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

요약

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.

초록

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.

서문

The PPC is a popular physics demonstration used to show the immense air pressure to which people are continually exposed^1,2,3,4,5. 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 PPC^7,8 (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 nozzle^9,10,11. 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 techniques^7,12 (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 study^1,2.

프로토콜

1. Building and assembly of the ping-pong cannon (PPC)

1. Assemble all the components of the PPC according to Figure 1.
2. Insert two high-clarity acrylic windows in the sides of the cannon to allow for optical probing across the interior of the cannon.
   1. Drill two 1/2 in holes through opposite sides of the PVC near the cannon's exit.
   2. Prepare two 1/8 in thick acrylic windows using a laser engraver. Download the three supplementary svg files.
      NOTE: There are three files labeled "JoVE_AcrylicWindows_Step1_Engrave.svg"
      (Supplementary File 1), "JoVE_AcrylicWindows_Step2_Engrave.svg"
      (Supplementary File 2), and "JoVE_AcrylicWindows_Step3_Cut.svg"
      (Supplementary File 3). These three files should be used in the order provided by using the process described in the title (engrave/cut). The laser speed and power settings should be set according to the manufacturer's recommended settings for acrylic. Each engraving step should remove approximately 1/3 of the thickness of the material.
   3. Add silicon sealant to the edge of the acrylic, being careful not to get any on the window. Then, place windows in the holes, ensuring they are perpendicular to one another. Leave ample time for the silicone to cure after this part of the process.
      NOTE: If a laser cutter is not available, a piece of clear tape can be wrapped around the circumference of the pipe to seal the 1/2 in holes and act as a window through into the interior of the pipe. Further experimentation can be carried out by inserting additional windows in the cannon to measure the velocity and acceleration of the ping-pong ball along the length of the driven pipe.
3. Using a belt sander, sand off the face of the flange at the exit of the cannon. Finish sanding with fine-grit sandpaper so that the tape can adhere well to the flange.
4. Using a laser cutter, cut an acrylic cap following "JoVE_AcrylicCap_Cut.svg" (Supplementary File 4). Attach a full-faced rubber gasket to the acrylic cap. The acrylic cap is a component of the pressure seal used when firing the PPC.
5. Firmly secure the cannon for firing, and position a sturdy container to safely catch the ping-pong ball with ample padding to minimize the impact with the back wall of the container.
   NOTE: There are many solutions for securing the ping-pong cannon and safely catching the ball. For the presented experiment, a custom clamping system was created to firmly secure the cannon with a horizontal orientation. These clamps can be constructed following "JoVE_CannonMountTemplate.png" (Supplementary File 5).
   1. Use Supplementary File 5 as a template to cut out 2 in x 6 in wood planks. Connect the upper and lower portions of the clamping system with a draw latch and hinge to secure the cannon.
   2. Line the insides of the clamps with rubber gasket material to prevent the slipping of the cannon during the firing process. Attach the connected upper and lower portions of the clamping system to the base using four corner brackets.
   3. Mount the completed clamping system to a tabletop using four C-clamps. Construct a 13 in x 13 in x 24 in plywood container, and back it with four 1 in plywood sheets to catch the ping-pong ball. Place a cushioning material in the container to prevent ball rebounds. Mount this container with C-clamps to a tabletop.

2. Building and assembly of the supersonic ping-pong cannon (SSPPC)

1. Assemble all the components of the driver pipe following Figure 2.
   NOTE: The primary difference between the PPC and the SSPPC is that the SSPPC is augmented with a driving, pressurized section of schedule 80 PVC pipe that is connected to the entrance of the PPC. Therefore, if the PPC has already been constructed, all that remains to be assembled to construct the SSPPC is the driver pipe section.
2. Firmly secure the cannon for firing and position a sturdy container that can safely catch the ping-pong ball with ample padding to minimize the impact on the back wall of the container.
   ​NOTE: The mounting and catching systems described in step 1.5 are the same systems used to secure the SSPPC.

