Old 02-23-2008, 05:27 AM
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AEAJR
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SIZING POWER SYSTEMS FOR ELECTRIC AIRPLANES
by Ed Anderson
aeajr on the forums
Revised November 2021

Preface

At the time this was originally written, 2005, most electric planes were
using some kind of brushed motor as brushless motors were still very
expensive. Today, brushed motors are seen mostly in micro models
and brushless motors are the standard in most applications.

We are still working from a Watts/pound target and designing
around the desired performance.

Likewise today you are more likely to be using LiPo or some other
Lithium-based battery than NiCd or NiMh, but the chemistry doesn't matter
to the motor. It only sees volts and amps. So, if I use NiMh or Lithium in the
examples the math still holds and the concepts still hold.

Volts X Amps = Watts no matter what kind of motor or battery you use.

==============================

This may get a little technical but I will try to keep it as simple as I
can. I will draw parallels to cars and bicycles in many places as most
people can relate to these and know at least a little about how they work.
I will use round numbers where I can and will use some high-level examples.
If you are an engineer you will see that I am taking some liberties here for
the sake of simplicity. I will go through the parts of the power system,
then, toward the end, I will show you how we tie these all together to come
up with a complete power system.


POWER = WATTS

I will be using the terms Volts, Amps, and Watts throughout this discussion.
You will see watts abbreviated as W.

Let me define them.

Volts = the pressure at which the electric energy is being delivered - like
pounds per square inch or PSI in a fuel system or water from a garden hose.
Volts is about pressure, it says nothing about flow. You will see volts
abbreviated as V.

Amps = the quantity or flow of electricity being delivered, like gallons per
minute in a fuel system or that same garden hose. Amps is about flow, it
says nothing about pressure. You will see amps abbreviated as A.

Watts = V x A. This is a measure of the energy or power being delivered.
This is how we measure the ability of that electricity to do work, in our
case the work of turning a propeller to move our airplane through the air.
Watts is about both pressure and flow. This serves the same purpose as
the horsepower rating of your car's engine. In fact 746 watts = 1
horsepower.

If you have an electric car, the strength of its motor(s) could
be reported in either watts or horsepower.


If you want more depth on this, visit this thread.
http://www.wattflyer.com/forums/showthread.php?t=1933


MOTOR EFFICIENCY - Brushed vs. Brushless

Whether brushed or brushless, the motor's job is to convert electricity into
mechanical motion to turn the propeller to move air. Efficiency is how we
measure how much of the power, the watts, that our battery delivers to the
motor is actually turned into useful work and how much is wasted as heat.
A higher efficiency motor delivers more energy to the propeller and wastes
less as heat.

A typical brushed motor, say a speed 400, is only about 40-50% efficient.
Only about half the watts delivered to the motor actually end up as useful
work turning the propeller. The rest is wasted. Motors that have "speed"
designations, like speed 400, are generally brushed motors. There are other names for
brushed motors but the "speed" term is a common one. They are inexpensive
and they work. Today brushed motors are typically only seen in micro models.

Brushless motors tend to be more efficient. They typically deliver 70-90%
of that input power to the propeller, Thus you get better performance per
watt with brushless motors. Seen a different way, if you use a brushless
motor, then, for the same flying performance you will use less energy which
means your battery will last longer. Or you can use a smaller size and
weight brushless motor/battery combo to get comparable performance
because the motor turns more of the watts from the battery into useful work
of turning the propeller.

Today brushless motors are the standard based on their higher efficiency and
higher useful power to weight ratio.


THE BATTERY IS MORE THAN JUST THE FUEL TANK

Think of the battery as the fuel tank plus the fuel pump all rolled into one.
It feeds/pushes energy to the motor. So you have to balance the battery
and the motor to achieve the power level we want.

Motors have a rating called kV. This is an indication of how fast the motor will
try to turn based on the voltage applied. More on this later.

Higher voltage turns the motor faster which turns the prop faster. The motor will draw more
power, more watts (Volts x Amps) to try to reach its designed kV speed. But this only works well
if the battery has the ability to deliver more amps.

Again using the car analogy, if you put a big motor in a car and put a tiny
fuel line and a weak fuel pump, the motor will never develop full power. In
fact, the motor might starve and stall once you got past idle. Such is the
same with batteries. We need voltage, we need capacity, but we also need to
know how many amps the battery is capable of delivering at peak.

The motor/speed control does not know whether the power is coming from a NiCd
NiMh or a Lipo pack. All the motor sees are volts and amps. so the illustrations
that follow still hold whether we are using NiMh, NiCd. or LiPo packs. The
cell count will differ at a given voltage but the math is the same.

