Electric Power Systems
By Jim Kitt

Determining the motor, speed controller, and battery pack that I will use in an RC airplane will be decided by one of two ways. If I am going to use the manufacturer’s recommended motor, speed controller, and battery pack setup, then there is very little I have to know, or calculate, to find the matching components. All I have to do is take out my credit card and be willing to spend more money. But now that I have begun accumulating electric components, the last thing I want to do is spend money a second time on something that I may already have.
The process of matching the right components to a new model is a bit time consuming, but in this economy, I would rather spend the time, than the money. In many instances, it is cheaper to find an airframe that suits my electronic components than the other way around.
The important components of the process are the Watts, volts, and Amps. To simplify the electric processes of the battery, ESC, and motor, I have always considered what I first learned in physics, which was the water faucet analogy. If I think of the flow of electricity as water from a tank, through a hose, to a faucet, I can easily understand that I have three variables that will define the force, flow, and power, of the water coming out the faucet.
Volts: The water pressure available from the holding tank to my faucet is generally constant, with some relief as the tank empties.  This is conceptually the same as the number of volts available from a specific battery pack.  Electromagnetic force is the technical term for voltage, and it represents the force of electron flow.
Amps: The faucet value controls the amount of water flowing into the sink. The amount of electrons flowing past a specific point is measured in Amps.
Watts: Watts is the measure of power.  The more I open the faucet allowing more water to flow (increasing the Amps), the more power is available given the same voltage.  Power is not a function of Work, though, so some motion needs to result from the applied power in order for power to be translated to work.
So if I have a finite amount of volts, like a minimum of 14.8 from my 4-cell pack, then my power will be determined by the number of electrons I allow to flow, which is measured in Amps. The more Amps, the more power I will generate from the finite amount of volts. Since the power generated by the system is measured in Watts, then the more Amps, the more Watts.
Additionally, since I can not regulate the diameter of the water pipes, I will get to a point where no matter how far I open my faucet valve, then amount of water will no longer increase. This analogy helps me to understand the C-rating of my system, as my water pipes can only discharge a finite amount of water. Once I know this capacity, I will also know the flow limit, the power limit, and how long it will take to empty a certain amount of water.
With all four of these variables in mind – the volts, Amps, Watts, and the discharge rate – I can begin to calculate how much force I will need to effectively power the weight of my airplane for a reasonable amount of time.
[1] Airplane Weight:
The first thing I do is try to determine the all-up weight of my airplane.  This is usually easy because every manufacturer will give you some flying weight range, glow, gas, or electric. This information is usually enough to get through the process of determine the power you will need for a specific airframe.
So for this example, let’s say that the manufacturer says that my expected weight is between 5 and 5.5 pounds, or 88 ounces, max. The very next thing I do is try to determine the power that I will need to fly this airplane.
[2] Motor Watts:
It is a generally accepted rule of thumb that 100 Watts per pound is acceptable for scale flying, 125 to 150 Watts per pound is acceptable for sport aerobatics, and a minimum of 150 to over 250 Watts per pound is acceptable for hard core 3D flying.
So for this example, if I want to fly 3D (which is nothing more than wishful thinking) with a 5.5 pound airplane, I will need a power system that can deliver at least 825 Watts.
Watts is the motor’s power and is virtually the horsepower of the motor world.  In fact, 745.7 Watts is considered 1 horsepower.  The wrinkle here is that there are two Watts variables... Watts-in and Watts-out.

Watts-in represents the total amount of Watts (power) it takes to drive the entire electrical system.  This includes heat, magnetic fields, the power lost through resistance, and other factors.

Watts-out represents the power needed at the prop shaft to actually spin the prop to a certain level of RPMs.  This required power is the less than what your Watts meter will register, but represents more accurately the power required, and is more in line with the HP value.  The 825 Watts needed is a representation of Watts-in, but the amount of Watts we could expect at the prop will typically be 80% less, or 660 Watts-out, or 0.88 HP.
The next thing I will do is look at the motors that are available in my price range that will deliver the Watts my system will require.
For this example, let’s say I have a 950 Watt motor in mind.
[3] Kv Rating:
I will then consider the Kv rating of the motors because this value will tell me how many volts I will need to obtain a respectable RPM.  The Kv rating tells me how many revolutions per minute my motor will deliver on each volt I input to the system. So for this example, let's say that my 950 Watt motor has a Kv rating of 600.

