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Sizing Power Systems

From EFlightWiki  by Ed Anderson

Intro

Based on an article called "SIZING POWER SYSTEMS FOR ELECTRIC AIRPLANES"
by Ed Anderson

How do they fly?

Flight

From EFlightWiki


This may get a little technical but aimed at someone trying to choose a power system for the first time.

Math's is kept to a minimum and parallels are drawn to cars and bicycles in many places as most people can relate to these and know at least a little about how they work. It uses round numbers where possible and gives some high level examples. If you are an engineer you will see that I am taking some liberties here for the sake of simplicity. It goes through the parts of the power system, then, toward the end, shows you how we tie these all together to come up with a complete power system.


POWER = WATTS
The terms Volts, Amps and Watts are used throughout this discussion.

Volts = the pressure at which the electric energy is being delivered - like pounds per square inch (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 power; the rate that energy is 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. [1]

How much power do we need?
The simplest approach 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.

25 W/lb = minimum for level flight, with a reasonably clean plane.
50 W/lb = Trainer/Casual/scale flying
75 W/lb = Sport flying and sport aerobatics
100 W/lb = aggressive aerobatics and mild 3D, effortless loops from level flight.
150 W/lb = all out performance.
200 W/lb = Unlimited high-speed vertical flight.
Remember that Watts = Volts X Amps. This is a power measurement. In case you were wondering, 746 watts equals 1 horsepower. (If you've ever been near a horse you'll know that it's far less power than a horse can provide; the original measurement was supposed to equate to the amount a work a pit pony could do all day, and it was set by the makers of steam engines, who were understandably biased.)

For a ducted fan you need something like 1.5 to twice the power of a prop, because ducted fans don't work well at low speeds.

What about thrust?
You might think that the thrust (or force) applied by the propeller is all that matters, but what really matters is the ability to carry on producing thrust when the plane is moving at speed.

For many planes, if they have enough power the thrust will come automatically. However for 3D flight and hovering you need thrust as well as power. At least 1.5 times the AUW, ideally twice the AUW.

Deltas really need at least thrust equal to their weight, or you can get 'stuck' with the nose up at low altitude with no way to gain speed.

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.

Batteries have

A nominal voltage - it's more than this when charged, and less than this (not zero) when used.
A capacity - in Amp Hours (Ah) i.e. they can provide this many amps for one hour, or twice that many for half an hour.
A C rating. This determines the maximum current you can get from the battery. It's expressed as a multiplier of the capacity to make it easier to compare batteries.
A 1C 1Ah battery can only provide 1 Amp and will do so for an hour.
A 2C 1Ah battery may look the same but it can provide 2 Amps (but if you do that, it'll only last half as long)
A 10C 1Ah battery can provide 10Amps for 6 minutes.
So, if after using the chart above you decide you need 100W, you could buy:

a 100v 1Ah 1C battery - if you didn't mind the risk of killing your self with that much voltage
a 10v 10Ah 1C battery - you'd get hour long flights, but it would be so heavy you may never get off the ground.
a 1v 1Ah 100C battery - it would only last 36 seconds and they don't make them.
a 10v 1Ah 10C battery - a sensible choice
a 20v 0.5Ah 10C battery, just as good but might be more expensive because it's made of lots of small cells.
a 10v 0.5Ah 20C battery - half the weight and half the flight time. Probably more expensive too. Great for racing but not as practical for sport flying.
Generally it's worth buying batteries rated at 10C or more. You don't have to fly at full throttle all the time, and they still contain the same amount of energy, it's just that you can get it out quickly if you want.

The actual amount of energy stored in a battery is the voltage times the capacity, although this is rarely calculated. It would be expressed in Watt hours, or Joules.

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 * 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.

Notice that at this point we aren't too bothered about how long the battery will last (that should tell you that it really is more than just a fuel tank!) but that it's capable of providing the amount of power we want.

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.

Pitch speed MPH = pitch (in inches) * RPM (in thousands) * 0.95

When a plane is flying at it's pitch speed, the prop is generating no thrust, so if you want to reach (for example) 100mph, you've got to pick a power system with a pitch speed higher than this.

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.

When experimenting with different props, there's a rule of thumb that says you can swap an inch of pitch for an inch of diameter, and keep roughly the same power draw. So if your plane currently flies with a 9x7, you could also try a 10x6 (rapid climb but reduced top speed) and a 8x8 (slow climb but fast dives!)

GEARBOXES
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.

While unusual on glow or gas planes, gearboxes are common on electric planes because electric motors are often not specifically designed for RC flight, but mass produced for other uses and only efficient at speeds far higher than we need.

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.

Motor Basics
If you ran a car engine with no load (e.g. wheels off the ground) at full throttle, it would turn faster and faster until something broke (unless there's a rev limiter to stop you doing this) but the electric motors used for E-flight behave differently. When you apply a voltage to an electric motor with no prop, the motor will run quite happily a certain speed, drawing very little current (because it's not doing any work, it doesn't need much power input). If you double the voltage, the speed will roughly double.

