We describe a method for the construction of a supersonic ping-pong cannon (SSPPC) along with optical diagnostic techniques for the measurement of ball velocities and the characterization of propagating shock waves during the firing of the cannon.
The traditional ping-pong cannon (PPC) is an educational apparatus that launches a ping-pong ball down an evacuated pipe to nearly sonic speeds using atmospheric pressure alone. The SSPPC, an augmented version of the PPC, achieves supersonic speeds by accelerating the ball with greater than atmospheric pressure. We provide instructions for the construction and utilization of an optimized PPC and SSPPC.
Optical diagnostics are implemented for the purpose of investigating the cannon dynamics. A HeNe laser that is sent through two acrylic windows near the exit of the pipe is terminated on a photoreceiver sensor. A microprocessor measures the time that the beam is obstructed by the ping-pong ball to automatically calculate the ball’s velocity. The results are immediately presented on an LCD display.
An optical knife-edge setup provides a highly sensitive means of detecting shock waves by cutting off a fraction of the HeNe beam at the sensor. Shock waves cause refraction-induced deflections of the beam, which are observed as small voltage spikes in the electrical signal from the photoreceiver.
The methods presented are highly reproducible and offer the opportunity for further investigation in a laboratory setting.
The PPC is a popular physics demonstration used to show the immense air pressure to which people are continually exposed1,2,3,4,5. The demonstration involves the placement of a ping-pong ball in a section of pipe that has an inner diameter that is approximately equal to the diameter of the ball. The pipe is sealed off on each end with tape and evacuated to an internal pressure of less than 2 Torr. The tape on one end of the pipe is punctured, which allows air to enter the cannon and causes the ball to experience peak accelerations of approximately 5,000 g's. The ball, which is accelerated by atmospheric pressure alone, exits the cannon at a speed of approximately 300 m/s after traveling 2 m.
Although the PPC is commonly operated as a simple demonstration of atmospheric pressure, it is also an apparatus that exhibits complex compressible flow physics, which has resulted in numerous open-ended student projects. The dynamics of the ball are influenced by secondary factors such as wall friction, the leakage of air around the ball, and the formation of shock waves by the accelerating ball. The substantial acceleration of the ball introduces a large-amplitude compression wave that travels down the tube in front of the ball. These compressions travel faster than the local sound speed, resulting in a steepening of the compression wave and the eventual formation of a shock wave6. Previous work has studied the rapid buildup of pressure at the exit of the tube due to the reflections of the shock wave between the ball and the taped exit of the tube and the resulting detachment of the tape prior to the exit of the ball2. High-speed video using a single-mirror schlieren imaging technique has revealed the response of the tape to the reflecting shock waves and the eventual detachment of the tape at the exit of the PPC7,8 (Video 1). Thus, the PPC serves as both a simple demonstration of air pressure that intrigues audiences of all ages and as a device exhibiting complex fluid physics, which can be studied in great detail in a laboratory setting.
With the standard PPC, the ping-pong ball speeds are limited by the speed of sound. This basic version of the PPC is covered in the scope of this paper, along with a modified cannon used to boost the ball to supersonic speeds. In previous work by French et al., supersonic ping-pong ball speeds have been achieved by utilizing pressure-driven flow through a converging-diverging nozzle9,10,11. The SSPPC presented here utilizes a pressurized (driver) pipe to provide a larger pressure differential on the ping-pong ball than is provided by atmospheric pressure alone. A thin polyester diaphragm is utilized to separate the driver pipe from the evacuated (driven) pipe containing the ball. This diaphragm ruptures under sufficient gage pressure (generally 5-70 psi, depending on the diaphragm thickness), thus accelerating the ping-pong ball to speeds up to Mach 1.4. The supersonic ping-pong ball produces a standing shock wave, as can be seen using high-speed shadowgraph imaging techniques7,12 (Video 2).
