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Values from research (if you disagree, change them here - but you probably don't need to)
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Symbol
|
Description
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Value
|
Units
|
Source
|
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Cr1
|
Rolling Resistance
|
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0.015
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from Brant
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Cr2
|
Brake and Steering Resistance
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0.003
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from Brant
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Cd
|
Coefficient of Drag
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0.603
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A
|
Frontal Area
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6
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sqft
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Crw
|
Relative wind factor
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1.6
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from Brant
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Edt
|
Drive train efficiency
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0.9
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guesstimate
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Values from bike (set them for your bike on the summary page)
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Symbol
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Description
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Value
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Units
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Source
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W1
|
Motorcycle Weight - w/o batteries (frame, wheels, motor, controller etc.)
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230
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lbs
|
guesstimate
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W2
|
Battery weight
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360
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lbs
|
manufacturer spec sheet
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W3
|
Rider Weight
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160
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lbs
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bathroom scales!
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Tc
|
Tire circumference
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80
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in
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as measured
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Environmental Factors (do you live in the windy city? adjust as needed on the summary page)
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Symbol
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Description
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Value
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Units
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Source
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w
|
Wind speed
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5
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mph
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US average wind speed (according to Brant)
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Constants (surely these are OK? Don't change them)
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inches in a mile
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63360
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1 Nm in lb-ft
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0.737
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lb-ft
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REQUIRED TORQUE
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Calculated Values - Speed & Incline Independent (don't change these - change the values above)
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rev per mile
|
wheel revolutions per mile
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792
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inches in a mile / Tc
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Wt
|
total weight
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750
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W1 + W2 + W3
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Tm
|
torque mutliplier
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1.06
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840.34 / rev per mile
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Fr
|
Total rolling force
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13.50
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lbs
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Wt * (Cr1 + Cr2)
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Calculated Values - Speed & Incline Dependent (don't change these - change the values above)
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Description
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Level Ground
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10
|
20
|
30
|
40
|
50
|
60
|
70
|
80
|
90
|
100
|
mph
|
|
Fd1
|
still air drag force
|
|
lbs
|
(CdAV^2)/391
|
0.93
|
3.70
|
8.33
|
14.81
|
23.13
|
33.31
|
45.34
|
59.22
|
74.95
|
92.53
|
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|
Cw
|
relative wind factor (0.98*w/V)^2+0.63(w/V))Crw-0.4(w/V)
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|
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|
0.54
|
0.21
|
0.13
|
0.09
|
0.07
|
0.06
|
0.05
|
0.04
|
0.04
|
0.03
|
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|
Fd2
|
relative wind drag force
|
|
lbs
|
CwFd1
|
0.50
|
0.78
|
1.07
|
1.35
|
1.63
|
1.91
|
2.19
|
2.47
|
2.75
|
3.04
|
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|
Ft
|
Total force
|
|
lbs
|
Fd1 + Fd2 + Fr
|
14.93
|
17.99
|
22.89
|
29.65
|
38.26
|
48.72
|
61.03
|
75.19
|
91.20
|
109.07
|
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|
Tl
|
Required torque on level
|
|
ft-lbs
|
Ft * Tm
|
15.84