When you put a load on an electric motor, it runs more slowly than it's no-load speed, and starts drawing more current. Eventually you reach a point where it's going so slowly that it gets really inefficient.

Electric motors are often labeled with their Kv value, this is the RPM at which the motor will turn for each volt supplied. For example, a 1000Kv motor, attached to a 6v battery and no load will turn at 6,000rpm. If you plugged the same motor into a 12v battery, it would turn at 12,000rpm. So if you want a higher speed motor, you can either buy one with a higher Kv, or use a higher voltage battery.

The Kv of a motor is determined by many things but the easiest thing for the manufacturer to change is the number of turns of wire in the coils. Thus two motors look identical but may be described as '8-turn' or '16-turn' or whatever; the fewer the turns, the higher the Kv. This isn't much use for comparing motor between manufacturers because of all the other factors.

Brushed motors are often only available in a single variant, and a gearbox is required to turn a prop at the desired speed. Brushless motors tend to be specifically designed for RC flight, so you can pick a suitable 'Kv' and save the power that would be lost in the gearbox.

Motors are also often labeled with a four digit number like '2208', this usually refers to the size of the stator in the motor - that's the bit the coils are wound around. Often the first two digits are the diameter (in mm) and the second are the length, in this case, 22mm diameter and 8mm long. Again the exact numbering scheme can differ from one manufacturer to another but it's usually safe to assume that a bigger motor is going to be able to handle more power and will weigh more.

Although you can predict the speed at which a motor will run when there is no load, it's much harder to predict how much thrust it will develop with a prop, and how far below the no-load speed it'll run. For this you generally look for charts provided by the motor manufacturer.

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 could cost 3 to 4 times that much, or you could buy a cheap one for little more than the brushed motor (but it's unlikely to be super efficient)

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.

For example, if a 50% efficient brushed motor can dissipate 50W of heat, it can only provide 50W of power (and this would require 100W of power from the battery). If the motor was 75% efficient the same 100W from the battery would be providing 75W of power and only 25W of wasted heat

The wasted energy becomes heat in the motor, if it gets too hot the insulation on the wires melts and the magnets become demagnetized. The rate that a motor can dissipate this heat determines the maximum power that the motor can handle. So, a more efficient motor can handle more power before it overheats. In the above example, you could put 200W into the more efficient motor before it would be as hot as the 50% efficient motor, and you'd then be getting 150W (three times as much!) power out.

Also, brushed motors are limited by their brushess (that make contact with the spinning coils). If they go to fast the brushes start to skip over the contacts and spark (causing radio interference) so there's a maximum voltage. Also there's a maximum current density for the brushes, so if your voltage is too low, the current required may be too high.

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.



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 (50 watts per pound) we need about 75 watts input to your motor for this 1.5 pound plane. If you want a little more spirited plane, we could use 75 w/lb X 1.5 lb which is about about 112.5 watts.

Lets use 100 watts as the total target, just to be simple, shall we?

The Battery:
If we use an 8 cell NiMh battery pack (9.6V) 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 rated at 10C then I need a pack rated at 1100 mAh to be able to deliver 11 amps. Sounds about right.

The motor
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.

The prop
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! GWS EDP400 Direct Drive power system]

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.

The gearbox
However the chart also says I can only expect 12oz of thrust from this set up. The pitch speed will probably be very high but if there isn't enough thrust the plane will never get anywhere near it. This might be suitable for a really clean racing plane but if you want a really good climb and lots of low end pull (maybe to help out a new pilot who is in training) you need more thrust.

Fortunately there are charts for gearboxes too. GWS EPS400

The same speed 400 with a 2.38 gearbox 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, the pitch speed will be lower.

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 -1500 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 lithium's, 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 it doesn't cover any props big enough to make this motor draw 13 amps at 7.4V. This may just be because they didn't both testing it, or because the motor just isn't efficient like that. So the 2 cell lithium won't meet my performance goal of 100 watts+ per pound using this motor and gear box.




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

Further reading
A series of posts on electric power system basics [2] [3]

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

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

Motor Wizard  http://www.commonsenserc.com/page.php?page=motor-wizard.php

Battery Packs

NIMH http://www.cheapbatterypacks.com/ma...d=445976&ctype= http://www.hobby-lobby.com/hydride.htm

 LiPo http://www.cheapbatterypacks.com/ma...pgid=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

Retrieved from "http://www.eflightwiki.com/eflightwiki/index.php?title=Sizing_Power_Systems"

Some Tools to help with choosing the system

Static Thrust Calculator   Ever wanted to know how much thrust your engines giving ?

Choose the right motor for your plane by describing you plane with MOTOR WIZARD @ comment sense RC

NEW POWER

A look at the other power options and technologies

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