Assignment 2.5 - Explanation for the spreadsheet
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Fig 1. Shows the velocity vs time graph of IDC for a 2W and a 3W
Figure 1: 2 wheeler Indian Drive cycle
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Fig 2. Explains what is the vehicle state in these 108 seconds of drive cycle. Whether the
vehicle is accelerating, decelerating, steady state or idling.
o Column “acceleration” denotes the vehicle acceleration in that operation.
o Column “speed” mentions the starting and ending speed in that operation.
o Column “duration of operation” denotes the number of seconds the operation
lasted for.
o Column “cumulative time” gives the cumulative time (1 to 108 seconds)
Figure 2. Figure showing various states of acceleration, deceleration, Idling and steady state at various instances of
IDC
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Fig 3. Contains all the vehicle specs and other parameters which can be taken as variables.
Figure 3. Specs of 2 wheeler given in question
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Next job is to expand the drive cycle given in Fig 2. at 1 second interval, so as to compute all
the forces at granularity of 1 sec. This is illustrated in fig 4. Highlighted is the operation no 2
of fig 2. Acceleration = 0.65, velocity goes from 0 to 14, duration of 6 sec and cumulative
time 22 sec. In this fashion build the entire spreadsheet for 108 seconds.
time(s)
vel(km/h)
dist (meters)
vel (m/s)
dv/dt = a
0
0
16
0
0
0
0
17
2.3333
0.6481
0.6481
0.6481
18
4.6666
1.2962
1.2962
0.6481
19
7
1.9444
1.9444
0.6481
20
9.3333
2.5925
2.5925
0.6481
21
11.6666
3.2407
3.2407
0.6481
22
14
3.8888
3.8888
0.6481
23
16
4.4444
4.4444
0.5555
24
18
5
5
0.5555
25
20
5.5555
5.5555
0.5555
0
Figure 4. A section of drive cycle.
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Next setup a spreadsheet to compute all the traction forces. Take small intervals of ΔT (say 1
second).
Figure 5. Spreadsheet derived using IDC
Below formulas are used to compute the required forces:
◦
Distance: Vel (m/sec) * ΔT (sec) at each point
◦
Acceleration = ΔVel / ΔT in m/sec2
◦
Acceleration Force Fa = M * Acceleration (Newtons)
◦
Rolling Resistance Force Fr = M*g*μ
◦
Drag Force FD = 0.5* Cd * ρ* A * v2
◦
Traction Force Ftrac = Fa +Fr + FD (Newtons)
◦
Traction Torque (Nm) = Ftrac * wheel radius (m)
◦
Ptrac (Watts) = Ftrac* V (Nm/sec)
and Ptrac (Watts) = (R * Ftrac) * V with Regeneration Efficiency R, when Ftrac is –ve
(Ptrac computation in spreadsheet uses average speed of time instance t and
instance (t-1), hence you will find factor of 0.5 in formula realized in spreadsheet.)
◦
Energy (Wh) = Ptrac * ΔT, Integrate to give drive-cycle energy
USE MS Excel formulas to realize above equations.