[4] RPM’s:
This means that I will theoretically obtain 600 RPM’s on my unloaded motor for every volt I connect to it.  Since each LiPo cell, as a rule of thumb, will deliver 3.7 volts, then I will obtain 2,220 RPM’s for every LiPo cell I use.  8,000 RPM’s will require 13.3 volts, which is 3.6 cells (13.3 / 3.7) so I’m now thinking about a minimum of 4 cells.
(3.7 volts x 4 cells) x (600 RPM’s per volt) = potentially 8,880 RPM’s
The load created by the propeller’s weight, diameter and pitch, will have some effect on the volts and the RPM’s. But as we load the motor with a bigger and bigger prop, the motor will do all it can to maintain the RPM's relative to volts and Kv.  In order to maintain the RPM's with a higher load, the current, and the Amps, will increase because more electrons will be needed to maintain the RPM’s with the added resistance.

A general rule of thumb is that an average propeller will load the motor to about 80%.  Anything over that is good, and anything substantially less will probably mean we are asking too much from the motor.  So I would expect the right propeller on this motor to develop between 7,100 and 7,500 RPMs as full throttle in a static test using a tachometer.
 [5] Amps:
Now that I have some idea of the Watts and the volts I may be using in this power system, I will calculate the Amps.  This is a vital part of my power system since it represents the current, which is the part of the equation that can be the most dangerous to the life expectancy of my investment.  This is where resistance and heat come into play and not managing Amps correctly is where most problems begin.
The formula for calculating Amps is simple.  I divide the Watts by the volts.
So for this example, my 950 Watt motor with 14.8 volts will theoretically generate 64 Amps when turning about 7,100 RPM’s.
I use the word ‘theoretically’ because some fine tuning is required to produce real-world values because different propellers will produce different results.  In the long run, measuring the Watts, Amps and volts with a meter will be the only way to determine the actual values, and to make sure the parts of the power system are performing as expected.
I will continue using these calculations to determine the parts of my motor system, and in the end, I can always use the meter to verify that I have done this correctly before putting my airplane at risk.  Predicting the meter readings is the trick and if the calculations are done correctly, the expectations will be very close to reality.
With these preliminary values, I can hypothetically say that I can fly my 5.5 pound airplane using my 950 Watt motor with a 4 cell battery and a 70 Amp speed controller, and obtain somewhere around 7100 to 7500 RPM’s.
[6] Propeller Selection:
All variables in my setup will change according to the load I put on my motor.  The load is also very simple to determine because it is only calculated using the diameter and pitch of my propeller and the RPM’s that I expect to achieve.  There is one other small variable, which is the propeller constant (pK), but this will only change if we are using an APC propeller designed for electric flight, or another brand intended for electric flight, such as a Xoar PJN Beechwood propeller   These load values are published in a few locations, so you may want to find them for your specific prop brand to help fine tune this understanding.
The next step is to determine the diameter and pitch of my propeller.
Most motor manufacturers will publish the recommended propeller diameter and pitch, which may vary by the number of cells they suggest to use with the motor.  Considering our 950 Watt, 600 Kv motor, I will say that most motors manufactures of motors with this power will recommend 3 to 5 cells and prop sized between 13x8 and 16x8.  With this information, we can make the most complex calculation in the entire process.  The result will be a true representation of the amount of power we will need to actually sustain RPMs with the right propeller without burning up the system.

In this example, the preliminary setup would include a 950 Watt, 600 Kv motor with a 4 cell LiPo pack, a 15x10 propeller and a 70 Amp ESC, and I may obtain an RPM in a range somewhere in the 7100 to 7500 RPM range.
Let’s now do some fine tuning and see how expectations will change relative to the load created by my propeller selection, and how it affects my perfect-world scenario.
[7] Real Watts:
Using a new formula, we will determine the Watts needed to drive this system (Watts-out), and as a result, we will have a much better understanding of our Watts, Amps, volts, and RPMs.
We calculate the actual number of Watts we will need in order to turn our propeller at a specific RPM value using the following variables:
A = Propeller Constant (pK)
B = Propeller Diameter measured in feet (so a 15 inch propeller will be represented in this formula as 1.25)
C = Propeller Pitch measured in feet (so a 10 pitch propeller will be represented in this formula as 0.83)
D = The RPM’s that we wish to obtain
The formula looks like this:
Watts = (Propeller Constant) x (Propeller Diameter to the 4th power) x (Propeller Pitch) x (RPM’s to the 3rd power), or
Watts = A x B x B x B x B x C x D x D x D
So using my preliminary values of a 15x10 APC propeller with a 1.03 pK load value, and 7100 RPM’s, we find that we actually need 750 Watts-out of power.  Considering that Watt-out may be only 80% of the total amount of Watts needed to run the entire electrical system, my actual meter reading of this system could be around 900 Watts.

