MECHANIKA LOTU

PROJEKT 5

,,CHARAKTERYSTYKI ZESPOŁU NAPĘDOWEGO’’

WYKONAŁ : KAROL WŁOSIK 187220

DATA ODDANIA: 15.01.2015

V.1 Dane potrzebne do obliczeń :

$$\mathbf{V}_{\mathbf{d}}\mathbf{=}\mathbf{500}\frac{\mathbf{\text{km}}}{\mathbf{h}}\mathbf{=}\mathbf{1}\mathbf{38,88}\frac{\mathbf{m}}{\mathbf{s}}$$

h_d=6000m

N(0)=1412 kW

n_s(0)= 40 obr/s

N_sd= 973, 38 kW

n_sd=27, 6 obr/s

V.2 Obliczenie cechy bezśrednicowej śmigła C_d

Gęstość powietrza na wysokości h_d=6000 m :

$$\mathbf{\rho}_{\mathbf{d}}\mathbf{= 1,225}{\mathbf{(1 -}\frac{\mathbf{6000}}{\mathbf{44331}}\mathbf{)}}^{\mathbf{4,256}}\mathbf{= 0,}\mathbf{659}\frac{\mathbf{\text{kg}}}{\mathbf{m}^{\mathbf{3}}}$$

$$\mathbf{C}_{\mathbf{d}}\mathbf{=}\mathbf{V}_{\mathbf{d}}\mathbf{*}\sqrt[\mathbf{5}]{\frac{\mathbf{\rho}_{\mathbf{d}}}{\mathbf{N}_{\mathbf{d}}\left( \mathbf{n}_{\mathbf{\text{sd}}} \right)^{\mathbf{2}}}}\mathbf{=}\mathbf{1}\mathbf{38,88}\mathbf{*}\sqrt[\mathbf{5}]{\frac{\mathbf{0,659}}{\mathbf{973,38}\mathbf{*}\mathbf{10}^{\mathbf{3}}\mathbf{*}\mathbf{27,6}^{\mathbf{2}}}}\mathbf{=}\mathbf{2,}\mathbf{14}$$

Dla obliczonej wartości cechy bezśrednicowej śmigła dobieram śmigło 3-ramienne 5868-g o profilu typu Clark Y.

V.3 Obliczenie średnicy śmigła

$$\mathbf{D =}\frac{\mathbf{V}_{\mathbf{d}}}{\mathbf{J*}\mathbf{n}_{\mathbf{\text{sd}}}}$$

Parametr J dobieram do obliczeń z wykresu dla kąta nastawienia łopat β, przy którym wartość sprawności jest największa. Jest to kąt β=45°.

• V_d=138,88 m/s

• J=1,75 , zatem :

$$\mathbf{D =}\frac{\mathbf{V}_{\mathbf{d}}}{\mathbf{J*}\mathbf{n}_{\mathbf{\text{sd}}}}\mathbf{=}\frac{\mathbf{138,88}}{\mathbf{1,}\mathbf{75}\mathbf{*}\mathbf{2}\mathbf{7}\mathbf{,}\mathbf{6}}\mathbf{=}\mathbf{2,}\mathbf{87}\mathbf{\text{\ m}}$$

V.4 Sprawdzenie liczby Macha na końcu łopaty śmigła

Dla H=6000m a_dd=316,3m/s

V_max=1,2V_d=166,65m/s

$$\mathbf{\text{Ma}}_{\mathbf{\text{kl}}}\mathbf{=}\frac{\sqrt{\mathbf{V}_{\mathbf{\max}}^{\mathbf{2}}\mathbf{+}{\mathbf{(\pi*}\mathbf{n}_{\mathbf{\text{sd}}}\mathbf{*D)}}^{\mathbf{2}}}}{\mathbf{a}_{\mathbf{\text{dd}}}}\mathbf{=}\frac{\sqrt{\mathbf{166,65}^{\mathbf{2}}\mathbf{+}{\mathbf{(\pi*}\mathbf{27,6}\mathbf{*}\mathbf{2,}\mathbf{87}\mathbf{)}}^{\mathbf{2}}}}{\mathbf{316}}\mathbf{=}\mathbf{0,}\mathbf{94}$$

V.5 Wyznaczenie mocy rozporządzalnej

N_r=N*η_s

h,m	ρ, kg/m^3
0	1,225
1000	1,111
2000	1,006486
3000	0,909115
4000	0,819122
5000	0,736107
6000	0,659688
8000	0,525157

