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.
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
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