Since my motor is rated to 950 Watts, I feel I have made an acceptable motor selection.  If I find that my selection did not result in acceptable values, my alternatives are to change the number cells (volts) or alter the load on the motor (prop size and/or pitch), or find a different motor with a different Kv rating.
Using this formula again, we can move the prop value down until it comes in line with the Watts rating of our motor.  For 3D flying, I will usually try to keep the diameter as high as possible because this factor plays a much more important role in developing power, vectored thrust, and torque.
[8] Real Volts:
Using my motor’s Kv rating, I can now predict that I will need a minimum of 14.8 volts to spin a 600 Kv motor 7100 RPM’s.
Volts required = RPM’s divided by the Kv rating, or

(8,880 / 600) = 14.8 volts

Since my LiPo cells have a 3.7 volt per cell rating, I know that I will need 4 cells.

14.8 volts / 3.7 volts = 4 cells

[9] Real Amps:
Now that we know the volts we will use, and the Watts we need, we can check the Amps to make sure we are still safe with regard to current and heat.  Since Watts equals volts times Amps, then Amps equals Watts divided by volts:
900 Watts / 14.8 volts = 60.81 Amps
So nothing has changed here, and a 70 Amp speed controller should be safe, and an 80 Amp ESC will be safer.  Nothing wrong with a little headroom.
We now know with some finer accuracy, that our 950 Watt, 600 Kv motor, with a 4 cell battery, a 70 or 80 Amp ESC, and a 15x10 APC propeller, should provide our 5.5 pound airplane with just over 7100 RPM’s.  When I use a Static Thrust calculator, I can also determine that this setup will generate over 7 pounds of static thrust.  Personally, I would try to shoot for a 1.67-to-1 thrust to weight for hard core 3D flying, but that's just me.
We now need to determine the milliamp and discharge ratings of the 4 cell battery that we will use to make sure it can deliver the Amps when we need it.
[10] Discharge Rate:
The first thing we must do is calculate the discharge rate to make sure we can safely obtain an Amperage value of our peak Amps of 61.  Without the Amps, the Watts are not obtainable with this voltage setup. To do this, we have to consider the batteries, and the milliamp per hour rating, that are available to us.  The calculation will require that we change milliamps per hour to Amps per hour by dividing milliamps by 1,000.  So if my battery is a very light 2650mAh 4 cell, then I will calculate the “C” rating by dividing Amps of my system but the Amps per hour of my battery:
60.81 Amps / 2.65 Amps per hour = 23C
This means that I need a 2650mAh battery with a 25C rating to safely provide the 61 Amps my system may require at peak RPM’s.

As a side note, all batteries are not created equal, and C rating can usually seem like an imaginary number.  I personally trust some brands, and don't trust others, but it is always a good idea to leave a little headroom without going overboard.

Going overboard in C rating will mean adding both weight and expense when neither are really necessary,

[11] Flight Time:

The final calculation of our project is to determine the flight time. This will be determined by the battery I have chosen to power my motor system, and to do this, I will use my C-rating once again.
The actual C-rating tells me the safe discharge rate of the battery.  We determined the C-rating by dividing the Amps by the milliamps per hour.  So the result is a discharge rate that is a function of time.  The 23.1 value we calculated in section [10] means that the battery will discharge in approximately 1/24th of an hour.  If we multiply the 60 minutes that are in an hour by our C rating fraction, we find that 1/24th of an hour is 2.5 minutes. Instead of multiplying a whole number with a fraction, the simple way is to divide 60 by the 23.1.
60 minutes / 23.1C = 2.6 minutes
So for this example, our 950 Watt, 600 Kv motor, with a 4 cell, 2650mAh battery, a 70 or 80 Amp ESC, and a 15x10 APC propeller, should provide our 5.5 pound airplane with just under 7100 RPM’s for about 2 minutes and 36 seconds at wide open throttle (WOT).

Considering that I will probably fly my airplane at half throttle and less, on average, I can easily double that time.

In reality, I have found that my son, who is an experienced 3D pilot, will average about 48% of the WOT Amps, and I will average about 35%  of the WOT Amps.  This means that I can predict that he would need to set his timer to 4:20, while I can get 6 minutes and use 80% of the full battery capacity.

60.81A x .48 = 29.2A
2650mAh x 0.8 = 2120mAh or 2.12Ah
29.2A  / 2.12Ah = 13.8C

60 minutes / 13.8C = 4.36 minutes
0.36 minutes is about 22 seconds, so 4 minutes and 20 seconds should be okay.

Some people will use 70% of the total capacity to be safer, and those using telemetry can really cut it close, and set their system to alert them at 75% to 80% capacity.

So, our 950 Watt, 600 Kv motor, with a 4 cell, 2650mAh battery, a 70 or 80 Amp ESC, and a 15x10 APC propeller, should provide my 5.5 pound airplane with a safe flight for about 6 minutes with me at the controls, and about 4 minutes and 20 seconds with my son at the sticks.