A low-power (class II) HeNe laser is used to carry out optical diagnostic studies on the performance of the cannon. The HeNe laser beam is split into two paths, with one path traversing through a set of acrylic windows near the exit of the cannon and the second path traversing just past the exit of the cannon. Each path terminates on a photoreceiver, and the signal is displayed on a dual-channel oscilloscope. The oscilloscope trace recorded during the firing of the cannon reveals information about both the speed of the accelerated ping-pong ball and the compressible flow and shock waves that precede the exit of the ball from the cannon. The speed of the 40 mm diameter ping-pong ball at each beam location is directly related to the time the ball blocks the beam. A sensitive "knife-edge" shock detection setup is achieved by covering half of the detector with a piece of black electrical tape and positioning the edge of the tape at the center of the beam2. With this setup, slight deflections of the He-Ne laser beam, produced by the compressible flow-induced index of refraction gradients, are clearly visible as voltage spikes on the oscilloscope trace. The shock waves traveling toward the cannon exit and the reflected shock waves deflect the beam in opposite directions and are, therefore, identified by either a positive or negative voltage spike.
Here, we provide instructions for the construction and utilization of an optimized PPC and SSPPC, as well as optical diagnostic techniques (Figure 1, Figure 2, and Figure 3). The optical diagnostic techniques and measurements have been developed through previous years of study1,2.
1. Building and assembly of the ping-pong cannon (PPC)
2. Building and assembly of the supersonic ping-pong cannon (SSPPC)
3. Optical diagnostics
4. Automatic velocity measurements
5. Setup and firing of the ping-pong cannon
6. Setup and firing of the supersonic ping-pong cannon
Here, we provide instructions for the construction and utilization of a PPC and an SSPPC, along with the implementation of the optical diagnostics for shock characterization and velocity measurements. Representative experimental results are also provided. The completed systems of the PPC and SSPPC, along with necessary accessories, are shown in Figure 1 and Figure 2. The SSPPC is an augmented version of the PPC, where a driving, pressurized section of pipe is connected to the driven pipe of the PPC. The optical diagnostics setup for the knife-edge detection of shock waves and ping-pong ball velocity measurements is shown in Figure 3. A sample oscilloscope trace demonstrating the effectiveness of the optical diagnostics for shock characterization and velocity measurements is shown in Figure 4, along with conceptual sketches showing the motion of the ball and the reflecting shock waves corresponding to the oscilloscope trace. The raw and processed signals received by the microprocessor, along with a depiction of the LCD-displayed velocity calculations, are presented in Figure 5. A representative dual-channel oscilloscope trace from a successful firing of the SSPPC is shown in Figure 6. The oscilloscope traces demonstrate the effectiveness of the knife-edge setup for the detection of shock waves inside and just past the exit of the cannon. The traces also display a clear cutoff in the signal as the ball passes, which is used for accurate ball velocity calculations. Tests were carried out for the firing of the SSPPC under different diaphragm rupture conditions. The correlation between the ping-pong ball velocities and SSPPC diaphragm rupture conditions is plotted in Figure 7.
Figure 1: Schematic of the standard ping-pong cannon. This figure shows the setup and layout of the standard ping-pong cannon. Please click here to view a larger version of this figure.
Figure 2: Schematic of the supersonic ping-pong cannon. This figure shows the setup and layout of the supersonic ping-pong cannon. Please click here to view a larger version of this figure.
Figure 3: Schematic of the optical diagnostic hardware setup. This figure shows the setup and layout of the components for optical diagnostic measurement. Please click here to view a larger version of this figure.
Figure 4: Representative oscilloscope trace with illustrated shock wave propagation. This figure depicts a propagating shock wave reflecting throughout the firing process of the cannon, which is represented by a change in voltage with respect to time. The five snapshots of the cannon portray the direction of the shock propagation in conjunction with the position of the ball in the cannon. The direction of the shock wave is determined by a positive or negative spike in the signal. The velocity can be measured through the width of the "square" pulse caused by the ball cutting off the beam. Please click here to view a larger version of this figure.
