7/21/2019 AE140 S14 Problem 6.5.1 Solution

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Spin and Precession of a Football

The angular velocity of a football which has just beenkicked is horizontal. The axis of symmetry q 3 is !

above the horizontal.and H are both in the q 12 " q 3 plane.

H

N B

#$

#%Find the orientation of H and

the spin and precession rates.

& %'! rpm

31

AC

II

transverse

axial==

Problem (.).%Solution

BN

7/21/2019 AE140 S14 Problem 6.5.1 Solution

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Space cone

Body cone

Hn z

q 3

* + ,- irect Precession

7/21/2019 AE140 S14 Problem 6.5.1 Solution

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Solution

/ody cone angle & & !

H

N B

q 3

q 12

& !0

rpm169.1cos20rpm61.6sin20

312

====

+=

3

12

312

qq

7/21/2019 AE140 S14 Problem 6.5.1 Solution

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H

N B

q 3

q 12

& !0

= 5.47===

+=

tan203tanCA

HH

tan3

12

312

HH 312 qqH

7/21/2019 AE140 S14 Problem 6.5.1 Solution

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H

!0

12.)0

n z

2.)0

%'!03 4 !0 3 2.)05

6aw of Sines

=

=

5.27sin

20sin

5.132sin

7/21/2019 AE140 S14 Problem 6.5.1 Solution

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=

=

5.27sin

20sin

5.132sin

112. rp

!3."rpm

=

=

7/21/2019 AE140 S14 Problem 6.5.1 Solution

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*lternate Solution

7ecall that-

!3."rpm

#$% ."sinrpm61.6

s

s

&

12

&12

=

==

=

112. rpm#."!3."cos$%169.1

c'

c

&3

&3

==

=

+=