The Math and the Science of ESK8, or ESK8 IQ

This isn’t an easy topic if you don’t have a background in math and/or engineering.  That being said, most of these are individually fairly simple.  You will need to put them together and understand the interoperations to be able to define the values discussed here.  It’s not as hard as it sounds, I walk you through it.

This is a list of the formulas and processes that can be used to define the values associated with building and riding an electric skateboard, aka ESK8.  Here you will find methods for defining gear ratio, range, battery WH usage, etc.  If you have a question, don’t understand something or see that I missed something please leave a comment.

If your not interested in understanding the math behind these calculations, or your just in a hurry, I have built a spreadsheet that will calculate everything for you.

Get it Here!

Battery Pack Voltage Values

 Nominal Peak 6S 21.6v 25.2v 8S 28.8v 33.6v 9S 32.4v 37.8v 10S 36.0v 42.0v 11s 39.6v 46.2v 12S 43.2v 50.4v

Battery Type Voltage Values

 Type Nominal Full Li-ion 3.6v per cell 4.2v per cell Lipo 3.7v per cell 4.2v per cell

Formulas

Watt Hours

mAh * V / 1000 = WH

Example with Nominal Voltage:
9000 mAH * 36v / 1000 = 324 WH
Example with Peak Voltage:
9000 mAH * 42v / 1000 = 378 WH

Range

WH / 30 * Efficiency % = Range in Miles
WH / 30 * 1.6 * Efficiency % = Range in Kilometers

Example:
9000 mAH / 30 * 85% = 10.71 Miles
Example:
9000 mAH / 30 * 1.6 * 85% = 17.14 Kilometers

ERPM (Electrical RPM)

KV * Max Voltage * 7 = ERPM

Example:
190 KV * 42.0v (10S) * 7 = 55,860 ERPM
Example:
260 KV * 25.2v (6S) * 7 = 45,864 ERPM

Maximum KV

8600 / Max Voltage = Max KV

Example:
8600 / 42.0v (10S) = 204.76 KV (Max)
Example:
8600 / 25.2v (6S) = 341.26 KV (Max)

Maximum Voltage

8600 / Motor KV = Max Voltage

Example:
8600 / 170 KV = 50.58v
Example:
8600 / 190 KV = 45.26v
Example:
8600 / 260 KV = 33.07v

Maximum Watts

Max Battery Amps * Volts per Cell * Cells = Max Watts

Example:
60a * 4.2v * 12 = 3024 Watts
Example:
80a * 4.2v * 12 = 4032 Watts
Example:
60a * 4.2v * 10 = 2520 Watts
Example:
80a * 4.2v * 10 = 3360 Watts

Maximum Charge Rate

mAh / 1000 = 4a
* Maximum Charge Rate always = 1C

Example:
9000mAh / 1000 = 9a
Example:
12000mAh / 1000 = 12a

* Charging at rates over 2a will lessen the lifetime of your pack
* Charging at rates over 5a can be dangerous

Motor RPM

Mav Voltage * KV = RPM

Example:
42.0v (10S) * 190 KV = 7,980 RPM
Example:
25.2v (6S) * 260 KV = 6,552 RPM

Gear Ratio

Wheel Pulley Teeth / Motor Pulley Teeth

Example:
15t / 36t = 0.42 Gear Ratio

Wheel Circumference

Diameter * PI = Wheel Circumference

Example:
90mm * 3.14 = 282.6mm

Maximum Speed (MPH & KMH)

Motor RPM * Gear Ratio = Wheel RPM * Wheel Circumference = MM/Min
MM/Min * 0.000037 = Maximum MPH
MM/Min * 0.000060 = Maximum KM/H

Example:
7,980 * .42 = 3351.6 * 282.6 = 947,162.16 MM/Min
947,162.16 * 0.000037 = 35.04 Max MPH

Example:
7,980 * .42 = 3351.6 * 282.6 = 947,162.16 MM/Min
947,162.16 * 0.000060 = 56.83 Max KM/H

Max Speed w/ Efficiency
35.04 * 85% = 29.78 Max MPH
56.83 * 85% = 48.31 Max KM/H

Constant Discharge Rate

AH * C = Constant Discharge Rate
* 1000mAh can deliver 1 Ampere (1000mA/1000) for 1 hour(s) or 1AH
* 8000mAh can deliver 8 Ampere (1000mA/1000) for 8 hour(s) or 8AH

Example:
8AH (8000mAh) * 30c = 240a Constant Discharge Rate
Example:
8AH (8000mAh) * 60c = 480a Constant Discharge Rate