Figure 5: Microprocessor signal conversion and display. Here, we show the trace of the internally sensing photoreceiver caused by a typical shot of the PPC. The pulse caused by the traveling ball is inverted by a comparator, extra noise is removed, and railed to 0 V and 5 V so that it can be easily read by the microprocessor. The width of the processed square pulse is read by the microprocessor and used to calculate the velocity, which is then displayed on the LCD. Please click here to view a larger version of this figure.
Figure 6: Representative oscilloscope trace for the firing of the SSPPC. The dual-channel oscilloscope trace shows the knife-edge signal for the beams traversing the interior (red) and exterior (blue) regions near the exit of the cannon. Please click here to view a larger version of this figure.
Figure 7: Dependence of the SSPPC ping-pong ball exit speeds on the diaphragm rupture conditions. The SSPPC was fired for a series of cases utilizing single sheets of 0.0005 in, 0.001 in, and 0.002 in polyester film. The membrane pressure differential upon rupture was plotted versus the Mach number for each case. The cannon was fired eight times for each diaphragm thickness, and the vertical and horizontal error bars represent the standard error in the differential pressure and Mach number, respectively. Please click here to view a larger version of this figure.
Video 1: Schlieren imaging technique. The video reveals the response of the tape to the reflecting shock waves and the eventual detachment of the tape at the exit of the PPC. Please click here to download this Video.
Video 2: High-speed shadowgraph imaging technique. The supersonic ping-pong ball produces a standing shock wave. Please click here to download this Video.
Supplementary File 1: JoVE_AcrylicWindows_Step1_Engrave.svg Please click here to download this File.
Supplementary File 2: JoVE_AcrylicWindows_Step2_Engrave.svg Please click here to download this File.
Supplementary File 3: JoVE_AcrylicWindows_Step3_Cut.svg Please click here to download this File.
Supplementary File 4: JoVE_AcrylicCap_Cut.svg Please click here to download this File.
Supplementary File 5: JoVE_CannonMountTemplate.png Please click here to download this File.
Supplementary File 6: JoVE_AutomaticVelocityDisplay.ino Please click here to download this File.
Supplementary File 7: JoVE_MylarDiaphram_Cut.svg Please click here to download this File.
We have presented a method for the construction of a PPC and an SSPPC along with optical diagnostics for the measurement of ball velocities and for the characterization of shock propagation near the exit of the cannon. The standard PPC is constructed with a 2 m section of 1.5 in schedule 80 PVC pipe. The pipe is fitted with flanges at each end, quick-connect vacuum fittings, and acrylic windows near the exit for laser diagnostics. A detailed schematic of the PPC is shown in Figure 1. Prior to firing, a ping-pong ball is inserted into the cannon, and the ends are sealed. The exit end is sealed by securing tape directly onto the flange. At the other end of the pipe, tape is secured over an acrylic cap with a 1.5 in cutout, and the pipe is sealed using the acrylic cap with a rubber gasket. The PPC is firmly secured, and a sturdy container is positioned to safely catch the ping-pong ball. The cannon is fired by evacuating the pipe to a reduced absolute pressure of less than 2 Torr and puncturing the cannon with a sharp object. The SSPPC is an augmented construction of the PPC that produces increased accelerations and supersonic ping-pong ball velocities by securing a pressurized section of 4 in schedule 80 PVC pipe to the standard PPC. A detailed schematic of the SSPPC is shown in Figure 2. One end of the pressurized pipe is sealed with a cap, whereas the other end is connected to the PPC with a reducer coupling and flange. The pressurized pipe is fitted with a 1-100 psi pressure gauge, quick-connect fittings to an air compressor, and a safety pressure relief valve. Prior to firing, the ball is inserted into the cannon and the exit end is sealed by securing tape onto the flange. Then, the driver and driven sections are securely connected with a thin polyester diaphragm and rubber gasket in between them. The SSPPC is secured, and a sturdy container is positioned to safely catch the ping-pong ball. After reducing the pressure in the driven pipe to less than 2 Torr, the cannon is fired by releasing pressure from the air compressor into the driver pipe until the diaphragm bursts.
