Enunciado

Um avião tem massa de 20.000   k g e voa a   175   m / s a 5.000   m de altitude padrão. A asa retangular tem uma corda de 3   m e um aerofólio simétrico a 2,5 ° de ângulo de ataque. Avalie (a) a envergadura da asa, (b) a razão de aspecto e (c) o arrasto induzido.

Passo 1

E aí, tudo bem? Bora matar essa questão!

a)

Para o ar a 5000   m , temos ρ = 0 , 736   k g / m 3 , agora calculando b temos:

Lembrando que:

P = 20.000 ⋅ 9,81   N

P = C S ρ V 2 b C = 2 π sen ⁡ 2,5 ° 1 + 2 ⋅ 3 b ⋅ 0,736 k g m 3 2 ⋅ 175 m s 2 ⋅ b ⋅ ( 30   m )

Reajustando a equação temos:

b 2 - 21,2 b - 127 = 0

b ≈ 26,1   m

Passo 2

b)

Agora calculando AR:

A R = b C = 26,1 3

A R ≈ 8,7

Passo 3

c)

Pra matar de vez calculando o arrasto induzido:

C S = 2 π sen ⁡ 2,5 ° 1 + 2 ⋅ 3 8,7 = 0,223

C A ∞ = C S 2 π A R = 0,223 2 π ⋅ 8,6

C A ∞ = 0,00182

F A , i n d = 0,00182 2 0,736 k g m 3 ⋅ 175 m s 2 ⋅ 21,6   m ⋅ 3   m

F A , i n d = 1,6   k N

Isso é tudo pessoal, conseguimos mais uma! \o/

Resposta

a)

b ≈ 26,1   m

b)

A R ≈ 8,7

c)

F A , i n d = 1,6   k N

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