SIZING POWER SYSTEMS FOR ELECTRIC AIRPLANES

by Ed Anderson

aeajr on the forums

Revised 7/11/2011

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 $30. A comparable brushless motor/ESC combination

would

typically cost 2 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 your battery will last longer. Or you can use a similar 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.

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.

Electric motors also have a value associated with them that you will see as kV.

This number tells us that for a given voltage the motor will try to turn a given number

of RPMs. So a 500 kV motor will want to turn 500 RPMs for every volt applied. So

10 volts would turn that motor 5000 RPM with no load (propeller) imposed on the

motor. So the higher the voltage of the battery the faster our motor wants to turn.

In order to turn faster it takes more amps to support the motor turning at that speed.

The motor is doing more work when it turns faster.

You can think of this as higher voltage pushes more electricity into the motor.

However this is true IF AND ONLY 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 what flow, how many amps the battery is capable of delivering at peak.

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 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 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, i.e.: 8.4V x

10A. If you bump up the voltage to 9.6 volts, the battery can ram in more

amps into the motor, 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 (remember kV discussed above) 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 bump it up to 12 volts and ram 15 amps

down its throat and you will likely burn it out.

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.

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 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. How this is done is beyond the scope

of this article.

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 perhaps 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 as a starting point. GWS has good charts!

http://www.gwsus.com/english/product/powersystem/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/powersystem/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 but a lower top speed typically. This is a

common strategy for 3D planes and gliders where we care more about thrust

to weight for climb rather than speed.

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 1000 -1300 mah capacity. Some examples here:

http://www.cheapbatterypacks.com/?me...D738&sid=10890
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

may 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? ( 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 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.

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 brushelss motors these days. Costs are reasonable and their higher

efficency

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.

For those who like to be even more analytical about it, there are packages

like MotoCalc that will allow me to play with all sorts of combinations and

make suggestions on what I should use. There is a link for MotoCalc below.

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

Good video that talks about some of the same topics covered in the article

http://www.youtube.com/watch?v=YJ7qqYRifzU
Brushed Motors

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

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

http://en.wikipedia.org/wiki/Brushle...electric_motor
Lithium Balancers and Balancing Chargers

http://www.rcgroups.com/forums/showthread.php?t=599287
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
This reader says Keith Shaw originated the watts per pound rule

http://www.rcgroups.com/forums/showpost.php?p=6156600&postcount=39
MotoCalc

This program 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/
This club has some interesting links on their home page that may be helpful

in planning props and power systems.

http://www.srcmc.co.uk/
Drive Calculator Version 2.21

Based around a Microsoft Excel spreadsheet This includes a propeller thrust

and power database, in a similar form to MotorXL, a motor database, and

tools for predicting home made motor performance. With these tools it is

possible to predict the performance of motor and prop combinations - even

with custom motors!

http://www.badcock.net/motorcalc/