If we compare an 8 cell AAA battery pack to an 8 cell C battery pack we get
9.6 V for both packs. However, the AAA pack may only be able to deliver 6
amps. After that, the cells will heat up and the voltage will drop. The cells are
likely to be damaged as they try to deliver the power the motor is demanding.
The C pack, also 9.6 V, might be able to deliver 60 amps without damage. So
we have to size not only by voltage but by the ability to deliver amps to the motor.
Again, think of the fuel line and the fuel pump as your image of what I am trying to explain. If the
motor needs 12 ounces of fuel per minute to run but the fuel line can only
deliver 8, the engine will starve and die.

In the lithium battery world, we would be looking at the C raging on the packs.
A 2000 mah pack rated at 30C can deliver three times the amperage of a 2000
mah pack rated at 10 C. If the motor is going to need 60 amps to deliver
full power, the 10C pack will not meet the demand as it an only deliver 20 amps
before it heats up and is damaged. The 30C pack can deliver the required
60 amps.

A given motor may want to draw 10 amps
( the quantity of electricity flowing ) at 8.4 volts ( the pressure at which
the electricity is being delivered) to spin a certain propeller. We would
say that the battery is delivering, or that the motor is drawing 84 watts,
i.e.: 8.4V x 10A. If you bump up the voltage to 11.1 volts, the motor will
try to spin faster which will turn the prop faster. In order to do this the
motor will draw and the battery must deliver more amps into the motor, more
energy to the motor, which will produce more power to the propeller but it
will also produce more heat in the motor. In this example, if we move from
an 8.4V battery pack to an 11.1V battery pack the motor may now take 13 amps.
But can this particular electric motor handle 13 amps? Can the electronic
speed control (ESC) handle 13 amps?

If you bump up the pressure, the voltage, too much, you can break something.
Putting a big supercharger on an engine that is not designed for it will
break parts of the engine. Too much voltage can overpower your electric
motor and damage it. So there is a balance that has to be struck.

Different motors can take different amounts of power, watts, volts X amps,
without damage. For example, a speed 400 motor might be fine taking 10 amps
at 9.6 volts or 96 watts. However bump it up to 12 volts, while spinning
the same prop, and it might draw 18 amps which could burn it out. The same
would be true for brushless motors.

Our goal is a balanced power system. If you match the right battery with
the right motor, you get good performance without damage to the motor, batter and
speed control.

In some cases, airplane designers will design planes around a specific
motor/battery combination so that they match the size and weight of the
plane to the power system for good performance.

REVOLUTIONS PER VOLT - kV

An important fact about electric motors is that they tend to want to spin
at a certain speed for every volt that we apply to them. We won't go into a
lot of depth here, but it is important to understand that if you apply 5
volts to a motor, it will try and spin at a given speed. If you apply 10
volts. it will try to turn twice as fast. This fact is noted on the specs of
your motor in the form of the kV rating. Basically a kV rating of 1000
means that the motor will spin at 1000 RPMs for every volt applied.

If you apply 10 volts, it will try to spin at 10,000 rpms. It will try to
achieve this RPM level regardless of the load we put on it. It will draw
more and more amps from the battery trying to hit this number.

By boosting the voltage on a motor, and getting it to spin faster we can get
it to produce more power, but we must be careful not to overwork the motor.
Even if it is 80% efficient, 20% of the power that goes into it turns into
heat. Too much heat can melt insulation, cause shafts to expand in bearings
and all sorts of bad things can happen. So, as we change the voltage we
apply to our airplane motors we sometimes change the propeller too.


PROPELLERS

Propellers are sized by diameter and pitch.

The diameter and pitch of the propeller determine the volume of air the propeller
will move, producing thrust, or pushing force.

Pitch refers to the angle of the propeller blade and refers to the distance
the propeller would move forward if there were no slippage in the air. So a
7-inch pitch propeller would move forward 7 inches per rotation if there
were no slippage in the air.

If we combine pitch with the rotational speed
of the propeller we can calculate the pitch "speed" of the propeller. So,
at 10.000 revolutions per minute, that prop would move forward
70,000 inches per minute. If we do the math, that comes out to a little
over 66 miles per hour.

By changing the diameter and the pitch of the propeller we can have a
similar effect to changing the gears in your car or a bicycle. It will be
harder for your motor to turn a 9X7 propeller than an 8X7 propeller. And
it would be harder to turn a 9X7 propeller than a 9X6 propeller. The
larger or steeper pitched propellers will require more energy, more watts,
more horsepower, to turn them. Therefore we need to balance the diameter
and pitch with the power or wattage of the motor/battery system.

Fortunately, we don't actually have to do this ourselves as motor
manufacturers will often publish suggested propellers to use with a
given motor/battery combination. We can use these
as our starting point. If we want we can try different propellers that are
near these specifications and use a wattmeter to measure the results. More
on wattmeters later.


GEARBOXES

While unusual on glow or gas planes, gearboxes are more common on electric
planes. Their primary function is similar to the transmission on a car. The
greater the gear ratio, the higher the numerical value, the slower the
propeller will turn for a given motor speed.

