Tuesday, January 18, 2022

Zero-g and Me


Enjoying free fall on G-Force One


I have always been fascinated by the space program. I grew up during the space race in the 1960s. I remember Mrs. Williamson taking my kindergarten class upstairs to watch Gemini launches. I admired the astronauts and followed their missions closely. However, it was the people that built their spacecraft that inspired me to pursue a career in aerospace engineering. The astronauts frequently acknowledged that the engineers and technicians were the true space explorers so I wanted to be one of them. I joined their ranks in 1982 at the Lockheed Missiles and Space Company (now Lockheed/Martin) where I worked on many NASA and DoD spacecraft. Some of these satellites will be orbiting the Earth for thousands of years. Although I was exploring space as an engineer, I wanted to travel into space someday. I am still waiting for that day but I have traveled into the stratosphere aboard NASA's Stratospheric Observatory for Infrared Astronomy (SOFIA). That was an amazing experience, but a 12 km altitude is far from traveling into space. My hometown was somewhat confused about that.

Boente Shell Sign in Carlinville, IL

I flew twice onboard NASA's SOFIA 747 in 2015












There are two unique experiences for those who are fortunate to travel into space. The first is seeing the planet Earth from a distance. The other is to experience what has been called zero gravity, zero-g, weightlessness, or microgravity. More about these terms later. The best description is free fall. Free fall is the motion of an object acted on only by gravitational forces. Recently I had the opportunity to experience extended periods of free fall aboard the Zero-G company's G-Force One plane. Free fall is frequently misunderstood. I put a lot of effort into helping my students understand free fall during my physics teaching career. I continue my efforts as the physics curriculum and training developer for PASCO scientific. I will describe my approach to teaching about free fall and my trip on G-Force One in this post.


Zero-g in the Physics Classroom

My aerospace engineering expertise was in astrodynamics, sometimes called orbit mechanics. It is the study of the path of objects in space. I was excited about teaching it when I became a high school physics teacher. I soon learned that there are powerful misconceptions that are barriers to student understanding. One misconception is that the laws of physics in space are different than on Earth. Students think that once you enter space, gravity turns off. To help them overcome this, I put a 400 km tall ladder on an Earth globe. I made its height to scale with a 12" diameter globe. That is a scale height of about 3/8". 400 km is approximately the orbital altitude of the International Space Station (ISS). Students are usually surprised about how short the ladder is. Does it make sense for the gravitational pull of the Earth to drop to zero after moving such a short distance away? Most students start to question their belief from this simple visual aid. 


Drawn to scale, a 400 km tall ladder represents only 8/125th of an Earth radius

Imagine a space-suited astronaut climbing the ladder into space. What would the astronaut observe if they stood at the top of the ladder on a scale? We calculated the gravitational force on the astronaut at the bottom and the top. The top was 88% of the surface value. This would be measurable but hardly noticeable. The astronaut might be very disappointed after expecting the scale to read zero. What would happen if they dropped a screwdriver from the top of the ladder? Would it float? No! It would fall straight down. The astronaut is doubly disappointed. They dreamed about floating in space all their life. They have climbed a 400 km tall ladder and things are not very different, save for the lack of atmosphere. How could they see the screwdriver float? Usually at least one student will figure this out. They will if the astronaut dropped it after jumping off the ladder. The screwdriver would appear to float from the falling astronaut's perspective. The astronaut could finally achieve their dream of floating in space. But for how long? After a few minutes they will encounter the atmosphere while moving very fast. That would not end well unless they were protected by much more than a spacesuit as depicted by this gruesome FoxTrot cartoon.

I stopped showing this for a few years after the Space Shuttle Columbia disaster, is it still too soon?

Students can use kinematics or energy conservation to determine the astronauts speed as they encounter the atmosphere. Assuming g is constant gives a reasonable answer or use Ug = -GMm/r for gravitational potential energy. For a happier high dive from space see my YouTube video about one that takes a lifetime. How could the astronaut experience floating in space but avoid this fate, or at least prolong it? I pose this question after displaying an image that is not drawn to scale. This made it more likely a student will offer an idea.