3. Optical diagnostics

1. Set up the laser, beam splitter, mirror, and photoreceivers by mounting the components on an optical breadboard, according to Figure 3. Orient the laser perpendicularly to the cannon, with the first beam traversing the interior of the pipe through the acrylic windows and the second passing just outside of the cannon exit.
2. Power the photoreceivers and laser module by connecting them to a 15 V current limited power supply and laser power supply. Connect the photoreceivers to the two channels of the oscilloscope using BNC cables.
3. Place black electrical tape over half of the photoreceiver sensor. The tape serves as a "knife edge" to create a sensitive shock detection setup.
   NOTE: The sensitivity of the knife-edge detection can be further enhanced using a converging lens to focus the beam on the knife edge. The sensitivity can also be enhanced by increasing the distance the beam travels to the photoreceiver, resulting in a greater refractive displacement of the beam.
4. Prior to setting the trigger level on the oscilloscope, pay special attention to avoid clipping, which can result from the sensitivity of the knife-edge setup. To avoid clipping, adjust the position of the beam on the knife edge so that the baseline voltage is approximately 50% of the maximum voltage. The maximum voltage is the voltage when the full beam is on the unobstructed detector.
   1. Adjust the settings on the oscilloscope to collect 20 million data points. Set the data acquisition rate to 500 MHz by adjusting the horizontal scale knob. Turn the trigger knob to trip at a voltage slightly below the baseline voltage acquired from the photoreceiver.
      ​NOTE: The velocity of the ping-pong ball can be found through simple mathematics using the photoreceiver modules. The velocity is the diameter of the ping-pong ball divided by the time the beam is obstructed by the ball. A microprocessor is utilized to process the signal received from the interior photoreceiver module to automatically measure the velocity of the ball at the end of the cannon.

4. Automatic velocity measurements

1. To utilize a microprocessor for automatic velocity measurements, convert the signal from the photoreceiver module to a 0-5 V pulse, as shown in Figure 5, using a comparator that triggers at approximately 10% of the baseline voltage. Connect the converted signal to port 7 of the microprocessor.
2. Download "JoVE_AutomaticVelocityDisplay.ino" (Supplementary File 6), and upload it to the microprocessor.
3. Connect the RA8875 display and driver board to the designated ports on the microprocessor.

5. Setup and firing of the ping-pong cannon

1. Put on ear and eye protection before firing the cannon.
2. Insert a ping-pong ball into the exit of the cannon. Blow lightly into the end of the cannon until the ball hits the vacuum fitting near the entrance of the pipe.
3. Secure a 3 in x 3 in square of tape onto the flange at the exiting end of the cannon and a second square onto the acrylic cap. Seal the tape such that it adheres to the surface of the flange and cap.
   NOTE: If there are any wrinkles or large bubbles, the tape needs to be discarded. If the tape does not sufficiently adhere to the surface, the vacuum can be lost, and the cannon can fire prematurely. If at any point the vacuum is lost, the needle valve connected to the vacuum pump can be opened to bring the system to equilibrium.
4. Ensure the laser beam is centered on the knife edge, the trigger is properly set, and the catching container is secure.
5. Turn on the vacuum pump to evacuate the pipe to a reduced absolute pressure of less than 2 Torr. Once a sufficient vacuum has been reached, puncture the tape at the entrance with a sharp object such as a broadhead or razor tip.
6. After firing, turn off the vacuum pump. Remove the tape from the exit flange and the acrylic cap.

6. Setup and firing of the supersonic ping-pong cannon

1. For safety, wear hearing and eye protection throughout the firing process.
2. Cut sheets of 0.0005 in, 0.001 in, and 0.002 in polyester film that match the dimensions of the flange. These sheets can be cut by hand or, preferably, using a laser cutter. Use the supplementary file "JoVE_MylarDiaphram_Cut.svg" (Supplementary File 7) as an outline.
   NOTE: For the purpose of this experiment, the cannon was fired with single sheets of 0.0005 in, 0.001 in, and 0.002 in polyester film, and the results are recorded in Figure 7. A template to laser-cut the polyester film can be found as an SVG file (Supplementary File 7).
3. Ensure the valve from the air compressor to the driver pipe is closed. Prefill the air compressor to allow for faster filling of the driver pipe when the cannon is ready to be fired.
4. Insert a ping-pong ball into the exit of the cannon. Blow lightly into the end of the cannon until the ball is stopped by the vacuum fitting near the entrance of the driven pipe.
5. Secure a 3 in x 3 in square of tape onto the exiting end of the cannon. Seal the tape such that it adheres to the surface of the flange.
   NOTE: If there are any wrinkles or large bubbles, the tape needs to be discarded. If the tape does not sufficiently adhere to the surface, the vacuum can be lost, and the cannon can fire prematurely. If the vacuum leaks or other complications arise, use the pressure release valve on the driver pipe and the needle valve on the vacuum pump to bring the system to equilibrium.
6. Insert a precut thin polyester diaphragm between two rubber gaskets. Place the diaphragm and rubber gaskets between the driver and driven sections of the cannon. Tightly connect the two sections using 4 cam clamps.
7. Ensure the laser beam is centered on the knife edge, the trigger is properly set, and the catching container is secure.
8. Turn on the vacuum pump to evacuate the pipe to a reduced absolute pressure of less than 2 Torr. Release the pressure from the air compressor into the driver pipe. Allow the pressure to rise until the diaphragm bursts and the compressed air within the driver pipe rapidly fills the evacuated driven pipe.
9. After the cannon fires, turn off the air compressor and the vacuum pump. Remove the burst polyester diaphragm and tape from the cannon.

결과

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...

토론

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...

자료

Name	Company	Catalog Number	Comments
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