Physics question (Power for acceleration at a certain speed)

[Chriull]

I had in my graphs a discrepancy between my power calculations for accelerations versus the real log data from wheellog. (http://forum.electricunicycle.org/topic/7855-anatomy-of-an-overlean/?do=findComment&comment=107766)

Data from wheellog: timestamp, speed and current.

Acceleration is Delta v / Delta t. As current power for this acceleration i used F = m * a, Pa = F * v.

On the other side i have the motor output power which is Pmotor = I * U Back EMF.

Both power should the same (ignoring friction&magnetic losses, air drag, etc and the "sampling inaccuracy" ) but here is an average error factor of ~2!

I am tempted to just use Pa = m * a * v / 2 as formula , but imho that would be the average power to reach the speed v with an acceleration a. Pa = m * a * v should imho be the power needed to keep up an acceleration a at a speed v?

Anyone has an explanation for this? If this power for acceleration formula is corect, then imho the only other possibility should be, that the reported currents from the KS16C are off by the factor of ~2 and i'd have to look if this can fit again somehow with the other measured data...

m	100	kg
timestamp	speed	voltage	current		speed	Accel m/s²	Pa		Pmotor		Error Factor		U Back EMF
s	km/h	V	A		m/s	dv / dt	Pa=F*v=m*a*v		I * U Back EMF		Pa/Pmotor
0,056	8,58	60,4	11,24		2,3833333								12,0978
0,244	9,42	59,84	15,16		2,6166667	1,241134752	324,7635934		201,358152		1,61287		13,2822
0,474	10,98	58,55	23,34		3,05	1,884057971	574,6376812		361,345212		1,59027		15,4818
0,667	13,29	56,7	31,93		3,6916667	3,324697755	1227,367588		598,333077		2,05131		18,7389
0,85	15,92	55,62	33,53		4,4222222	3,992106861	1765,398367		752,654616		2,34556		22,4472
1,038	18,61	56,65	30,53		5,1694444	3,974586288	2054,640301		801,110253		2,56474		26,2401
1,278	20,18	57,49	25,19		5,6055556	1,81712963	1018,602109		716,751222		1,42114		28,4538
1,459	21,5	55,38	28,38		5,9722222	2,025782689	1209,842439		860,3397		1,40624		30,315
1,64	24,09	53,04	33,81		6,6916667	3,974831185	2659,824535		1148,420889		2,31607		33,9669
1,899	26,47	52,28	34,93		7,3527778	2,552552553	1876,835168		1303,681911		1,43964		37,3227
2,044	28,72	53,52	30,7		7,9777778	4,310344828	3438,697318		1243,20264		2,766		40,4952
2,243	30,25	54,17	26,86		8,4027778	2,135678392	1794,563093		1145,64615		1,56642		42,6525
2,449	31,69	55,06	23,41		8,8027778	1,941747573	1709,277238		1046,026689		1,63407		44,6829
2,644	32,66	55,73	20,67		9,0722222	1,381766382	1253,569167		951,865902		1,31696		46,0506
2,913	33,66	56,23	18,22		9,35	1,032631144	965,5101198		864,732132		1,11654		47,4606
3,056	34,96	56,94	15,78		9,7111111	2,525252525	2452,300786		777,853008		3,15265		49,2936
3,251	36,14	57,97	13,02		10,038889	1,680911681	1687,44856		663,465348		2,54339		50,9574
										Average	1,92774

[meepmeepmayer]

Nothing substantial to say, just thoughts:

• "Pa" is not a good variable name if there's an "a" somewhere else, that was a bit confusing 
• "P_a = mav" should only apply to the actual accelerating.
  At constant speed, this is =0 because that's just the power needed to change the speed.
  At constant speed, you have tire and wind friction. While you may assign to this a formal acceleration a_const so that
  P_friction= m a_const v,
  this isn't the same "a" as the actual acceleration which you get from speed changes and which you can measure directly.
  Shouldn't the formula be more like
  P = P_a + P_motor + P_friction
  where I'd guess P=IUc (c some efficiency) which the battery produces/ends up at the motor, and the right hand terms what that has to work against (acceleration, friction, back EMF).
  So why are you expecting the two powers to be the same?
  No idea how the model for wheels is
• Maybe the wheel numbers are just not very precise. Especially current can change quickly, so you could average some values (instead of the current at a point in time, average it with everything in 10 milliseconds around it, or so). Same with the other data. Aka "clean it up" in some way.

[Circuitmage]

Looks like your acceleration is off (??).

Example, for your first data point, dv = (2.62-2.38)=0.24 m/s . dt = 0.1s

dv/dt= 0.24m/s  /  0.1 s  = 2.4m/s^2 

And why do Europeans insist on using "," when it should be a "." ?   

