# Battery math



## dodger (Feb 10, 2004)

Commencal Meta Power with Shimano Steps 8000, 500WHr battery

Love the bike but something that my feeble mechanical engineering mind can't grasp is the battery math. How can I fully drain a 500WHr battery in 1 hour with a 250W motor?

My maths says I should be able to get 2 hour at full boost (2 Hr x 250 W = 500W Hr).

I have two batteries and I can drain either in 1 hour at full Boost.

I've got over 3,000 miles and 800,000 ft of climbing in it now in about 1 year. Tangentially there has been more battery degradation than Shimano purports. My best guess is maybe 15% less than initially but that still doesn't explain where those watts are going. I'm sure there are some heat losses and inefficiencies, but 50%?


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## ninjichor (Jul 12, 2018)




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## dodger (Feb 10, 2004)

Thanks, I had seen some of these dynos long ago and forgotten about them. I kind of assumed they were peak, not nominal charts.

So a 250W nominally rated motor can produce 500W for as long as an hour?


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## ninjichor (Jul 12, 2018)

Nominal - in name only.

Here's a clue to answer that: watch your display. The boost meter tops out often in Boost mode a lot, right? How long can you keep it there? Has it ever tried to limit that as if it were overheating?

P.S. note that 500W output is different from 500W input, and there are sensors to be powered, like the torque sensor for Trail and Boost mode* (and the smart controller that manages current based on the info from sensors). If you're getting 500W output with a motor that has 80% efficiency at best...

* assumption on my part here, that Eco mode doesn't use this fancy stuff to use less energy. Could explain why Trail mode displays far lower estimated range than Eco on flat pavement, despite similar levels of assist. I don't understand why it would seem to decimate range that much though...


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## matt4x4 (Dec 21, 2013)

Fully drain the 500W Hour battery, easy, go up steep hills on the highest assist. Probably get very high wh/distance #'s and drain the battery quickly that way. How much power do the store bought ebikes put out, I have no clue. Does it depend on speed alone, then it could very well get into the 40wh/distance or 50wh/d or more, until the motor heats up and turns off the power from the controller to the motor.



dodger said:


> Commencal Meta Power with Shimano Steps 8000, 500WHr battery
> 
> Love the bike but something that my feeble mechanical engineering mind can't grasp is the battery math. How can I fully drain a 500WHr battery in 1 hour with a 250W motor?
> 
> ...


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## 33red (Jan 5, 2016)

With a display that shows how much energy is being drained from the battery in real time it easily multiply by 20X. You can pedal on flat using allmost nothing from your stored energy and sprint up a hill in top gear with max assist and BAM in 10 seconds you just lost the energy that you would have used on flat in 3 minutes. I am only 130 pounds, imagine a heavy rider. The smart thing to do is modify the transmission for easier gearing. That allows slower climbing to stretch distance and if you need to use muscles only it also helps, so less fear of an empty battery.
With a new 500Wh 3 hrs is easy unless you expect a motorcycle.
These are bicycles with some assist.


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## b1rdie (Mar 11, 2011)

It seems to me that the boost level of assistance is supposed, by design, to be used like 10-20% of the time only.
Designers have to assume some paradigma and I guess that designing a bike that can take any unfit rider to the top of a 4.000 foot hill faster than Nino Schurter could ever dream of, is good enough for most of us.
The boost mode, i guess, was designed to just make it possible to clear a climb where changing to a lower gear is not possible. It does not mean to be used as a "faster climb" mode because it will drain the batteries abnormally fast in trade for some abnormal power.


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## richj8990 (Apr 4, 2017)

ninjichor said:


> Nominal - in name only.
> 
> Here's a clue to answer that: watch your display. The boost meter tops out often in Boost mode a lot, right? How long can you keep it there? Has it ever tried to limit that as if it were overheating?
> 
> ...


Isn't it also because most peak power is 200-250% more than the nominal power? As in 250W nominal and 550-600W peak? So when he uses boost then it's at 500+ Watts, assuming his cutoff fuse is rated for at least 20-25 amps for a 24V battery, or 15-20 amps for a 36V battery? I think that's what you were getting at but didn't specify it this way.


