GoldenMotor.com Forum
General Category => General Discussions => Topic started by: stevo on September 02, 2008, 03:54:30 PM
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I have a question about how electric bike motors work. As background, I don't have an electric bike conversion kit yet.
I would like to know how electric bike motors work in conjunction with pedaling. For example, assume I have a motor that can propel me (and my bike) at 32km/hr at full throttle. Say I start with the throttle at half-power without pedaling- so I would get up to 16km/hr. Then I start to pedal such that I bring the bike up to 20 km/hr, keeping the throttle at half. Would the motor then "speed up" to match its RPM to 20km/hr? (i.e. the bike speed would be a combination of my pedaling power + the motor's power). Or would the motor itself continue to spin at an RPM that matched 16km/hr? (i.e. the 4km/hr increase from 16 to 20 was completely my own power). If this is the case, then the power input to drive the bike is really binary - either the motor or myself but not both. In other words, whenever I pedal faster than the throttle speed, I might as well turn the throttle off because it will be all my own pedaling power driving the bike. I suppose if I pedal at exactly the throttle speed, I would reduce the amperage drawn from the battery by the motor.
Thanks,
Steve
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G'day Stevo
Its more to do with power than speed and the power is not contant over the speed range, if you suddenly went up a hill at half throttle your speed would decrease but power would increase to keep you going up hill, see the picture below (grabbed from http://www.ebikes.ca/simulator/ for a GM 36v 12ah, 26" and 20a controller). Power or torque is greatest at lower speeds and then reduces as you go faster. To answer your question, if you hold the throttle at half and start pedalling, yes the motor would "speed up", or the rpm of the whole wheel, as you are adding power from your own legs, then yes "the bike speed would be a combination of my pedaling power + the motor's power". Lets take a tandem bike for example. If you were going up a slight incline which necessitated some effort from both riders to maintain a certain speed and then one rider stopped pedalling, you would probably lose half your speed or the first rider would have to pedal twice as hard to maintain the same speed. So when you say "In other words, whenever I pedal faster than the throttle speed, I might as well turn the throttle off because it will be all my own pedaling power driving the bike." it depends on the load, ie if you are on a flat or a hill. From the above mention site: "The average power that a typical cyclist will deliver is on the order of 150 watts, or 1/5th of a horsepower. A fit individual can sustain 350 watts for about 10 minutes and up to 600 watts for a few seconds, but for continuous riding between 100-200 W is typical. You might think then that 150 watts would be all you need for an ebike, but if you ever ride a 150 watt bike it will feel unimpressive. When a cyclists hits a hill, they switch to an easy gear and the speed drops to 10-15 km/hr as they work hard and move at a slow pace. However when an electric bike does the same thing and slows to walking speed on the hills it seems way under powered. To maintain nice speeds over 30 kph while going uphill requires on the order of 400-500 watts or more. On the flat, 400 watts (about 1/2 horsepower) will move a typical bicycle about 40 km/hr."
I hope my explanation was clear enough and helpfull.
Muzza.au
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Thanks Muzza. That sounds good. However, despite the statement in your post that "On the flat, 400 watts (about 1/2 horsepower) will move a typical bicycle about 40 km/hr.", my understanding is that in order to be street legal, electric bike motors are designed to have a maximum unassisted speed of 32km/hr. So does this mean that they are somehow "mechanically governed" such that the motors will not spin faster than X RPM (where X is whatever RPM translates into 32 km/hr for the size of the wheel). I'm hoping not but I wanted to confirm this.
To give context to this question, I tried out an e-bike recently (Crystalyte, 400W, 36V 10 Ah Battery) and I noticed that at full throttle, after the bike reached its top speed (presumably around 32 km/hr) it "seemed" that when I started to pedal, it was all my own power (I'm hoping I was mistaken).
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Thanks Muzza. That sounds good. However, despite the statement in your post that "On the flat, 400 watts (about 1/2 horsepower) will move a typical bicycle about 40 km/hr.", my understanding is that in order to be street legal, electric bike motors are designed to have a maximum unassisted speed of 32km/hr. So does this mean that they are somehow "mechanically governed" such that the motors will not spin faster than X RPM (where X is whatever RPM translates into 32 km/hr for the size of the wheel). I'm hoping not but I wanted to confirm this.
