This isn’t a joke.

Since hitting crazy speeds with the VX1 and VXR-190, I have been doing a bit of thinking and observing. How were those builds able to hit 154.5 and 165.8 mph on a 5s lipo with 2450kv motors while the fastest quad on a 6s with 2750kv motors “only” managed to hit 145mph? Of course the VX1 and VXR-190 are much more aerodynamic, but something told me that there is something else going on to cause such a huge discrepancy. I will admit that hitting this speed was a shock, but careful number crunching and observing has revealed how it was possible.

The Sound Barrier

I am not sure how many in the multirotor community have done this, or even realize this, but it’s true: we are knocking on the sound barrier. Specifically, the helical tip speed of our props are going transonic. Transonic speeds (between mach 0.8 and 1.2) has traditionally been called the sound barrier due to the abrupt differences in the nature of subsonic air flow vs. supersonic air flow. When an object reaches speeds of approximately mach 0.8, localized regions of airflow will actually hit mach 1.0. This is due to the fact that the speed of the air flow around an object varies at different points on the object (example: air moves over the top of an airplane wing faster than the air below the wing).

So what?

They call it the sound barrier for a reason. Once transonic speeds are hit, the pressure differences between the super and subsonic regions start wreaking havoc and don’t play well together. This leads to vibration, distortion, and a skyrocketing drag coefficient which in turn requires a skyrocketing amount of torque. To sum it up: transonic flight not only requires loads of power, it is extremely unstable. This is EXACTLY what happened to WWII fighter planes and why supersonic flight was once thought to be unbreakable. However, all air flow is supersonic once an object is over (approximately) mach 1.2. From here, things begin to stabilize and the drag coefficient drops.

Helical tip speed

Example:

Helical tip speed = (prop tip velocity² + quadcopter velocity²)^1/2

If we observe during a speed run using a 5s lipo, the RPM reaches 31,500 and the quad is at 150 mph using 5 inch props:

Prop tip velocity = 31,500 RPM/1 minute x 5 inches x Pi x 60 minutes/1 hour x 1 ft/12 inches x 1 mile/5280 ft = 468.6 mph

Helical tip speed = ((468.6 mph)² + (150 mph)²)^1/2 = 492 mph

To figure our mach number: 492mph/767 mph = mach 0.64

Propellers and transonic speeds

Why don’t we just chuck on another cell or 2, add more kv’s, and blow through the barrier? As noted above, the further out from the center of the prop, the faster its speed (angular velocity). The problem with this is that the propeller will always be in a state of transonic speed (unless, of course, the object it is attached to is going supersonic). The tip of the prop can hit supersonic speeds at relatively low RPMs compared to the root of the prop. So basically, once a propeller hits transonic speeds, we are doing no favors by having them go any faster. As a side note, the first time we encountered problems associated with the sound barrier were on airplane propellers (a propeller driven airplane cannot go supersonic since the prop cannot reach supersonic speeds). Here is a great link about the history of the sound barrier:

https://history.nasa.gov/SP-4219/Chapter3.html

Too Much Power

Of course we want the most amount of RPMs possible for speed. Of course, the easiest way to get more RPMs is to increase voltage (volts x motor kv = RPMs). Now we know that we can have too many RPMs. With a 2750kv motor and a 5 inch prop, we are already hitting mach 1 at 18.65 volts! Of course that is assuming the prop is fully unloaded. In reality we will have some RPM loss. However, we still haven’t taken into account the speed of the quad which adds to the problem.

The Significance

What does it all mean? Basically this means we are limited (for a given prop size) to a maximum RPM. This is extremely significant since this will enable us to mathematically figure out how much motor kv and lipo cells we need to obtain our maximum RPM. Anything more will only serve to decrease efficiency and overload our electronics – this is why it has been observed that adding more cells and motor kv has resulted in very little if any gain in speed.

Conclusion

It appears that we have more than enough power to spin our props to their physical limits which leaves us with 2 factors left that affects speed: prop pitch and drag. However, prop pitch is relatively limited too as most prop manufacturers only produce props within reason (if pitch is too high, the prop will stall at low RPM and you won’t be able to take off). Now we are only left with drag. Once optimum motor kv, prop diameter, and prop pitch are determined, I believe that the quad with the lowest drag coefficient will end up being the fastest. I’m hoping the VXV project will help solidify this conclusion.