Lithium Battery knowledge

There is much to know about lithium batteries.  Whether you are shopping for a factory made bike, or planning a DIY kit, some basic knowledge goes a long way.
 
Batteries and electricity are mysterious things to most people, so I will start with the basics.
 
Voltage: Put simply, this is the force with which electrons are pushed around in an electrical circuit. Think of this like the pressure in a water hose.  Measured in Volts (V). A higher Voltage will make a motor turn faster, or a light bulb burn brighter.

Amps: A measure of how much electricity is used, or is available to be used at any one time.  Think of this like the size of a water hose.  Measured in Amps (A). A higher Amperage will give a motor more torque and faster acceleration.

Watts:  Amps multiplied by Volts gives you Watts; a measure of the work that electricity does per second. 

1 Amp at 2 Volts = 2 Watts
1 Amp at 200 Volts = 200 Watts

A motor producing 350 Watts of power could be supplied from a 35 Volt battery supplying 10 Amps, or a 70 Volt battery supplying 5 Amps.

Capacity or Amp hours: When talking about a battery, the capacity is measured in Amp hours (Ah) or Watt hours (Wh).  This is a measure of how long the battery can supply a certain amount of Amps or Watts.
 
When talking Ah, we would say this battery is 10Ah (10,000 milliamp hours): it can supply 1 Amp for 10 hours, or 10 Amps for 1 hour, etc.  This is a not useful, however, unless we also know the voltage because the voltage is the multiplier.  A more immediately useful term is Watt hours, because it inherently takes into account the Voltage and the Amp hours. For example:
 
A 2 Watt hour battery will supply 1 Amp at 2 Volts for 1 hour

Another example:

 A 10 Amp hour, 48 Volt battery has 480 Watts hours of power available. (10 X 48 = 480)

This battery will supply 5 Amps at 48 Volts for 2 hours. 

Still with me? Read on, you will start to get more familiar with the terms.  

When shopping for batteries or e-bikes there will be different voltages and capacities listed. Converting them into Watt hours levels the playing field as far as the energy available to help you get from A to B.  You may see two models: one with a 48 Volt 9 Amp hour battery, and the other with a 36 Volt 12 Amp hour battery.  They both have the same amount of Watt hours available: 432. There are lots of other variables that will affect the performance of the bike, but at least as far as the battery capacity goes, they are equal.

With batteries, all of these numbers are not exact and will change over time & with changes in temperature. We have to start somewhere though, so that we can compare and estimate range, so we go with the manufacturers specifications of Voltage and Amp hours or Watt hours.
 
How batteries are made, and why it matters.

The batteries used in electric bikes are made up of cells. As of early 2016, they have largely standardized to the 18650 cell. This cell is 18mm in diameter and 65mm long (the 0 is for round) and looks just like an AA flashlight battery, only larger.

There are many other shapes and sizes of cells, but these cells are produced in enormous quantity, and used in everything from laptops to Tesla cars. There is tough competition amongst the big players, so they are constantly improving.

The cells are arranged in parallel groups and series strings in order to produce the required Voltage and capacity.

When you slide a couple of batteries into a flashlight, you have to be careful to put them in the right way around, or it won’t work. What you are doing is putting cells in series. The first cell goes in with the + side down, and the next the same way, that means the + contact of the second battery is touching the - of the first. When you stack cells like this the Voltage adds up.

In the case of a common lithium cell, the Voltage is said to be “nominally” 3.6 to 3.7 V. When it is fully charged it will be 4.2 Volts, and when it is fully discharged is might be 2.75 to 2.9 Volts (Lithium Iron Phosphate cells have a slightly lower Voltage).

For an electric bike, we need at least 24 Volts and as much as 72 Volts (or more) to do the work of propelling the bike, so we need to stack a bunch of cells in series.

A 36 Volt lithium battery is made up of 10 cells, or groups of cells, in series. (10 cells X 3.6 V = 36 V)

Sometimes the Voltages don’t quite add up, for instance 13 cells in series (13S) should be described as a 46.8 Volt battery, but is almost always classed as 48 V. The 24, 36, and 48 Volt standard is a holdover from the days of lead acid batteries that often come in 12 Volt packages.

The common 18650 cells have a capacity of between 1.2 and 3.6 Amp hours at this time, so a single series string of 10 of these batteries might add up to 36 V, 2.5 Ah.

From my experience with many common e-bikes, ridden by all sorts of people, the power consumption is something like 8 to 20 Watt hours per kilometer (Wh/km). Let’s use 10 as a likely number. There are all sorts of bikes and riders that fall either lower and higher than this, of course. Either way, let’s do the math:

36 Volts X 2.5 Ah = 90 Watt hours. 90 Watt hours / 10 Wh per km = 9 kilometers.

Not really enough to make a practical e-bike, even if our rider is more economical with the power, and doubles that to 18 km.

Instead of putting a single cell in series, we parallel a number of cells by connecting them plus to plus, and minus to minus. Instead of adding to the Voltage, this adds capacity, or Amp hours. About the least that you will see with 18650 cells in an e-bike is 3 or 4 in parallel, so if we stick with 36 Volts, we might have a 10 series, 4 parallel (10S4P) battery, so lets look at that:

36 Volts X 2.5 Ah X 4 parallel = 360 Watt hours. 360 Watt hours / 10 Wh per km = 36 kilometers.

That is looking more practical now. Of course, you don’t want to run the battery down all the way on your commute (just like you wouldn’t want to run a car out of gas), so if you had a 25-30 km trip, this 360 Wh battery would be sufficient.

