MECHANIKA LOTU
PROJEKT 4
,,LOT SZYBOWY. BIEGUNOWA PRĘDKOŚCI’’
WYKONAŁ : KAROL WŁOSIK 187220
DATA ODDANIA: 04.12.2014
DANE POTRZEBNE DO OBLICZEŃ :
Pułap maksymalny Hmax=9085m
Maksymalna masa startowa samolotu m=11990 kg
Pole powierzchni nośnej samolotu S=39,4 m2
| H1 | H2=1/2Hmax | Hmax | |
|---|---|---|---|
| ρ | 1,225 kg/m3 | 0,773 kg/m3 | 0,461 kg/m3 |
IV.1 OBLICZENIE PRĘDKOŚCI LOTU
$$V = \sqrt{\frac{2*m*g}{\rho*S}*\frac{1}{\sqrt{C_{z}^{2} + C_{x}^{2}}}}$$
PRZYKŁADOWE OBLICZENIE DLA H1= 0m Cz=-1,381, Cx=0,131
$$V = \sqrt{\frac{2*m*g}{\rho*S}*\frac{1}{\sqrt{C_{z}^{2} + C_{x}^{2}}}} = \sqrt{\frac{2*11990*9,81}{1,225*39,4}*\frac{1}{\sqrt{{- 1,381}^{2} + {0,131}^{2}}}} = 59,25\ \frac{m}{s}$$
IV.2 OBLICZENIE PRĘDKOŚCI OPADANIA
$$w = \sqrt{\frac{2*m*g}{\rho*S}*\frac{C_{x}^{2}}{\sqrt{{(C_{z}^{2} + C_{x}^{2})}^{3}}}}$$
PRZYKŁADOWE OBLICZENIE DLA H1= 0m Cz=-1,381, Cx=0,131
$$w = \sqrt{\frac{2*m*g}{\rho*S}*\frac{C_{x}^{2}}{\sqrt{{(C_{z}^{2} + C_{x}^{2})}^{3}}}} = \sqrt{\frac{2*11990*9,81}{1,225*39,4}*\frac{{0,140}^{2}}{\sqrt{{({- 1,381}^{2} + {0,131}^{2})}^{3}}}} = 5,59\frac{m}{s}$$
IV.3 OBLICZENIE KĄTA TORU LOTU γ
$$\gamma = arctg\frac{C_{x}}{C_{z}}$$
PRZYKŁADOWE OBLICZENIE DLA Cz=-1,381, Cx=0,131
$$\gamma = arctg\frac{C_{x}}{C_{z}} = arctg\left( - \frac{0,131}{1,381} \right) = - 0,094$$
IV.5 PRZYBLIŻONE WARTOŚCI EKONOMICZNYCH I OPTYMALNYCH WARTOŚCI LOTU SZYBOWEGO
| H1 | H2 | Hmax | |
|---|---|---|---|
| ρ | 1,225 kg/m3 | 0,773 kg/m3 | 0,461 kg/m3 |
A.)
$$V_{\text{opt}} = \sqrt{\frac{2mg}{\rho*S*\sqrt{\pi*\Lambda_{e}*C_{x0}}}}$$
Dla H1
$$V_{\text{opt}} = \sqrt{\frac{2*11990*9,81}{1,225*39,4*\sqrt{\pi*6,41*0,016}}} = 92,66\frac{m}{s}$$
Dla H2
$$V_{\text{opt}} = \sqrt{\frac{2*11990*9,81}{0,773*39,4*\sqrt{\pi*7,2*0,019}}} = 116,65\frac{m}{s}$$
Dla Hmax
$$V_{\text{opt}} = \sqrt{\frac{2*11990*9,81}{0,461*39,4*\sqrt{\pi*8,84*0,022}}} = 151,05\frac{m}{s}$$
B.)
$$w_{\text{opt}} = \sqrt{\frac{8mg*\sqrt{0,016}}{\rho*S*\left( \sqrt{\pi*\Lambda_{e}} \right)^{3}}}$$
Dla H1
$$w_{\text{opt}} = \sqrt{\frac{8*11990*9,81*\sqrt{0,016}}{1,225*39,4*\left( \sqrt{\pi*6,41} \right)^{3}}} =$$
Dla H2
$$w_{\text{opt}} = \sqrt{\frac{8*11990*9,81*\sqrt{0,016}}{0,773*39,4*\left( \sqrt{\pi*6,41} \right)^{3}}} =$$
Dla Hmax
$$w_{\text{opt}} = \sqrt{\frac{8*11990*9,81*\sqrt{0,016}}{0,461*39,4*\left( \sqrt{\pi*6,41} \right)^{3}}} =$$
C.)
$$V_{\text{ek}} = \sqrt{\frac{2mg}{\rho*S*\sqrt{3*\pi*\Lambda_{e}*C_{x0}}}}$$
Dla H1
$$V_{\text{ek}} = \sqrt{\frac{2*11990*9,81}{1,225*39,4*\sqrt{3*\pi*6,41*0,016}}} = 70,40\frac{m}{s}$$
Dla H2
$$V_{\text{ek}} = \sqrt{\frac{2*11990*9,81}{0,773*39,4*\sqrt{3*\pi*6,41*0,016}}} = 88,63\frac{m}{s}$$
Dla Hmax
$$V_{\text{ek}} = \sqrt{\frac{2*11990*9,81}{0,461*39,4*\sqrt{3*\pi*6,41*0,016}}} = 114,77\frac{m}{s}$$
D.)