If the astronaut ran and jumped, the Earth would curve away as they fell. This would prolong their time in free fall. If they could run fast enough, they would not hit the Earth and fall all the way around! To be in orbit, the astronaut must be moving sideways fast enough so that their path doesn't intersect the Earth. To complete an orbit they must be above the bulk of the atmosphere. If the astronaut releases the screwdriver after running and jumping, it will fall with them as they circled the Earth, appearing to float. A return to the scale size ladder on the Earth globe makes it clear it will have to be moving sideways very fast! This is clearly too fast to run and faster than a bullet. Rockets are the only technology we currently have that can accelerate an object the size of an astronaut or spacecraft to the required speed. Although most rockets launch vertically, they soon pitch over and add most of the velocity in a direction parallel to the Earth's surface.

Now that we have established that objects appear to float in space only if they are in free fall together, I put up this clicker question:

An astronaut lets go of a screwdriver while orbiting the Earth. It floats before her eyes. The same thing can be done

        A. In an airplane
        B. On an amusement park ride
        C. In a high school classroom
        D. All of the above 
        E. None of the above

The answers are usually well distributed. Not because they didn't understand the previous discussion, but because few students think C can be correct. Some have heard of airplanes that fly parabolic arcs, some have heard of or been on free fall rides at the amusement park. They don't think it can be done in an ordinary classroom, so they are confused by the other choices. After letting them discuss their answers with their peers and re-voting, a few switch to D but most stick with their original answer. I pick up a screwdriver, get on a stool and jump while releasing the screwdriver in front of my face. For a fraction a second it floats in front of my eyes. The only difference between that and the astronaut's experience is the duration. How could I increase the duration? I can jump up and release the screwdriver. We are in free fall together on the way up and on the way down. If I could jump as high as the stool, I would double the duration. I encourage them to try it themselves but with something softer than a screwdriver. A trampoline is ideal for seeing objects float with you on the way up and down. Just release it after losing contact with the fabric. Free fall is a loaded term for students because they think of each term separately. Some assume "free" means there are no forces acting. Some think "fall" only describes something getting closer to the ground. It is important to make sure they understand that when used together, free fall means motion under the influence of just gravitational forces. It can be moving toward or away from the ground. An object in free fall at the highest point of its motion or in a circular orbit is doing neither.

Zero-g on Earth
Can the duration of free fall on Earth be increased further? Amusement park rides have braking systems that allow for free fall up to about 3.5 seconds on the way down. The Superman ride in Southern California's Magic Mountain launches riders horizontally at about 100 mph. The track curves up so riders are in free-fall for about 3.2 s on the way up and 3.2 s on the way down. I have ridden it several times but prefer the Drop Tower at Santa Clara's Great America park for experiencing free fall. The Superman ride is great, but by the time you have recovered from the acceleration to 100 mph the ride is over. The Drop Tower releases riders from rest for about 3.5 s of free fall. This isn't quite right because free fall is the motion of an object acted on only by gravitational forces. The Drop Tower riders are traveling 35 m/s at the end of the drop. That is almost 80 mph. The cars are heavy but at some point, air resistance reduces the acceleration. To overcome this, the ride would need to be in a vacuum. I doubt amusement parks will be constructing such a ride anytime soon, but NASA has. The Zero G Research Facility at the Glenn Research Center has a 132 m evacuated drop tower that allows for 5.18 s of true free fall. Although it is large enough to hold a person, I don't recommend trying it because of the 65 g peak acceleration at the end! NASA does a lot of experiments using this facility. It is less expensive to first test equipment on Earth before sending it into orbit. There are many research questions that can be answered in 5.18 s. Below is a short video about the Zero Gravity facility:

There is another option for those that need longer duration free fall. Instead of getting rid of the air, additional forces can be applied. If they have a sum that is equal in magnitude and opposite in direction to air resistance, the object will move like it is in free fall. These forces can be supplied by an airplane using the lift of the wings and the thrust of the jet engines. The airplane can also use these forces to pull up at the end of the free fall to avoid hitting the ground. This technique was first suggested in 1950 by German rocket scientists Fritz and Heinz Haber. The paper they authored together is a fascinating and short read. They were working for the US government following WW II as part of Operation Paperclip.
Figure from F. Haber and H. Haber's paper originating what they call weightless flight

