I recently presented my work on the real-time sound synthesis of a propeller at the 12th International Audio Mostly Conference in London. This sound effect is a continuation of my research into aeroacoustic sounds generated by physical models; an extension of my previous work on the Aeolian harp, sword sounds and Aeolian tones.
A demo video of the propeller model attached to an aircraft object in unity is given here. I use the Unity Doppler effect which I have since discovered is not the best and adds a high-pitched artefact but you’ll get the idea! The propeller physical model was implemented in Pure Data and transferred to Unity using the Heavy compiler.
So, when I was looking for an indication of the different sound sources in a propeller sound I found an excellent paper by JE Marte and DW Kurtz. (A review of aerodynamic noise from propellers, rotors, and lift fans. Jet Propulsion Laboratory, California Institute of Technology, 1970) This paper provides a breakdown of the different sound sources, replicated for you here.
The sounds are split into periodic and broadband groups. In the periodic sounds, there are rotational sounds associated with the forces on the blade and interaction and distortion effects. The first rotational sound is the Loading sounds. These are associated with the thrust and torque of each propeller blade.
To picture these forces, imagine you are sitting on an aircraft wing, looking down the span, travelling at a fixed speed and uniform air flowing over the aerofoil. From your point of view the wing will have a lift force associated with it and a drag force. Now if we change the aircraft wing to a propeller blade with similar profile to an aerofoil, spinning at a set RPM. If you are sitting at a point on the blade the thrust and torque will be constant at the point you are sat.
Now stepping off the propeller blade and examining the disk of rotation the thrust and torque forces will appear as pulses at the blade passing frequency. For example, a propeller with 2 blades, rotating at 2400 RPM will have a blade passing frequency of 80Hz. A similar propeller with 4 blades, rotating at the same RPM will have a blade passing frequency of 160Hz.
Thickness noise is the sound generated as the blade moves the air aside when passing. This sound is found to be small when blades are moving at the speed of sound, 343 m/s, (known as a speed of Mach 1), and is not considered in our model.
Interaction and distortion effects are associated with helicopter rotors and lift fans. Because these have horizontally rotating blades an effect called blade slap occurs, where the rotating blade passes through the vortices shed by the previous blade causing a large slapping sound. Horizontal blades also have AM and FM modulated signals related with them as well as other effects. Since we are looking at propellers that spin mostly vertically, we have omitted these effects.
The broadband sounds of the propeller are closely related to the Aeolian tone models I have spoken about previously. The vortex sounds are from the vortex shedding, identical to out sword model. This difference in this case is that a propeller has a set shape which more like an aerofoil than a cylinder.
In the Aeolian tone paper, published at AES, LA, 2016, it was found that for a cylinder the frequency can be determined by an equation defined by Strouhal. The ratio of the diameter, frequency and airspeed are related by the Strouhal number, found for a cylinder to be approximately 0.2. In the paper D Brown and JB Ollerhead, Propeller noise at low tip speeds. Technical report, DTIC Document, 1971, a Strouhal number of 0.85 was found for propellers. This was used in our model, along with the chord length of the propeller instead of the diameter.
We also include the wake sound in the Aeolian tone model which is similar to the turbulence sounds. These are only noticeable at high speeds.
The paper by Martz et. al. outlines a procedure by Hamilton Standard, a propeller manufacturer, for predicting the far field loading sounds. Along with the RPM, number of blades, distance, azimuth angle we need the blade diameter, and engine power. We first decided which aircraft we were going to model. This was determined by the fact that we wanted to carry out a perceptual test and had a limited number of clips of known aircraft.
We settled on a Hercules C130, Boeing B17 Flying Fortress, Tiger Moth, Yak-52, Cessna 340 and a P51 Mustang. The internet was searched for details like blade size, blade profile (to calculate chord lengths along the span of the blade), engine power, top speed and maximum RPM. This gave enough information for the models to be created in pure data and the sound effect to be as realistic as possible.
This enables us to calculate the loading sounds and broadband vortex sounds, adding in a Doppler effect for realism. What was missing is an engine sound – the aeroacoustic sounds will not happen in isolation in our model. To rectify this a model from Andy Farnell’s Designing Sound was modified to act as our engine sound.
A copy of the pure data software can be downloaded from this site, https://code.soundsoftware.ac.uk/hg/propeller-model. We performed listening tests on all the models, comparing them with an alternative synthesis model (SMS) and the real recordings we had. The tests highlighted that the real sounds are still the most plausible but our model performed as well as the alternative synthesis method. This is a great result considering the alternative method starts with a real recording of a propeller, analyses it and re-synthesizes it. Our model starts with real world physical parameters like the blade profile, engine power, distance and azimuth angles to produce the sound effect.
An example of the propeller sound effect is mixed into this famous scene from North by Northwest. As you can hear the effect still has some way to go to be as good as the original but this physical model is the first step in incorporating fluid dynamics of a propeller into the synthesis process.