To give context to this question, I tried out an e-bike recently (Crystalyte, 400W, 36V 10 Ah Battery) and I noticed that at full throttle, after the bike reached its top speed (presumably around 32 km/hr) it "seemed" that when I started to pedal, it was all my own power (I'm hoping I was mistaken).
Yes I do believe that some brands in some markets are governed to be legal (not sure about GM), but most likely electrically in the controller. You could probably get around this by finding a kit where they say its for off road use only. Have a look at what you can get for off road use only here (in Aus): http://www.emtb.com.au/ (http://www.emtb.com.au/) The above quote I got from the website I mentioned in my last post was probably refering to ungoverned theoretical top speed.
Muzza.au
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hi stevo,
your question can be answered with a few simple equations. are you looking for that kind of answer?
the system is equivalent to a brushed DC motor directly driven by a voltage source (modulated by the throttle input and with a constant-current current limiter). and the non-regen equivalent circuit has a series diode.
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Thanks again Muzza.
Hi Lanchon,
Re your reply, I wasn't really looking for equations (at least, not at this time). I was just wanted to understand conceptually how the motors work. So assuming an electric motor is "un-governed" (in terms of maximum rpm), if I lifted the bike off the ground and held it in place (ie no wind/rolling resistance) and put the throttle at full, the wheel should be able to spin at incredibly high speed - it would be limited only by its own internal mechanical resistance. Is this correct?
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By the way Muzza, I am having difficulty interpreting the graph you attached in your earlier post (the one called torqeugraph). For example, why do all 3 lines drop to 0 at 45 km/hr? Also, re your statement "Power or torque is greatest at lower speeds and then reduces as you go faster", this makes sense for the torque line. However, the power line seems to start low and rise and peak at about 29 km/hr then start dropping.
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G'day Stevo,
go to http://www.ebikes.ca/simulator/ (http://www.ebikes.ca/simulator/) and have a play with it. There is an explanation of how it works and what the plot lines mean. Other sections of the site also have alot of useful information.
Muzza.au
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cool. thanks Muzza
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> So assuming an electric motor is "un-governed" (in terms of maximum rpm), if I lifted the bike off the ground and held it in place (ie no wind/rolling resistance) and put the throttle at full, the wheel should be able to spin at incredibly high speed - it would be limited only by its own internal mechanical resistance. Is this correct?
no.
sorry, I need equations to explain. assume an open loop controller in which the throttle directly controls the modulation width of the PWMed FETs (valid for my 2006 GM controller). ignoring transients, the steady state is something like this:
call the actual rotational speed of the wheel "w".
there's also a rotational speed target "wt" that linearly depends on battery voltage "vbat" and modulation index "x" (0 to 1, controlled by throttle position):
wt=k1*(x*vbat)
(the proportionality constant k1 is a parameter of the motor.) think of it as if the throttle regulated the batt voltage from 0 to max batt voltage. so the throttle regulates target speed from 0 to max target speed (if vbat is constant).
the torque exerted by the motor depends on the difference between target and actual speed:
tu=k2*(wt-w) ("unlimited" version of torque)
t=tmin, if tu<tmin
t=tmax, if tu>tmax
t=tu, if tmin<tu<tmax
this means that the torque is proportional to the speed difference, but within limits. the motor current is proportional to torque:
imotor=k3*t
and so tmax and tmin are implemented as simple motor current limits (except tmin in nonregen mode, which is zero and is implemented by FET diodes that come to bare due to the noncomplementary PWM switching strategy used). FYI, the batt current is:
ibat=x*imotor (so ibat<=imotor)
note that k1, k2, k3, tmin and tmax are constants depending on motor and controller. (actually if you idealize vbat as constant, k2 also depends on the batt's internal resistance, which you could consider constant on your setup.)
so, back to your question, full throttle with wheel lifted up means:
-t=0 (zero torque on wheel)
-thus w=wt
-wt is the max speed attainable (since x=1)
-wt depends only on vbatt (linearly)
-imotor=0 and ibatt=0
of course there are various losses (electronic, magnetic, friction and drag) and the currents are not really zero, but they are low. this situation corresponds to the origin of the torque graph in the pdf published at GM's website. this graph corresponds to full throttle (x=1), so:
-you can verify the low ibat at the origin
-you can compute k1 from max speed and vbatt
-you can compute k2 from how the increase in torque results in a decreasing real speed "w" (wt is constant and is the max speed, since vbatt and x are (mostly) constants).
