Consider a rigid aircraft observed by optical sensors giving the inertial velocities of the masscenter and right wing tip points Vem and Vwt indicated below. Position of the right wing tiprelative to the mass center frwt/cm is also known and indicated below."TAViwt = 74î – 21j + 68k ft/sVem =100î – 10j + 1ok ft/sFrwt/cm = -2î + 10ĵ + 1k ftCompute aircraft angular velocity vector (in units of rad/s) when the angular velocity vectormagnitude equals 502 rad/s.

V→Icm=100i^-10j^+10k^ ft/sVI→rwt =74i^-21j^+68k^ ft/sV→rwt/cm=-2i^+10j^+1k^ ft/swe know from…

Answered: Consider a rigid aircraft observed by…

Related questions

Question

100%

Consider a rigid aircraft observed by optical sensors giving the inertial velocities of the mass
center and right wing tip points Vem and Vwt indicated below. Position of the right wing tip
relative to the mass center frwt/cm is also known and indicated below.
"TA
Viwt = 74î – 21j + 68k ft/s
Vem =
100î – 10j + 1ok ft/s
Frwt/cm = -2î + 10ĵ + 1k ft
Compute aircraft angular velocity vector (in units of rad/s) when the angular velocity vector
magnitude equals 502 rad/s.

Expert Solution

Step 1

${\vec{V}}^{I}_{c m} = 100 \hat{i} - 10 \hat{j} + 10 \hat{k} f t / s {\vec{V^{I}}}_{r w t}^{} = 74 \hat{i} - 21 \hat{j} + 68 \hat{k} f t / s {\vec{V}}_{r w t / c m} = - 2 \hat{i} + 10 \hat{j} + 1 \hat{k} f t / s w e k n o w f r o m k i n e m a t i c s r e l a t i o n t h a t {\vec{V}}_{r w t} = {\vec{V}}_{c m} + {\vec{V}}_{r e l} + {\vec{V}}_{c m / w r t} \times \vec{ω} \vec{ω} = x \hat{i} + y \hat{j} + z \hat{k} r a d / s e c {\vec{V}}_{r e l} = 0 (R i g i d b o d y k i n e m a t i c s) {\vec{V}}_{r w t} = {\vec{V}}_{c m} + 0 + {\vec{V}}_{c m / w r t} \times \vec{ω} {\vec{V}}_{r w t} - {\vec{V}}_{c m} = {\vec{V}}_{c m / w r t} \times \vec{ω} . . . . . . . (i) (74 \hat{i} - 21 \hat{j} + 68 \hat{k}) - (100 \hat{i} - 10 \hat{j} + 10 \hat{k} f t / s) = (y - 10 z) \hat{i} - (x + 2 z) \hat{j} + (2 y + 10 x) \hat{k} = (- 26 \hat{i} - 11 \hat{j} + 58 \hat{k}) = (y - 10 z) \hat{i} - (x + 2 z) \hat{j} + (2 y + 10 x) \hat{k} T h e r e f o r e, (y - 10 z) = - 26 x + 2 z = 11 (2 y + 10 x) = 58 f r o m e q u a t i o n (i) w e h a v e, |- 26 \hat{i} - 11 \hat{j} + 58 \hat{k}| = \vec{r} \times \vec{ω}, \vec{r} = {\vec{r}}_{c m / r w t} |\vec{ω}| = \frac{\sqrt{26^{2} + 11^{2} + 58^{2}}}{2^{2} + 10^{2} + 12^{2}} x^{2} + y^{2} + z^{2} = \frac{1387}{35} o n s o l v i n g e q u a t i o n s (y - 10 z) = - 26 x + 2 z = 11 (2 y + 10 x) = 58 a n d x^{2} + y^{2} + z^{2} = \frac{1387}{35} w e g e t, x = \frac{197}{35} y = \frac{6}{7} z = \frac{94}{35} \vec{ω} = \frac{197}{35} \hat{i} + \frac{6}{7} \hat{j} + \frac{94}{35} \hat{k} r a d / s e c \vec{ω} = \frac{197}{35} \hat{i} + \frac{6}{7} \hat{j} + \frac{94}{35} \hat{k} \times \frac{180}{π} d e g / s e c = 322.49 \hat{i} + 49.11 \hat{j} + 153.88 \hat{k} d e g / s e c$

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here