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## 33red (Jan 5, 2016)

Personaly without a car, i use boost/max assist in streets and roads going to the trails. Than i lower 1 notch to play in the woods. I like to climb so i do not want a motorbike. Many want a motorbike less the insurance so they need Huge batteries, loose the light feel of a bike.


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## matt4x4 (Dec 21, 2013)

Typically on min assist you use about 6-8 Wh/km
Typical assist at 40kph with pedaling and motor on all the time 9-12Wh/km
No pedaling is 14-20Wh/km

I'd be sure interested to see the controller design for the boost function. How would it latch to give more amp discharge. I just open up a controller to find the lvc pads, or the shunts.


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## ninjichor (Jul 12, 2018)

Sorry if I wasn't clear earlier, supplying the data but only hints to help figure out the answer yourself. Here the answer:

Output: 475W* of assist from motor from full boosting, without any power fade due to overheating.

Input: 593.75W drawn from the battery if the motor has 80% efficiency* (divide 475 by .8). Consider sensors and display, round up a little...

This explains how a 504 Wh battery draining in 1 hour with boost is a realistic result, if the battery really did have that much capacity**. 

* from source in post #2.

** a number of things reduce full/max capacity, such as temp fluctuations and charger design. Charging to fuller capacity fatigues the capacity sooner, than charging to 70-90%, getting maybe only 500 cycles before capacity drops to 70% rather than thousands. Smart chargers recognize that it's harmful to charge to full if you're not going to run the risk of running out of charge. Non-smart chargers probably just charge to whatever voltage is marked on the back (Shimano runs a 36V system). Winter weather has severely reduced capacity in electric cars, permanently in early gen Nissan Leafs. I was given the impression that cells physically expand and contract as they are charged and discharged, and temps can affect this, which is why lithium cells are recommended to be stored at room temp with 50% charge. Being stored at 100% and being exposed to hot weather can lead to bad juju maybe--charging to 100% in cold temps can possibly lead to overcharge as the battery warms up too.


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## matt4x4 (Dec 21, 2013)

There is no consistent discharge, due to the terrain and wind dynamics. You also have to take into consideration the age of the battery and the type of chemsitry it is.


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## b1rdie (Mar 11, 2011)

I took the easy math: buy an extra batterie and got
New range = (Old range)x2


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## matt4x4 (Dec 21, 2013)

You can also just look at any 18650 discharge curve, lots at lygte. I chose the 25R for a link to post.

Obviously you dont want to be doing 20A per string as the life span of the battery pack would suffer greatly. Also the older the battery, the # of discharges, the depth of those discharges, how its stored (/cycle of temperatures) all have an impact on the internal resistance of the battery. The higher the IR the worse off the battery is. The lower the IR the better that battery is.

https://lygte-info.dk/review/batteries2012/Samsung INR18650-25R 2500mAh (Cyan) UK.html


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## ninjichor (Jul 12, 2018)

b1rdie said:


> It seems to me that the boost level of assistance is supposed, by design, to be used like 10-20% of the time only.
> Designers have to assume some paradigma and I guess that designing a bike that can take any unfit rider to the top of a 4.000 foot hill faster than Nino Schurter could ever dream of, is good enough for most of us.
> The boost mode, i guess, was designed to just make it possible to clear a climb where changing to a lower gear is not possible. It does not mean to be used as a "faster climb" mode because it will drain the batteries abnormally fast in trade for some abnormal power.


I attached what Shimano intended Boost to be used for, relative to the other modes. I tried using Boost simply just to get used to using boost. The 50+ lb bike is not something I want to push/lift on steep loose terrain, so I want the best chance of making it up through riding. Is Trail mode smart enough to do it? I don't know, as I haven't tested. I stayed in Eco for most of the time, since Boost was a bit too much and it kept boosting for at least 0.5 seconds after I stopped pedaling, which was worrisome to me (I'm not used to motorized bikes).