-you can compute k3 from the total current "ibat" (since x=1, imotor=ibat)
-with k3 and the controller current limit you can calculate tmax (in my controller, imotormax is around 22A or 23A).
so,
> I would like to know how electric bike motors work in conjunction with pedaling.
pedaling reduces the torque requested from the motor
> Say I start with the throttle at half-power without pedaling- so I would get up to 16km/hr. Then I start to pedal such that I bring the bike up to 20 km/hr, keeping the throttle at half. Would the motor then "speed up" to match its RPM to 20km/hr?
of course, otherwise the tire would be burning rubber and neither you nor the motor have enough power to do that.
> Or would the motor itself continue to spin at an RPM that matched 16km/hr? (i.e. the 4km/hr increase from 16 to 20 was completely my own power).
neither of these sentences make sense.
since you're reducing the difference between w and wt, the torque output of the motor will be reduced. if the current angular speed target wt (according to batt and throttle) corresponds to a bicycle linear speed target higher than 20kph, then the motor would still be putting in some torque and power.
otherwise torque would be zero and you'd be doing all the work. or in regen mode torque would be negative and you'd be doing all the bicycle work plus you'd also be charging the battery.
> If this is the case, then the power input to drive the bike is really binary - either the motor or myself but not both.
assuming non-regen: no, the transition speed range is governed by k2. (note that k2 decreases with increasing batt internal resistance.)
> In other words, whenever I pedal faster than the throttle speed, I might as well turn the throttle off because it will be all my own pedaling power driving the bike.
this is valid only if you are passed wt, the current target speed, and in non-regen mode.
> my understanding is that in order to be street legal, electric bike motors are designed to have a maximum unassisted speed of 32km/hr.
limiting vbat limits the speed. so a street legal 36V kit ceases to be such if operated at 48V. it seems many kits are underspecified to make them compliant (I suspect there's no difference between the GM 36V and 48V motors, yet they are marked differently).
> I tried out an e-bike recently (Crystalyte, 400W, 36V 10 Ah Battery) and I noticed that at full throttle, after the bike reached its top speed (presumably around 32 km/hr) it "seemed" that when I started to pedal, it was all my own power (I'm hoping I was mistaken).
assuming no feedback loop (my first assumption in this post), then this just means a large k2, which is a good thing for reasons not spelled here.
EDIT: some implementation caveats...
note that if w>k1*vbat, many non-regen controllers effectively start acting as if they were regen (due to the FET diodes changing the effective switching strategy away from noncomplementary). so,
> I noticed that at full throttle, after the bike reached its top speed (presumably around 32 km/hr) it "seemed" that when I started to pedal, it was all my own power
in this case, when past wt (the point at which you provide all the power), you may start to charge the batt even with a non-regen controler.
plus, when entering this "mode" there's really no current limiting in force. so if you short-circuit the power input to the controller when the wheel is turning fast... kaboom!
also, I said:
> tu=k2*(wt-w) ("unlimited" version of torque)
> t=tmin, if tu<tmin
> t=tmax, if tu>tmax
> t=tu, if tmin<tu<tmax
> imotor=k3*t
> and so tmax and tmin are implemented as simple motor current limits
but note that due to limitations in common controller implementations, the controller loses its ability to accurately measure imotor as x approaches zero. in particular, it tends to underestimate it. so when using low modulation indexes (low throttle) it is possible that imotor, and thus torque, both exceed their limits (but not ibat, since x is low). all sorts of problems could arise...
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OMG! Lanchon, although I recognize the terms that you are using from my introductory university physics classes, I have to admit that you lost me in the equations (but that's ok). You obviously understand how these motors work in great detail.
