# Control Tower - September 1998

## First in a series: Understanding Electric Power Systems. Also, Jim shares email from our readers.

Understanding Electric Power Systems

It seems that a lot of e-flight beginners have trouble understanding electric power systems.  If you are confused about how electric motors work then follow along with me as I present a simplified electric motor model.  Why simplified?  Because the real world is darn confusing and complex that's why!  Plus, we don't need to worry about every little loss and friction in the real world if all we are trying to do is understand the basics.

Lets imagine a simple electric motor which we will call the Ideal Motor.  We call it "ideal" because it has extremely simple characteristics and is 100% efficient in operation.  Our motor has a single quality: for every volt of energy applied to it, the motor will turn at exactly 1000 RPM.  On 5 volts the motor will turn 5000 RPM, on 25 volts the motor will turn 25000 RPM.  The RPM will always be equal to the amount of volts applied to the motor times the constant of 1000.

 Volt to RPM Relationships for our Ideal Motor Volts RPM 1 volt 1000 RPM 2 volts 2000 RPM 3 volts 3000 RPM 4 volts 4000 RPM ...and on and on...

Now we need a power source for our motor.  Lets imagine that we have an Ideal Cell to match our Ideal Motor.  For now, our Ideal Cell can be defined by just a single characteristic: the amount of voltage it produces.  Since I am a lover of simple things (and some would say its because likes attract), lets choose a really easy to understand voltage for our Ideal Cell.  Each Ideal Cell produces exactly 1 volt of electricity.

So now we can make up a pack of Ideal Batteries and attach them to our motor.   Lets see what the results would look like:

 Cell Count to RPM Relationships for our Ideal Motor # of Ideal Cells RPM 1 1000 RPM 2 2000 RPM 3 3000 RPM 4 4000 RPM ...and on and on...

Careful observers will note that the table above looks a lot like the first table.  Our Ideal Motor and Ideal Cell make life very easy for us, don't they?   We can almost use the words "cell" and "volts" interchangeably because of our contrived values.  Naturally, the real world isn't quite this simple, but its not entirely unlike our Ideal world either.  Keep that in mind as we go along.

The relationship between volts (cells) and RPM for our Ideal power system can work backwards as well as it does forwards.  So if I measure that my Ideal Motor is spinning at 4000 RPM I can bet my sweet patootie that the input voltage is precisely 4 volts.  That in turn means that 4 cells are being used.  Simple so far.

But!  You may notice that our motor is just happily spinning away and doing nothing!  We need to add something to the output shaft so that it can twirl around and move lots of air.  So lets put a propellor on our motor and watch what happens to the RPM.  In fact, lets compare two different propellers with the same motor given various cell counts.

If you are really new to R/C then you might need to know how propellers are specified.   Each propeller has a diameter and a pitch.  I assume you know what "diameter" means, but the word "pitch" can be a little confusing.   The "pitch" is the distance the propeller would travel forward in one revolution in a perfect medium.  The higher the pitch the more angled the blades of the propeller are and the farther it would travel in a single revolution.  A high-pitch prop is usually used on a fast airplane while a low pitch prop is usually used on a slow airplane.  In the US, where I am from, propellers are specified in inches.   Lets use two propellers for our example.  One will have a 5 inch diameter and a 5 inch pitch, which we'll designate as 5x5.  The other will have a 12 inch diameter and an 8 inch pitch, which we'll designate as 12x8.

 Cell Count to RPM Relationships for our Ideal Motor and two different props # of Ideal Cells Propeller RPM 1 5x5 1000 RPM 2 5x5 2000 RPM 3 5x5 3000 RPM 4 5x5 4000 RPM ...and on and on... 1 12x8 1000 RPM 2 12x8 2000 RPM 3 12x8 3000 RPM 4 12x8 4000 RPM ...and on and on...

Nothing in the above table should surprise you because our Ideal Motor always turns 1000 RPM for every volt regardless of what kind of load is placed on the output shaft.  This is a crucial point and its real-world analogy is one of the hang-ups that keeps many beginners from understanding electric power completely.