I know that the bike's not bad to be ridden with assist turned off totally, as the motor has virtually no resistance.

Not sure if this is normal, but the motor's internal gears kind of feel notchy when accelerating from a standstill--this is the same feeling I get when the bike roll backwards with pressure on the pedals.


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## 33red (Jan 5, 2016)

ninjichor said:


> I attached what Shimano intended Boost to be used for, relative to the other modes. I tried using Boost simply just to get used to using boost. The 50+ lb bike is not something I want to push/lift on steep loose terrain, so I want the best chance of making it up through riding. Is Trail mode smart enough to do it? I don't know, as I haven't tested. I stayed in Eco for most of the time, since Boost was a bit too much and it kept boosting for at least 0.5 seconds after I stopped pedaling, which was worrisome to me (I'm not used to motorized bikes).
> 
> I know that the bike's not bad to be ridden with assist turned off totally, as the motor has virtually no resistance.
> 
> Not sure if this is normal, but the motor's internal gears kind of feel notchy when accelerating from a standstill--this is the same feeling I get when the bike roll backwards with pressure on the pedals.


The obvious thing is biking uphill we use gears.
Other obvious thing some want a motor bike disguised as a bicycle.
Eco goes everywhere with a proper gearing.
There are facts and marketing, not the same.
Some systems are better than others by design.


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## b1rdie (Mar 11, 2011)

*@ninjichor*

Yes, trail mode is enough for most climbs and I also found that 0,5 seconds of extra assist even when you stall the pedals is annoyng but it also helps a lot to clear technical steps. I wish I could adjust that extra "timing" for some special purposes and then control it with the brakes ?
If you want to stop that extra 0,5 s of assistance you can make just an infinitesimal backpedal and it stops immediately I have been doing this when need to do a fast shift under power and it works well for me.


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## matt4x4 (Dec 21, 2013)

You raise an interesting situation.
The store bought ebikes, if the hill is too steep and not wanting to stall the motor then how does a rider walk a store bought bike up a steep hill if its pedal only for power?
I am used to using a little throttle then using the brakes, then walk up then a little throttle, then brakes, then walk up. Its a smooth motion, but the first time was quite awkward.



ninjichor said:


> I attached what Shimano intended Boost to be used for, relative to the other modes. I tried using Boost simply just to get used to using boost. The 50+ lb bike is not something I want to push/lift on steep loose terrain, so I want the best chance of making it up through riding. Is Trail mode smart enough to do it? I don't know, as I haven't tested. I stayed in Eco for most of the time, since Boost was a bit too much and it kept boosting for at least 0.5 seconds after I stopped pedaling, which was worrisome to me (I'm not used to motorized bikes).
> 
> I know that the bike's not bad to be ridden with assist turned off totally, as the motor has virtually no resistance.
> 
> Not sure if this is normal, but the motor's internal gears kind of feel notchy when accelerating from a standstill--this is the same feeling I get when the bike roll backwards with pressure on the pedals.


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## Twilight70 (May 24, 2019)

33red said:


> The obvious thing is biking uphill we use gears.
> Other obvious thing some want a motor bike disguised as a bicycle.
> Eco goes everywhere with a proper gearing.
> There are facts and marketing, not the same.
> Some systems are better than others by design.


I have a few questions on this gearing issue...

1. I've noticed a lot of the specs...bikes are being sent out w/ 34T or 36T front rings w/ the 10/11-50/51 cassettes. Why can't it be tweaked so that a combo like a 32T w/ a 10-51 setup be used in trade for higher RPM (like roadie RPM in the 90 range) and less boost to extend the battery range? I have knee issues and less torque and higher revs works really well to keep my knees happy.

2. I understand that the above might shorten the life of the ring/chain. But if I consistently use less boost and thereby less torque at the motor, shouldn't it in theory maintain, or even extend, the life of these parts? I guess a stainless ring might help w/ longevity here?

3. I also understand that a gear ratio too far reduced might put too much torque at the rear wheel and cause spin-outs too easily. But I think this can be addressed by shifting. What I can see is that because the boost helps you when you peak and drop off when you're not laying into the pedals, an uneven pedal stroke becomes very exaggerated. Can this be remedied by going to an oval ring?

