Monday, March 23, 2015

Building a Better Multirotor - Propeller Selection

Building something that flies? Start by selecting your props

Let me tell you why. On any aircraft without fixed wings, the propellers are what hold the vehicle in the air. If you wanted to build a plane instead, wouldn't you be picking an airframe that met your needs? High wing, low wing, low profile symmetrical wings, or thick flat bottomed wings? What kind of flying do you want to do? You pick the airplane with the wings to match. So, what kind of flying do you want to do with your multirotor? Let me explain the different wings, and why you'd pick them.

The Basics

To understand what props you want, you need to understand the basics of flight. How does any helicopter stay in the air? A helicopter works just like an airplane. It redirects air, creating a change in momentum of the air mass.

or Force = mass * acceleration. Notice that there are two variables here, mass and acceleration. Generally, your multirotor doesn't change mass while flying. So, in order to hover in the air we can easily calculate the force needed.

Force needed to fly = mass of multirotor * gravitational acceleration. Now we can look at the mass of air, and the acceleration needed to create to force that keeps the multirotor in the air. Guess what? We can control both of these variables. We can choose a large mass of air and accelerate it a little, or we can choose a small mass of air and accelerate it a large amount. Let me summarize this in terms of propellers.

A large propeller spinning slowly will create the same force as a small propeller spin very fast.

Getting a little more complicated

Now that you understand the basics, let us go to the next step, and understand some of the implications of having a large prop spinning slowly, or a small prop spinning fast.

Power Requirements

Let's pick a large propeller, and spin it real slow. How about this as an example?

Okay, now how about a small propeller spinning very fast.

Do you notice any difference in those aircraft? One is powered by a guy on a bike frame. The other has a monstrous jet engine. Both fly. In fact, once you boil down the math of flight, you can generate an equation that directly relates the effective size of the propellers (disc area) to the amount of power required to produce the force required to keep the aircraft in the air. Why is this? Doubling the acceleration of an object, keeping the mass equal, requires four times the energy. So, back to F=ma,

if we cut the mass in half and double the acceleration, the force stays the same. Even though we've kept the forces (F) equal, the second equation requires double the energy. Why? Look at the equation for kinetic energy.

Here we start with our initial kinetic energy E_k0 in terms of mass and velocity. Let's rewrite this in change of energy in terms of change of velocity.

For this example, let's double the velocity and compare the change in kinetic energy

Now substitute that into our previous equation and rearrange things...

Wow! A 2x change in velocity increases the energy by 4x!

Do you recognize what a change in velocity is? Change in velocity is acceleration. So, doubling our acceleration in F=ma means that we will require more energy to keep the same force. More energy in a given time means more power. More acceleration means more power to create the same amount of force. Now that we know this, we can relate our math to what this means in term of propellers. A larger propeller moves more air mass, requiring smaller acceleration, therefor requiring less power. Let me emphasize this.

Power required to fly is proportional to the size of prop

Now, let's flip that around a little. If we want to be able to carry a certain amount of weight, such as, say, a camera, you need less power if you simply use larger propellers. Here is an even larger realization.

Given the same battery capacity, larger propellers will yield longer flight times.

Yup. That simple. Do you want 1 hour flight times? Pick really large propellers and spin them incredibly slow. Want to move bricks from point A to B? Pick really large props and spin them slow.

Efficiency

You just learned that spinning a large prop slowly means longer flight times based solely on the difference in required energy. Guess what? A large propeller spinning slowly is also more efficient than a small prop spinning fast. Why? Have you heard of the sound barrier? As the tip of the propeller approaches the speed of sound, the resistance of air increases. The increase in resistance isn't just a straight line, either. Look at the equation for drag

Do you notice that v2 term? Have you seen that before? Drag force quadruples when you double the velocity. More drag, means more energy wasted, more energy not contributing to lift. Again, big prop spinning slowly will be more efficient than a small prop spinning fast creating the same amount of lift.

Speed

We've just learned that a big slow prop gives longer flight times and more lift. Why would we ever want a small prop spinning insanely fast? If you think of a spinning propeller travelling through the air, the tips would draw a screw pattern. Propellers have a radius, and a pitch. The pitch is usually given in distance the propeller would travel after a single rotation of the propeller. If you want to travel more distance, you either need more pitch or to spin the propeller more times in the same amount of time. There are limits to how steep we can make the pitch. The best compromise is to spin a small propeller faster. Simply put, if you want to fly fast, you need to spin your props fast. There is no way around it. You can't have your cake and eat it too. Real life always has trade offs.

Multirotors and helicopters have another problem. Forward flight. When you move your aircraft in a direction, a portion of the lift goes toward accelerating the aircraft in that direction. Say your prop pitch and prop RPM says that you push air at 50mph. You can't direct all that airflow into forward flight. Only a portion of it goes toward forward flight. Some of it has to be used for lift. Even if you can push air at 50mph, your aircraft will only go a portion of that speed.

One more thing... Multi-blade props

Why do multirotor aircraft often have propellers with 3 or more blades? We know that moving more air mass means more lifting power, right? Adding more blades to a propeller without changing the pitch or diameter means that you can move more air in the same amount of space. Now, there are diminishing returns. Adding 100 blades won't give you 100x more lift. However, a multiblade prop will act like a larger 2-blade prop in a smaller amount of space. Just to be clear, though, the equivalent 2-blade propeller will be more efficient.

Conclusions

  • Large Slow-fly propellers with low KV motors will give you long flight times and more carrying capacity
  • Small sport propellers with high KV motors will allow you to fly fast, but require more power and cut flight times
  • Multi-blade propellers can give you more lift in a smaller area without increasing power requirements geometrically

Ok, any person who flies planes is saying, "Duh. I already knew this." However, sometimes we think that helicopters work on the principles of magic and that the same rules don't apply. The same rules do apply. Hopefully next time you build a multirotor you will use this knowledge to build one that meets all your requirements.