ok I made it into a spreadsheet…
I went through the equations. They seem right. I have 3 questions though.
 Under what assumptions is motor_current == battery_current_per_motor/duty
 Is KV = 1/KT always true?
 Lv^3 +vK = J has three solutions. How did you choose the right one?
 “So, for example, stepping 12 V down to 3 V (output voltage equal to one quarter of the input voltage) would require a duty cycle of 25%, in our theoretically ideal circuit.”
“The stored energy in the inductor’s magnetic field supports the current flow through the load. This current, flowing while the input voltage source is disconnected, when concatenated with the current flowing during onstate, totals to current greater than the average input current (being zero during offstate). The “increase” in average current makes up for the reduction in voltage, and ideally preserves the power provided to the load. During the offstate, the inductor is discharging its stored energy into the rest of the circuit. If the switch is closed again before the inductor fully discharges (onstate), the voltage at the load will always be greater than zero.”

KT = 1/KV when kv is stated in terms of rad/sec per volt

If memory serves I believe the other 2 solutions to L * v^3 + v * K = J used negative numbers or imaginary units
also to verify you could watch this video and most times the throttle is being used, you can use battery current / duty cycle % to get the motor current:

I asked this question because you haven’t considered the battery IR. SO the total voltage available to the motor will drop under current draw.

sorry I had the units flipped in my brain. I was thinking in terms of volts/radianpersecond. But I remember reading something related to KV proportional to 1/KT but equal under some assumptions.

Gotcha.
The battery voltage selected should be the voltage including voltage sag at the battery current limit chosen factoring all motors. ie 4 motors @ 60a battery current limit = 240a battery amps… ie what is the battery voltage including sag?
I haven’t gone through the equations but something caught my eye.
200w copper losses is going to end up in a boiling motor in a few minutes if not seconds.
I believe the max current value should be lowered as these settings would result in throttling very soon.
*use these equations at your own risk
As far as esk8 goes, I have come to the conclusion that everything I do is at my own risk
most interesting/surprising finding so far:
if you have 2 motors, 46v, 190kv, 0.05ohm, 205lbs, 90mm tires trying to surmount a 30% grade with only 30a battery amp limit per motor, your best gear ratio is 4.05:1 for 20.8mph…
I’ve made a new calculator as an apple numbers spreadsheet for predicting peak speeds and optimal gear ratios for a variety of load conditions and vehicle parameters:
^basically you fill in the numbers at the top and it spits out the charts.
Losses factored are wind, slope, copper loss and max duty cycle (which affects the max effective battery voltage to the motor). Motor saturation, rolling resistance, iron, controller and battery losses are ignored.
Any interested parties can download the apple numbers speadsheet file here for the next few weeks:
How would/do you use it for your own setup?
It’s cool it’s here don’t get me wrong but I’d rather ride with a setup and explore in practice.
Let’s say I am completely new to this, where would I start.
If I was looking at the above chart with the same hardware (42v battery, 2 motors, 190kv, 100mm tires…
First I’d consider am i riding entirely on the flats or do I climb hills? How steep are the hills?
Suppose I won’t be seeing any hills and want to use 30a battery limit per motor and have max flatland speed for this battery amp limit. Looking at the above chart I’d use 1.85:1 ratio for 46.1mph top speed (48.0mph no load speed).
But suppose I’ll frequently be climbing 25% grade hills and willing to use 60a battery limit per motor… In this case 2.57:1 is called for to enable climbing 25% slopes at the max possible 31.8mph for this battery current limit. This change will reduce my no load speed to 34.6mph.
Thanks. Now that’s some good info I can relate to.
Why would you vendorlock the spreadsheet? ODS file format is much better.
would this be an addition to or a companion to the current esk8 calculator? I could link both in the new nav bar if we wanted.
The calculator has one tab (at the bottom) labeled “saul” because it was a copy of the one he made that everyone used to use before it disappeared from the internets and he’s unreachable. I planned on adding more tabs with different folks’ calculators. When I find an hour or two I will add another tab. It’s easiest to turn a spreadsheet into a calculator.
I had envisioned “calc.esk8.news” as a “suite of esk8 calculators” and not really a single one.
I’m a big fan of https://calc.3dservisas.eu/, is this one you were considering adding? IDK if Kugelis would mind, probably best to ask.
that is the dopest shit yet.