Katou's Math

[katou]

RC Motors - How to Choose Kv

Here's the thing, if I choose a kv that is super low, I need a high voltage to get max power out. But what if we plan on keeping the voltage down? Then a kv should be chosen that gets full RPM out of the motor by the time full battery voltage is applied.

Right?

Does it make sense to run a bike on high voltage? If we can choose whatever voltage we want, and whatever kv we want, how high is high enough? And which should be high, voltage or Kv?


Here's what I found out:

The limiting factor in all of this is the controller. You can not just specify a voltage and get everything else to fit. Controllers do not come in every voltage you might want.

Currently, sensored controllers can be found up to 100v, but sensorless controllers (RC type) go up to 50v max.

I want to use a RC type controller, specifically the Castle HV 160 which has a max operating voltage of 50v.

Here are some other RC controllers, take notice of their voltage limits

hextronik 120A 25V
total power 3000 watts
$60

Turnigy 2000 200A 48V
total power 9600 watts
$190

Turnigy Sentilon 100A 48V
total power 4800 watts
$116

Hacker X-70 70A 24V
total power 1680 watts

Castle HV85 85A 50V
total power 4250
$210

Castle HV110 110A
50V total power 5500
$270

Castle HV140 140A
50V total power 7000
$360

As you can see, if you want to use a RC controller, max battery voltage must be 50v or below, preferably 48v or less to allow some headroom just in case.

If we assume that we will use a 48v limit, and a 130 kv motor, how fast would that get us going? The reduction ratio determines this, so lets do an example:

Given:

Wheel: 700 C wheel
Motor: Turnigy TR80-100-A
Motor kv: 130
Max voltage: 48v

distance wheel travels in one revolution

= pi x diameter
= 3.14 * 70cm
=2.2 m/wheel revolution

Given:
1st stage reduction: 4 motor to 1 jackshaft
2nd stage reduction: 6 jackshaft to 1 wheel

Total reduction
= 4 * 6
= 24 or 24:1

Given:
motor rpm at 1volt = 130 rpm

Min motor rpm
= motor kv x voltage
=130 x 1volt
=130 rpm

Min wheel rpm after reduction?

= motor rpm / reduction ratio
=130 / 24
=5 rpm

5 rpm is how fast in km/hr?

= rpm x distance wheel travels in one revolution
= 5 rpm* 2.2 m/wheel revolution
= 12 m/min (or 0.7 km/hr)

Max motor rpm at 48v

= 130 kv * 48v
= 6240 rpm

Max wheel rpm after reduction?

=6240/24
=260 rpm

260 rpm is how fast in km/hr?

= rpm x distance wheel travels in one revolution
=260 rpm * 2.2 m/wheel revolution
= 572 m/min (or 34.3 km/hr)


How to choose a Reduction Ratio


Minimum reduction means lowest losses to friction, soI think that the minimum reduction possible is the way to go. Single stage if possible, double if necessary. The highest ratio I've seen so far in one stage is about 10:1 while double stage reduction (using a jackshaft or planetary gears) can get up to 30 or 40:1

We want a Kv that is high enough to hit the mechanical limits of the motor at the max voltage of 48v. Astro motors being custom wound come in a variety of winds, with many different Kv choices. Let's take a look at the chart.




Lowest kv is:
12 turn for 113 rpm/volt

but the highest rated controller is 50 v, so actual top rpm would be
50v x 113 = 5650 rpm

Apparently, these motors are good up to 12,000 rpm, so we are losing some power by limiting the rpm.

how much of an RPM loss is this?
12000-5650 = 6350 rpm
6350/12000 = 53%

Wow, that's huge!

lets try a higher kv winding:
8 turn for 169 rpm/volt
50v x 169 = 8450

Still too low! So what voltage would get us to max rpm?

12000 / 48v = 250 rpm/v

Now, this is the calculation to get max power from a given motor. I you want less power, you have two choices: be gentle on the throttle, choose a lower kv so that the motor runs slower at the max voltage that the controller puts out.