The knife-edge optical diagnostics are set up on an optical breadboard with a laser, beam splitter, mirror, and two photoreceivers, as shown in Figure 3. The laser is oriented perpendicular to the cannon, with one beam traversing the interior of the pipe through the acrylic windows and another beam (from the beam splitter) passing just beyond the exit of the cannon. The intensities of the beams are collected by two photoreceiver modules, and the signal is displayed on a two-channel digital oscilloscope. Black electrical tape is placed on the photoreceiver sensors to block approximately half of each beam. The tape serves as a knife edge and increases the sensitivity to detect small transverse deflections produced by shock waves or other density variations in the flow. Data from the photoreceivers are automatically recorded when the cannon is fired by triggering the oscilloscope when the ball traverses the first beam. Prior to setting the trigger level on the oscilloscope, special care must be taken to avoid clipping, which can result from the sensitivity of the knife edge system. Clipping can be avoided by adjusting the position of the beam on the knife edge such that the baseline voltage is approximately 50% of the maximum voltage. The ping-pong ball velocities are calculated using the traces from the photoreceiver modules. A simple and accurate calculation for the velocity is made by dividing the diameter of the ping-pong ball by the time the beam is obstructed by the ball. A microprocessor is utilized to process the signal received from the beam traversing the interior of the pipe to automatically calculate and display the velocity of the ball near the exit of the cannon.
The results of this method are highly reproducible and provide an immediate digital display of the ping-pong ball velocities, enhancing the value of the cannon as a demonstration device. The oscilloscope trace using the knife-edge setup contains a rich visual depiction of the compressible flow and shock waves associated with the cannon. This method focuses on an experiment that is influenced by many secondary factors that can be studied further in a laboratory setting, such as wall friction, the leakage of air around the ball, the formation of shock waves by the accelerating ball, the rapid buildup of pressure produced by the reflection of shock waves between the ball and the taped exit, and the subsequent detachment of the tape prior to the exit of the ball. A representative oscilloscope trace from the firing of the SSPPC is shown in Figure 6. The upper trace in the figure corresponds to the beam that traverses the interior of the cannon near the exit. The lower trace corresponds to the beam that traverses the ping-pong ball’s path just after exiting the cannon. A clear cutoff in the signal is evident as the ball passes by and obstructs each beam. Voltage spikes prior to the ball passage, introduced by propagating shock waves, are enhanced by the knife-edge detection setup and can be seen on each trace. The successive voltage spikes in the upper trace invert due to the reflection of the shock waves inside the cannon between the ball and the tape. In contrast, each voltage spike on the lower trace is in the same direction because the shock waves outside the cannon do not reflect and pass through the exterior beam a second time.
In addition to the experiments that have been presented, follow-on student projects could be designed to provide additional control over the test conditions during the firing of the cannon. For example, the current SSPPC fires upon natural rupture of the diaphragm after a sufficient pressure differential builds up between the two sections of pipe. The development of a user-controlled rupture mechanism that is initiated by the user or automatically triggered at a desired driver pressure would allow for greater precision in controlling the test conditions. Other follow-on projects could be aimed at measuring the velocity of the ping-pong ball at multiple positions in a single firing of the cannon to provide a more complete description of the velocity and acceleration of the ball as it travels down the pipe. Velocity measurements in the PPC as a function of position have been previously studied, but with each velocity data point obtained from separate firings of the PPC1.
The ping-pong cannon will continue to be a demonstration that generates intrigue and curiosity for audiences of all ages and types. The complex fluid physics exhibited by the cannon will continue to provide a seemingly limitless supply of follow-on studies that can be investigated in physics and engineering laboratory projects. In the classroom, it will continue to serve as a popular demonstration that stimulates excitement and intrigue about the magnitude of atmospheric pressure. We anticipate that the methods for the construction of the SSPPC and the optical diagnostics that we have presented will enhance the value of the cannon both as a demonstration device and as a useful apparatus for exciting laboratory experiments.
The authors have nothing to disclose.
This work is supported by the NSF Division of Undergraduate Education (award # 2021157) as part of the IUSE: EHR program
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