$$w_{\text{ek}} = \sqrt{\frac{32mg*\sqrt{C_{x0}}}{\rho*S*\left( \sqrt{3\pi*\Lambda_{e}} \right)^{3}}}$$
Dla H1
$$w_{\text{ek}} = \sqrt{\frac{32*11990*9,81*\sqrt{0,016}}{1,225*39,4*\left( \sqrt{3\pi*6,41} \right)^{3}}} = 4,58\frac{m}{s}$$
Dla H2
$$w_{\text{ek}} = \sqrt{\frac{32*11990*9,81*\sqrt{0,016}}{0,773*39,4*\left( \sqrt{3\pi*6,41} \right)^{3}}} = 5,76\frac{m}{s}$$
Dla Hmax
$$w_{\text{ek}} = \sqrt{\frac{32*11990*9,81*\sqrt{0,016}}{0,461*39,4*\left( \sqrt{3\pi*6,41} \right)^{3}}} = 7,47\frac{m}{s}$$
IV.6 BIEGUNOWA PRĘDKOŚCI
| α∞ (st) | Cx | Cz | Vh=0 | Vh=4542 | Vh=9085 | wh=0 | wh=4542 | wh=9085 | γ |
|---|---|---|---|---|---|---|---|---|---|
| -19 | 0,131 | -1,381 | 59,25 | 74,59 | 96,59 | 5,59 | 7,05 | 9,13 | -0,094 |
| -18 | 0,118 | -1,381 | 59,28 | 74,62 | 96,63 | 5,06 | 6,37 | 8,25 | -0,085 |
| -17 | 0,106 | -1,362 | 59,74 | 75,20 | 97,38 | 4,65 | 5,86 | 7,59 | -0,077 |
| -16 | 0,102 | -1,321 | 60,65 | 76,35 | 98,87 | 4,66 | 5,86 | 7,59 | -0,076 |
| -15 | 0,093 | -1,280 | 61,62 | 77,57 | 100,44 | 4,47 | 5,62 | 7,28 | -0,072 |
| -14 | 0,086 | -1,230 | 62,89 | 79,16 | 102,51 | 4,37 | 5,51 | 7,13 | -0,069 |
| -13 | 0,078 | -1,169 | 64,51 | 81,21 | 105,16 | 4,28 | 5,39 | 6,98 | -0,066 |
| -12 | 0,072 | -1,108 | 66,27 | 83,42 | 108,02 | 4,30 | 5,42 | 7,01 | -0,064 |
| -11 | 0,062 | -0,996 | 69,89 | 87,99 | 113,93 | 4,35 | 5,48 | 7,09 | -0,062 |
| -10 | 0,055 | -0,904 | 73,34 | 92,33 | 119,56 | 4,47 | 5,63 | 7,29 | -0,060 |
| -8 | 0,043 | -0,711 | 82,70 | 104,11 | 134,82 | 4,95 | 6,23 | 8,06 | -0,059 |
| -6 | 0,032 | -0,508 | 97,85 | 123,18 | 159,50 | 6,17 | 7,77 | 10,06 | -0,063 |
| -4 | 0,025 | -0,305 | 126,23 | 158,90 | 205,77 | 10,46 | 13,17 | 17,05 | -0,082 |
| -2 | 0,021 | -0,091 | 227,79 | 286,76 | 371,33 | 51,98 | 65,44 | 84,74 | -0,230 |
| -1 | 0,021 | 0,010 | 457,59 | 576,05 | 745,93 | 411,69 | 518,26 | 671,10 | 1,119 |
| 1 | 0,023 | 0,234 | 144,05 | 181,34 | 234,82 | 14,33 | 18,04 | 23,37 | 0,099 |
| 2 | 0,026 | 0,345 | 118,61 | 149,31 | 193,35 | 8,86 | 11,15 | 14,44 | 0,074 |
| 4 | 0,033 | 0,569 | 92,47 | 116,41 | 150,74 | 5,41 | 6,81 | 8,82 | 0,058 |
| 6 | 0,044 | 0,782 | 78,86 | 99,28 | 128,56 | 4,45 | 5,60 | 7,25 | 0,056 |
| 8 | 0,057 | 0,986 | 70,26 | 88,45 | 114,53 | 4,08 | 5,14 | 6,65 | 0,058 |
| 10 | 0,077 | 1,209 | 63,42 | 79,84 | 103,39 | 4,03 | 5,07 | 6,56 | 0,063 |
| 11 | 0,084 | 1,280 | 61,63 | 77,59 | 100,47 | 4,03 | 5,07 | 6,57 | 0,065 |
| 12 | 0,090 | 1,331 | 60,44 | 76,09 | 98,53 | 4,09 | 5,15 | 6,67 | 0,067 |
| 13 | 0,100 | 1,402 | 58,88 | 74,12 | 95,98 | 4,19 | 5,27 | 6,82 | 0,071 |
| 14 | 0,108 | 1,453 | 57,84 | 72,81 | 94,28 | 4,28 | 5,39 | 6,98 | 0,074 |
| 15 | 0,118 | 1,504 | 56,84 | 71,56 | 92,66 | 4,45 | 5,60 | 7,25 | 0,078 |
| 16 | 0,128 | 1,534 | 56,26 | 70,83 | 91,71 | 4,69 | 5,90 | 7,64 | 0,083 |
| 17 | 0,137 | 1,534 | 56,25 | 70,81 | 91,69 | 5,02 | 6,32 | 8,18 | 0,089 |
| 18 | 0,151 | 1,524 | 56,41 | 71,01 | 91,96 | 5,55 | 6,98 | 9,04 | 0,098 |
| 19 | 0,168 | 1,453 | 57,72 | 72,67 | 94,10 | 6,63 | 8,35 | 10,81 | 0,115 |