From what I did understand from your explanation, I have a question about your statement "note that if w>k1*vbat, many non-regen controllers effectively start acting as if they were regen". I plan to buy a kit that is non-regen. If I pedal fast enough such that w>k1*vbat, (and/or I am going down a really steep hill) would turning the throttle off prevent the controller from acting as if it were regen? Or would it start to regen regardless?
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> I recognize the terms that you are using from my introductory university physics classes
well you asking physics questions! I hope I made it more or less clear though.
> would turning the throttle off prevent the controller from acting as if it were regen?
no, it would regen. the controller software can't do a thing to prevent it, and the throttle is just a input to the software. you can disconnect the motor from the controller. you could also disconnect the controller from the batt, but some losses will remain and you could zap the controller if you overvolt it.
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thanks Lanchon
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Hi Lanchon,
I've got a few more questions if you don't mind:
1) Re your note "the proportionality constant k1 is a parameter of the motor", is there any way to modify k1 for a motor? For that matter, is there any way for me to find out what the k1 is for a particular motor?
2) Re your notes about un-intended regen when w>k1*vbat, assuming I am pedaling fast enough such that w>k1*vbat, if I wanted to "limit" the un-intended regen, would it be better to keep the throttle on full rather than turning the throttle off? (ie to reduce the difference between target and actual speed). Conversely, if I wanted to "maximize" the un-intended regen, would it better to turn the throttle off?
3) re your note "when entering this 'mode' there's really no current limiting in force", I find it odd that controllers are not made to be able to limit current in "regen" mode (even if they aren't regen controllers) because I'm sure it's quite common for riders to exceed k1*vbat e.g. on steep downhills. Is the risk of "short-circuiting the power input to the controller when the wheel is turning fast" a risk that people should be concerned about?
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I love these threads where everyone puts a math equasion to every living breathing thing... :D
I think it also depends on the riders strength and fitness, it would even depend on how much the rider had to drink the night before.
Dont forget to use La in the constance of your equasions.
-1La = how much sitting you been doing over the last 20 odd years.
-1Fi = how much smoking and drinking you do inyour spare time
-Fat = how fat you are.
-St = strength, how much elbow grease you put into life.
To me these tend change the final figure in a massive way.
Sorry it had to be said... :-|
I get 30 kms with 36v 18ah sla's and they weigh a 15kgs, I ride on flats most of the time and find I can over double my distance with a little pedal on the take offs and keep my max speed up.
I really don't see much differance in speed on my setup as I seem to use more power to keep the speed constant as mentioned before,
I honestly see more advantage with distance and power not the speed when pedaling...
I find if im feeling fit the distance figure increases logarithmic upwards on decreasing slope with wind resistance factor. I think the fitness thing can not be ignored or else you are waisting your time. you need to be able to measure the torque "you" can apply on your cranks and how long you can sustain this for in relation to your battery size, power disipation of the motor and efficiency of the controller, total wind resistance, also the size of the wheel, type of tyre (knobby or slick) Air pressure in relation to the total weight of the bike and rider can make is a huge difference and the list goes on ....
My PWM controller seems to have a speed fix on it as I don't go faster when I add pedals I go further... Controllers shmaloalas.
You really have taken on a a huge task making a formula for all this....
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hi stevo,
> 1) Re your note "the proportionality constant k1 is a parameter of the motor", is there any way to modify k1 for a motor?
only by physically altering the motor. for example removing loops from the windings, using weaker magnets, and removing some of the magnets, all would increase k1 (make it go faster on same voltage). but of course there's a reason people take the trouble of using these strong magnets made of rare materials: if you do any of this, you'd be killing torque (you'd be diminishing k2). like most engineering tasks, motor design involve trade-offs.
> For that matter, is there any way for me to find out what the k1 is for a particular motor?
with a test bank, but usually the manufacturer provides these basic constants. GM does better, it provides the output of a real life test run (for the HBS-36, see http://www.goldenmotor.com/hbs-36.pdf). please reread my long post, it tells you how to obtain the constants from this graph.
> 2) Re your notes about un-intended regen when w>k1*vbat, assuming I am pedaling fast enough such that w>k1*vbat, if I wanted to "limit" the un-intended regen, would it be better to keep the throttle on full rather than turning the throttle off?
in theory there should be no difference. in practice, zeroing the throttle could be marginally better (less regen). (let me say this without proof, you don't need it anyway.)
