0

2

1 + γ (γM 0 2 n 1 − γ − 1

2 )

M 1 n = 1 + γ− 2 1 M 0 2 n 1

γM 0 2 n 1 − γ − 2 1

! 1 2

M 1 = M 1 n

sin(σ 1 − ϑ)

ν(M ) =

r γ + 1

γ − 1 arctan

r γ − 1

γ + 1 (M 2 − 1) − arctan √

M 2 − 1

ν(M 1 ) = ν(M 0 ) + ϑ

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20 ^◦

• a 0 = 0.0, 2.0, 4.0, ...20.0 ^◦

• θ = arctan ² _l ^h

1 + ^γ ⁻ 2 ¹ M 0 ²

1 + ^γ ⁻ ₂ ¹ M 1 ²

! _γ ₋₁ ¹

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1 + ^γ ⁻ ₂ ¹ M 1 ²

! _γ−1 ^γ

tan(σ ¹ ) = 2 γ + 1

M 0 ² sin ² ( σ 1 ) + γ − 1 γ + 1

tan(σ ¹ ) tan(σ ¹ − ϑ)

M 0 n 1 = M 0 sin(σ ¹ )

1 + γ (γM 0 ² n 1 − γ − 1

M 1 n = 1 + ^γ− ₂ ¹ M 0 ² n 1

γM 0 ² n 1 − ^γ ⁻ 2 ¹

! ¹ ₂

sin(σ ¹ − ϑ)

γ + 1 (M ² − 1) − arctan √

M ² − 1

ν(M ¹ ) = ν(M ⁰ ) + ϑ