1. $\mathbf{N}\left( \mathbf{h = 8000}\mathbf{m} \right)\mathbf{= N}\left( \mathbf{h = 0}\mathbf{m} \right)\mathbf{*}\left( \frac{\mathbf{\rho}}{\mathbf{\rho}_{\mathbf{0}}} \right)^{\mathbf{0,6}}\mathbf{= 1412*}\mathbf{10}^{\mathbf{3}}\mathbf{*}\left( \frac{\mathbf{0,525}}{\mathbf{1,225}} \right)^{\mathbf{0,6}}\mathbf{= 849,27*\ }\mathbf{10}^{\mathbf{3}}\mathbf{\text{\ W}}$

n_{sh = 8000}=24, 1 obr/s

$$\mathbf{C}_{\mathbf{N}}\mathbf{=}\frac{\mathbf{N}}{\mathbf{\rho*}{\mathbf{\eta}_{\mathbf{\text{sd}}}}^{\mathbf{3}}\mathbf{*}\mathbf{D}^{\mathbf{5}}}\mathbf{=}\mathbf{0,593}\mathbf{5}$$

1. $\mathbf{N}\left( \mathbf{h = 6000}\mathbf{m} \right)\mathbf{= N}\left( \mathbf{h = 0}\mathbf{m} \right)\mathbf{*}\left( \frac{\mathbf{\rho}}{\mathbf{\rho}_{\mathbf{0}}} \right)^{\mathbf{0,6}}\mathbf{= 1412*}\mathbf{10}^{\mathbf{3}}\mathbf{*}\left( \frac{\mathbf{0,659}}{\mathbf{1,225}} \right)^{\mathbf{0,6}}\mathbf{= 973,38*\ }\mathbf{10}^{\mathbf{3}}\mathbf{\text{\ W}}$

n_{sh = 6000}=27, 6 obr/s

$$\mathbf{C}_{\mathbf{N}}\mathbf{=}\frac{\mathbf{N}}{\mathbf{\rho*}{\mathbf{\eta}_{\mathbf{\text{sd}}}}^{\mathbf{3}}\mathbf{*}\mathbf{D}^{\mathbf{5}}}\mathbf{=}\mathbf{0,3}\mathbf{60}\mathbf{7}$$

$$\mathbf{C.)}\mathbf{N}\left( \mathbf{h =}\mathbf{5}\mathbf{000}\mathbf{m} \right)\mathbf{= N}\left( \mathbf{h = 0}\mathbf{m} \right)\mathbf{*}\left( \frac{\mathbf{\rho}}{\mathbf{\rho}_{\mathbf{0}}} \right)^{\mathbf{0,6}}\mathbf{= 1412*}\mathbf{10}^{\mathbf{3}}\mathbf{*}\left( \frac{\mathbf{0,}\mathbf{736}}{\mathbf{1,225}} \right)^{\mathbf{0,6}}\mathbf{=}\mathbf{1040,11}\mathbf{*\ }\mathbf{10}^{\mathbf{3}}\mathbf{\text{\ W}}$$

n_{sh = 6000}=29,4 obr/s

$$\mathbf{C}_{\mathbf{N}}\mathbf{=}\frac{\mathbf{N}}{\mathbf{\rho*}{\mathbf{\eta}_{\mathbf{\text{sd}}}}^{\mathbf{3}}\mathbf{*}\mathbf{D}^{\mathbf{5}}}\mathbf{= 0,}\mathbf{2838}$$

$$\mathbf{D.)}\mathbf{N}\left( \mathbf{h = 4000}\mathbf{m} \right)\mathbf{= N}\left( \mathbf{h = 0}\mathbf{m} \right)\mathbf{*}\left( \frac{\mathbf{\rho}}{\mathbf{\rho}_{\mathbf{0}}} \right)^{\mathbf{0,6}}\mathbf{= 1412*}\mathbf{10}^{\mathbf{3}}\mathbf{*}\left( \frac{\mathbf{0,819}}{\mathbf{1,225}} \right)^{\mathbf{0,6}}\mathbf{= 1108,97*\ }\mathbf{10}^{\mathbf{3}}\mathbf{\text{\ W}}$$