Why would you want to do that? Well, if you run the motor at max rpm, it's going to be louder, and have a higher pitch to the noise. Maybe you don't like that? Or perhaps you want to maximize efficiency. If so, you'll want a Kv and gearing for your motor that puts it in the zone of highest efficiency most of the time. What is that zone for your motor? I have no idea, ask the manufacturer.

I am designing for max power, so someone else with experience in that direction will have to jump in here to discuss the alternatives.

 

[katou]

Looks solid! I like the little coloured arrows, it draws the attention from the cool photos to the text. The only thing I might change is your summary could use a title.

As a newb, what I really want is to know what you think, the expert. So, your summary is very important to me because it contains your distilled knowledge. I'd give that last little summary a nice big title with some underlining or something.

I said it before, but I'll say it again, those are AWESOME pictures that you found. I wish I had as good pix for the FAQ's I've written (there are a couple more that I'm working on for this section)

Katou

 

[katou]

First a bit of Background:

An amp represents 6.25 x 10 exponent 18 electrons (or a COULOMB) flowing through a wire.

An amp hour means that one coulomb's worth of electrons is passing through a wire, for a period of one hour.

a battery that is rated for 10 ah can produce 10 coulombs of electrons, over a period of 10 hours.

Problem here is that due to the Peukert Effect, batteries do not produce what they should, when discharged over shorter periods of time.

Batteries are rated by discharging them over a really long period of time, like 20 hours or longer.

However, in the real world, we discharge them in a period of 5 hours. The shorter the period of discharge, the more pronounced the loss of power.

So, our 10 ah battery was tested for the 10 ah rating by discharging over 20 hrs, 1/2 amp load, voila, 10 ah.

We discharge it in 5 hours, and we find we get 8 ah out. Hmm, Peukert effect sucks.

We discharge it in 2 hrs, and we find we get 6 ah out. Peukert really sucks.

We discharge it in 1 hr, and we get 5 ah out. Dang.

The C rating of a battery indicates how fast it can be discharged without damaging the battery, or showing wicked voltage sag.

10 ah batt with 2c rating = spikes of up to 20 amps
10 ah batt with 10c rating = spikes of up to 100 amps
10 ah batt with 30c rating = spikes of up to 300 amps

Motors require power in uneven patterns. They are not constant load devices. They need power, a boatload of of it to combat the slight rise in the road, and a slight headwind, and all of a sudden, they don't need it anymore because the road flattened out. The spike or surge capacity of batteries is very important because of this.

Perfect example is here: viewtopic.php?t=15704#p233590

He's got a monster motor, but it is doing poorly because the batteries are SLA and can't handle the 300A spikes that the motor needs. Performance was very poor, realizing only a fraction of the massive power that the Etek is capable of.

C rate is very, very important. If you use a larger battery, you can compensate for low C rate:

10 ah 15C A123 pack = 150a surge capacity
30ah 5c Emoli pack = 150a surge capacity

The capacity of the packs aren't equal, but the surge capacity is.

Hope this helps, I've learned from this place, just trying to give some back. If you want more about Peukert, check this site out:

http://www.smartgauge.co.uk/peukert_depth.html

Katou

 

[katou]

Pack Building Math Part 1:

How many amp*hours do you want your pack to be?

I will assume that you will have 50 A123 M1 cells for the example. This could be arranged in many ways.

25 in series, 2 parallel, 5 series, 10 parallel, 50s 1p, whatever you want.

*********************************************
Let's assume you want 48v, how many in series would be needed for that?

To find out how many cells you need in series, and you want 48v, then divide 48v by 3.3v
************************************************
Let's assume that you want a 10 ah pack. How many cells would you need in parallel?

to find out how many cells you need in parallel, divide 10ah by 2.3ah/cell

Multiply these #'s together to make sure you have enough cells.

Let's do an example:

48v 10ah pack will require:
48v/3.3v per cell = 14.5s
10ah/2.3ah per cell = 4.3p

Now clearly we can't use half-cells, so we round down to 14s and 4p.