[jbwheel]

8 hours ago, Chriull said:

Acceleration is Delta v / Delta t. As current power for this acceleration i used F = m * a, Pa = F * v.

On the other side i have the motor output power which is Pmotor = I * U Back EMF.

Force and acceleration depends on the mechanical power outputof the wheel. Mechanical power is not constant depending on the speed and the load (wind resistance, weight...). Relationship between mechanical power and used electrical power also depends on the motor efficiency. Motor efficiency for brushless motor is not constant and depends on the rotational speed... you need at least two graphs for your calculation : mechanical power output and motor efficiency plotted against speed.

Hope I am clear and good luck ! 

[Chriull]

6 hours ago, meepmeepmayer said:

Nothing substantial to say, just thoughts:

• "P_a = mav" should only apply to the actual accelerating.
  At constant speed, this is =0 because that's just the power needed to change the speed.
  At constant speed, you have tire and wind friction.

As written for the first step i did not care for finetuning and by this ignored the losses, friction, etc - i wanted to understand the error factor of ~2

Quote

• 
  where I'd guess P=IUc (c some efficiency) which the battery produces/ends up at the motor, and the right hand terms what that has to work against (acceleration, friction, back EMF).
  So why are you expecting the two powers to be the same?
  No idea how the model for wheels is

 if you are interested in this topic there is a quite perfect script for e-bikes, but covers all the basics needed for EUC's in german:

https://ces.karlsruhe.de/~BUB/Umwelttechnik/Elektromobilitaet_TGJ14_2012.pdf

(3 phase BLDC's can be simplified to normal DC motors as written in this script and by this easily understood)

Or my steps towards this direction: http://forum.electricunicycle.org/topic/7549-current-demand-versus-battery-voltage/. But i'd recommend the former link - is much better explained and understandable

 

Quote

• Maybe the wheel numbers are just not very precise. Especially current can change quickly, so you could average some values (instead of the current at a point in time, average it with everything in 10 milliseconds around it, or so). Same with the other data. Aka "clean it up" in some way.

That's why i made an average over all the values and compared this. This should sort out sampling problems, also it's just for 16 values. By now i'm thinking of logging with wheellog driving some slow and fast cirlces (in/declines get sorted out) and average the power consumptions and accelerations to get a correction coefficient for the current... (without really knowing why).

- on reason could be the current flowing through two coils with 120° difference. If one makes a vector addition of the two "forces" created by this the sum is by the squareroot of 3 bigger (1,7...). Maybe i have overdone with the 100kg weight and additionally some sampling variations did the rest and this is the factor? That kingsong reports just one phase current and the effective motor current goes by this factor?

- the measurement of the motor current is just inaccurate and has to be corrected for each wheel/batch?

6 hours ago, Circuitmage said:

Looks like your acceleration is off (??).

Example, for your first data point, dv = (2.62-2.38)=0.24 m/s . dt = 0.1s

dv/dt= 0.24m/s  /  0.1 s  = 2.4m/s^2 

Sorry - that's the excel time/date formatting. It only shows a max of 1 digit after the comma (decimal point ). I've made a recaluclation and formatting of this in the sheet and going to edit the above posting to the full 3 digits after the point/comma.

Thanks for looking at this in this kind of detail level!

Quote

And why do Europeans insist on using "," when it should be a "." ?   

Because it's called comma here - don't know why you call it decimal point... 

1 hour ago, jbwheel said:

Force and acceleration depends on the mechanical power outputof the wheel.

Thats motor current times the Back EMF Voltage (or also called motor induced voltage). Minus some magnetic losses and internal friction.

Quote

Mechanical power is not constant depending on the speed and the load (wind resistance, weight...).

Resitances are, as written ignored by now - that's finetuning once i understand or give up understanding  They would just count for some (major) percentages but not for an factor of 2.

The mechanical output power of the motor which is as written above motor current (direct proportional to the torque) times Back EMF Voltage (direct proportional to the speed) is by this formula/definition direct proportional (dependend) on torque (load) and speed.

Quote

Relationship between mechanical power and used electrical power also depends on the motor efficiency. Motor efficiency for brushless motor is not constant and depends on the rotational speed... you need at least two graphs for your calculation : mechanical power output and motor efficiency plotted against speed.

