Initial performance calculations

Completed initial performance spreadsheet, results are listed below. Assumptions are as follows:

• 26" rear wheel
• rolling resistance coefficient  = .01
• Cd = .3
• frontal area = 9ft^2
• net weight = 385# (250# rider)

These are initial assumptions and will need to be verified as the design develops. Using these assumptions, the best gear ratio to satisfy the 10% grade requirement was 19.1. This value would give a top speed on level ground of about 25 MPH. The limiting factors are the 10 minute current rating of the motor of 115 amps, and the motor torque vs. required torque.

The gear ratio is higher than I was anticipating so the next step will be to design a gear train to produce a 19.1:1 reduction -  the initial design goal of 20 MPH up a 10% grade looks feasible, but the level cruise top speed is limited to 25 MPH rather than the desired 30 MPH because of the gearing. Optimizing the aero and drag might allow the top speed to be increased.

Performance Spreadsheet Results:

	Gear Ratio	19.1
Speed (MPH)	Grade (%)	Tire rolling resistance (Cr)	Total rolling force (lbs)	Still air drag force (lbs)	Relative wind factor (Cw)	Relative wind drag force (lbs)	Incline force (lbs)	Rolling drag force (lbs)	Total drag force (lbs)	Motor Torque Reqd  (ft-lbs)	Motor RPM	Max Motor Torque (ft-lbs)	Current Draw (amps)
5	0	0.011	5.19	0.17	2.74	0.47	0.00	5.19	5.84	0.32	1278	9.84	21.0
10	0	0.011	5.38	0.69	0.82	0.57	0.00	5.38	6.64	0.36	2555	7.59	22.8
15	0	0.012	5.57	1.55	0.42	0.66	0.00	5.57	7.79	0.43	3833	5.35	25.4
20	0	0.012	5.77	2.76	0.27	0.75	0.00	5.77	9.28	0.51	5110	3.10	28.7
25	0	0.013	5.96	4.32	0.20	0.84	0.00	5.96	11.12	0.61	6388	0.86	32.9
30	0	0.013	6.15	6.21	0.15	0.93	0.00	6.15	13.30	0.73	7666	0.00	37.8
35	0	0.014	6.34	8.46	0.12	1.03	0.00	6.34	15.83	0.87	8943	0.00	43.5
40	0	0.014	6.54	11.05	0.10	1.12	0.00	6.54	18.70	1.03	10221	0.00	50.0
45	0	0.015	6.73	13.98	0.09	1.21	0.00	6.73	21.92	1.20	11498	0.00	57.3
50	0	0.015	6.92	17.26	0.08	1.30	0.00	6.92	25.49	1.40	12776	0.00	65.3
5	10	0.011	5.19	0.17	2.74	0.47	38.26	5.16	44.07	2.42	1278	9.84	107.2
10	10	0.011	5.38	0.69	0.82	0.57	38.26	5.36	44.87	2.46	2555	7.59	109.0
15	10	0.012	5.57	1.55	0.42	0.66	38.26	5.55	46.02	2.52	3833	5.35	111.6
20	10	0.012	5.77	2.76	0.27	0.75	38.26	5.74	47.51	2.60	5110	3.10	115.0
25	10	0.013	5.96	4.32	0.20	0.84	38.26	5.93	49.34	2.70	6388	0.00	119.1
30	10	0.013	6.15	6.21	0.15	0.93	38.26	6.12	51.53	2.82	7666	0.00	124.0
35	10	0.014	6.34	8.46	0.12	1.03	38.26	6.31	54.05	2.96	8943	0.00	129.7
40	10	0.014	6.54	11.05	0.10	1.12	38.26	6.50	56.93	3.12	10221	0.00	136.2
5	20	0.011	5.19	0.17	2.74	0.47	75.40	5.09	81.14	4.45	1278	9.84	190.8
10	20	0.011	5.38	0.69	0.82	0.57	75.40	5.28	81.94	4.49	2555	7.59	192.7
15	20	0.012	5.57	1.55	0.42	0.66	75.40	5.47	83.08	4.55	3833	5.35	195.2
20	20	0.012	5.77	2.76	0.27	0.75	75.40	5.66	84.57	4.64	5110	0.00	198.6
25	20	0.013	5.96	4.32	0.20	0.84	75.40	5.84	86.40	4.74	6388	0.00	202.7
30	20	0.013	6.15	6.21	0.15	0.93	75.40	6.03	88.58	4.86	7666	0.00	207.6
35	20	0.014	6.34	8.46	0.12	1.03	75.40	6.22	91.11	4.99	8943	0.00	213.3
5	25	0.011	5.19	0.17	2.74	0.47	93.25	5.04	98.93	5.42	1278	9.84	231.0
10	25	0.011	5.38	0.69	0.82	0.57	93.25	5.22	99.73	5.47	2555	7.59	232.8
15	25	0.012	5.57	1.55	0.42	0.66	93.25	5.41	100.87	5.53	3833	0.00	235.4
20	25	0.012	5.77	2.76	0.27	0.75	93.25	5.60	102.36	5.61	5110	0.00	238.7
5	30	0.011	5.19	0.17	2.74	0.47	110.48	4.97	116.10	6.36	1278	9.84	269.7

Motor Torque Curve: