The information in this post was recovered from a back-up archive of posts by user @devin after some of the information was hidden, deleted or removed from the Electric-Skateboard.builders forum.
Link to Original Thread @ Electric-Skateboard.builders
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The "Is My Math Right?!" Thread
It was suggested by @treenutter

forum moderator, that, since I

often observe mathematical errors and misstatements (and respond to them), maybe I should

start a thread devoted to Math Mistakes and Misstatements.

So here it is.

In an effort to avoid "ruining other people's discussions with math," whenever I see

misstatements being made about products I care about, I will post my observations here, preserving the "

sanctity" of other people's threads.

@devin
2017-02-01 17:17:11 UTC
Ackmaniac, post:6, topic:17037, full:true Wrote:Your right, sorry. My question was wrong. I meant what is the highest no load motor voltage (no load duty cycle) at which i still can achieve 1440 watts at 95% duty cycle.For example at a standstill the motor has a no load voltage of 0V. And we feed i with some volts and amps to achieve 1440 W at a stand still.But now i want to know at which no load motor voltage i still can achieve 1440 watts when my maximum duty cycle with that i can feed the motor is 95% (34.2V).My calculations tell me that this is somewhere around 92,33% duty cycle (33,24 V) but that seems to be wrong.

@Ackmaniac

Question: What is the

highest no load motor voltage (no load duty cycle) at which i still can achieve

1440 watts at

95% duty cycle?

Answer: The

pack voltage is

36V The

highest duty cycle which you can achieve

1440 watts electrical is

95% at

one particular RPM determined by

VESC-detected ohm resistance, pack voltage, user chosen batt/motor/absolute amp limit settings, and motor KV.
@devin

2017-02-02 11:45:54 UTC

Ackmaniac, post:8, topic:17037, full:true Wrote:When the motors no load is already at 95% duty cycle and you power the motor with 95% duty cycle then the power output is 0 W. Think if a ideal world without any resistance. The means when you spin the motor with 1000 rpm then it will spin forever with that speed.A 100 kv motor will spin at 95% (32.4 V) no load with 3240 rpm. When you power that motor now with 32.4 V it won't spin any faster. You remember the donkey/carrot picture. So in this scenario the donkey reached already the carrot.

My question is now at which no load duty cycle (actual motor speed) you can still get a power output of 1440 W when your maximum duty cycle is 95% (32.4 V). Because when the motor spins already at 94.9 % duty cycle you can't achieve 1440 watts anymore (at least not when you have a realistic resistance).

@Ackmaniac

I am confused by your use of the term "

no load duty cycle".

My understanding is the term "

no load" generally refers to a

maximum RPM the motor reaches with

no mechanical load.

This

RPM is determined by:

No Load RPM = Pack V x Motor KV

@devin

2017-02-02 11:59:58 UTC

Ackmaniac, post:10, topic:17037, full:true Wrote:Correct. But lets imagine that the motor spins at no load with 94 % duty cycle. And now we want full power and feed the motor with 95% duty cycle. So my question is at which no load can i still achieve 1440 watts when i fed the motor with 95% duty cycle.

@Ackmaniac

Question: At which

no load can I

still achieve 1440 watts when i fed the motor with

95% duty cycle.
Answer:

Very close to

No Load RPM, you can only achieve

maximum ~1 W,

even with 95% duty cycle.
Extended Answer: Very

close to No load RPM, the

voltage produced by the spinning magnets, opposing battery voltage (called

Back EMF V), is

almost equal to Pack V. As a result of this,

even with 95% duty cycle, only maximum ~1 W will flow to the motor.
",0,2,http://www.electric-skateboard.builders/t/the-is-my-math-right-thread/17037/11,2017-02-02 12:20:23 UTC
Ackmaniac, post:12, topic:17037, full:true Wrote:That's not a answer to my question. You repeat what i explained already.

Ackmaniac, post:10, topic:17037 Wrote:So my question is at which no load can i still achieve 1440 watts when i fed the motor with 95% duty cycle.

@Ackmaniac

Since

you said "no load" I understand this to mean "

no load rpm".

At no load rpm, you

can't achieve 1440 W @ 95% duty.
If you are asking:

Which RPM does

1440W electrical = 95% duty cycle?

The answer is

determined by

Pack V, Ohm Resistance, Batt/Motor/Absolute Max Amp Limit Settings, and

Motor KV.

",0,5,http://www.electric-skateboard.builders/t/the-is-my-math-right-thread/17037/13,2017-02-02 12:37:09 UTC
devin, post:13, topic:17037 Wrote:If you are asking:

Which RPM does 1440W electrical = 95% duty cycle?

The answer is determined by Pack V, Ohm Resistance, Batt/Motor/Absolute Max Amp Limit Settings, and Motor KV.

Ackmaniac, post:14, topic:17037 Wrote:Pack V = 36V, Ohm Resistance = 0.016, Batt = 1000 /Motor = 1000 /Absolute Max = 2000 Amp Limit Settings, and Motor KV = 190

@Ackmaniac this is a

good question and I'll admit

I don't know how to calculate the answer precisely.

",0,1,http://www.electric-skateboard.builders/t/the-is-my-math-right-thread/17037/15,2017-02-02 12:40:56 UTC
Ackmaniac, post:20, topic:17037, full:true Wrote:I just experienced that the power output at higher speeds gets less the more resisance the motor has. But on the other side the motor has more torque at very low speeds of you limit the motor max to for example 50 A.So at low speeds the motor max plays a role. But at close to 95 % duty cycle the motor max can't even be reached.

@Ackmaniac

In my view, this is really the all-important equation:

battery amps =

motor amps x (% duty cycle / 100)
in simple terms battery amps is a whole second avg,

motor amps is an avg for "ON" duration only (seconds).

battery

dc is

pulsed.
or you could say:

battery amps: ON + OFF time AVG

motor amps: ON time AVG

",0,1,http://www.electric-skateboard.builders/t/the-is-my-math-right-thread/17037/21,2017-02-02 13:02:44 UTC