# Do quadcopter propellers break the sound barrier?

I recently bought a quadcopter and noticed every time I fly it there is this weird buzzing noise. I have heard this noise on other quadcopters around the same size as mine(4in by 4in). On an airliner turbofan engine you can sometimes hear this weird buzzing sound from the engines, which this sound is the n1 fan spinning faster than the speed of sound and resulting in this loud buzzing sound. So is my little quadcopter motors going supersonic or is it something else?Source:(dynomodels.co.uk)

• I cant find good tags for this question. If there is a good tag for this question besides supersonic than please add it to the question thanks. – Ethan Oct 20 '15 at 18:45
• @mins does that mean length of the blade. If is that I measured 0.5in in lenght of each of the 16 blades. – Ethan Oct 20 '15 at 21:25
• @Ethan diameter means twice the radius (i.e. the width of the entire circle through which the blades spin.) If you have an even number of blades on the prop, you can measure this as the distance from one blade tip to the tip of the opposite blade. Otherwise, you can measure it as 2 x the distance from the center of the drop to a blade tip. – reirab Oct 20 '15 at 21:28
• The "buzz saw" noise from jet engine fans is created by high vibration amplitudes in the blades, not from supersonic airflow. A common cause is aerodynamic flutter creating a feedback loop which excites the vibration modes. This doesn't necessarily occur at the maximum N1 speed. Eliminating these problems can be challenging - for example I was once involved with a situation where less than 1 part in 1 million of the total power output of the engine was "getting into the wrong place" and generating the nasty noise. – alephzero Oct 20 '15 at 22:00
• Is that your actual quadcopter on the picture? – mins Oct 21 '15 at 0:59

Almost certainly not. Given the comments specifying a $0.5$ inch radius (blade length,) that means the circumference of the path of the blade tips would then be

$$2 \pi \cdot 0.5 \, \text{inches} \approx 3.1415 \, \text{inches} \approx 0.2618 \,\text{feet}$$

To get to the speed of sound (which is approximately $1,126 \,\frac{\text{ft}}{\text{s}}$ at sea level,) that means you'd need to have the fan spinning at

$$\frac{1,126}{0.2618} \approx 4,301 \,\text{Hz} \approx 258,060 \,\text{rpm}$$

Needless to say, that's not happening unless you have one seriously expensive quadcopter.

The buzzing you hear is probably either the frequency at which the motor is spinning or, perhaps, the frequency of some oscillation of the fan blades. Most likely, though, it's just the frequency of the motor/fan.

• Each rotor has its own motor, so each prop will rotate a close-to but not necessary the same rate. This may produce a beat note which could be the audible artifact the OP is noticing. – Digital Trauma Oct 20 '15 at 22:01
• To give an idea of what 258,000 RPM is: the electrons in the Large Hadron collider are doing about 666,666 RPM (0.00 009 seconds per rotation). – Nzall Oct 20 '15 at 22:11
• @NateKerkhofs: Isn't that mostly just a function of the LHC's size? I'd expect smaller accelerators to have much higher RPMs, since the track is so much shorter. – user2357112 Oct 21 '15 at 0:25
• Arg. That should say "accelerate electrons," not "accelerate electronics." One would hope that they don't accelerate their electronics. :) – reirab Oct 21 '15 at 1:29
• @mins Kv, not kV - confusing constant – user2813274 Oct 22 '15 at 20:23

It's possible, but I would say unlikely. Supersonic propeller tips really mess with efficiency.

The tip speed of many aircraft propellers is close to supersonic, and if not properly controlled can exceed the speed of sound, but most models don't get up that fast (and your blade tips don't have to be supersonic to be annoyingly loud).

There is a formula to figure out the speed of the blade tip. For your quadcopter multiply the blade RPM by the diameter (in inches), and multiply that by 0.00426

$TipSpeed = RPM * Diameter * 0.00426$

The result is in Feet per Second.
Anything over 1125 feet per second (343 meters per second) and your tips are supersonic.
Anything over about 650 feet per second (200 meters per second) and the propeller is probably really loud and annoying.

• Can you provide this equation in meters too? Thanks! – Gabriel Brito Oct 20 '15 at 21:08
• @Ethan With a 0.5" blade length, that's extremely unlikely. See my answer. I've updated it to reflect the 0.5" blade length you mentioned recently in a comment. – reirab Oct 20 '15 at 21:37
• What is this magic number, 0.00426? – Brad Oct 20 '15 at 23:48
• @Brad: It's pi divided by 60 and 12. Required to convert rpm to rps, then in to ft. In meters: 3.14 * d * rpm / 60. – mins Oct 21 '15 at 0:23
• @mins Well, it's 3.14 * d * rpm / 60 regardless of whether you're using meters, feet, furlongs, or megaparsecs. :) – reirab Oct 21 '15 at 0:52

It is entirely likely that your quadricopter, based on the picture, is not even in the range of expensive supersonic models. They do exist, but they're mostly modded or privately made. The buzzing, if it is underlying the whine of the fan, is probably either the motor itself or some other internal friction. Fortunately, this isn't a huge problem. It is, however, annoying. On the other hand, if it is the whine of the rotors, which you described as a "buzz", that's just the way they sound at that size and type, evidenced by your knowledge of the sounds of similar copters. But a model of that size and apparent cost could never reach the sound barrier. There would be something on the package about that, because producers like bragging about speed.

Also note the shape and size of your average turbofan.