Starting from this point on, we can see what physical changes we can make to our frame/layout to optimize our speed. Also, we will see why a heavier balanced quad can be faster (top speed and acceleration) than a lighter unbalanced quad.
Update October 28, 2017:
Although the above statement is still true, I falsely claimed that CG/CT alignment in the z-axis (in the direction of gravity) also mattered. This isn’t the case (thanks to Peter Gunnarson for the insight!). This is commonly known as the Rocket Pendulum Fallacy. I also came across this master thesis paper that helped to clarify the subject:
Although I removed any misleading info, I will have to update the page and illustrations when I get a chance (I say that a lot)…
Center of Thrust and CG:
The Gravity of the Situation
To ensure that our quad is able to use all available power of the motors, it’s important to have the CG as close to the center of thrust (I’ll call it CT) as possible. The technical way to put it: any difference in the x, or y axis between the two centers creates a moment which is a force that creates a torque. Whenever a moment is created, something needs to offset it to keep things stable.
A Dumb Example
Think of a dumb bell, which is normally symmetrical, and your grip is at the center of the handle which is pretty much at the center of gravity. Now take some of the weight off of one side and it will cause your wrist to twist. To keep the handle level, the muscles on one side of your forearm have to work harder than the other side. The same thing goes for a quad. To avoid this twisting, some motors will be working harder than others.
The idea here is somewhat hard to follow when it comes to quads, but it’s one that is frequently overlooked, especially when it comes to battery placement.
Keep it Centered
Looking from the top, we’ll call front to back the Y (or roll) axis, and left to right the X (or pitch) axis. To find the center of thrust in this view, draw an imaginary line from the upper right motor to the lower left, and another line from the upper left to lower right. Where the lines cross is where the CT is.
Looking from the side, draw an imaginary line from the base of the front propeller to the base of the back propeller. The midpoint of that line is the CT for the Z-Y plane.
In this case, the torque is working against the right side motors which will have to work harder than the left motors. How does this affect speed? Let’s say the right motors are working 20% more than the left motors. Once the right motors reach 100%, the leftt motors will only be at 80%. Doing the math, we see the quad is only able to utilize 90% of its total power: (80%+100%)/2 = 90%. This is the reason why a heavier balanced quad can be faster than a lighter unbalanced quad. In other words, adding weight to your quad (to balance it) can make your quad faster. Luckily, for most of us, our battery is an easy way to keep things balanced and is normally already placed in the center of the X-Y plane. If anybody has an issue with this, let me know and I will show the calculations.
Lining up the CG and CT will give you a better top speed, but it will also give you a more balanced flying experience in terms of responsiveness to movements (more specifically, angular acceleration). As we saw above, if we have a torque that favors right roll, rolling right will occur faster than rolling left (since the torque will favor angular acceleration to the right). However, I am assuming this will only be the case when the PID rates, etc. are set to max values. Also, I am unsure of how much of a time difference there would be between the two and if it’s even humanly detectable.
Balance the Power With Blackbox
Blackbox is a great tool to use when it comes to balance (and in my case, motor alignment!). When checking for balance, 2 easy tests should be done in acro mode:
- Do at least a 2 second climb. Start from a hover and then pin the throttle to 100%. This will tell you your balance in the X-Y plane (top view).
View the blackbox results and see if any motors are working harder than the rest. if so, adjust the battery (easiest to do) position away from this motor or motors.
Other Balance Factors:
- Cross Section: Another factor that can cause unequal power is asymmetry of the quads cross section. For example, having one of those large “saucer” type vtx antennas hanging to one side of the quad will cause greater air resistance on that side. Keep the antenna centered, or better yet, use a naked antenna.
- Motor Alignment: If weight is centered and the cross section is symmetric, then motor alignment is the next likely cause in unbalanced power (when I say motor alignment, I mean that all motors should be perpendicular to the frame).
As of this writing, I am still finalizing the SK1. Today I did a couple WOT climbs to get some blackbox data for tuning and balance:
Just by looking at the motor graphic in the upper left corner, you can see that motors 2 and 3 are working harder than 1 and 4. This means something is causing the quad to turn counter clockwise and motors 2 and 3 will always have to work harder in order to keep the quad going into a counter clockwise spiral. Once I took a closer look at the motors, it was obvious. The motor 2 pylon was bent outwards which was causing a counter clockwise movement.
Balance by Inversion
I have found one of the best ways to get the CG and CT in better alignment is to strap the battery to the bottom of the frame and to invert the front motors. If the rear motors are inverted, I would imagine that the propwash from the front motors would affect the rear props.
Center of Pressure:
Since the center of pressure on a quadcopter is constantly changing, this is not really worth looking into. This mainly helps with aircraft in which the airflow is travelling in (generally) the same direction relative to the surface.
As mentioned briefly above, the next part of this series will introduce the drag equation to gain a better understanding of how to reduce drag.