Quick check to see if we have enough cells:
14s x 4p = 56 cells !!

That's no good. How about 14s and 3p?
14s x 3p = 42 cells, this works.

But how many amp*hours do we have now?
3 cells in parallel x 2.3 ah per cell = 6.9 ah

Hmm, that's a little low, I think I might rather go the other way and get 6 more cells to meet the original design goal of a 10 ah pack.

HTH, that's about as clear as I can make it. I wish someone had laid it out for me like this. Good luck!.

Katou

 

[katou]

Pack Building Math 2

The higher the C-Rate, the smaller capacity (ah) the pack can be, and still provide juice for the big current spikes.

The lower the C-rate, the larger capacity (ah) the pack has to be to provide juice for big current spikes.

The rest of it is just how hard you ride (watt hours per km) multiplied by how far you want to go. You can also look at it as watt hours per hour.

Eg, I like to ride WOT for about 30 minutes. Other people say that with my 5304, I can expect to expend 720 watt hours in that time.

How big of a pack at 72 v would that take?

720 / 72v = 10 ah

You need a 72v 10 ah pack to JUST get that power. In general, you don't want to drain a pack down, best to aim for max 70% discharge.

720 wh / 0.7 = 1029 wh

1029 / 72v = 14 ah pack

Everything equals, but fun. More fun, bigger battery. More fun for longer time = much, much bigger battery.

Katou
****************************************************

FAQ Pack Building Math 3

Let's look at this example, but now throw C rate into the mix.

What is max current spike I can expect from 5304 WOT running off 72v?

(I'm guessing here) 100A

Example pack from example in previous post = 14 ah

Assume C rate of cells (A123) is 30c (conservative, manufacturer states up to 50c for short periods)

max current draw = 30c x 14ah = 420a

Looks like we're okay for pack size!!

But what if we use Moli cells, generously 5c?

5c x 14ah = 80a Uh oh.

So how big would a pack of moli cells have to be then?

100a / 5c = 20 ah

So, our biggest problem in sizing this pack was not overall amount of energy needed, but in surge capacity of 100a.

To get the surge capacity that we want, using low C rate cells, we need a 72v 20 ah pack.

As you can see, when riding a bike like a madman, you either need:
a) small pack of high c rate cells
b) really big pack of low c rate cells

So basically, we're juggling
1. energy required as a whole (distance or time riding)
2. c rate of cells used in pack
3. size of amperage spike expected with a given riding style

Katou

 

[Erogo]

First a bit of Background:

An amp represents 6.25 x 10 exponent 18 electrons (or a COULOMB) flowing through a wire.

An amp hour means that one coulomb's worth of electrons is passing through a wire, for a period of one hour.

a battery that is rated for 10 ah can produce 10 coulombs of electrons, over a period of 10 hours.

This needs clarifying up a bit. Instead, I'll post my understanding

An amp represents a coulomb of electrons flowing through a wire every second. A coulomb of electrons is an amount, just like a bucketful, so it's important to mention how long it takes this bucketful of electrons to pass through the wire. With a current of one amp, the coulomb of electrons passes through any cross-section in the wire in one second. Or, in any second, one coulomb of electrons passes any point in the wire.

An amp-hour means that one coulomb's worth of electrons is passing through the wire every second, and keeps it up for one hour. By the end of the hour, 60*60 = 3600 coulomb's worth of electrons will have dropped out the end of the wire.

A battery that is rated at 10 ah can produce 10 amps for one hour. Or, 1 amp for 10 hours! It can release 10 coulombs of electrons per second, for 1 hour. Or, 1 coulomb of electrons per second for 10 hours. If it lets them out fast it can't do it for long, and if it lets them out slow, it can do it for longer. Just like a bucket! Only usually batteries are smaller.

E

 

[katou]

I am earnestly trying to spread "good" information, so if you have a correction LFP, make it.

I'm not an EE, just doing my best.

