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.

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, y, or z 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. Most quads have their CG in line with the CT in this plane.

C Top 0 CT

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.

C Side 0 CT
Since the battery sits inside this frame, the CT and CG are aligned

Most racing quads (that I’ve seen) have the battery below this CT point which (depending on the layout) puts the CG below the CT. As long as the CG is aligned with the X and Y axes, this will work fine while hovering. Now to better understand the effect of the CG being above the CT, think of a vertical line drawn through the CG and imagine that this line will always be vertical with respect to the earth; it will pivot at the CG as the quad pitches.

Here Comes the Pitch

While hovering, the line passes through the CT. Now when the quad pitches forward, our vertical line no longer passes through the CT. This creates a moment (torque). If you draw a horizontal line from the CT to the pivoting vertical line, this distance is the moment arm which gets longer as the pitch angle increases. In short, torque is being created around the X (pitch) axis.

X Side 45 CT
The horizontal blue line is the moment arm. The length of this arm times the weight of the quad generates a torque relative to the center of thrust.

In this case, the torque is working against the back motors which will have to work harder than the front motors. So whenever the quad is pitched forward, the flight controller will always send a higher throttle signal to the back motors to keep the quad stable. For example, We’ll say the back motors are working 20% more than the front motors. Once the back motors reach 100%, the front 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. If anybody has an issue with this, let me know and I will show the calculations.

Other Benefits

Lining up the CG and CT will give you a better top speed, but it will also give you a more balaced flying experience in terms of responsiveness to movements. As we saw above, if we have a torque that favors backward pitch, pitching backward will occur faster than pitching forward (since the torque will be working against forwards pitch). 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.Once the X-Y plane is balanced, do the next test:

  • Do a speed run. For at least 2 seconds of the run, make sure that the altitude stays relatively the same and that there is no yaw or roll input.

Once again, view the blackbox data. If the front motors are working harder, then the CG is too high. If it’s the rear motors working harder, the CG is too low.

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.

Example:

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:

blackbox-yaw

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:

Work in Progress…

Moving On

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.

Part 5: Drag

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