Electric Go Kart motors.. the essence

itsid

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Hi,
I think it might be easier -for me at least-
to have a thread where I can point you to,
to explain the basic math behind motors, power ratings,
and the magic of finding the ideal motor for your task ;)

Within this thread I'll be using strictly metric values
namely kilogram (kg), meter (m) and sometimes kilometers per hour (km/h).
In case you want to convert:
10 lb = 4.536 kg
10 ft = 3.048 m
10 mph = 16.094 km/h
and
10 mph = 4.47 m/s

Also you want to make sure you know the difference between
Power -Watt (W)- and Force -Newton (N)- :D


What kind of motor to choose?

First of all, to have some clarification;
there's a minimum of TWO different power ratings for each motor.

Pm [ mechanical Power, W ] and
Pe [ electrical Power, W ]

Do not mix those two up.

The electrical Power is the amount of power a motor draws from your batteries,
where as the mechanical Power is the amount of power
you can pick up at the motorshaft to turn your wheels.
that is the number you want to know.

It's about the motor efficiency,
which for modern motors is above 80% in their recommended powerband,
the speed(rpm) and load at which you can run it until your batteries are drained.

If you do not know it's efficiency rating,
you should assume an efficiency of said 80% for a calculation,
although it's most likely better than that.
That way your motor will either have a tiny bit more power,
or it'll draw a tiny bit less from the batteries than expected...
Both mistakes are not really an issue for us ;)

Math:
Pm = 0.8 * Pe

Attention:
All motors have a limit, and the closer you get to that, the worse will be it's efficiency.
Some companies cheat and tell you the peak power
that's an amount that will kill your motor when applied for too long.
Whatever too long means; can be as little as just 10 seconds.
And it's best efficiency rating (at a very different speed and load).
That's fairly common for RC motors for example.

At it's peak power the efficiency of nearly every motor is worse than 50%
That means at least half the power applied is converted to heat.
You don't want that!​

So whenever possible, choose a motor that is specifically made for electric vehicles
(EV motors) those are -to my knowledge- always rated in mechanical power, and they always rate the constant power
(some list the peak too, some don't)
If that is impossible for some reason, be sure to know it's continuous power if you need to calculate!

If you do not need to calculate, this thread will be of no interest to you :D

'sid
 
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itsid

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yeah.. stop babbling.. what Power do I need?

What power do you need?

This is the most painful question to answer,
since it's based on a lot of different informations for various tasks.

You need to know what you want the kart to do
or even better, know it all.

Just like Star Wars.. this is all about the Force!

Let's just start with a something really simple
the way I calculate a value as a suggestion in case you asked.

Say you do not care much about acceleration but more about
the possibility to climb road inclinations without slowing down too much.

The main factor to judge the power is said road inclination.
Nearly all roads in the western world have an inclination of less than 10%
most even less than 5%...
So all you need to know basically is the force required to move up that hill.

Fi [ Force inclination, N ]
m [ total mass of the kart incl passengers, kg ]
g [ gravitational force, 9.81 m/s² ]
alpha [ road inclination angle ]

Math:
Fi = m * g * sin(alpha)

This is a very easy way to find motor specs,
just assume an alpha of 5° -almost 9% inclination-
that'll cover most of your roads,
if you want to go offroad you can assume 10°,
and if you really need to climb a steep hill, you need to know it's inclination ;)

Example:
Fi = 150 kg * 9.81 m/s² * sin(5) = 128.25 N

If you do not want to spend much time on finding a number, this is the way.:D

You do not need to climb a hill,
you just want to ride on a level surface

Well in that case you need to know the rolling resistance of your kart
and the force to counteract that ;)

Fr [ Force rolling resistance, N ]
Cr [ Coefficient rolling resistance ]

Math:
Fr = m * g * Cr * cos(alpha)

See, not too difficult either, but you need to know the coefficient.
here's a short list:
Code:
[B]Cr		Wheel -> Surface[/B]
0,015-0,02	Motorcycletyre on asphalt
0,011–0,015	Cartyre on asphalt
0,01–0,02	Cartyre on concrete
0,020		Cartyre on gravel
0,015–0,03	Cartyre on cobblestone
0,03–0,06	Cartyre on potholes
0,050		Cartyre on dirt track
0,04–0,08	Cartyre on compacted sand
0,2–0,4		Cartyre on loose sand

Example:
Fr = 150 kg * 9.81 m/s² * 0.02 * cos(0) = 29.43 N

See how small this number is compared to the other one?
If you decide by that number, your result will be disappointing,
no matter how low your expectations were ;)

Okay now.. you want to go much quicker than it'd be possible with that amount of force.
Let's find out what you need for a good acceleration

Fa [ Force acceleration, N ]
Ca [ Coefficient accelerative resistance ]
a [ acceleration, m/s² ]

Math:
Fa = Ca *m *a
Now that looks easy... doesn't it,
we just need to know the coefficient..

