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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 March 2016

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. As of today, brushed motors are seen mostly in micro models
and brushless motors are the standard.

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, while I use NiMh 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.
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. So if you had an electric car, the strength of its motor could
be reported in either watts or horsepower. You will see watts abbreviated as
W.

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 prop, and wastes
less.

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 a "speed"
designation, like speed 400, are brushed motors. There are other names for
brushed motors but the "speed" term is a common one. They are inexpensive
and they work. For example, you can buy a speed 400 motor and electronic
speed control, ESC, for $20. A comparable brushless motor/ESC combination
would likely be 1.5 to 3 times that much, but prices have been coming down fast.

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 you will most likely be working with brushless motors for new installations
or to replace older brushed motors.


THE BATTERY IS MORE THAN JUST THE FUEL TANK

Think of the battery as the fuel tank plus the fuel pump and a supercharger
all rolled into one. It feeds/pushes energy to the motor. So you have to
look at the battery and the motor as one unit when you are sizing power
systems for electric planes. In many cases we start with the battery when
we size our systems because the motor can't deliver the power to the prop if
the battery can't deliver the power to the motor.

The higher the voltage rating of the battery, the higher the pressure, like
a supercharger on a car engine. More pressure delivers more air/fuel
mixture to the engine which allows the engine to produce more power to turn
the wheels of the car.

Higher voltage turns the prop faster which places more load on motor which will
cause it to pull more amps. But this only works well
if the battery has the ability to deliver more electricity.
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 do not know whether the power is coming from a NiCd
NiMh or a Lipo pack. All the motor sees is volts and amps. so the illustrations
that follow still hold whether we are using C Cell NiCds 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 either be damaged or the
voltage will start to drop fast. 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.

Using our electric motors, 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 9.6 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 a 9.6V battery pack the motor may now take 14 amps.
But can this particular electric motor handle 14 amps? Can the electronic
speed control handle 14 amps?

If you bump up the pressure 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 over power 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, inrunner or outrunner.

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. In
many 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 over work 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 of the propeller determines the volume of air the propeller
will move, producing thrust, or pushing force. Roughly speaking the
diameter of the propeller will have the biggest impact on the size and
weight of the plane that we can fly. Larger, heavier planes will typically
fly better with larger diameter propellers.

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 10000 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 but the larger the propeller we can turn. 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 slow, 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.

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. How this is done is beyond the scope
of this article.

Today with a choice of inrunner or outrunner motors you have more of a choice.
Inrunners tend to have higher kV ratings so they will turn smaller propes faster
or large props with a gearbox. Outrunners tend to have lower kV ratings and
can spin larger props without a gearbox but turn it more slowly for a given
voltage. Which you choose can be a matter of preference or a matter of how the
plane is built.

In the skinny nose of a glider a gearbox may be needed just to get things to fit.
On a larger electric plane an outrunner may have plenty of room to spin and therefore
eliminate the need for the gearbox. These are design choices.



NOW WE CAN START TO MATCH UP THE PIECES!

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.
In case you were wondering, 746 watts equals 1 horsepower.


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 your 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, shall we? 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 8 cell NiMh battery pack at 9.6 V it will have to deliver 10.4
amps to hit our 100 watts input target ( 100 watts/9.6 V = 10.41amps) If
my battery pack cells are NiMh cells that are rated at 10C then I need an 8
cell pack rated at 1100 mah to be able to deliver 11 amps. Sounds about
right.

Now I select a motor that can handle 100 watts or about 10.4 amps at 9.6
Volts. From experience we know this could be a speed 400, a speed 480 or
some kind of a brushless motor.

We now need a propeller that will cause the motor to draw about 100 watts. I
don't know off the top of my head what that would be. I would go to some mfg
chart as a starting point. GWS has good charts!
http://www.gwsus.com/english/product...tem/edp400.htm

I see that if I use a direct drive speed 400 with a 5X4.3 prop at 9.6V then
the motor will draw about 12.4 amps or about 119 watts. This would be a
good candidate motor/prop for the plane using a 9.6V pack that can put out
12.4 or more amps. This would be a set-up for a fast plane as that motor
will spin that small prop very fast.

However maybe I don't want such a fast plane but one with a really good
climb and lots of low end pull to help out a new pilot who is in training or
to do more low speed aerobatics

I can also use a speed 400 with a 2.38 gearbox and run it at 9.6V spinning a
9X7 prop and run at about 12.8 amps for 120 watts.
http://www.gwsus.com/english/product...em/eps400c.htm

The larger prop will give this plane a strong climb, but since the prop
speed has been reduced by 2.38 times, it won't be as fast. Spinning a
bigger prop gives me more thrust. Also note went from a pitch of 4.3 on the
direct drive set-up to a pitch of 7 with the gearbox. This is because the
prop is turning 2.38 times slower now so we increase the pitch to somewhat
balance that.