4. Is it a good idea to buy a battery charger/conditioner? Do the chargers that comes along w/ these $6K+ bikes have a battery conditioning mode?

Disclaimer: I don't have an ebike, yet. I'm in research mode, as well as selling some of my pedal bike mode to fund an ebike purchase. Eyeballing the YT Decoy Pro Race, and building a set of custom wheels to run full 29.

Thanks in advance.


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## matt4x4 (Dec 21, 2013)

You should be able to install whatever crank gear you want, so a 32T is fine if thats what you think you want. 

The less power you use, the more power is retained in the battery to go longer distances. On the KT kits there are different levels of assist, 0 to 5. The less power used, the longer distnace you can ride. You want 100% assist, set to that level and you will get less distance. Set to 10% assist forces you to pedal and break a sweat which means you get much more distance out of each charge. 

Remember that store bought ebikes are proprietary, meaning you have to buy everything from them and no one else. They set high prices for parts, knowing they got you by the balls.

I am currently using 3 laptop 330W chargers, spitting out 16A at 20.50V, on a 54V pack. I use XT90 connectors from Hobbyking.com I can use my battery chargers on anything I wish to. With proprietary systems, there are electronic handshakes that make certain the charger and the battery were purchased for extremely high prices from the same manufcaturer as the store you purchased the bicycle from. Alright for rich people, but I'd be too paranoid of having a $6k ebike locked up while I grab groceries.


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## 33red (Jan 5, 2016)

Twilight70 said:


> I have a few questions on this gearing issue...
> 
> 1. I've noticed a lot of the specs...bikes are being sent out w/ 34T or 36T front rings w/ the 10/11-50/51 cassettes. Why can't it be tweaked so that a combo like a 32T w/ a 10-51 setup be used in trade for higher RPM (like roadie RPM in the 90 range) and less boost to extend the battery range? I have knee issues and less torque and higher revs works really well to keep my knees happy.
> 
> ...


OK, here i am a 62 YO outdoor guy not an expert but semi-retired so i ride a lot and have nothing to sell, i am just sharing what i have learned and experienced.

I do not trust Shimano way too many reports from riders on their second motor, on their third motor. This is a new system that has proven to be not reliable.
Start reading a whole list of excuses like happy customers do not write, many sold so tiny failure % well a third engine in 6 months is HUGE.

Let say you find a bike that comes with 36, 11/46 nothing stops you from using a 32 front.

If you do not trust the system as is do not buy a system that needs a patch. Buy a system you trust.

Oval is clearly a patch, with the range you like you will like your bike.
I have very little power so i have a fat with an easier cassette, and a summer bike with a smaller front ring, we are not all average.

Here is an example, my older HT was 11S 28 front with 10-42 for 21 pounds. It makes no sense to pull a 36 front with an Ebike.
What if i run out of batttery or any electrical problem that 48 pounds will need a tow truck.


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## PierreR (May 17, 2012)

Battery math is straight forward. Marketing is not.

Your battery is rated in amp hours not really in watt hours. The difference in range is related to battery voltage sag. The voltage of a battery drops as power is removed. The higher the amp draw the greater the drop in voltage. If you are pulling high amps from a battery you will not get the rated watt hours out of the battery, you will get the rated amp hours. Quit pulling amps and the battery voltage recovers.

Say your bike is 36 volts, 500 watt hours is 14 amp hours. Most battery BMS's cut power to the bike when the voltage drops to 20% of remaining battery. Some systems go by amp hours remaining. In any case if your battery is 100% charged you only have 80% available max. But wait, there is more. At high power draw the voltage will sag to the cutoff limit long before the 20% is reached. You might only be draining 60% of that battery before it cuts out.

Now at the top end of the battery its hard even new to get above 95% charged with most chargers.

But wait, there is more. Some systems will power the bike to a full 250 watts output. The motor might only be 70% efficient so the battery might be putting out 350 watts. Again many things depend on how your system operates.