Well....you got me!:surrender:
This is nearly impossible to calculate correctly for any of us.
To do it correctly you will need to know the exact weight of all rotating parts of your kart, the internals
of your motor, the chain, the sprockets, axles, wheels ... everything!
And how fast they rotate, and their angular acceleration,
then calculate the inertia and add those values up until you bang your head on the keyboard of yours :mad2:

Long story short: We can at least guesstimate a value.
We know that number must be bigger than 1;
and we also know it must be smaller than 2 (most likely smaller than 1.6)
(you do not rotate inside the kart, do you? :D)
And the biggest and most likely heaviest rotating parts of your kart are the wheels.
So, to have a good idea of the force in this scenario,
just assume one tenth of your wheeldiameter in inches
(for wheels between 11 and 16 inches, which should cover a fair amount of karts)

Example:
Fa = 1.2 * 150 kg * 2 m/s² = 360 N
you want an acceleration of 2 m/s²
(hitting 7.2 km/h after one second)
and you have 12" wheels mounted.

Attention:
This is not the correct number -it's too big-, it's just a simplification to at least have a good guess.
I might change my mind one day, if I can make a better guess for the coefficient here ;)
So in case you decide by that number your motor turns out to have too much power.
:lolgoku: as if...​

But you want top speed, don't you
Yes, I kept the best for last ;)
How well do you know your kart, and are you really sure you want to know it all?
Well then...

Fw [ Force wind AKA drag, N ]
Da [ Air density, kg/m³ ]
Cw [ Coefficient wind resistance ]
A [ Area facing the wind kart plus passengers, ]
v [ Velocity (relative), m/s ]

Math:
Fw = 0.5 * Da * Cw * A * v²

Most likely you will have to assume most of those numbers
(oh dear.. how accurate can that be?)
average air density at 20° C is 1.2 kg/m³
depends on your altitude, temperature and humidity.. but 1.2 is close enough ;)
The Cw for a modern sprint kart is 0.62
the one for a typical person on a bike is 0.9
chopper with ape hangers 1.1
you'll be in between ;)
The area of a person on a bike is 0.5 m²
an adult in a racing kart 0.82 m²
a chubby on a chopper 1.1 m²
again I hope you're in between ;)

And if you do not know the exact values for you and your kart,
you'll have to guess.

Example:
Fw = 0.5 * 1.2 kg/m³ * 0.7 * 0.9 m² * (9 m/s)² = 30.62 N
9 m/s are 32.4 km/h btw (~20 mph)
Again another small number.
So not much power involved...
True, but see what happens if we double the speed to 18m/s (64.8 km/h or 40.2 mph)
we end up with 122.472 N (that's four times the original value)

if your intention is to hit the 100km/h mark (~60 mph)
this is the reason you'll have a hard time achieving it.
Said kart would need 291.667 N; at a top speed of 27.778 m/s that's 8101.852 Watts of mechanical power.

Now what.. you wanted to know the Power and all you got was Force...

I know.. but it's not all wasted time ;)
Just multiply the Force by velocity...

Math:
Pm = F * v

Now that was easy, wasn't it?
And to pick up our previous examples...
Example:
Pm(Fi) = 128.25 N * 9 m/s = 1154.25 W
Pm(Fr) = 29.43 N * 9 m/s = 264.87 W
Pm(Fa) = 360 N * 9 m/s= 3240 W
Pm(Fw) = 30.62 N * 9 m/s = 275.58 W


Now that's confusing, isn't it?
So many different values, which is the one I need to choose a motor?
And on the way here most of it are just assumptions.

Well it gets worse..
the correct (the ultimatively correct value)
would be calculated by this term:


Math:
Pm = m * g * sin(alpha) * v + m * g * Cr * cos(alpha) * v + Ca * m * a * v + 0.5 * Da * Cw * A * v³
And you need to recalculate that for any given speed and acceleration

So let's simplify it again to "top speed reached" (no further acceleration)
leveled road (alpha = 0°)
and you'll end up with this

Math:
Pm = m * g * Cr * v + 0.5 * Da * Cw * A * v³

Example:
150 kg * 9.81 m/s² * 0.02 * 9 m/s + 0.5 * 1.2 kg/m³ * 0.7 * 0.9 m² * (9 m/s)³
= 540.432 W

See, that's why I choose to calculate either inclination or acceleration.
both of these numbers are always bigger than the top speed result on a levelled asphalt road.

it's a compromise you have to make.. it's up to you, but choose wisely :D

'sid
 

itsid

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...the he11?