If the question "how do I size a battery pack" isn't a FAQ Ypedal, then tell me, and I will delete what I wrote.

I'm not into ego, I'm just trying to get started. If I need to change something, I will.

Katou

EDIT: just read your comments re: equations in the other thread Ypedal. I hear what you are saying. I guess I'm confused what would be left if I took them out.

I was trying to use the math in a pretty simple way, with examples, so that the reader could use the equations for their own project.

I'll read over your stuff and see if I can get a handle on what level you would deliver at. I also did tech support for debit/credit cardswipe machines for about 2 years, but that was a while back.

 

[Ypedal]

alright, i split this off from the FAQ, we can refine this and link it into the FAQ later but i find this a bit too heavy for an faq..

 

[katou]

Voltage and Amperage, what's the difference?

Here are the dictionary definitions:

Voltage: the potential difference between to points

Amperage: the strength of the electric current

These definitions are not very helpful. Are they correct? Absolutely, but will they help us understand? No. So, on with the tutorial.

If you prefer a more advanced tutorial, check here: http://endless-sphere.com/forums/viewtopic.php?f=16&t=1580

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I will give you several metaphors. None of them are exact. All of them will help. You must use your imagination here. I've taught about 2000 students (successfully) the difference between Voltage and Amperage using these few metaphors.

***********************************************************************************

Water:

The voltage is the pressure of the water, amperage is the amount of water coming out.

eg: high voltage, low amperage: SQUIRT GUN (lots of pressure, small amount of water)
eg: low voltage, high amperage: RIVER FLOWING BY (very low pressure, but lots and lots of water)

eg: high voltage, high amperage: FIRE HOSE (lots of pressure, lots of flow)

*****************************************************************************
People running:

You are walking along the hall, you get hit by people running in the hall. How badly will you get hurt?
In this metaphor, voltage is the speed of the runners, amperage is how many runners.

eg: high voltage, low amperage: One person running, but sprinting really, really fast (high speed, only 1 runner)
eg: low voltage, high amperage: 50 people walking (low speed, but lots and lots of people)

eg: high voltage, high amperage: 50 people sprinting straight at you (high speed, many people)

*************************************************************************************
Electricity

eg: high voltage, low amperage: you get a shock from touching a doorknob. It sort of smarts a bit (electrons really want to get to you, but very, very few electrons make the trip)
eg: low voltage, high amperage: this one you probably have never experienced, so I can't give you an example. If anyone can think of one, let me know

eg: high voltage, high amperage: Lightening strike (electrons really, really want to go from the clouds to the ground, and a boatload of electrons go for the ride)

***********************************************************************************

Hopefully you are starting to get the idea. Voltage is how badly the electrons want to go somewhere. Amperage is how many electrons make the trip.

You probably are starting to understand as well that either high voltage or high amperage can hurt you. Power is the combination of Voltage and Amperage. There is a slight difference in danger between voltage and amperage though.

***************************************************

High Voltage is more dangerous!

The electrons in any circuit (light switch, flashlight, ebike battery pack) are more than happy to take a shortcut through you to get to the ground. Voltage is how bad the electrons want to get out of the circuit and detour through you.

Imagine a high voltage (but low amperage) flow as a mad man behind bars, shaking and screaming to get out. He really, really wants to get out.

Imagine a low voltage (but high amperage) flow as room full of 100 people who are all feeling a bit sleepy. They don't care much about doing much of anything.

Which one is more dangerous to you?

This is why you have seen DANGEROUS HIGH VOLTAGE stickers on machines or electric utility boxes. Think now, have you ever seen one that said: DANGEROUS HIGH AMPERAGE? Now you know why.

**************************************************************

This explanation is meant to give you a feel for voltage and amperage. You will need to understand some basic electrical math before you can use this "feel" for something more constructive.

*************************************************************
In Ebikes,

Voltage is usually discussed as a measurement of the size of the battery pack.
Amperage is usually discussed as a measurement of how large the electrical flow is for various components like motors and such.