Scott Crossfield and Chuck Yeager were the first to try their idea for an extended duration in 1951. Both reported signs of disorientation during the 20 seconds of free fall. NASA configured a C-131B cargo plane to fly parabolic trajectories so experiments could be conducted in a volume larger than a jet cockpit.
Mercury astronauts train on a C-131B, the original vomit comet

Flying parabolas can play havoc with a passenger's inner ear because of the many periods of downward acceleration during free fall and upward acceleration while pulling up. That is how the planes got the nickname vomit comet. Technically, the plane is not in free fall but the people and objects inside are. The plane has forces acting on it in addition to gravitational forces, but they add up to zero. If a person tried the same thing using a jet pack, they would not feel like they were floating. They would feel the force of air resistance on one side and the push of the jet pack engine on the other, squeezing them. The plane rotates through about 90 degrees during the parabolic arc. This produces a small centripetal acceleration on objects attached to the plane that increases the further from the center of rotation. It is below the accelerations caused by vibration.

Zero-g Terminology

The words used to describe the experience of free fall can be misleading. NASA originally used the term "zero gravity". This naturally led people to believe that in space there is no gravitational force. The 400 km ladder helps dispel this idea. Ideally those using this term would say "it is as if there is no gravity". Unfortunately, this is seldom done. We are stuck with this term, but all is not lost for physics teachers. According to Einstein's equivalence principle, there is no difference between being in free fall and being in a place where there is no gravity. From this perspective gravity is not a force. It is the curvature of spacetime. Objects follow this curvature unless acted on by forces. A person in free fall is not accelerating. A person at rest on the surface of the Earth is accelerating up at 9.8 m/s2 or 1 g. This is an interesting and valid perspective but might be counter-productive to use in an introductory physics course. I will assume there are gravitational forces for the remainder of this post. Veritasium's "Why Gravity is NOT a Force" video is a good introduction to this other way of thinking.

Another problematical term used to describe free fall is "Zero-G". Or is it "Zero-g"? G is the universal gravitational constant and g is the acceleration due to gravity. If either were zero, the gravitational force would be zero. As far as I can tell, these terms are used interchangeably, often by people who would not understand the difference. The term "zero-g" is more commonly used by NASA and other space researchers. Those using zero-G appear to be doing so for aesthetics like the Zero-G company that flies a parabolic arc plane for paying customers. g is sometimes used as a unit of acceleration where 1 g = 9.8 m/s2. However, if you use an accelerometer to measure acceleration you will discover something surprising. In free fall the reading will be 0 m/s2 or 0 g. If it is at rest it will measure the vertical acceleration to be upward at 9.8 m/s2. Toss it into the air and it will measure more than 1 g while your hand is speeding it up and while catching it. Students using accelerometers in their physics class should know this, preferably finding out through their own experience in the lab.
The term weightlessness is used to describe free fall. Weight is an imprecise term in physics. Most textbooks define it as the gravitational force acting on an object. However, some define it as whatever a scale reads. The latter definition is more common outside the USA. It is a good idea to make your students aware of these two definitions and make it clear which one you will use. Weightlessness is an accurate term for free fall using the scale definition because a scale would read zero in free fall. But if weight is the gravitational force on an object, weightlessness is not an accurate term. There is a gravitational force on an object in free fall. A better term would be apparent weightlessness. This is sometimes used but it begs the question, why not describe what it is rather than what it appears to be? An object in free fall has no supporting force acting on it. For a person standing on the floor, the supporting force is the push of the floor on their feet. This force is called the normal force. If the person is in free fall, the normal force is no longer acting on them. Instead of weightlessness, why not name it for the force that is missing? It should be called normalforcelessness. As far as I know, I first coined this term in the 1990s. I have promoted normalforcelessness to my students for decades. I had a colleague write a page in Wikipedia about normalforcelessness. After a few years they removed it because normalforcelessness was not used in any peer-reviewed papers. Since then I have asked my students to include normalforcelessness in any paper they submit for peer review. None have done it yet, but some have promoted it in other ways online. Search "normalforcelessness" and every reference originated from my student's efforts.
NASA started using another term in the 1970s. They started calling it microgravity. It may have been partially due to a desire to stop using zero gravity. Its main purpose was for researchers wanting to do experiments in free fall. On spacecraft and other free fall research facilities there are small deviations from pure free fall. A pivoting solar array, circulating cooling fluid, an exercising astronaut, or drag in low Earth orbit can produce tiny forces that cause micro-accelerations. Even solar radiation can cause measurable acceleration on a high-altitude spacecraft. Some experiments are more sensitive to these deviations and scientists want to know what the maximum values are. Preferably these deviations from free fall acceleration are in the micro realm.