What now? I'm confused?

Well, I do not know your requirements, and I'm sure there are
some things left you need to think about yourself.

Like controllers and batteries.

let's talk about the batteries

Most motors have a voltage rating in multiples of 12.
12V, 24V, 36V, 48V.... 96V even 144V.

Let's assume we have a 36V motor
So you need to stack three 12V batteries in series to end up with 36V.

Keep in mind, that stacking batteries in series, will NOT increase the capacity (time you can drive the kart).
3 * 12V, 30Ah batteries make ONE 36V, 30Ah batterypack.

If you want to increase the capacity you need to add batteries in parallel.
which will turn your 3 batteries into 6 batteries.
And you know how heavy and big one battery is.. six of them :eek:

What's that to do with the motor?

We calculated the mechanical power above;
now we need it's electrical power

Math:
Pm = 0.8 * Pe
or
Pe = 1.25 * Pm

say we choose a 1200W motor
Example:
Pe = 1.25 * 1200 W = 1500 W

Math:
Watt = Volt * Ampere

Our motor needs
Example:
1200 W / 36V = 41.667 A

The motor will draw 42 Amps.
With just one batterypack with 30Ah,
that's less than 43 minutes of driving time

And just think of what would happen if we choose a 3000 W motor ;)
or how many batteries we'll need with a 72V motor.

So my best advice would be:
get a lower voltage motor and choose one not too powerfull,
that way you don't have to carry around dozens of batteries;
also, since this is serious weight we're talking;
that needs to be included in the calculations of course :stir:

Speaking of lower voltage motors..

Overvolting

Don't!
Not if you can avoid it.

I read fairly often, that some of you PLAN to overvolt a motor to get more power...
And that's true.. you could get more power by overvolting the motor,
but that comes at a price.

Motors are specifically wound for a certain amount of voltage and current, and for those they're rated.

If you overvolt a motor (say apply 48V to a 36V motor)
you effectively draw the same amount of currents making our 1500W motor a 2000W motor (Pe).
Sounds great, but it's not.

In fact most of the additional power is converted to heat, not mechanical power.
And that means the efficiency will be worse.
So your gain might be as low as just 100W additional mechanical power.

not even 10% more power, but draining the batteries 25% faster.
Plus - the additional heat can shorten its lifetime significantly.

If you're spending money on a project like this, do it right,
get the motor rated for the task!

Last thing to consider is the controller..

The lower the Voltage, the higher the currents,
say we have an option for a 1200W 24V motor

instead of 42 Amps it will draw 62.5 Amps
that not only affects the number of batteries required, but also the controller.

So make sure there is a controller for the motor in question!

In order to make a wise decision,
you should know the price (and availability) for a controller that matches the motor.


'sid

PS And yes, in case you wonder:
for the example kart I'd suggest a 1200-1250W 36V motor ;)
 

itsid

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Thanks Paul.. I'm flattered :D

Seeing how long this got in the end -so much for the essence part :roflol:-,
I actually doubt anyone will make it down here ;)

But maybe it helps to get an idea of what motor you need,
or in case you have the motor already, what it can do for you :D


Although it says "electric motor" in the topic,
that's exactly the same principles for any engine!

And that's why you will not hit 60mph with a stock 6.5HP engine
(absolute minimum is 8919.352 Watts or 12 HP! for our example kart)

'sid
 

Krash

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A comment on adding batteries in series won't increase your range...
If you select the same power motor with batteries in series (i.e. higher voltage) then you will draw a lower current, thus you will increase your range. To work out your range independent of volts and amps, convert your battery pack size to Watt hours and this will give you an indication of how many watts motor to chose for a given run time or what run time you will get from a given size motor.

Also a word on efficiency and current, higher currents require larger wires, thus a system with a higher voltage and lower current can use smaller wires or will be more efficient than lower voltage and higher current which is the same reason power transmission lines operate a high voltages. Also a higher voltage motor for a given power output will be smaller than a lower voltage motor for the same reason - the wires inside it can be smaller, so I would differ from the advice above and recommend a higher voltage motor, although for safety reasons I would suggest limiting voltage to about 60 Volts max.
You can get 60 volts from 18 lithium cells which are a lot lighter, faster recharging and will do a lot more cycles than a lead acid battery. If you consider cycle life, lithium will typically be cheaper on a cost per charge cycle basis. The other great thing about lithium is they deliver next to maximum current until they run down on charge, where as lead acid voltage slowly drops off and your kart gets slower.
 

