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JDH: CB750 Conversion - Motor Math
Submitted by jdh2550_1 on Tue, 10/16/2007 - 17:38
OK, so I found a round tuit down the back of the sofa and decided to use it for calculating some numbers for my CB750 conversion. I've created a spreadsheet based off of Bob Brant's Build Your Own Electric Vehicle and John Bidwell's Secrets of El-Ninja. I used BYOEV for the required torque formulas, and I used El-Ninja for the available torque formulas (they were presented as a nice short list in the Bidwell book!). I used the co-efficient of drag and frontal area figures from the defaults on the electricmotorcycles.net calculator (http://electricmotorcycles.net/modules/toolbox/battery_worksheet.php)
You can see the spreadsheet at: http://www.editgrid.com/user/jdh2550/CB-72V - if you want to use it yourself then you can get a free edit grid account (takes 5 minutes to setup) and do a Save As ... and create your own copy because you can't edit this sheet directly. BTW, the graph is on the summary tab and all the gory details are on the calcs tab. The other tabs are all work in progress.
Here's the pretty picture I drew:
The lines that run "left to right" are the required torque for various gradients (from level through 25%). The lines that run "up and down" are the available torque for a Perm 132 @ 72V - these are plotted for 3 different ratios (1) the original ratio on the bike right now; (2) the ratio Bidwell uses for El-Ninja & (3) the ratio I'm thinking will be best for me. So, where the "up-down" line crosses the bottom "left-right" line is my theoretical top speed - around about 66mph. The tick marks are at 25A intervals - so I'll be drawing around 120A @ 66mph. The Perm is rated for 110A continuous - so I reckon 60mph should be fine. I figured the available torque by calculating y=mx+c equations for the speed and torque values off of the 72V Perm chart. I only had a small chart so I upsized it and then used a ruler to measure off the values - it's close but it certainly isn't spot on (I don't even know if the torque and speed lines are really 100% linear).
Bottom line is that this exercise tells me that I'm not crazy - I should be able to get a 60mph cruising speed out of the beast without frying the motor. It also tells me that I'll likely be out accelerated by a Festiva :( By my reckoning I'll be able to accelerate at around 3.5 mph per second - which gives a 0 to 60 time in 17.1 seconds (btw, does anyone know why it's the de facto standard to use 0 to 60? - just curious). With that accel I'll be drawing 400A which will push the poor little Perm if I do that too much.
OK, so I used the chart provided for this motor: http://www.evparts.com/shopping/product_details.php?id=533&product_id=1107 (as suggested by Andrew - thanks!). I read off the values for torque and rpm given amps between 25 and 325 in steps of 25 - yes I am that anal! Added them to the graph above. Getting kind of hard to read now. A couple of points to mention - the top two speeds for the original ration for the ADC have been truncated - so when counting "ticks" one has to start at 75A not 25A. The relationship between amps, torque and speed is clearly not linear for the ADC - yet I calculated as linear (and it's darn close according to this graph which I used as the basis for the calculation).
I'm a little nervous that my available torque curves are bogus. But, what the heck - at least it's not a billion dollars worth of Mars rover... So, I'm pressing onwards with what I've got.
Approximate values for top speed for both motors for my proposed ratio are:
|Perm 132 @ 72V||ADC MT2113 @ 72V|
|Amps (A)||Speed (MPH)||Amps (A)||Speed (MPH)|
So, the ADC will turn faster at higher amps - however, at 150amps I'm 50% over the continuous rating (listed as 100A). The Perm will give me a top speed of 65 at 125amps, this is only 13% over the continuous rating (listed as 110A).
In Summary: At the moment I plan to use a Perm 132 @ 72V with UB121100 batteries - using a 13 tooth cog on the front sprocket and sticking with the 48 tooth cog on the rear wheel.
Of course after doing some battery math I might change my tune...
1) Start poking at Peukert's law to try and figure some expected ranges (although Bidwell offers twovery simple rule of thumb calculations (a) 30mph steady state range = pack kWhours * 9.8 & (b) stop-and-go range = pack kWhours * 7). This will be the subject of an exciting new blog entry... (I bet you can hardly wait, eh?)