Of course we must also realize that it takes far more energy to spin a 12x8 propeller at 4000 RPM than it does to turn a 5x5 propeller at the same rate.  There must be something missing from our simplified motor model or all those Speed 400 pylon racers out there would be flying with 18x18 propellers.

Indeed, the thing we are missing is called current.  Current is the other half of the energy equation.  Sadly, we can go no further without introducing some kind of formula into the discussion.  I promise I wouldn't do this to you if I didn't have to but its an easy formula and shouldn't cause anyone any trouble:

Watts = Volts x Amps

The above formula is the most important formula you will ever encounter and may someday save your life.  Ok, I'm exagerating here, but these articles are really boring if I don't take poetic license once in a while.  The fact is, though, that I use this formula in some way almost every day (man, I just realized what a dork I am...but I digress).

The formula relates energy as a product of Volts and Amps.  You see, volts is only part of the energy equation.  Without Amps, you don't have any energy at all.

The word "Watts" is just a fancy way of saying "energy" or "power".  Over time, watts can perform work.  Y'know, work: that stuff that all your co-workers are doing while you read this web page.

Lets put Watts to work right now, in fact.  Remember the last chart that showed our Ideal Motor mated with a variable number of Ideal Cells to turn two different propellers?  Remember how the RPM was always dependent solely on how many volts were applied to the motor, even though it takes a lot more effort to turn a big prop than it does a small one?  Lets use watts to show just how much effort is involved:

 Amount of Enery Required to Spin Two Different Propellers 5x5 12x8 1000 RPM 1 watt 10 watts 2000 RPM 4 watts 40 watts 3000 RPM 10 watts 100 watts 4000 RPM 25 watts 250 watts Note that these are mythical values!

Please note that the watt values I gave in the above table are not actual values.  I'm just using simple values (that mirror reality in a few key ways) to demonstrate a point.  And that point is that it takes a lot more power (energy) to turn a 12x8 prop at 4000 RPM than it does to spin a 5x5 prop.  Also it takes more than twice as much power to spin a prop at twice as much RPM.

Since we now know how to express energy (watts = volts x amps), we can pull an example out of the table above and see what is going on with our Ideal Motor. Lets concentrate on the table entry which shows that it takes 100 watts to spin a 12x8 propeller at 3000 RPM.  Since we know that watts is the product of volts and amps this means that we would need a combination like the following examples:

• 100 watts = 1 volt x 100 amps
• 100 watts = 2 volts x 50 amps
• 100 watts = 3 volts x 33 amps

...and on and on...

So we can actually get 100 watts in many different ways.  Our motor, though, is hard-wired to give us exactly 1000 RPM per volt regardless of anything else.  Since we are trying to spin our prop at 3000 RPM, this means we need 3 volts.  And, therefore, our motor must be drawing 33 amps of current from our Ideal Cells.  This is an inescapable conclusion.  For our motor to turn 3000 RPM with that prop it must have 3 cells and it must draw 33 amps because 100 watts are required to perform that demanded task.

Lets take a look at one of our tables and fill in values for current and watts as appropriate:

 Cell Count to RPM Relationships for our Ideal Motor and two different props # of Ideal Cells Current Propeller RPM Power 1 1 5x5 1000 1 watt 2 2 5x5 2000 4 watts 3 3 5x5 3000 10 watts 4 6 5x5 4000 25 watts # of Ideal Cells Current Propeller RPM Power 1 10 12x8 1000 10 watts 2 20 12x8 2000 40 watts 3 33 12x8 3000 100 watts 4 63 12x8 4000 250 watts

So here is what we've leared so far:

• Our motor turns exactly 1000 RPM for every volt regardless of load
• Our motor draws the current necessary to make the watts of electrical energy equal the watts of power it takes to turn the prop at the rate demanded by the voltage.
• Watts is the product of volts and amps
• A big propeller requires a lot more power to spin at a specific RPM than a small propeller does
• Given a fixed propeller and motor, increasing voltage will increase current at an exponential rate.

Based on what you've learned, can you answer the following questions?