From the editor: Check out all Rod’s videos at https://www.youtube.com/channel/UCIB4yxyZcndt06quMulIpsQ
A copy the paper published at Audio Mostly 2017 can be found here >> Propeller_AuthorsVersion
Synthesising the Aeolian harp is part of a project into synthesising sounds that fall into a class called aeroacoustics. The synthesis model operates in real-time and is based on the physics that generate the sounds in nature.
The Aeolian harp is an instrument that is played by the wind. It is believed to date back to ancient Greece; legend states that King David hung a harp in the tree to hear it being played by the wind. They became popular in Europe in the romantic period and Aeolian harps can be designed as garden ornaments, part of sculptures or large scale sound installations.
As air flows past a cylinder vortices are shed at a frequency that is proportional to the cylinder diameter and speed of the air. This has been discussed in the previous blog entry on Aeolian tones. We now think of the cylinders as a string, like that of a harp, guitar, violin, etc. When a string of one of these instruments is plucked it vibrates at it’s natural frequency. The natural frequency is proportional to the tension, length and mass of the string.
Instead of a pluck or a bow exciting a string, in an Aeolian harp it is the vortex shedding that stimulates the strings. When the frequency of the vortex shedding is in the region of the natural vibration frequency of the string, or one of it’s harmonics, a phenomenon known as lock-in occurs. While in lock-in the string starts to vibrate at the relevant harmonic frequency. For a range of airspeed the string vibration is the dominant factor that dictates the frequency of the vortex shedding; changing the air speed does not change the frequency of vortex shedding, hence the process is locked-in.
As with the Aeolian tone model we calculate the frequency of vortex shedding for a given string dimensions and airspeed. We also calculate the fundamental natural vibrational frequency and harmonics of a string given its properties.
There is a specific area of airspeed that leads to string vibration and vortex shedding locking in. This is calculated and the specific frequencies for the FM acoustic signal generated. There is a hysteresis effect on the vibration amplitude based on the increase and decrease of the airspeed which is also implemented.
A used interface is provided that allows a user to select up to 13 strings, adjusting their length, diameter, tension, mass and the amount of damping (which reduces the vibration effects as the harmonic number increases). This interface is shown below which includes presets of an number of different string and wind configurations.
When we watch Game of Thrones or play the latest Assassin’s Creed the sound effect added to a sword being swung adds realism, drama and overall excitement to our viewing experience.
There are a number of methods for producing sword sound effects, from filtering white noise with a bandpass filter to solving the fundamental equations for fluid dynamics using finite volume methods. One method investigated by the Audio Engineering research team at QMUL was to find semi-empirical equations used in the Aeroacoustic community as an alternative to solving the full Navier Stokes equations. Running in real-time these provide computationally efficient methods of achieving accurate results – we can model any sword, swung at any speed and even adjust the model to replicate the sound of a baseball bat or golf club!
The starting point for these sound effect models is that of the Aeolian tone, (see previous blog entry – https://intelligentsoundengineering.wordpress.com/2016/05/19/real-time-synthesis-of-an-aeolian-tone/). The Aeolian tone is the sound generated as air flows around an object, in the case of our model, a cylinder. In the previous blog we describe the creation of a sound synthesis model for the Aeolian tone, including a link to a demo version of the model.
For a sword we take a number of the Aeolian tone models and place them on a virtual sword at different place settings. This is shown below:
Each Aeolian tone model is called a compact source. It can be seen that more are placed at the tip of the sword rather than the hilt. This is because the acoustic intensity is far higher for faster moving sources. There are 6 sources placed at the tip, positioned at a distance of 7 x the sword diameter. This distance is based on when the aerodynamic effects become de-correlated, although a simplification. One source is placed at the hilt and the final source equidistant between the last tip source and the hilt.
The complete model is presented in a GUI as shown below:
Referring to the both previous figures, it can be seen that the user is able to move the observer position within a 3D space. The thickness of the blade can be set at the tip and the hilt as well as the length of the blade. It is then linearly interpolated over the blade length so that each source diameter can be calculated.
The azimuth and elevation of the sword pre and post swing can be set. The strike position is fixed to an azimuth of 180 degrees and this is the point where the sword reaches its maximum speed. The user sets the top speed of the tip from the GUI. The Prime button makes sure all the variables are pushed through into the correct places in equations and the Go button triggers the swing.
It can be seen that there are 4 presets. Model 1 is a thin fencing type sword and Model 2 is a thicker sword. To test versatility of the model we decided to try and model a golf club. The preset PGA will set the model to implement this. The golf club model involves making the diameter of the source at the tip much larger, to represent the striking face of a golf club. It was found that those unfamiliar with golf did not identify the sound immediately so a simple golf ball strike sound is synthesised as the club reaches top speed.
To test versatility further, we created a model to replicate the sound of a baseball bat; preset MLB. This is exactly the same model as the sword with the dimensions just adjusted to the length of a bat plus the tip and hilt thickness. A video with all the preset sounds is given below. This includes two sounds created by a model with reduced physics, LoQ1 & LoQ2. These were created to investigate if there is any difference in perception.
The demo model was connected to the animation of a knight character in the Unity game engine. The speed of the sword is directly mapped from the animation to the sound effect model and the model observer position set to the camera position. A video of the result is given below: