JDH: CB750 Conversion - Motor Math

jdh2550_1's picture

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.

Update
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)
125 65 150 68

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...

Next Up:
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?)

before comments

Comments

echuckj5's picture

jdh,
I used to do a lot of these calculations. On a piece of paper I just write it down, solve it, takes a minute or so. I guess I do a lot of it in my head, skip steps.

HP=[Torque*(speed)]/t
speed is measured in radians. Most motors are rated at revolutions per minute. So a long time ago, since I never had a calculater that would handle radians for quick calculations, I took the radians out, by dividing both sides of the above equation by 2 pi. Using minutes HP is 33000/2pi=5252

HP=torque*rpm/5252

This is the easiest way to do it, that I have found. I always work in feet, pounds and seconds, except for the initial hp calculation since motors are rated at revolutions per minute. This number has always stuck in my head, I remember it because it is like miles, 5280 feet.

From your calculations at 60 mph, total forces are 88.77ftlb.
Wheel radius is 80"/2pi=12.73"=1.06feet
Reduction ratio=48/13=3.69
speed is 60mph=88ft/sec

From the web, pmg specs
12 - 72 Volt, 9.5 HP on 72 volts systems, 19.3 HP peak for 10 minutes
Current: 110 Amps
72 Volts, 3480 RPM, 9.7 HP maximum efficiency
Temporary service: 10 min = 200 Amps

Finding max torque at max efficiency
9.5hp=torgue*3480rpm/5252
torque available is 12.99ftlbs at the motor, at max efficiency

To go 60 mph, up a grade of 5% how much HP?
1hp=550ftlbs/sec
HP=Force*Distance/time
The Distance/time is the 88feet/sec
The force is 88.77 ftlbs
hp=88.77*88/550=14.2hp

Now, how much torque is available?

I am gonna sign off for now, is this making sense jdh? It usually just takes me a minute or two, to figure this out, but old thinker is tired, let me relax a little, see if I can get my brain working tonight

chuck

[b]AGM BATTERIES[/b]

echuckj5's picture

jdh,
This morning, I checked the 50 mph, additional force, from level ground to a 5% grade, got almost the exact same number you got, using Potential energy.

Playing around with your gear ratio's. 48/13=3.69 to 1
At 60 mph, and 3480rpm, I come up with an ideal ratio of 4.4 to 1? What am I missing?

chuck

[b]AGM BATTERIES[/b]

jdh2550_1's picture

You're not missing anything (well, at least as far as this calculation stuff goes - not that I can tell anyway).

I did the spreadsheet thing so that I could play with different numbers - I get bored really quickly with doing things with paper and pencil. It's kind of an old school (you) vs. new school (me) thing! I'm still working on the basis of 460+lbs of batteries - which part of me says is WAY too heavy and part of me says we can handle it! So, I'll likely play with different battery configs - change the battery weight and as if by magic all my figures are instantly updated. Yes, my brain is lazy - I haven't been able to do mental arithmetic worth sh*t for many, many years now - I've got this amazingly powerful computing machine in front of me - so I use it (all the time and at the expense of my mental faculties)

As far as my chosen ratio - it's kind of arbitrary. Although I said I wanted a top speed of 60mph to me "top speed" means "top usable speed which means still having a little bit to spare". I'm keeping 48 on the rear so that I can use the same rear sprocket. When I order the front sprockets I'll probably get three: a 13, 12 & 11 so that I can play with them and see which is the best compromise for my preferences. That will give me 3.69, 4 & 4.36 ratios to play with - I'm hoping that the chain adjustment on the bike will give me enough range so that one chain size will fit all.

Make sense?

John H. Founder of Current Motor Company - opinions on this site belong to me; not to my employer
Remember: " 'lectric for local. diesel for distance" - JTH, Amp Bros || "No Gas.

echuckj5's picture

OK
Thought I was losing it.

One thing I found out on my little 1 hp, since I went to a 9.1 from a 10.4 ratio. Now, going 20 mph, I get less range than when I go, 23, 24 mph. Ideally, to go 25 mph, I should gear at 9.7, then the slower speeds will be more efficient. Since I don't have a real need for range right now, I like the speeds of 28 to 30 mph.

20 mph is the speed limit unlicensed. 25 mph is probably pushing it. 30 mph, oh, I'll get a ticket in this town.

Anyway, the charts are nice, I like playing around with them, checking their accuracy, they look good on the things I've checked.

I am going to build a motorcycle, probably in the 40 to 50 mph range, I'll follow your build, anything and everything information wise is useful.

I need an efficiency chart for those 2 motors, with the range of efficient rpms. Post em, if you find em.

chuck

[b]AGM BATTERIES[/b]

echuckj5's picture

Just checking the above chart, need torque available at the wheel for a 5% grade at 60 mph for the perm motor.