There is another reason that cells are put in parallel in a battery, and that has to do with the ability of the battery to supply current (Amps). The cells in a battery are rated for how many Amps that they can deliver continuously. This is also described as a C rating. To find the Amp rating from the C rating, take the capacity and multiply it by the C rating:

A 2.5 Ah cell rated at 3C is capable of 7.5 Amps continuous discharge current. (2.5 X 3 = 7.5)

Look at the 36 Volt 10 Ah battery that we had examined earlier. If it was made of these 3C cells it would be capable of 30 Amps continuous discharge (4 cells in parallel, each with a 7.5 Amp maximum discharge rate). This battery might be mated with a 20 Amp motor controller and 500 Watt motor to produce an e-bike system capable of 720 Watts maximum power.

36V battery x 20A motor controller = 720W maximum motor power

(Electric motors can be run at more than their nominal rating for short periods of time with no problems)

There is a problem with this though, because those C ratings are the maximum the cell is capable of. When a cell is used this way it will usually heat up, and the supplied Voltage will sag. Heat and high current are a lithium battery’s worst enemies: they accelerate the chemical processes that happen as the battery ages. So a battery used near its maximum C rate will not last all that long, and it will also not supply the Watt hours that it is rated for, as it is sagging to a lower Voltage.

A better designed battery would use a higher C rate cell, or more cells in parallel, so that the cells are not operating anywhere near their maximum C rate.

When you are buying a factory made e-bike, information on which cell the manufacturer is using is generally not available, they will say something like “made with Samsung cells“. Samsung makes many different cells, so it does not tell you all that much, except that they are a name brand, so there an expectation of a certain level of quality and safety of the cells.

An easy, though initially more expensive way to prolong the life of a lithium battery is to use a higher capacity battery than you think you need to meet your range requirements. This battery will have more cells in parallel and /or series, so each cell is working at a lower C rate. It will also mean that you will not use anywhere near the full Amp hour capacity on your average trip.

Batteries of most any type will last longer if they are not deeply discharged on every cycle. In fact lithium batteries are happiest if they can stay between 80% to 20% charged. With a larger capacity battery, this kind of conservative use is possible day to day. Then, when you want to take a longer trip, you can use a full 100% charge to get to your destination worry-free.

Now if this is your first e-bike, or you don’t have the proper instrumentation, how do you know what your Wh/km figure will be? Here is a rough guide for an area with hills and or headwinds, move down a row or so for flat areas.

Usage Watt hours/km

Light/small person on a low power 250 Watt bike traveling 25 km/h 5-8
Light/small person on a low power 250 Watt bike traveling 25-30 km/h 8-12
Average person on a 350-500 Watt bike traveling 25 km/h 10-12
Average person on an average 500 Watt bike traveling 30-35 km/h 12-15
Heavy person on a 500 Watt bike traveling 25-30 km/h 15-20
Average person on an 500 Watt bike pulling a trailer traveling 30-35 km/h 15-20
Average person on an average 500 Watt bike traveling 38-43 km/h 15-20
Average person on a 1000-2000 Watt bike traveling 40-50 km/h 20-25
High power e-bike 3000-5000 Watts 25-35
Electric car 240-300

Lets look at a popular electric bike kit and see how this works out.

The specifications are as follows:

48 Volt, 8.8 Amp hour battery = 422 Watt hours
Claimed range 105 kilometers.

So 422 Wh divided by 105 = 4 Wh/km

I suspect that this range can be obtained riding this bike at one of the lowest assist level on flat ground, at a relatively low speed, say 20 km/h. Seems to me a more realistic rating in the real world would be 34 km. (422Wh/10Wh/km=42 X 0.8=34) The 0.8 multiplier is there because you do not want to run out of power, and running the battery all the way down will reduce the life of the battery.

Why do they tell you 105 km? The majority of manufacturers do this to some extent, so if one starts telling the truth, they won’t sell as many bikes! You can get a reasonable range estimate at the store by using this simple formula:

Watt hours (Volts X Amp hours) divided by 10

Don’t let the salesperson sway you by telling you that their motor technology is sooo much better than the others, therefore it doesn’t use as much power. There is maybe a maximum 20% difference between motor technologies on an open road course.

Having said that, do listen if they are talking about certain motor systems being better suited to the type of riding that you are doing. There are two types of motors systems:

The mid-drive motor (usually located near the crank) powers the bicycle wheel through the chain, allowing the motor to use the bike’s gears. This allows the motor to spin in it’s optimum range even when the bike is going slowly. Possible applications for this type of motor system would be off-road mountain biking (gnarly terrain), and towing a heavy trailer up hills.

The hub motor (built into the center of the wheel), is very simple with few moving parts to wear or break, and can be almost silent. Some hub motors can also act as a brake while supplying some power back to the battery. Applications for this type of motor system would be open road travel at speed, where it has the advantage of not stressing the bike’s chain and gears, as it is totally independent of the human powered part of the bike.

You can certainly stretch the range out on most any electric bike if you need or want to, just by pedaling harder and/or going slower. This is great if you are enjoying the scenery on a Sunday afternoon. The whole point of an e-bike though, is to ride either faster, or with less effort, or both. Expect to use some Watt hours in the process - that’s what the battery is there for!

There is a handy device called the Cycle Analyst that is somewhat of a standard in the DIY e-bike world. It can often be adopted to factory made e-bikes as well (there is an adaptor available to use the Cycle Analyst on the Juiced ODK U500). It calculates Wh/km for you automatically, as well as all sorts of other useful info and functions, highly recommended.