> 3) re your note "when entering this 'mode' there's really no current limiting in force", I find it odd that controllers are not made to be able to limit current in "regen" mode (even if they aren't regen controllers)
regen controllers should and probably do limit the current in regen mode, but this is not regen mode we're talking here, this is a parasitic and unwanted regen functionality that is a side effect of the power stage being the way it is. it's difficult to eliminate this parasitic function. this is a guess but probably all e-bike controllers display this property.
> because I'm sure it's quite common for riders to exceed k1*vbat e.g. on steep downhills.
actually they won't exceed it by much, their speed will be limited and excess "accelerating" force will be charging their batts instead of accelerating them. this happens regardless of whether they use a regen or non-regen controller, and regardless of whether they are aware of this. (btw, I've never seen this issue discussed anywhere before so most people must be unaware of it.)
> Is the risk of "short-circuiting the power input to the controller when the wheel is turning fast" a risk that people should be concerned about?
I really can't say. people are usually concerned about not missing "big brother". when you drive your car around town, should you be concerned that you're sitting on 60 liters of liquid high-yield explosive? should you be concerned that leaders of the most powerful armies of the world routinely invoke god to explain their actions? I don't know about you, but I'm not interested in starting any public awareness campaigns. and I guess people are already avoiding short circuits on the battery lines for other reasons anyway.
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you seem a bit hung up on the w>k1*vbat thing. why don't you try it yourself? disconnect the batt, wait a bit, short the power input to the controller, lift the bike, and turn the wheel; it's entirely safe.
given that equation, breaking should start at w>0. however, there will be a (slow) threshold speed below which no breaking will occur due to diode voltage drops.
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in 2006 I modeled the HBS-36 before buying it. I best-fitted the numeric data in the pdf into my model, so I should have all the constants laying around somewhere. do you really need this?
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some graphs of the HBS-36. first is a torque graph; the circles are Philip's samples taken from the pdf and the continuous lines come from the model. it's a good fit but the model is more complex including aero drag from the freely rotating wheel for instance (regressed from the data). second graph is torque vs. speed extrapolated to zero speed.
(both assume full throttle with a 36V non-regen controller (max imotor 23.81A) fed by a 36.167 V source with source resistance of 0.024 Ohm (this is the real source used by Philip, regressed from the pdf).)
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Smeee,
To your point, I was a bit overwhelmed by the equations at first but I don't really mind them. I took engineering in University so I recognize all of the terms and if I think about them hard enough, I can understand them.
However, its also nice to have simple real world experience ie your point "i can over double my distance with a little pedal on the take off"
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Thanks Lanchon.
> if you do any of this, you'd be killing torque
So would it be fair to say "if I modified a motor to be able to achieve a higher top speed, I would have to sacrifice torque which would mean that my hill climbing ability would be less and my overall acceleration (flats and hills) would be slower"?
> I'm not interested in starting any public awareness campaigns
I'm on the same wavelength as you. I just wanted to make sure that the short-circuiting scenario you described wasn't something that happens frequently and would therefore be a safety concern.
Re the w>k1*vbat thing, based on your explanations, I'm okay with it now.
Re the graphs, thanks.
BTW, after all this, I ended up buying a Crystalyte 408 w/36V 20A controller and Lithium Polymer 36V 10.5 Ah batt. (since this is a Golden Motor forum, my apologies to any die-hard GM'ers)
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> So would it be fair to say "if I modified a motor to be able to achieve a higher top speed, I would have to sacrifice torque which would mean that my hill climbing ability would be less and my overall acceleration (flats and hills) would be slower"?
not exactly; I said higher k1, not higher top speed. a fair amount of torque is needed when traveling at top bike speed. a higher k1 and lower k2 could just as easily increase or decrease top speed, depending on the torque vs. speed characteristic of the load. (one wants to imagine that these hubs are more or less tuned to a typical ebike load.)
> I ended up buying a Crystalyte 408 w/36V 20A controller and Lithium Polymer 36V 10.5 Ah batt
could you detail the costs? btw, I guess you are aware that the cobalt chemistry typically used in li-polys is quite dangerous. won't you consider using lifepo4?