Found the HP needed to be 14.2
Rpm at max efficiency=3480
Radius of wheel=1.06ft
Gear reduction=48/13 or 3.69
60mph=88ft/s
wheel rpm at 60mph, 3.69 ratio=791.6
Rpm of motor at 60mph and a 3.69 to 1 ratio=2921
Rpm of motor at 60mph and peak eff. 4.4 ratio=3480

Available Torque
HP=(torque*rpm)/5252 {at the motor}.
14.2*5252/2921=25.5ftlbs

To find torque at the wheel
{(Torque at motor)*(Gear reduction)}/(Wheel radius)
Torque at the wheel=25.5*3.69/1.06=88.76ftlbs

Available torque=25.5ftlbs
Available at wheel=88.76

Torque at peak efficiency of the motor

HP*5252/rpm=torque {at the motor}
14.2*5252/3480=21.43ftlbs

To find torque at the wheel
{(Torque at motor)*(Gear reduction)}/(Wheel radius)
21.43*4.4/1.06=88.95ftlbs

Available torque=21.43ftlbs
Torque at the wheel=88.95ftlbs

The chart says that the Torque needed at 60 mph is about 50 ftlbs, holding a piece of paper up to the computer screen.

So, conclusions? Can the motor put out 14.2 hp at 2920rpms, efficiently enough? I don't have that information. Can the batteries supply the amps at that hp requirement? Can't answer that one either. Stall torque is 28.37ftlbs.

Thats all,

chuck

ps, above about my first post, available torque at 9.5 rated horsepower at peak efficiency is 14.34ftlbs, I posted that it was 12.99ftlbs, sorry.

[b]AGM BATTERIES[/b]

In support of your motor choice, I have been using a Perm-132 and Universal 12550 (55ah AGMs), toal battery weight is 228lbs. 72 Volts, I am using the 300 Amp Alltrax. The Perm prefers to be run clockwise rotation so I have a jack shaft and am using the stock sprocket on the rear and a second chain with gears to drive the rear, net ratio is roughly 13:1, top speed is 60mph. Since I have made some changes I have not yet run to 80% depletion to check range, I will try to do that soon. I have over 1000 miles on her so far. Some chain stretch about the only issue. Yay!!!

The size and weight of the Perm lends itself to mounting in the area you specified (battery/air box), moreso than the ADC. I built a small air shround and mounted 6 small fans to force air into the motor, these fans run as soon as the power is turned on. They help keep the heat from saturating the motor internals. I did this as a preventative measure. The Perm is moving about 440 lbs of bike plus my weight around 190. I could gear this closer to 12:1 but I don't want to give up the acceleration I have now.

The Bike is the Franken'ceptor Honda VF500, on EVALBUM. My new website, no content yet is: www.dreamdesignbuild.net. Cheers. Jeff

jdh2550_1's picture

Thanks for the info Jeff.

I am currently considering 8 Universal 12550's for a 96V system. I can just about fit 6 121100's (4 up front two as paniers) but I'm about to mock up the 12550's and see if I can squeeze 'em in there!.

Do you know if the Perm can handle the higher voltage? I know the spec says 72V but I've heard of folks running other motors over spec. I know the ADC is rated for up to 96V.

I'm off to look at your EVALBUM entry...

John H. Founder of Current Motor Company - opinions on this site belong to me; not to my employer
Remember: " 'lectric for local. diesel for distance" - JTH, Amp Bros || "No Gas.

I got my 12550s from Battery Solutions in Texas, paid $63 each. IMO staying with a 72 volt pack will be to your advantage, I have not heard anyone running 96v on the PMG. I know before I added 6 mini-fans and it was hot out 90+ and I ran it hard the motor got pretty hot. I am using a 300 amp Altrax. I think if you run the 450 amp controller you might get the Perm to ignite!! Costly experiment. 228 lb of battery is reasonable, keeping the overall weight/mass down my idea of keeping the bike fun - like not a turd... Don't know if you caught the Aussies on TV riding around on an electric Harley in the US that weighs like 1000 lbs, that's not an EMC, definitely turd material.

jdh2550_1's picture

I'm currently considering the ADC at 96V. Not as efficient as the Perm, but reckoned to be more robust (more thermal mass). The trouble with 72V/55Ah is that it's a little too light on the range than my target of 50 miles (ballpark it seems to be around 30 miles). 96V/55Ah gets closer but is still a little light. Hmmm, now I'm wondering about 120V/55Ah - I could fit them - but at the moment I'm thinking I'll go with 96V and the ADC MT2113.

Turd definitions definitely depend on one's POV. Gas Harley's are up there in the weight department too. One of the reasons I chose an older, bigger bike was to do a slower, more stately cruiser (a turd in your eyes!). I've ridden everything from a race prepped 250cc (Kawasaki KR1S) through 750cc sports, current gas ride is a 450lb V-Strom 1000 (love it!).

John H. Founder of Current Motor Company - opinions on this site belong to me; not to my employer
Remember: " 'lectric for local. diesel for distance" - JTH, Amp Bros || "No Gas.

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