After going through these terms with my students, we watch a short clip from the old CNN show, Science and Technology Week featuring Miles O'Brien. Miles is flying with undergraduate students on the Vomit Comet. I have shown this video to my physics students and at teacher workshops since it first aired in 1994. I have seen it over 100 times but still enjoy watching it. I would sometimes quip that it would make a good drinking game if you did a shot every time they say zero-g, zero gravity, weightlessness, or microgravity. Miles describes free fall well at 2:40 just before he unexpectedly stops doing it.

 Zero-g Flight Opportunity
I like that they show undergraduate students doing research in the video. I advise my students to ask about opportunities to get involved in undergraduate research while choosing a college. A show of hands reveals that many students want to fly on NASA's KC-135 to experience normalforcelessness. I told them many people share their enthusiasm and would pay money to realize their dream of floating like the astronauts. I encouraged them to start a business to take advantage of this market. None of my students did, but some enterprising individuals started the Zero-G company. I watched their progress with interest hoping to avail myself of their services at some point. I considered applying to the teacher flight program that was sponsored by Grumman but they were seeking middle school teachers at the time. The teacher program ended. If I wanted to fly, I would have to purchase my own ticket. A colleague did and hearing about his experience made me want to fly even more.

My chance came as a surprise after I retired from teaching. I was working for PASCO scientific as the physics curriculum and training developer. Our Florida sales representative was contacted by Zero-G's Deb Houts about collaborating with PASCO. Deb is a retired physics teacher who flew with Zero-G as a flight attendant and later as flight director. They noticed her amazing ability to tolerate parabolic flight without any ill effects after she participated in the teacher flight program. She seems to thrive under those conditions and has been flying for Zero-G for 10 years. Zero-G is reviving their teacher flight program and wanted PASCO's help updating their experiments and activities. Deb used PASCO equipment throughout her career and knew JP Keener, PASCO's international director of curriculum and product development. I enthusiastically started working on the project. This included fulfilling Deb's request to fly a Kundt's tube on Zero-G's 727-200. The English pronunciation of Kundt is "koont". I do not recommend using the German pronunciation!

A Kundt's tube is a clear cylinder with a variety of lengths and diameters. It is sealed at one end and has a single frequency sound source at the other end. Kundt vibrated a metal rod to produce the sound when he invented it in 1866. Inside the tube is a fine powder or particles that form a standing wave pattern when the frequency of the sound resonates in the tube. The Exploratorium uses kerosene that splashes at the anti-nodes. There are many sources online that describe how to build one. The powder is disturbed most at the anti-nodes and least at the nodes. The fundamental frequency of the tube has a wavelength that is twice the length of the tube. Kundt used his tube to determine the frequency of the vibrating rod so he could determine the speed of sound in the metal. Modern Kundt's tubes use a speaker and frequency generator to produce the sound. They are primarily used for classroom demonstrations and physics lab activities. Deb was curious about what the standing wave pattern would look like in free fall. I started experimenting with different tubes. One commonly used tube is the clear cover used to store fluorescent light tubes. They are inexpensive but too flimsy for the Zero-G plane. Mounted experiments must be able to withstand high accelerations. Deb also wanted a larger diameter so it could be more easily seen. I found a 3.5" diameter, 0.92 m long acrylic tube in our spare stock room and decided to use that. I knew the duct tape I used to seal the end and attach the speaker would not survive high acceleration. I asked PASCO's resident engineering wizard, Jon Hanks, for help. He 3D printed an end cap and speaker mount in PASCO blue that worked perfectly. Now I had to find a suitable powder to use. Deb suggested Styrofoam beads because they are easy to see. I also saw Kundt's tubes online that used them.