However, this allows this motor to spin a larger propeller, just more slowly.
Larger propellers provide more thrust per rotation. So you can
use a gearbox to help provide more thrust so you can fly larger planes with
a given motor. However you will be turning the propeller slower so the
plane will not go as fast with the same propeller.

With direct drive, that is when the propeller is directly attached to the
motor shaft, we are running in high gear ( no gear reduction). Like pulling
your car away from the light in high gear. Assuming the motor doesn't stall,
acceleration will be slower, but over time you will hit a high top-end!
Typically direct-drive propellers on a given motor will have a smaller
diameter.

With the geared motor, it would be like pulling away from the green light in
first gear - tons of low-end power and lots of acceleration, but your top
speed is reduced.

Cars have transmissions that provide multiple gear ratios so that you can
match the gear to the speed of the car as you accelerate. However,
our model airplanes don't have transmissions

In effect, changing the pitch and diameter of the propeller also has a gear ratio
kind of effect. So, by matching up the right gear ratios made up of the propeller and,
optionally a gearbox, we can adjust the kind of performance we can get out
of a given battery/motor combination. I won't go into the math here. I pointed out
some calculators at the end of the previous chapter. So we would either follow the
manufacturer's recommendations or use one of the calculators to help us pick the right
motor/propeller/battery combination.

In the skinny nose of a glider a gearbox may be needed just to get things to fit.
On a larger electric plane, where you have more room, you will have more options as to
whether you wish to use a direct drive or gearbox set-up. These are design choices.


NOW WE CAN START TO MATCH UP THE PIECES!

Watts/Pound

The simplest approach I have seen to figuring power systems in electrics is
input watts per pound of "all up" airplane weight. The following guidelines
were developed before brushless motors were common but it seems to hold
pretty well so we will use it regardless of what kind of motor is being
used. You may see variations on these numbers but the concept is the same.

50 watts per pound = Casual/scale flying

75 watts per pound = Sport flying and light sport aerobatics

100 watts per pound = aggressive sport aerobatics

150+ watts per pound = High performance and 3D

Remember that Watts = Volts X Amps. This is a power measurement.


AN EXAMPLE!

This should be fun. Let's see where these formulas take us! We will use a
24 ounce, 1.5 pound plane as our example. If we want basic flight you will
need 50 watts per pound or about 75 watts input to the motor for this 1.5
pound plane. That is, 50 watts per pound X 1.5 pounds = 75 watts needed
for basic flying performance. If you want a little more spirited plane, we
could use 75 watts X 1.5 pounds which is about 112.5 watts.

Lets use 100 watts as the total target, just to be simple, I am
going to use a lot of round numbers here. I hope you can follow. Remember
the motor does not know what chemistry the battery is using, it only sees
volts and amps.

The Battery:

If we use an 11.1 V 3 cell lipo pack. To hit a 100 watt input target the battery
will have to deliver about 9 amps to the motor.

Now I select a motor that can handle 100 watts or about 9 amps or more at 11.1 volts.

We now need a propeller that will cause the motor to draw about 100 watts.

This would involve reading a lot of motor specs and battery specs and understanding the
implications of a change in propellers. This can get complicated.

What I do, and what I recommend you do is to go to one of the calculators, put in the specs and
see what they recommend. I tend to use eCalc which will allow me to play with all sorts of
combinations and make suggestions on what I should use. It will model different motors, batteries,
propellers, and even speed controls to help me come up with the right combination for my application.

These calculators are pretty good. I have found the predicted performance closly matches those predicted
by the calculator.


SUMMARY

So, in these few paragraphs, you have taken in basic knowledge of how
electric power systems are sized, the factors that are considered and how to
predict the outcome.

Of course, there is a lot more to know and time and experience will teach
you plenty, but with this basic understanding you are better prepared to
begin playing with the power systems you put in your planes.

Here are some additional resources that may be helpful.

RESOURCES

EVERYTHING YOU WANTED TO KNOW ABOUT ELECTRIC FLIGHT
an e-book by Ed Anderson
http://www.wattflyer.com/forums/showthread.php?t=31071

Maxx Products has a pretty good tip sheet on coming up
with a glow to electric power comparison. You can find it here:
http://www.maxxprod.com/mpi/tips3.html

MotoCalc
A commercial tool that will tell you everything you need to know: Amps,
Volts, Watts, RPM, Thrust, Rate of Climb, and much more! It is a popular
tool for predicting the proper motor, prop, battery pack for electric
planes. There is a fee but if you are going to do a lot of this kind of
work, it may be a good investment.
http://www.motocalc.com/

Electricalc
Like Motcalc, this is a commercial tool that is very extensive. Well worth
the money for anyone who is doing a lot of power system design.
http://www.slkelectronics.com/ecalc/index.htm
or
http://www.hobby-lobby.com/ecalc.htm...QueryId=447678

e-CALC - This is the one usually use. I like their prop calculator
http://www.ecalc.ch/

Last edited by AEAJR; 11-02-2021 at 06:55 PM. Reason: Made some minor updates to keep the article current
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