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SIZING POWER SYSTEMS FOR ELECTRIC AIRPLANES
by Ed Anderson
aeajr on the forums

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 motor, 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 $35. A comparable brushless motor/ESC combination
would
typically cost 3 to 4 times that much.

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
you battery will last longer. Or you can use a similar size and weight
brushless motor and get much higher performance because the motor turns more
of the watts from the battery into useful work of turning the propeller.

So, as with many decisions we make, this is a cost benefit decision. Am I
willing to pay more to get more? That is up to you.


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 pushes more electricity into the
motor
to produce more power.

Using our electric motors, a given motor may take 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, ie: 8.4V x
10A. If you bump up the voltage to 9.6 volts, the battery can ram in more
amps delivering more energy to the motor which will produce more power to
the
propeller. In
this example, if we move from an 8.4V battery pack to a 9.6V battery pack
the motor may now take 12 amps. This will typically spin the motor faster
with any given propeller or allow it to turn a larger propeller at the same
speed.

However, 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 a speed 280 motor will have a short life
with the same
combination of volts and amps.

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.


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 7000 inches 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, 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 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 to see how they work with our airplane.


GEARBOXES

While unusual on glow or gas planes, gearboxes are 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 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.


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.

50 watts per pound = Casual/scale flying

75 watts per pound = Sport flying and sport aerobatics

100 watts per pound = aggressive aerobatics and mild 3D

150 watts per pound = all out performance.

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.

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 ( 100/9.6 = 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 - 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.

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. 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 but
a lower top speed typically.

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 1100 -1300 mah capacity, depending on the
quality of the cells.

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
produce 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 I
have to go for the smaller but faster prop combo.

If this is a puller, then I can choose my prop by ground clearance or some
other criteria and match a gear box to it.


See, that was easy, right? 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 push
13 amps into this motor. 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.

Summary

So, in these few paragraphs 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

Brushed Motors
http://www.hobby-lobby.com/elecmot.htm

Brushless Motors
http://www.hobby-lobby.com/brushless-motors.htm

Battery Packs - NIMH
http://www.cheapbatterypacks.com/mai...=445976&ctype=
http://www.hobby-lobby.com/hydride.htm

Battery Packs - LiPo
http://www.cheapbatterypacks.com/mai...gid=tp&sort=PL
http://www.hobby-lobby.com/lithium-polymer.htm

Gearboxes - Speed 400 & 480 examples
http://www.hobby-lobby.com/gear400.htm
http://www.hobby-lobby.com/gear480.htm

A series of posts on electric power system basics
http://www.wattflyer.com/forums/showthread.php?t=1933
http://www.rcgroups.com/forums/showthread.php?t=417868

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
MotoCalc 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.
http://www.motocalc.com/