itsid

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well.. increasing the voltage will not decrease the currents, in fact you'll draw the exact same currents as before (with the exact same motor)
since that depends on the internal resistance which will not be changed noteworthy
(yes, more heat, higher resistance... blabla...)
So that part of your comment is BS!

true true higher currents require larger wires, no doubt!
But larger wires are much much more efficient than smaller wires, so that comment too is total crap.
the resistance of a wire is resistive constant (material based) times length divided by diameter
the longer the wire the bigger it's resistance (the higher the resistance the lower the efficiency)
the thicker the wire the lower the resistance (ergo the higher the efficiency)

lithium cells are nice ... for RC cars;
for full size karts they get very expensive very soon!
you cannot get away with 4Ah on a typical kart

now just calculate a bat pack of typically 60Ah and 36 volts...
the large cells I know are 100 US (85 €) for 10Ah @ 12 V
that's three cells in series to get 36 Volts
and six such batterypacks in parallel to get the 60Ah
that's 18 cell or $1800 US (1530€)
compared to three car batteries which come in 60Ah off a shelf for 65€ ($76 US)
so that'd be 228 US compared to 1800 US

Do I really need to say it????

But true they're lighter... 18 12V 10Ah Lithium cells weigh about 25.2kg whereas three car batteries drop in at about 45 kg; almost twice as much...

'sid
 

dcastillo

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Sid, wouldnt higher voltage to the controller mean lower current draw?

if the motor, say, takes 24V @ 10 amps to cruise at 'X' speed and you are supplying the controller with 24V then it would need about 10 amps as well (240W in the controller to get 240W out to the motor)
(obviously overlooked the efficiency of the controller for now)

if you input 48V to the same controller and wanted to continue cruising at the same speed 'X', then the batteries would only need to deliver 5A to give the controller the same 240W needed to power the motor with 24V at 10A... right, or am I missing something?

thanx
Danny
 

itsid

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Unfortunately that's not true.
You forgot to take motor efficiency into account.
and what happens if you overvolt a motor.

But let's see in a greater detail;
let's assume we reuse absolutely everything from before.
since we have a controller that allows for higher voltage
(that's very possible, but not always true.. nevermind we just assume things here)

and we have your 24V 10Amp motor

if we set the throttle to 50% the motor will be switched off for 50% of your driving time
(it's no voltage cutoff nor current cutoff it's just switching the motor on and off)
So over any given period the average is 5Amps @24V

if you double the voltage the 50% toggle STILL delivers an average of 5Amps over any given time.

And now here's the thing:
very few motors that are eligible to power an electric vehicle increase their rpms with voltage;
instead they regulate their rpms by levelling the power between the power they need to move the shaft and the speed they turn the shaft.

And as we know by now (well should know ;))
if we overvolt a motor most of the extra power is converted to heat not mechanical power,
so the actual gain in torque can be very minimal ,
what means, that to end up with the same speed we need the exact same amperage as before to keep the motors rpm at the desired pace.

Even IF we have a sweet spot in the motors performance and by doubling it's voltage (the motor itself will not survive that.. but let's keep that example)
we can reduce the throttle a bit, since
we gain 20% more torque -which is in fact more than you could expect- and have a little higher rpm as a result;
but you'll still draw slightly more than 4Amps instead of 5 to keep your speed.
(192W instead of 125W)
and not just 2.5 I'm afraid.

If you consider a different motor (one specifically wound for the higher voltage)
THEN it's true, assuming it has about the same efficiency rating it'll draw
about the same amount of electrical power to produce the same mechanical power
(torque and speed)

But his statement was:
...
If you select the same power motor with batteries in series (i.e. higher voltage) then you will draw a lower current, thus you will increase your range.

and that remains BS!

you need (60AH 24V)
2 batteries (120Ah @ 12V) in series to have a 24V pack with 60Ah
to get 48V you need 4 batteries in series,
and even if you pick 30Ah batteries (which would be the same 120Ah @12V)
you end up with no more than HALF the capacity (30Ah @ 48V);

so you do NOT increase your range!

if you take 4 60Ah cells you'd double the range of course (60Ah @48 or 240Ah @ 12V);
but you would too if you add the very same two 60Ah cells to the 24V set up ending up with 120Ah @ 24V;)

'sid
 

Krash

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Maybe to simplify the comparison we should be comparing watt hours (wh) which takes into account both the voltage and the current. My experience with headway cells puts the lithium at $0.6 per wh which is similar to Sid's figures above ($0.83 per wh)