n_{sh = 4000}=31, 4 obr/s

$$\mathbf{C}_{\mathbf{N}}\mathbf{=}\frac{\mathbf{N}}{\mathbf{\rho*}{\mathbf{\eta}_{\mathbf{\text{sd}}}}^{\mathbf{3}}\mathbf{*}\mathbf{D}^{\mathbf{5}}}\mathbf{= 0,}\mathbf{2}\mathbf{246}$$

$$\mathbf{E.)N}\left( \mathbf{h = 3000}\mathbf{m} \right)\mathbf{= N}\left( \mathbf{h = 0}\mathbf{m} \right)\mathbf{*}\left( \frac{\mathbf{\rho}}{\mathbf{\rho}_{\mathbf{0}}} \right)^{\mathbf{0,6}}\mathbf{= 1412*}\mathbf{10}^{\mathbf{3}}\mathbf{*}\left( \frac{\mathbf{0,909}}{\mathbf{1,225}} \right)^{\mathbf{0,6}}\mathbf{= 1180,56*\ }\mathbf{10}^{\mathbf{3}}\mathbf{\text{\ W}}$$

n_sh=3000=33, 4 obr/s

$$\mathbf{C}_{\mathbf{N}}\mathbf{=}\frac{\mathbf{N}}{\mathbf{\rho*}{\mathbf{\eta}_{\mathbf{\text{sd}}}}^{\mathbf{3}}\mathbf{*}\mathbf{D}^{\mathbf{5}}}\mathbf{= 0,}\mathbf{173}\mathbf{8}$$

$$\mathbf{F}\mathbf{.)}\mathbf{N}\left( \mathbf{h = 2000}\mathbf{m} \right)\mathbf{= N}\left( \mathbf{h = 0}\mathbf{m} \right)\mathbf{*}\left( \frac{\mathbf{\rho}}{\mathbf{\rho}_{\mathbf{0}}} \right)^{\mathbf{0,6}}\mathbf{= 1412*}\mathbf{10}^{\mathbf{3}}\mathbf{*}\left( \frac{\mathbf{1,006}}{\mathbf{1,225}} \right)^{\mathbf{0,6}}\mathbf{= 1254,61*\ }\mathbf{10}^{\mathbf{3}}\mathbf{\text{\ W}}$$

n_{sh = 2000}=35, 5 obr/s

$$\mathbf{C}_{\mathbf{N}}\mathbf{=}\frac{\mathbf{N}}{\mathbf{\rho*}{\mathbf{\eta}_{\mathbf{\text{sd}}}}^{\mathbf{3}}\mathbf{*}\mathbf{D}^{\mathbf{5}}}\mathbf{= 0,}\mathbf{1431}$$

G.)$\mathbf{N}\mathbf{\ }\left( \mathbf{h = 1000}\mathbf{m} \right)\mathbf{= N}\left( \mathbf{h = 0}\mathbf{m} \right)\mathbf{*}\left( \frac{\mathbf{\rho}}{\mathbf{\rho}_{\mathbf{0}}} \right)^{\mathbf{0,6}}\mathbf{= 1412*}\mathbf{10}^{\mathbf{3}}\mathbf{*}\left( \frac{\mathbf{1,}\mathbf{111}}{\mathbf{1,225}} \right)^{\mathbf{0,6}}\mathbf{=}\mathbf{1331,62}\mathbf{*\ }\mathbf{10}^{\mathbf{3}}\mathbf{\text{\ W}}$

n_{sh = 2000}=37, 5 obr/s

$$\mathbf{C}_{\mathbf{N}}\mathbf{=}\frac{\mathbf{N}}{\mathbf{\rho*}{\mathbf{\eta}_{\mathbf{\text{sd}}}}^{\mathbf{3}}\mathbf{*}\mathbf{D}^{\mathbf{5}}}\mathbf{= 0,}\mathbf{1}\mathbf{167}$$

G.) (h=0m)

N(0)=1412 kW

n_s(0)= 40 obr/s

$$\mathbf{C}_{\mathbf{N}}\mathbf{=}\frac{\mathbf{N}}{\mathbf{\rho*}{\mathbf{\eta}_{\mathbf{\text{sd}}}}^{\mathbf{3}}\mathbf{*}\mathbf{D}^{\mathbf{5}}}\mathbf{= 0,}\mathbf{092}\mathbf{4}$$

h=0m
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h1=1000 m
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h2=2000 m
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h3=3 000 m
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h4=4000 m
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h5=5000 m
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h6=6 000 m
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h7=8000 m
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