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However, its also nice to have simple real world experience ie your point "i can over double my distance with a little pedal on the take off"
I studied electronics under some army guy in oz about 23 years ago and I could calculate the beta of a transistor as well as any one back then...
I Started to get back into it when I bought some evs.
My guess is that the ligthter batteries unlike mine :| wont advantage from the pedal power the same as I see the weight playing a big fat drain on my batteries, I do have 15 kgs of lead packed on my frame.... The advantage of the big batteries is to get more distance and the pedal power is used to off set the disadvantage of the weight. Ive done over 80 kms in a single day with a few short charges between a few short trips and a long one.
I cant see 4X 12ah LiFePO4 doing the what my 3X18 ah sla's with pedals but I think it would be pretty even with out the pedals.
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Lanchon,
I paid $465.95 CAD for the wheel/motor/controller and $535.00 CAD for the battery.
I considered lifepo4 but its more expensive. And my understanding is that the battery that I bought (from Its Electric) are Li(Ni-Mn-Co)O2 which are safer than pure Cobalt-based Lithium batteries due to the Manganese.
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that's true, spinel is much safer. but lifepo4 is much safer than spinel in turn. however I think you ought to know that spinel batts have a terrible shelf life spec. apparently the manganese reacts with and kills the other electrode very quickly.
the problem is serious. thundersky made the LMP cells based on manganese; here are some comments from endless-sphere:
LMP - 40 Ah
There's a reason that the LMP's are so cheap. Their lifecycles are simply terrible. No way would you want to only get 300 cycles for this kind of money. :(
Apparently "LMP" is an acronym for "Limping" as in:
"I was riding my bike when the cells cut out and I had to limp home."
You are talking about the old "LMP" cells. Those were junk (you had to "limp" your way home) and were rated at only 300 cycles, but the new ones are called "LFP" and are now made with LiFePO4 and are rated at 2000 cycles.
note that these 300 cycles are spec'ed at only 80% DoD. but never mind the cycles, the problem is shelf life. the manufacturer test cycle life by cycling back-to-back in a short period of time. but these cells will probably corrode in a matter of months, even if you don't cycle them.
I'd strongly advice that you cancel the batt order if possible; strongly. btw, 500 USD is not cheap, you can buy trusty lifepo4s for less. see http://cgi.ebay.com/Ping-Battery-48V-12AH-LiFePO4-Electric-Scooter-E-Bike_W0QQitemZ220276121942QQihZ012QQcategoryZ11332QQcmdZViewItem#ShippingPayment (http://cgi.ebay.com/Ping-Battery-48V-12AH-LiFePO4-Electric-Scooter-E-Bike_W0QQitemZ220276121942QQihZ012QQcategoryZ11332QQcmdZViewItem#ShippingPayment). that seller and product seem very trustworthy. research it on endless-sphere.
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crap. too late. I've already received the kit and battery (and started using it). Oh well.
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let's hope your batt does well. when it finally dies it's to be hoped that you'll be able to get very cheap and proven lifepo4s.
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Hi Lanchon,
If you're still available, I have some questions about one of your posts. You wrote:
there's a rotational speed target "wt" that linearly depends on battery voltage "vbat" and modulation index "x" (0 to 1, controlled by throttle position):
wt=k1*(x*vbat)
(the proportionality constant k1 is a parameter of the motor.) think of it as if the throttle regulated the batt voltage from 0 to max batt voltage. so the throttle regulates target speed from 0 to max target speed (if vbat is constant).
My understanding is that one of the implications of this is that the power delivered by the motor peaks at a little over half of wt and then drops to 0 at wt.
This seems like a very unintuitive design to me. I don't understand the purpose of having a rotational speed target "wt" ie why aren't controllers designed such that they regulate the battery voltage from 0 to max battery voltage (and/or regulate amperage from 0 to max amperage) based linearly on the modulation index "x". This way, the more you turn the throttle, the more power you would get. So at full throttle, you would get full power from the battery/motor.
As an aside, does a controller actually regulate the battery voltage? or does it regulate the amperage? or a combination of both?