wAo math

	A	B	C	D	E	F
1
2	Parameters
3	Yield Stress	6.09E+04	lbf/in^2	4.20E+08	Pa
4	Density	503	lbf/ft^3	8050	kg/m^3
5	Young's Modulus	3.12E+07	lbf/in^2	2.15E+11	Pa
6
7	Useful Conversions
8	Length	1	in	0.0254	m
9	Length	1	ft	0.3048	m
10	Pressure	1	lbf/ft^2	47.88	Pa
11	Pressure	1	lbf/in^2	6894.72	Pa
12	Force	1	lbf	4.44822	N
13	Mass	1	lb	0.4535	kg
14
15	Horizontal Axle
16	Length	8	ft	2.4384	m
17	Diameter	3.5	in	8.89	cm
18	Thickness	0.3	in	0.762	cm
19	Volume	0.1675516082	ft^3	0.004744525379	m^3
20	Mass	84.27845892	lb	38.1934293	kg
21	Moment of Inertia	3.894318253	in^4	162.0937638	cm^4
22	Force on Center of Beam*	2793.053246	lbf	12424.11531	N	*obtained from adding centrifugal forces from motion plus gravitational force of both beams and carriage
23	Deflection of Center of Beam**	0.308	in	1.08E-02	m	**obtained from Myosotis formulae
24	Max Stress	30123.07177	lbf/in^2	207690145.4	Pa
25	Safety Factor	2.02E+00
26
27	Vertical Axle
28	Length	6	ft	1.8288	m
29	Diameter	3	in	7.62	cm
30	Thickness	0.25	in	0.635	cm
31	Cross Sectional Area	0.01499892326	ft^2	0.001393445568	m^2
32	Volume	0.08999353956	ft^3	0.002548329061	m^3
33	Mass	45.2667504	lb	20.51404894	kg
34	Moment of Inertia	2.058602217	in^4	85.68549357	cm^4
35	Max Normal Force on Beam***	2793.053246	lbf	12424.11531	N	***assumed to be the same as the force at the center of the horizontal beam
36	Max Axial Stress	1293.179559	lbf/in^2	8916110.969	Pa
37	Max Hole Stress	3879.538677	lbf/in^2	26748332.91	Pa
38	Safety Factor	15.7
39
40	Frame Buckling
41	Largest Unsupported Length	100	in	2.54	m
42	Width	3.5	in	0.0889	m
43	Thickness	3.5	in	0.0889	m
44	Smallest Second Moment of Area (I)	12.50520833	in^4	5.21E-06	m^4
45	Young's Modulus	8.48	GPa
46	Critical Buckling Load	1.52E+04	lbf	6.75E+04	N
47	Maximum Load	698.2633114	lbf	3106.028827	N
48	Safety Factor	2.17E+01
49
50	Carriage
51	Number of Seats	4
52	Seat Mass	30	lb	13.60776	kg
53	Avg Rider Mass	200	lb	90.90909091	kg
54	Total Rider+Seat Mass	920	lb	418.0674036	kg
55
56	Rotating Pipe
57	Length	3	m	0.9144	m
58	Diameter	6	in	15.24	cm
59	Thickness	0.25	in	0.635	cm
60	Volume	0.09408415499	ft^3	0.0026641622	m^3
61	Mass	47.32432996	lb	21.44650571	kg
62
63	Other Carriage Parts Mass	350	lb	158.725	kg
64	Carriage Total Mass	1317.32433	lb	597.4065836	kg
65
66	Vertical Axle Bolt
67	Cross Sectional Area	0.306640625	in^2
68	Tensile Strength of Grade 8 Bolt	150000	lb/in^2
69	Shear Strength of Grade 8 Bolt	90,000	lb/in^2		~60% of tensile strength
70	Max Rated Shear Load on Bolt	27597.65625	lb
71	Max Shear Load on Bolt	1396.526623	lb
72	Safety Factor	19.76163991
73
74	Vertical Bearing Retaining Ring Bolt
75	Cross Sectional Area	0.306640625	in^2
76	Tensile Strength of Grade 8 Bolt	150000	lb/in^2
77	Shear Strength of Grade 8 Bolt	90,000	lb/in^2		~60% of tensile strength
78	Max Rated Shear Load on Bolt	27597.65625	lb
79	Max Shear Load on Bolt	1396.526623	lb
80	Safety Factor	19.76163991
81
82	Vertical Shaft Taper Bearing
83	Dynamic Radial Rating	68100	lbf	303000	N
84	Bearing K-Factor	1.44
85	Maximum Equivalent Radial Load****	4021.996674	lbf	17890.72604	N	****calculated at bottom of swing, at maximum possible velocity from gravity
86	Safety Factor	16.93188869				(the maximum thrust load for a bearing is less than the maximum radial load)
87
88	Horizontal Shaft Bearing
89	Dynamic Radial Rating	19153.72891	lbf	85200	N
90	Maximum Radial Load*****	2793.053246	lbf	12424.11531	N	*****never sees any axial load
91	Safety Factor	6.857631138
92
93	Motion
94	Starting Angle	1.047	radians
95
96	Carriage Rotation Radius	4.5	ft	1.3716	m
97	Height Difference	2.25	ft	0.6858	m
98	Carriage Max Velocity	12.034	ft/s	3.668	m/s
99	Carriage Centrifugal Force	1317.39	lbf	5860.05	N
100