For instance, I have a 700 watt hour 52 Volt battery. I went out yesterday riding roads. I started the trip at a voltage of 58.7 volts and finished the trip at 49.5 volts. I used 412.6 watt hours. The battery draw was 8.713 amp hours. With no battery sag, taking an average of my voltage and dividing the watt hours should have been 412.6 / 54.1 v= 7.63 amp hours. The actual average voltage I used was 412.6 / 8.713 or 47.35 volts My actual sag was 51.1-47.35 = 6.75 volts.

I was cruising at 20.5 mph pulling 350-550 watts for 21.8 miles. My battery now has about 300 charge cycles on it. Power measured from the battery, not the crank.

In short, the math is really immaterial. You can figure you have a 50% to 75% usable battery depending on how much amperage you are pulling from it.

If I want high power and long range I have a 14s23p GA battery 4,170 watt hours at 52 volts (80.5 amp hours) Sag is super low on that battery because of its size. My range is 180 to 380 miles depending on my speed. 
https://www.aliexpress.com/item/32966299785.html?spm=a2g0o.productlist.0.0.4d7777afz32Fxr&algo_pvid=71f30f88-f6eb-4de1-9ca3-8f85835d9253&algo_expid=71f30f88-f6eb-4de1-9ca3-8f85835d9253-6&btsid=0be3746c15859706145723590e9581&ws_ab_test=searchweb0_0,searchweb201602_,searchweb201603_


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## matt4x4 (Dec 21, 2013)

Don't forget about connection resistance, winding resistance, Turn Count of motor, lamination size, and internal resistances of the battery, temperature and chemistry. 




But 52V 80.5Ah WOW!!!!! Sounds like maybe a diy battery, how did you weld it up, or did you solder it which is a ghetto way but then there is also the solderless/weldless way.


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## PierreR (May 17, 2012)

matt4x4 said:


> But 52V 80.5Ah WOW!!!!! Sounds like maybe a diy battery, how did you weld it up, or did you solder it which is a ghetto way but then there is also the solderless/weldless way.


I put the link to the battery above. It's the floor of a small trailer. I looked at a DIY and I did not figure I could really beat the price enough to bother.


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## matt4x4 (Dec 21, 2013)

PierreR said:


> I put the link to the battery above. It's the floor of a small trailer. I looked at a DIY and I did not figure I could really beat the price enough to bother.


Yeah the cost does add up for building one yourself, 18650 holders, metal tabs, tab welder, bms, encasement materials. Thats why LiPo rc batteries have a following as they are just plug and play, but more sensitive to voltage fluctuations, over charging, and under charging etc.

However, too many people buy from unknown sources that are not reputable. People see some good price on ebay or aliexpress or alibaba or amazon and they dont have a clue how its built, what brand of 18650's are inside, if the bms is any good at all. There was a very knowledgeable fella on https://endless-sphere.com/forums/ who bought a battery on alie from an unknown seller, and it ended up exploding causing massive damage. Thats the problem with buying from unknown sources, and buying cheaply. But there are reputable companies out there selling very well built batteries but you arent getting them cheaply.


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## PierreR (May 17, 2012)

matt4x4 said:


> That's the problem with buying from unknown sources, and buying cheaply. But there are reputable companies out there selling very well built batteries but you arent getting them cheaply.


I here you. Even from Alibaba you are going to pay for quality, even from China. Just not as much. I could have bought a battery for damn near half the price I paid if I wanted a cheap Chinese cell. Some Chinese cells are down right a bargain though. Takes a lot of asking and research to find out which ones. Your first line of defense is to understand battery construction, chemistry and point of manufacture. Forget the factory photos in the web sites. Many are the same photo. In my case, the cells are made in Japan. 
We now make third world parts right here in the USA. We didn't get the refugees with great skills and there are lot of stupid people running factories here. No guarantee sourcing here in the states going to get you quality so I do my research. 
Just bought the battery in January and now this here virus is playin hell with giving it a workout. I bought it for touring off the beaten path on a fat bike with 26 X 4.8's


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