• How many RPM will my Ideal Motor spin if I apply 17 volts?
• How much current will my Ideal Motor draw if I bolt a 12x8 prop on it and attach it to an Ideal Cell? 2 Ideal Cells? 3 Ideal Cells?
• Suppose I had an Ideal Airplane that was lacking in power but I didn't want to add cells, what would you suggest that I do?

Thats probably enough learning for one month.  Lets continue the discussion next month.  As we progress we will add a little bit of "real world" effects until finally we have a complete understanding of an electric power system.

As always, I can be reached via email at jbourke(at)ezonemag.com for any questions you might have.

 From: Soren Kjaer Nielsen in Denmark Hi Jim I started flying with RC 1½ year ago. The plane that I started with was a simple stick-construction made by the editor of the danish magazine: Modelflyvenyt (model plane news).  The little plane is powered by a S600, 9 cells, 3:1 gearbox and 10x5 prop - that give up to 15 min. flying time (it will also fly with an S500 and 6-7 cells).   The name "El a' Stik" is a non correct Danish translation of "el" and "stick" - "Elastik" is the Danisk name for the rubber used to fix the wing! Since then I have built and flown a lot of different planes from a twin-motor Do228 (wingspan 6' weight 8Lb) to some fine S400 planes.  The Do228 is powered with 2 S600 race 7.2v motors, 18 cells, 4.8:1 gearbox and 12x13 APC-props. The static-stalled props give a very fine flying performance - a lot of flying time and a lot of power when that's meeded. The plane will ROG in 50' The good result with the static stalled prop started some thinking: What would happen if I used a big static stalled prop on a big slow flying plane?  I needed a big, easy to build plane for a test. The small plane was enlarged 2 times.  Wingspan is 8 feet.   All up weight is close to 12 Lb.  I have added ailerons and flaps - the flaps, just to have some fun while building, but they are working, and the plane is able to land at walking speed.  Obviously the name is El a' Big. The El a' Big and the El a' Stick I intend to try out four different power systems, based on my ability to run a single motor or use two motors in a homemade gearbox. 2 x S700 8.2v 1 x S700 8.2v, 2 x S600 race 7.2v (one of the best S600 for gearbox, it is easy to get more than 230 w out and still have a good efficiency) 1 x S600 race 7.2 v - to see if it will have sufficient power The next picture shows the 2 x S700 configuration, the homemade gearbox and speedcontroller and the prop 20x10 prop that I used for the test flying. The test flying was done with 24 cells.  The plane ROG with that motor in less than 10' 2 Speed 700 motors mated with a gearbox I an just now building a computer to put into the plane (from the German magazine: Elektro Modell).  The compuer is simple and relatively cheap. The computer is able to measure: Voltage, amp, rev/min, speed, hight, temp and calculate the mAH. If you are looking for a good computer-construction this one is the right one!  You can contact one of the constructors, Ingo Stahl: ingo.stahl(at)koeln.netsurf.de.   When I am ready with the computer I will start to test big stalled props like a 16x16 and 18x18 (APC) on the plane - the props will, like the 20x10, go approximately 4200 rev/min. Flying with E-power is fantastic, I love it. Soren Kjaer Nielsen Denmark

 Mar 27, 2014, 04:34 AM Registered User Joined Jul 2013 41 Posts Hay, Thanks for this post, it's absolutely incredible, I'm surprised no one else has commented? Cheers this is exactly what I have been looking for. Yours Tom
 Oct 27, 2014, 04:50 AM MudMaster The Netherlands, NB, Breda Joined Sep 2014 559 Posts Incredibly funny & interesting article Jim! Thank you very much for refreshing my high school knowledge :-)
 Oct 27, 2014, 08:36 AM Registered User Wallingford, Ct Joined Sep 2001 2,011 Posts This was a good series of articles. I always felt it needed one more chapter.
 Oct 27, 2014, 11:38 AM Y=C+I+G United States, CA, Rosemead Joined Jan 2012 10,001 Posts you guys may want to check out: http://theampeer.org/ the last one wasn't 16 years ago.