I can also increase his flight time to 6 minutes and my time to 8.3 minutes by going to a heavier 3700mAh battery, but this change in weight could change the power-to-weight requirements.  By increasing the weight, I may have to increase the power needed for the desired flight characteristics.

As a side note, adding more volts, such as a 5 or 6 cell battery, to this power combination, will provide additional efficiency.  More volts will result in less Amps, and less Amps will reduce resistance and heat, and therefore provide additional flight time since time is a function of C-rating, and the C-rating is a function of Amps.  A 5-cell, 2650mAh battery will reduce the Amps of this system to about 50, and increase the safe flight time.  Therefore, for 3D flying, I initially try find [1] the biggest prop I can use, [2] with the most number of cells, [3] with the least amount of weight.
[12] BEC:
As with most electrical systems in all applications, the motorized RC vehicle requires a device that regulates current in order to provide a save flow of electrons from the source, to the load. The Electronic Speed Controller is used to provide the correct current to the motor and to the receiver. The ESC’s we typically buy comes with a built-in Battery Elimination Circuit (BEC). This internal device provides voltage to the receiver, and therefore the servos, from the batteries that are powering the motor. This means that a separate receiver battery is not required if they are combines in the ESC.

The BEC will typically have programming logic monitoring the battery pack voltage, and as a precaution, it will channel power to the receiver and control surfaces and cut off the motor power when voltage is too low to power both. This is known as the LVC, or low voltage cutoff.

In most manufactured speed controllers, there is a limit to the amount of voltage where an internal BEC can be applied, and this is typically 6 cells, or 22.2 volts. If you need more than 6 cells to power your aircraft, you have two options: You will either use a high voltage ESC in tandem with a separate, external BEC, or use a separate battery to power your receiver.

ESC’s that require an external BEC will contain an OPTO switching mechanism to prevent high voltages, or rapidly changing voltages from the battery from damaging the motor.

If using a separate battery, the battery is connected to the battery port of your receiver and the ESC is connected to the throttle port. If a separate external BEC is used, the BEC is connected between the battery and the speed controller and connects to the battery port of your receiver. The ESC is then connected to the throttle port.

It may also be your preference to include a separate BEC on smaller planes for a few reasons. I have found that many ESC’s do not provide 6 volts to the receiver, which means my servos are operating on only 4.8 volts and not reaching their true potential for speed and torque. Because of this, I use an external BEC on all planes, even those being powered by only three cells. This means I typically buy OPTO ESC’s and add a $16 BEC to the setup.

I can also alter my ESC with an internal BEC to accommodate an external BEC by removing the power wire from the connector that attaches to my receiver – which is usually the middle wire of the three going to the connector. This disables the internal BEC, which is very important in order to keep the receiver from getting power from two separate sources. This is easy to do, but obviously necessary. The connector from the ESC is then plugged back into the receiver’s throttle port, and the external BEC is connected to the battery port.

With the external BEC attached, the circuit should be set up in this configuration: the battery is connected to the BEC, the BEC is connected to the ESC with the connector running to the battery port of the receiver, and the ESC is connected to motor with the connector running to the throttle port of the receiver.

There are really good BEC’s out there for under $20.

For bigger planes that can manage the additional weight, I truly recommend that you use a separate receiver battery. The newer A123 Systems, 6.6 volt, 2 cell, 1100mAh nanophosphate batteries weight only 3.3 ounces, and they extended the time between charges considerably compared to NiMH and NiCd batteries. They use safer battery chemistry than a LiPo, they eliminate the need for a regulator, they don’t self-discharge, and they provide a battery that you can safely recharge in about 5 to 7 minutes. Most of them now come without balancing plugs since most users are becoming comfortable with the fact that these batteries really don’t need to be balanced until they are old enough that you may as well discard and replace them after 1,000 cycles
[12] Ohms:
In the circuit defined above, the voltage coming from the battery will decrease linearly as current increases. The voltage reduction is, for the most part, related to the internal resistance of the wiring and cell construction and configuration. So when the volts go through a circuit, some of the energy is converted to heat because of the resistance, and our system will get warm or hot depending on how well, or how efficiently, we combined our motor, ESC, and battery, and how low or high the discharge rate is of our battery.

The bottom line here is that if we have a decent battery with a decent discharge rate, and we matched the Amp rating of our ESC to the motor and number of battery cells, we should get less of a voltage drop when we go to full throttle then if we did not configure the setup properly.

Finally, I hope this experience can help you too, so keep it in the back of your mind in case the day comes when you feel power is being lost to heat, instead of going to Watts from your motor.