Energy usage and motors and propellers

(this is in response to this thread - questions about props and pitch and diameter and so on)

You're correct so far about props, but it's fairly complicated. Here's the long explanation...

We know that energy can not be destroyed, right? So that means that any electricity you send into a motor will either be turned into kinetic energy by spinning the prop, or heat, which is the enemy of metal parts. That's beside the point really, but keep it in the back of your mind for when I talk about efficiency, because the losses due to lowered efficiency show up as heat, usually in the motor wires, some in the bearings too.

First some definitions:
A Newton is a unit of force - it is the force required to accelerate a one kilogram mass by 1 meter per second squared. So, if you apply 1 Newton of force to a 1 kilogram mass for one second, it's final speed will be 1 meter per second faster than it was before you started applying the force.

A Joule is a unit of energy - it is the amount of energy expended by a 1 Newton force over a distance of 1 meter.

A Watt is a unit of the rate of energy usage - it is one Joule per second.

The units of electricity usage were set up deliberately such that 1 volt times 1 amp will be one watt of energy usage - 1 Joule per second.

So, if you have a 1 kilogram airplane, and you want it to accelerate at 1 meter per second per second, you need to have one watt of power. If there was no drag or gravity or anything, your theoretical plane would be going 1 meter per second after 1 second of time, and speed would be 2 meters per second after 2 seconds of time, and so on.

When you measure the wattage of your power system, this is exactly what it means... so for example, my Brio draws 250 watts, and it weighs about 2 kilograms (4.4 pounds). This means that if all the energy put out by the battery were used to accelerate the plane, it would have acceleration of 125 meters per second per second. Obviously, the Brio doesn't go that fast... so there is some huge losses going on there.

The losses are due to the efficiency of the motor (about 85%), giving approximately 40 watts lost as heat in the motor. If you've ever put your hand on a 40 watt light bulb, you know that's a lot of heat. The rest of the losses are due to the drag of the plane and the propeller itself. Propellers are not very efficient - anywhere from 10% to 50% loss. On small planes at normal speeds it's closer to 50% losses. So now my Brio has about 100 watts remaining, and that is being turned into kinetic energy...

However, it is not all turned into forward momentum... some of it is lost to drag, and some of it is turned into lift by the wing. An airplane must consistently overcome the force of gravity time its own weight. That is 19.8 Newtons for my 2-kilo plane... every second - meaning I need 20 watts worth of lift just to stay in the air. Wings are horribly inefficient, so I'm wasting a ton of energy just turning forward momentum into lift.

It was a long journey, but here's where the propeller comes in...

A propeller has two measurements... diameter and pitch. Diameter is obviously just the length of the thing. Pitch is a little more complicated... it is defined as the linear distance that the propeller would move if it was turned one revolution in a thick fluid (air is not a thick fluid). A 10x6 prop will move 6 inches forward in one revolution, but a 50x6 prop will also move 6 inches forward in one revolution, but it will use a lot more energy - but it will use it more efficiently.

Thrust is the acceleration force of the propeller - it is the amount of Newtons that the prop creates. Multiply that by a distance, and you have Newtons times meters, and remember, that is the definition of a Joule. Multiply that by a unit of time, and you have Joules times seconds, which was the definition of a Watt. So, to bring that full circle, the Watts used by the prop are directly related to the thrust it creates, bigger diameter props use more Watts, have more Newtons, and we call that more thrust. The 50x6 propeller is going to have more of that, even though the pitch is still the same as the 10x6.

I know that was a convoluted explanation, and for those who don't want to know why things are the way they are, it's simple enough to say what Sir Raleigh said... more diameter, more thrust, even if the pitch is the same.

Pitch is indirectly related to speed, but it's fairly complicated. If the RPM is kept the same, more pitch will result in both more thrust and more speed, because the speed if there was no slipping or drag or anything, would be the pitch times the RPM... it would be 6 inches times the number of rotations, divided by a time period, and a distance divided by a time period is the definition of speed. It is not that simple though, and more pitch will only create more speed if you can keep the RPM the same. Due to losses from efficiency problems and drag and lift and so on, there is never a direct relationship between pitch and speed. Speed comes from thrust, so if you want the plane to go faster, you need more thrust (more Newtons of force). In practice, what we see is that increasing the pitch gives more force, and we realize an increase in speed, but it is not that simple. You only get more speed (which requires more thrust) when you can keep the RPM the same. With electric motors, the RPM will drop a little when you increase the pitch, but not by much, so we do see more speed.

I know that is more than what you wanted to hear, but these things are never simple. I just hope that if you could stand to read that all, you'll understand more why we have to measure things. It is not a guarantee that increasing the pitch will give more speed, but if you increase the diameter, you will have more energy usage, and that always translates to more power, more speed, more everything... but it also means you may overwork the motor.

SIG Riser

This is my SIG Riser - it was fun to build and I covered it myself. It is a 2 meter glider, but I'm going to put a motor on the front. This is the first plane that I built and covered myself, and I think it came out pretty good!