Sids figures for car batteries are $0.11 per wh. However car batteries are not suited to deep discharge so we either need to use a larger pack size relative to lithium (not recommended due to weight) or use a deep discharge cell which is more like $180 for a 60Ah battery or $0.25 per wh. However a deep discharge lead acid battery still cannot be discharged completely.
"A deep-cycle battery is designed to discharge between 45% and 75% of its capacity, depending on the manufacturer and the construction of the battery. Although these batteries can be cycled down to 20% charge, the best lifespan vs cost method is to keep the average cycle at about 45% discharge." from Wikipedia.
Thus we still need to oversize a deep discharge pack which increases cost per useable wh to $0.3 to $0.4 per wh.
The capacity of a lithium battery is based on what it can safely be charged and discharged to, so the full capacity can be realised.

Yes I agree, lithium is more expensive at about twice the price per wh compared to lead acid, (consistent with reported figures for electric car batteries) but the benefits make it more than worth the extra cost. This includes significantly lighter, higher peak current output (20C or 20x the 15A current for headway cells), voltage does not reduce as the cell discharges, smaller size, much faster recharging and will do 2 - 3 times the number of cycles of a lead acid. This is the reason why battery tools, RC hobby industry, bikes, laptops, cameras and phones have all moved to lithium batteries because they have far superior performance which warrants the higher initial cost, particularly in mobile applications where weight and power output is important.
 

itsid

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However a deep discharge lead acid battery still cannot be discharged completely.

true.. but WTFC?

modern motor controllers (not RC sh1t.. ev controllers!)
have a cutoff voltage embedded..
a 36V controller cuts off at 28V or something;
still enough juice inside your batpack to keep the cells from dying.
And it WILL cutoff; no matter what cells you use.
So I have eight batpacks as a backup for the same price ;)

But mind the thread topic: it's about motors.. not batteries!

I got, it you love Lithium cells...
(me too in some occasions btw)
but they're not the magic wonder that their price is implying they are.

And since this thread is about motors, not batteries nor controllers
(that's why I barely mentioned them)
I'd kindly ask to open your own thread if you want to talk about batteries.

'sid
 

itsid

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So I take it a 200w electric engine could not push a 100kg cart around at 10-20kms and hour?

funny question...the answer is it can..
but you need another much more powerfull motor to push the kart TO 10-20km/h

divide km/h by 3.6 and you get m/s
just use the formulas and you'll see ;)

'sid
 

dcastillo

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Incase anyone misread sid's post like I did, twice... heres a clearer version

but you need another much more powerfull motor to push the kart TO 10-20km/h
 

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i am new to this forum yet belong to others. i have been building pretty much anything that rolls for over 50 yrs. this thread interests' me as i can share some agony with others through the grief i've gone through. a chevy v-8 old school starter is viably equal to a 5 hp b&s gas. i viewed an youtuber vid on liquid cooling one of these starters. works like a charm. gearing for a kart starts at 20-1 and by using a jack shaft i find it easier to change ratios per idea/rider/speed. working on a cvt for an electric at this time and will keep you updated. i love mechanical anythings. you can contact me and i will share what pinched my finger so you don't have to!
 

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Where did the information come from for overvolting a motor?
Using a 36V motor on 48V will only lose a few % on efficiency.
I am running a 24V motor at 45V+ no problems with efficiency and more than double rated power. I am using a 36V 40A controller on it :)
You will see people on endless-sphere pushing 7kw on a 1kw motor :D
 

itsid

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Motors are slaves of their windings,
some motors allow to run fine at anything from x to y Volts;
very true.. but even those DO HAVE a sweet spot somewhere,
where they provide the best mechanical powerout per electrical input power.

for those the change in efficiency sometimes is gradual.
But the simple fact is: companies do test their motors, and motors for EV are tested very thoroughly.
Check the manufacturers diagram of the motor and you'll see the drop in efficiency.

And just because you are not aware of loosing efficiency, doesn't mean it's not happening, it just means you do not care enough to check on it (which is a valid thing to do or ignore in this case.. but it's not good advice!)

And btw.. with a 36V controller as you say, you do not provide 48V to your motor.. maybe to the controller, but not to the motor ;)
(maybe it's a 36-48V controller, but if it is, you'd said so, right??)

Anywhoo..
yes, there are people that do several things..
if that's a clever thing to do is just a completely different topic!

Oh, and I am aware of exactly ONE 7kw (6.something IIRC; electrical btw) motor that once was a 1kW (mechanical) motor..
that was rewound (new coils plus custom magnets)... can't find it ATM.. but if you talk about that one...
that's not overvolting, that's reconfiguration ;)

'sid
 
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