Summary

High-Speed Optical Diagnostics of a Supersonic Ping-Pong Cannon

Published: March 24, 2023
doi:

Summary

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.

Abstract

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.

Introduction

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.

Protocol

1. Building and assembly of the ping-pong cannon (PPC) Assemble all the components of the PPC according to Figure 1. Insert two high-clarity acrylic windows in the sides of the cannon to allow for optical probing across the interior of the cannon. Drill two 1/2 in holes through opposite sides of the PVC near the cannon's exit. Prepare two 1/8 in thick acrylic windows using a laser engraver. Download the three supplementary svg…

Representative Results

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 co…

Discussion

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 t…

Disclosures

The authors have nothing to disclose.

Acknowledgements

This work is supported by the NSF Division of Undergraduate Education (award # 2021157) as part of the IUSE: EHR program

Materials

15 V Current Limited Power Supply New Focus 0901 Quantity: 1
2" x 6" Plank Home Depot BTR KD-HT S Quantity: 1
5.0" 40-pin 800 x 480 TFT Display Adafruit 1680 Quantity: 1
Absolute Pressure Gauge McMaster-Carr 1791T3 0–20 Torr | Quantity: 1
Air Compressor Porter Cable C2002 6 gallon | Quantity: 1
Arduino UNO Rev3 Arduino A000066 Quantity: 1
ASME-Code Fast-Acting Pressure-Relief Valve
for Air
McMaster-Carr 5784T13 Nickel-Plated, 3/8 NPT, 125 PSI Set Pressure | Quantity: 1
Black Electrical Tape McMaster-Carr 76455A21 Quantity: 1
BNC Cable Digikey Number 115-095-850-277M050-ND Quantity: 2
Broadband Dielectric Mirror THORLABS BB05-E02 400–750 nm, Ø1/2" | Quantity: 1
C-Clamp McMaster-Carr 5133A15 3" opening, 2" reach | Quantity: 6
Cam Clamp Rockler 58252 Size: 5/16"-18 | Quantity: 2 (2 pack)
Digital Pressure Gauge Omega Engineering, Inc. DPG104S 0–100 Psi Absolute Pressure, With Output and Alarms | Quantity: 1
Digital Pressure Gauge Omega Engineering, Inc. DPG104S 0–100 Psi Absolute Pressure, With Output and Alarms | Quantity: 1
Draw Latch McMaster-Carr 1889A37 Size: 3 3/4" x 7/8" | Quantity: 4
Driver Board for 40-pin TFT Touch Displays Adafruit 1590 Quantity: 1
Full Faced EPDM Gasket PVC Fittings Online 155G125125FF150 Quantity: 2
Gasket Material McMaster-Carr 9470K41 15" x 15", 1/8" thick | Quantity: 1
Glowforge Plus Glowforge Glowforge Plus Quantity: 1
HeNe Laser Uniphase 1108 Class 2 | Quantity: 1
High Tack Box Sealing Tape Scotch 53344 72 mm wide 
Laser Power Supply Uniphase 1201-1 115 V .12 A | Quantity: 1
LM311 Comparator Digikey Electronics 296-1389-5-ND Quantity: 1
Mirror Mount THORLABS FMP05 Fixed Ø1/2", 8–32 Tap | Quantity: 1
Moisture-Resistant Polyester Film McMaster-Carr 8567K102 10' x 0.0005" x 27" | Quantity: 1
Moisture-Resistant Polyester Film McMaster-Carr 8567K12 10' x 0.001" x 40" | Quantity: 1
Moisture-Resistant Polyester Film McMaster-Carr 8567K22 10' x 0.002" x 40" | Quantity: 1
Mourtise-Mount Hinge with Holes McMaster-Carr 1598A52 Size: 1" x 1/2" | Quantity: 4
Needle Valve Robbins Aviation Inc INSG103-1P Quantity: 1
Non-Polarizing Cube Beamsplitters THORLABS BS037 Size: 10 mm | Quantity: 2
Nonmetallic PVC Schedule 40 Cantex A52BE12 Quantity: 2.5 m 
Oatey PVC Cement and Primer PVC Fittings Online 30246 Quantity: 1
Oil-Resistant Compressible Buna-N Gasket with Holes and Adhesive McMaster-Carr 8516T454 1-1/2 Pipe Size, ANSI 150, 1/16" Thick | Quantity: 1
Oscilliscope Tektronix TBS2102 Quantity: 1
Photoreceiver New Focus 1801 125-MHz | Quantity: 2
Ping Pong Balls MAPOL FBA_MP-001 Three Star
Platform Mount for 10mm Beamsplitter and Right-Angle Prisms THORLABS BSH10 4-40 Tap | Quantity: 1
Proofgrade High Clarity Clear Acrylic Glowforge NA Thickness: 1/8" | Quantity: 1
Sch 80 PVC Cap PVC Fittings Online 847-040 Size: 4" | Quantity: 1
Sch 80 PVC Pipe PVC Fittings Online 8008-040AB-5 Quantity: 5 ft
Sch 80 PVC Reducer Coupling PVC Fittings Online 829-419 Size: 4" x 1-1/2" | Quantity: 1
Sch 80 PVC Slip Flange PVC Fittings Online 851-015 Size: 1 1/2" | Quantity: 3
Silicone Sealant Dow Corning McMaster-Carr 7587A2 3 oz. Tube, Clear | Quantity: 1
Steel Corner Bracket McMaster-Carr 1556A42 Size: 1 1/2" x 1 1/2" x 1/2" | Quantity: 16
Vacuum Pump Mastercool  MSC-90059-MD 1 Stage, 1.5 CFM, 1/6HP, 115V/60HZ

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Cite This Article
Barth, T. J., Stein, K. R. High-Speed Optical Diagnostics of a Supersonic Ping-Pong Cannon. J. Vis. Exp. (193), e64996, doi:10.3791/64996 (2023).

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