What effect will different choices of
"Battery Amp Limit" and
"Motor Amp Limit" settings have on acceleration?
Anonymous ESK8 Rider ""A"" Shared these numbers:
500 watts desired from battery
full throttle
50V pack
0.2386 ohm windings
2 motors
x/x/x batt/motor/absolute amp limit settings
From the above values it is simple to calculate the settings that are necessary to reach various performance targets.
Only one set of batt/motor/absolute amp max settings gives the Rider's desired low speed 500w / all speeds under 500w values. Some values give uneven "low speed watt" / "all speed watt limit" values:
5/33/33 gives
500w total available electrical watts at low (under 200rpms) speeds, but at higher speeds, no more than
500w total available electrical watts
(500w/500w) <
even
20/50/50 gives
1193w total available electrical watts at low (under 200rpms) speeds, but at higher speeds, no more than
2000w total available electrical watts is available (
1193w /2000w) <
uneven/unequal
20/30/30 gives
429.48w total available electrical watts at low (under 200rpms) speeds, but at higher speeds, no more than
2000w total available electrical watts
(429.48w/2000w) <
uneven/unequal

the math to make these predictions is all very straightforward
ohm's law
volts = amps x resistance
volts x amps = watts
rider has 2 motors so desired 500 watts is 250 watts per motor
solve for 0.2386ohm and 250 desired watts:
volts = amps x
0.2386 ohm resistance
volts x amps =
250 watts
enter the 2 numbers into an ohm's law calculator to find the other 2 answers:
7.72 volts =
32.36 amps x
0.2386 ohm resistance
7.72 volts x 32.36 amps =
250 watts
this gives us 4 values:
7.72 volts
32.36 amps
0.2386 ohms
250 watts
how do these numbers tell us how to choose
battery amp limit and
motor amp limit?
the 32.36 amps value, rounded up to
33, turns out to be the
motor amp limit required to achieve 250 wattselectricalintomotor while accelerating full throttle at low (under 200rpm) speeds
since there are 2 motors, 2 x 250W = 500W (the desired battery draw limit)
since we don't want more than 250 watts per motor at any speed, the
battery amp limit is calculated as follows:
250W / 50V pack voltage =
5 battery amp limit
this gives us:
5 battery amp limit
33 motor amp limit
500w low speeds & no more than
500w any speed resulting in the evenest acceleration possible limited to desired 500w battery draw electrical (2 x 250W motor draw electrical)
in conclusion:
we started by knowing winding resistance, pack voltage, desired battery max wattage and number of motors
from this we calculated the appropriate battery amp limit and motor amp limit settings.
it is outside the scope of this particular thought experiment to say whether or not any particular values for these settings will or will not harm a VESC or other components.
but from a purely software perspective, the calculated 5 battery amp limit and 33 motor amp limit effectively achieves the rider's electrical power input and steadyacceleration goals.
devin, post:3, topic:15995 Wrote:Ultimately the numerical output of the software controls the "% Duty Cycle" or "% ON TIME" of the switches.
so
how do those 5/33 batt motor max limits we inputted into the VESC exactly mathematically determine the controller's onoff switching % Duty Cycle during the very first moments of acceleration?
remember those 4 numbers we got out of the ohm's law equation?
7.72 volts < divide this number by the battery pack voltage, then x 100
32.36 amps
0.2386 ohms
250 watts
this gives us 7.72 volts / 50 volts = 0.1544
0.1544 x 100 = %15.44
%15.44 will be the contoller's initial onoff % duty cycle during full throttle acceleration (under 200) rpms.
",3,1,http://www.electricskateboard.builders/t/understandingvescthedifferencebetweenbatteryampsandmotoramps/15995/6,20170113 05:06:34 UTC
long story short from last post:
choice of batt/motor/absolute amp limit settings directly determines the on time % duty cycle of the VESC during acceleration, which in turn directly controls electrical wattage into motor which in turn directly affects rate of acceleration.

what if 3 different riders all want 500 watts battery draw max with even acceleration, using completely different setups and boards? what batt/motor amp limit settings would each rider choose to get 500W battery max? (setups are immune to damage for thought experiment)
Anonymous ESK8 Rider "
A" Shares these numbers:
500 watts desired from battery full throttle
50V pack
0.2386 ohm windings
2 motors
result:
5/33/33 batt/motor/absolute amp limit settings for
500w
10/46/46 batt/motor/absolute amp limit settings for
1000w
Anonymous ESK8 Rider
"B" Shares these numbers:
500 watts desired from battery full throttle
35V pack
0.0415 ohm windings
1 motor
result:
15/109/109 batt/motor/absolute amp limit settings for
500w
29/156/156 batt/motor/absolute amp limit settings for
1000w
Anonymous ESK8 Rider
"C" Shares these numbers:
500 watts desired from battery full throttle
37V pack
0.02058 ohm windings
1 motor
result:
14/155/155 batt/motor/absolute amp limit settings for
500w
27/220/220 batt/motor/absolute amp limit settings for
1000w
Conclusion: widely different batt/motor/absolute settings are required to obtain 500W battery max & even acceleration wattage on differently configured ESK8 boards.
",0,0,http://www.electricskateboard.builders/t/understandingvescthedifferencebetweenbatteryampsandmotoramps/15995/7,20170113 06:23:36 UTC
Are there any other important and useful mathematical formulas for understanding the VESC software?
It turns out there is a very interesting mathematical relationship that always exists in a VESC between "motor amps" "battery amps" and "on time % duty cycle". If you know the true values of any 2 of these numbers, you can calculate the value of the 3rd number.
For example:
 if you know the instant "motor amps" and "battery amps" values, you can calculate the "ontime % duty cycle"
 if you know the instant "ontime % duty cycle" and battery amps values, you can calculate the motor amps
 if you know the instant "ontime % duty cycle" and motor amps values, you can calculate the battery amps
The formulas for the relationship between these values are:

battery amps x pack voltage =
wattage into motor
 (
motor amps x (% duty cycle / 100)) x pack voltage =
wattage into motor

battery amps = (
motor amps x (% duty cycle / 100))

% duty cycle = (
battery amps /
motor amps) x 100
^ these ratios will be true at all times & can be seen in any VESC data logging video during throttle use, such as this one by Benjamin Vedder:
",0,1,http://www.electricskateboard.builders/t/understandingvescthedifferencebetweenbatteryampsandmotoramps/15995/8,20170113 07:23:32 UTC