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Watts, Volts, Amps, Amp hours, Watt hours...a discussion


Tom Cole:
Here is some basic math and information that is good to know when researching ebike batteries, controllers, and motors.

Amps = I
Volts = V
Watts = W
Amp Hours = Ah

Amps x Volts = Watts
Watts/Volts = Amps
Watts/Amps = Volts
Amp hours x Volts = Watt hours

If we analogize these terms to a river, volts would be how many feet the water is going to drop from one point to another, or how fast the water will run, it is really about potential...kinda like water pressure.  Amps would be how big the gates in the dam are and the water behind the dam to be dumped into the river is amp hours (capacity).  Watts is a measurement of the power generated and watt hours tells us how long peak power is going to last.  A controller is what regulates the opening and closing of the gate based upon power requirements.

Tom Cole:
Using the information above for our purposes on ebikes...

A couple of rules:
* Your controller's maximum continuous wattage should NEVER exceed the maximum continuous discharge rate of your battery pack.  It is dangerous and will shorten the life of your batteries.
* Your motor's maximum continuous wattage capability should slightly exceed the maximum continuous wattage provided by the controller, assuming your battery meets the rule above.Let's say we have a 36 Volt, 10 Amp hour battery with a maximum continuous discharge rate of 30 amps.  This battery can continuously provide a maximum  of 1080W (36V x 30I = 1,080W).  But for how long?  It will provide 360Wh (36V x 10Ah = 360Wh) which means it will provide 360W of power for 1 hour.  If the battery is run at peak output (1080W), it can only do that for 1/3 of the time (360Wh /1080W = .333), which is 20 minutes.    WAIT, WHAT!?!?

Don't fret!  This DOES NOT mean that your 36V10Ah battery is only going to give you a 20 minute ride.  Assuming the two rules above,  your controller provides the motor with power based upon both need and the programmed max RPM of the motor.  Your controller will usually only draw maximum amps from the battery when you hit the throttle from a dead stop.  The amp draw from that point on will depend mostly upon if you are pedaling or not, bike/rider weight, number of stops/starts, throttle position, hill incline and drag(headwind and rolling resistance)...pretty much in that order too.
So if you and your fat tire bike weigh 400+lbs and are riding full throttle up steep hills of sand into a 30 MPH headwind without pedaling, you are probably only going to get 20 minutes out of that battery.  But an average person on an efficient bike at 20 mph riding on a paved road in light winds while pedaling will easily get 2 hours out of this system.  The controller opens the gate as the motor requires power.

Whether you are pedaling or not and to what extent you are adding support to the system MECHANICALLY is a factor that must be considered.  You can add anywhere from 100 to 300 watts of continuous power to this system.  A professional bicycle rider will produce 200-400 watts continuously for 4 hours and can peak around 1800W in a 30 second sprint.   You should be able to easily add an additional 120W.

Tom Cole:
Taking all of this into consideration, you can make an informed decision about what your needs really are in a battery, controller, and motor.  Let's go through deciding on a bike or motor kit for commuting.

If you are going to convert a regular bicycle into an ebike, I suggest, for commuting rides, that you consider a more traditional frame design with the horizontal top tube, vertical seat tube, and straight down tube completing the triangle.  Most bike racks on cars and buses are designed around this standard, and your battery mounting capability is maximized.  This pretty much eliminates rear suspension bikes.

Your first consideration about the "e" part of the bicycle should be the law where you are going to ride it.  Let's say you live in a state that just follows the Federal laws Federal laws .  Paraphrasing -Less than 750 watt(1 HP) motor, and no more than 20mph without pedaling.  Most often, meeting this requirement is pre-programmed into the controller's default.  It limits the wattage supplied to the motor to 750 and limits the RPM to what will drive a specific wheel size to 20mph.  Many systems have an "off road" setting as well, and some systems have multiple settings that enhance either performance (top speed and/or acceleration) or economy(distance capability).  A motor that can handle 750w to 1000w would be your choice here, just in case you decide to take her off road a bit.  But it is better to ask before you buy.

The next consideration will be your battery.  I am a fan of keeping the center of gravity low on a bicycle, so I prefer my battery to mount on the down tube.  This allows the battery to be attached securely using the water bottle mounting screws and keeps it protected inside the frame.  For commuting, you do not need to go crazy with the battery's voltage or energy density and this is great since the battery is often the most expensive part of the system.  The battery packs we use are almost always made up of 3.7v  "18650" cells wired in various configurations.  There are a lot of different 18650 batteries with varying features.  The latest greatest are 3.5Ah 10 amp batteries that allow the production of smaller battery packs without sacrificing energy density or the ability to draw a lot of current at once.The "Shark" or the bottle battery it the way to go.  A 36V pack with 40 cells in a "10S4P" configuration will provide 14Ah.  This will yield a 504Wh battery.  Couple that with a 30 amp controller and you have 1080W peak.  The 750 watt setting on the controller would need to be at 20 amps and you have 40 minutes at peak watts.  If you pedal at this "legal" setting, you will easily cover 20 miles at top speed.


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