|
19.08
|
24.29
|
31.46
|
40.60
|
51.70
|
64.76
|
79.78
|
96.77
|
115.72
|
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5%
|
incline (approximately equivalent to 1mph/sec accel on level ground)
|
|
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|
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|
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|
theta
|
arc tan % incline
|
|
0.0500
|
|
|
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|
|
|
|
|
|
|
|
|
Sin theta
|
|
|
0.0499
|
|
|
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|
|
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|
|
|
|
|
|
Cos theta
|
|
|
0.9988
|
|
|
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|
|
|
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|
Fi
|
Incline Force
|
|
37.45
|
lbs
|
Wt * SinTheta
|
|
|
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|
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|
Fr
|
Rolling Drag Force
|
|
13.48
|
lbs
|
CrWCosTheta
|
|
|
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|
|
|
|
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|
Ft
|
Total Force
|
|
lbs
|
Fi+Fr+Fd1+Fd2
|
52.37
|
55.42
|
60.33
|
67.09
|
75.70
|
86.16
|
98.47
|
112.63
|
128.64
|
146.50
|
|
|
T05
|
Required torque at 5%
|
|
ft-lbs
|
|
55.56
|
58.81
|
64.01
|
71.18
|
80.32
|
91.42
|
104.48
|
119.50
|
136.49
|
155.45
|
|
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|
|
|
|
|
10%
|
incline (approximately equivalent to 2mph/sec accel on level ground)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
theta
|
arc tan % incline
|
|
0.0997
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Sin theta
|
|
|
0.0995
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Cos theta
|
|
|
0.9950
|
|
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|
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|
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|
Fi
|
Incline Force
|
|
74.63
|
lbs
|
Wt * SinTheta
|
|
|
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|
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|
|
|
|
|
Fr
|
Rolling Drag Force
|
|
13.43
|
lbs
|
CrWCosTheta
|
|
|
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|
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|
Ft
|
Total Force
|
|
lbs
|
Fi+Fr+Fd1+Fd2
|
89.49
|
92.55
|
97.45
|
104.21
|
112.82
|
123.28
|
135.59
|
149.75
|
165.77
|
183.63
|
|
|
T10
|
Required torque at 10%
|
|
ft-lbs
|
|
94.95
|
98.20
|
103.40
|
110.57
|
119.71
|
130.81
|
143.87
|
158.89
|
175.88
|
194.84
|
|
|
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|
|
|
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|
|
|
|
|
|
|
15%
|
incline (approximately equivalent to 3mph/sec accel on level ground)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
theta
|
arc tan % incline
|
|
0.1489
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Sin theta
|
|
|
0.1483
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Cos theta
|
|
|
0.9889
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Fi
|
Incline Force
|
|
111.26
|
lbs
|
Wt * SinTheta
|
|
|
|
|
|
|
|
|
|
|
|
Fr
|
Rolling Drag Force
|
|
13.35
|
lbs
|
CrWCosTheta
|
|
|
|
|
|
|
|
|
|
|
|
Ft
|
Total Force
|
|
lbs
|
Fi+Fr+Fd1+Fd2
|
126.03
|
129.09
|
134.00
|
140.76
|
149.37
|
159.83
|
172.14
|
186.30
|
202.31
|
220.17
|
|
|
T15
|
Required torque at 15%
|
|
ft-lbs
|
|
133.73
|
136.97
|
142.18
|
149.35
|
158.48
|
169.58
|
182.64
|
197.67
|
214.66
|
233.61
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
20%
|
incline (approximately equivalent to 4mph/sec accel on level ground)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
theta
|
arc tan % incline
|
|
0.1974
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Sin theta
|
|
|
0.1961
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Cos theta
|
|
|
0.9806
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Fi
|
Incline Force
|
|
147.09
|
lbs
|
Wt * SinTheta
|
|
|
|
|
|
|
|
|
|
|
|
Fr
|
Rolling Drag Force
|
|
13.24
|
lbs
|
CrWCosTheta
|
|
|
|
|
|
|
|
|
|
|
|
Ft
|
Total Force
|
|
lbs
|
Fi+Fr+Fd1+Fd2
|
161.75
|
164.81
|
169.72
|
176.48
|
185.09
|
195.55
|
207.86
|
222.02
|
238.03
|
255.89
|
|
|
T20
|
Required torque at 20%
|
|
ft-lbs
|
|
171.63
|
174.87
|
180.08
|
187.25
|
196.38
|
207.48
|
220.54
|
235.57
|
252.56
|
271.51
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
25%
|
incline (approximately equivalent to 5mph/sec accel on level ground)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
theta
|
arc tan % incline
|
|
0.2450
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Sin theta
|
|
|
0.2425
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Cos theta
|
|
|
0.9701
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Fi
|
Incline Force
|
|
181.90
|
lbs
|
Wt * SinTheta
|
|
|
|
|
|
|
|
|
|
|
|
Fr
|
Rolling Drag Force
|
|
13.10
|
lbs
|
CrWCosTheta
|
|
|
|
|
|
|
|
|
|
|
|
Ft
|
Total Force
|
|
lbs
|
Fi+Fr+Fd1+Fd2
|
196.43
|
199.48
|
204.39
|
211.15
|
219.76
|
230.22
|
242.53
|
256.69
|
272.70
|
290.57
|
|
|
T25
|
Required torque at 25%
|
|
ft-lbs
|
|
208.42
|
211.66
|
216.87
|
224.04
|
233.17
|
244.27
|
257.33
|
272.36
|
289.35
|
308.30
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Available Torque for Perm 132 @ 72V
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Constants
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
1 Nm
|
0.737
|
lb-ft
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Calculated from graph
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
WARNING:
|
Assumes strictly linear relationship, working from a small low definition graph
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Equation for straight line
|
|
y = mx + c
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Data read from graph
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
20
|
110
|
200
|
A
|
|
|
|
|
|
|
|
|
|
|
|
|
|
3511
|
3480
|
3111
|
RPM
|
|
|
|
|
|
|
|
|
|
|
|
|
|
3.6
|
20.5
|
38.3
|
Nm
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Calculated gradient and offset
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
mRPM
|
-2.22
|
gradient
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
cRPM
|
3466
|
offset
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
mTorque
|
0.18
|
gradient
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
cTorque
|
0.06
|
offset
|
|
|
|
|
|
|
|
|
|
|
|
|
|