Back to battery packs and motors

So if I shop for a 9.6V pack to be able to handle about 15-20 amps, I should
do just fine and not over stress the batteries. In NiMh that would probably
be a 2/3 or 4/5 A pack of about 1500 -1600 mah capacity.

If I am working with LiPo packs I might be looking at 2 cell or 3 cell packs
in this application and adjust the motor kV and prop size according to the
manufacturers recommendations.

We view the battery and motor as a linked unit with a target power profile,
in this case about 100 watts. We use the prop and gearbox, if any, to
adjust the manner in which we want to deliver that power to the air to
pull/push the plane.

If this is a pusher, I may not have clearance to spin that big prop so we
may have to go for the smaller but faster prop combo.

If this is a puller, then we can choose our prop with more flexibility but
we may have to limit it by ground clearance or some other criteria.


See, that was easy, right? ( well sorta but ....)


But we are not done! Oh no!

I could try to do it with a 2 cell lithium pack rated 7.4V. To get 100 watts
I now need a pack that can deliver 13.5 amps and a motor/prop combination
that will draw that much. So if I have 10 C rated lithiums, then the pack
better be at least 1350 mah. Probably use a 1500 mah pack to be safe.

Well, when I look at the chart for the geared speed 400 I see that,
regardless of prop, at 7.4V I am not going to have enough voltage (
pressure) to draw 13 amps based on the propellers they tried. So the
2 cell lithium won't meet my performance goal of 100 watts+ per
pound using this gear box.

If I go back to the charts and look at a different gear boxes. I can't hit
my power goals using 7.4V. Maybe we go back to direct drive.
http://www.gwsus.com/english/product...tem/edp400.htm

We see that the best I can get this speed 400 to do is a total of 70 watts
at 7.2V ( close enough ) so I can't hit my power goals using a speed 400 at
this voltage. but 70 watts would be about 48 watts per pound so I could have
a flyable plane, but not an aerobatic plane using this two cell pack.


REALITY CHECK!

Now, in fact that is NOT how I would do this. I would decide on the watt
target, go to the chart, find a combo that meets my goals, then select a
battery that will meet the demand and see if my weight comes up at the
target I set. A little tuning and I come up with a workable combo.

I often use the MaxxProd combos for reference. If you read the details on
each package they have wonderful information. And, the fact is that I
generally go with brushless motors these days. Costs are reasonable and
their higher efficiency gives me more performance and longer flight times.
http://www.maxxprod.com/mpi/mpi-264.html

Following the example above, the combo 10 on that page would be an excellent
fit for my 1.5 pound plane for sport flying. The Combo 049 might be a good
fit for a slow flyer. Either way the package has all I need.

If I wanted the plane to have all out performance, the 15A or 19A package
would be my pick. Note that these would need either higher voltage or
higher amperage battery packs. The flyers/PDF for the packages make
recommendations.

Another approach is to use one of the available motor/prop/battery calculators
like eCalc that will allow me to play with all sorts of combinations and
make suggestions on what I should use.


SUMMARY

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

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.

Good luck e-pilot!

Clear Skies and Safe Flying!
Ed Anderson


RESOURCES

EVERYTHING YOU WANTED TO KNOW ABOUT ELECTRIC FLIGHT
an e-book by Ed Anderson
http://www.wattflyer.com/forums/showthread.php?t=31071
http://www.rcuniverse.com/forum/m_7100376/tm.htm


Battery Packs
http://www.cheapbatterypacks.com

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

This reader says Keith Shaw originated the watts per pound rule
http://www.rcgroups.com/forums/showp...0&postcount=39

MotoCalc - Fee
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 - Fee
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 - A free power system sizing tool
http://www.ecalc.ch/


Webocalc - Free
A free calculator that can help you get close to the proper design. You put
in certain parameters and it will give you the proper prop combo for that
motor set-up. It does not list by brands and it is not as full featured as
the
programs that charge a fee, but hey, it's free. This is the one I use most
of the time.
http://flbeagle.rchomepage.com/softw.../webocalc.html


What's Inside an Electronic Speed control?
[media]http://www.youtube.com/watch?v=22CpRl2_TRI&feature=digest_sat[/media]

Last edited by AEAJR; 03-11-2016 at 09:11 PM. Reason: Made some minor updates to keep the article current
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