The electrical power supplied by the battery and/or the electrical motor input power in relation to the motor output power depends on this motor efficiency and cannot be ignored (would lead to error factors much higher than two). But here this is not looked at. By just taking the motor output power (i_motor times back_emf_voltage) just some small magnetic losses and internal friction are "ignored" (some percents of efficiency)

[Chriull]

1 hour ago, jbwheel said:

Force and acceleration depends on the mechanical power outputof the wheel. Mechanical power is not constant depending on the speed and the load (wind resistance, weight...). Relationship between mechanical power and used electrical power also depends on the motor efficiency. Motor efficiency for brushless motor is not constant and depends on the rotational speed... you need at least two graphs for your calculation : mechanical power output and motor efficiency plotted against speed.

Hope I am clear and good luck ! 

The "power system" of on EUC works as follows:

The battery supplies some "ideal" power = "ideal" battery voltage times battery current

Then there is somy power dissipated internally in the  battery = internal battery resistance times battery current ^ 2

Then some wire/contact power disspation

mainboard/mosfet power disspation

After the mosfets the battery voltage is "stepped down" by the PWM duty cycle, the motor inductance and the freewheel diodes (mosfet body diodes) or active freewheeling. By stepping down the battery voltage to the motor voltage the motor current has to be this same factor higher than the battery current.

(**)This stepped down battery voltage is the motor input voltage

Again some wire/contact power dissipation

Then there is the power dissipated by the coil resistance: coil resistance times motor current ^ 2

After the voltage dropped at the motor coil resistance the back emf voltage is "left" (motor induced voltage).

(*) This back emf voltage times motor current is almost the motor output power, there just some magnetic losses and internal friction.

This now mechanical output power left now "satisfies" the external friction (tire on road) and air drag.

The rest of the power is for acceleration(and/or inclines).

I just looked at the system after the (*) - and there the losses/efficiency are for the concerned speed way below this error factor of 2 i had in my calculations.

If one would look at the whole system, the main losses are as you stated at low speeds and high loads are the losses at the motor coil resistance (more or less the motor efficiency).

(**) This motor input voltage  is "regulated" by the firmware (PID feedback loop which sets the PWM duty cycle) to get the right motor current (torque) to keep the driver upright ("self" balancing)

[jbwheel]

8 hours ago, Chriull said:

They would just count for some (major) percentages but not for an factor of 2.

Use of average is not good, your error factor is between 1,5 and 3,5. 

As for brushless motor, efficiency is between some % to 80% depending on the speed. It can not be considered as constant.

This is a dynamic system  and  phase you are studying (acceleration) and you might not have enough plot (3/second ?) Which is needed since it is nearly impossible to have a constant acceleration (motor power output increasing then decreasing but motor efficiency increasing with speed.).

You might want to try at constant speed first but different speed between 0 and 30km/h... (Ebike model would fit, adding some wind resistance)

 

[Chriull]

1 hour ago, jbwheel said:

Use of average is not good, your error factor is between 1,5 and 3,5. 

As for brushless motor, efficiency is between some % to 80% depending on the speed. It can not be considered as constant.

In because of this i just looked at the system "after the motor coil resistance", so this high losses are not in effect for this consideration.

1 hour ago, jbwheel said:

This is a dynamic system  and  phase you are studying (acceleration) and you might not have enough plot (3/second ?) Which is needed since it is nearly impossible to have a constant acceleration (motor power output increasing then decreasing but motor efficiency increasing with speed.).

Could easily be, that with this sampling intervall some "main values" are "missing". Also one does not know if the values are all from the same point in time or from some point within the timespan, or averaged, or whatever... ;(

This "example" above was choosen, because it was a phase of a somewhat "constant" acceleration phase. And my question arose if the available current data from the wheel is just off by some factor or my formulas are wrong...

This 16 data points are however a very low number and chances are high that by some "asynchronity" of the sampling the deviation gets quite high/renders the data quite unmeaningfull...

1 hour ago, jbwheel said:

You might want to try at constant speed first but different speed between 0 and 30km/h... (Ebike model would fit, adding some wind resistance)

 

With constant speed and "no acceleration" i cannot "calibrate" the current(torque) leading to an acceleration. With constant speed just the torque to overcome friction, air drag and the provide balancing is existing. And all this values are new "unknowns"...

Maybe some 5 to 10 minutes accelerating up and down in the underground garage gives some nicer data...

[jbwheel]

6 hours ago, Chriull said:

With constant speed and "no acceleration" i cannot "calibrate" the current(torque) leading to an acceleration. With constant speed just the torque to overcome friction, air drag and the provide balancing is existing. And all this values are new "unknowns"...

Sure, but you will know if you are using the right tools and will have an easier reading on electrical power (some would say that you need a proper ammeter on battery side). Also a way to identify the motor efficiency factor.

Have you seen this (GT16 there is an old version , some other wheels are boosted but still informative)

http://ecodrift.ru/wiki-article/rockwheel-gt16-review/