# ESK8 IQ: The Math and the Science of Electric Skateboarding – Part 2

Originally published at: http://dev.esk8.news/2018/12/14/esk8-iq-the-math-and-the-science-of-electric-skateboarding-part-2/

If you haven’t read ESK8 IQ Part 1 read it here.

Lets get right to the meat and potatoes.  The first thing I am going to school you fine folks on today is watt hours.  This is the method that we, as members of the electric skateboarding community, have decided is the most accurate way to measure battery capacity.  Here’s the formula to find your watt hours:

`mAh * V / 1000 = Wh`

Let’s break this down. First we have “mAh”, which means Milliamp Hour and is a unit that measures (electric) power over time.  Sounds daunting, but don’t be afraid.  Just think of it as a gas gauge.  As an example, a 3000 mAh battery could power a device drawing 1000 mA (milliamp), or 1 amp,  for 3 hours, a device drawing 2000 mA, or 2 amps, would last only 1.5 hours.

Seems easy enough, but the key here is knowing the draw, and that’s damned near impossible with an esk8.  Why, you ask?  Let me take you on a trip and show you by example:

I’m riding in my brothers neighborhood, a fairly standard american suburb with nice sidewalks (I’m not riding on that crap!) and fresh asphalt (hrnghhh, oh yeah).  It’s a well used board, so I start off cruising at around 15 mph, that lasts about 1.25 minutes, then I slam the throttle (because, you know, it’s important to KNOW that I can hit 35 mph).  That lasts for about 30 seconds, then it’s back to cruising (for a minute).

I think you can see how figuring this in you head can be a little difficult, that’s why we use volt meters (for the most part).  You can use the volt meter to give you a percentage of battery left or voltage left, I prefer voltage because I know where my cutoff is and I am a bit of a control fiend.

You can get an approximate value based on how and where you ride for the entire ride or across a range of rides.  If you make the effort to record this value, or at least remember it, you will eventually be able to make a pretty good guess about how long you will be able to ride on your board with your battery pack.  For now, just use the voltmeter, or a mobile app and an HM-10 or METR Bluetooth module. More on those modules will come at another time.

Now back to the math.  Here’s a couple of examples:
Let’s assume a 10s4p battery pack, since that what we used in part 1.

`12,000 mAh * 36v / 1000 = 432 Wh`

You have a total of 12,000 mAh because its a 4p pack, meaning 4 cells in parallel at 3,000 mAh each.  You use 36v because that is the nominal voltage (or middle voltage) of a 10s pack.  Using the formula above you have a pack that has 432 Wh.

The reason we divide the mAh value by 1000 is to get amp hours. Watt hours are calculated by multiplying the stated nominal voltage by the stated amp hours. However, most cells rate their capacity in milliamp hours, which are one thousandth of an amp hour.  In order to account for this labelling trend and to keep things simple, we just add ” / 1000 ” in the calculation so you can just plug in the numbers you see on the cells or packs you’re using.

We use the watt hours value to define multiple things, the most important of which is range.  This is the holy grail of esk8 (and speed of course, oh and weight, and then there’s wheel size…ok, maybe not the holy grail but you get what I mean right?)  Here’s the formula to define range:

`Wh / 30 * efficiency % = range in milesWh / 30 * 1.6 * efficiency % = range in kilometers`

I live in the land of eagles, freedom and a McDonalds on every other block, so we will use miles.  It’s just as easy to use the metric formula, just add a ‘x 1.6’ to the end to get the value in kilometers.  Using the Wh value we discovered above with this formula we can define a tentative range for your battery pack of roughly 13 miles.

Whoah whoah whoah, you say.  How did I do that?  I’ll show you.

I used a value of 432 Wh divided by 30 (30 is the average Wh per mile value that I use for pneumatics)  multiplied by 90% efficiency (or .9) and you get 12.96 miles.  This makes some assumptions though.  Based on your wheels, weight, terrain, etc. the value of 30 Wh per mile may be higher or lower.  I have found that 30 is good medium estimate for urethane wheels of medium durometer on decent asphalt.  I use the efficiency value to account for weight of the board and my own fat ass.  You can find your own Wh per mile value with some experimentation.

Its important that you understand this because next time we get into RPM, ERPM, motor KV, max voltage, etc. All of that is needed to define the ever illusive, three horned, gold coin pooping ‘Max Speed’ unicorn, and that one is a pain to calculate.

Until next time…

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