I had a problem with static electricity when I tried 0.01" diameter Styrofoam beads. The beads would levitate and zip around as I opened the bag, defying gravity before they were on the Zero-G plane. They stuck to the inside of the tube making the standing wave pattern harder to see. I tried different sizes and cork dust but had no luck. I ordered some anti-static spray and that worked well. I made a few videos and sent Deb a report of the results.  She asked me to ship it to Ft. Lauderdale so she could get it approved for a November 2021 flight. After I let he know it was shipped I got this email.

Whoo hoo! I was going to get to fly on a Zero-G plane after watching others do it for many years. Unfortunately, PASCO was still in a COVID induced employee travel ban. I told Deb I would go and pay my own expenses if needed. Eventually it was approved after supplying a doctor's note attesting to my medical suitability for the flight. I had less than 2 months to prepare more experiments because the actual flight date was 11/19. I solicited ideas from my colleagues, searched online, and reviewed free fall activities I used in my classroom.


Zero-g Experiments

One simple activity I did for many years comes from the Conceptual Physics Lab Manual authored by my friend Paul Robinson. Poke 2 holes in the side of a cup near the bottom. Fill it with water and hold it over a container, keeping the holes covered with your fingers. Ask students what will happen if you remove your fingers. After some discussion, take your fingers off and the water streams out. Now ask what would happen if you carefully filled it on the International Space Station and removed your fingers. Many students will know but don't verify their predictions. Instead, ask how we could do it ourselves. If you discussed how orbiting is the same as free fall, they will suggest dropping it. Tell them you won't drop it, but they can. Doing a demo of this can backfire as the cup will fall with the water that previously came out. Students in the back may not notice that the water stops coming out. If you drop the cup yourself, you easily see the water stop. I prepared a cup for each student in advance using a drill to create 4-5 at a time. I grab a couple of buckets filled with water and take the class outside. My campus was hilly and made finding a spot to drop them easy. Even if your campus is flat, it is worth dropping them from just above your head. Students won't complain about getting their feet wet. Once they see what happens when they hit the ground, even the shyest student will get a cup and try it themselves. I had many students say this was their favorite activity on my year-end survey. Below is a video teacher guide showing students dropping the cups. There is some good slo-mo at 5:50.

I had to figure out how to do this on the Zero-G plane without spilling a lot of water. It would be harder than on the ISS because of the changes in acceleration and pressure. I came up with the idea of using a PASCO water bottle with a valve on the top. I drilled holes and covered them
with tape. During free fall I would equalize the pressure with the valve, remove the tape, and open the valve to see if the water came out. There will be no need to let go as it will be falling with me.

An good choice for a Zero-G flight experiment is the PASCO wireless acceleration/altimeter. Measuring the acceleration of the Zero-G plane should yield interesting data. This device has a 3-axis accelerometer and altimeter. It also measures angular velocity about 3 axes. The lowest acceleration range is ±16g, accurate to ±0.04g. The ±100g, ±200g and ±400g ranges are accurate to ±1g. The low g range would work best for the flight. The altimeter does not measure altitude accurately in a pressurized jet. However, measurements of the cabin pressure while the air is accelerated by flying parabolas should be interesting. The acceleration/altimeter is perfect for teachers to use in the lab before their Zero-G flight. It is encased in a durable housing that allows students to throw it as high as they can to measure their own parabolic flights. It can be attached to carts and rotating platforms with the included thumb screw or Velcro strap. It has a remote logging feature like most of PASCO's wireless sensors. You can configure the sensor while connected to a computer, then disconnect and start collecting data right away or later. This feature allows for the sensor to be used outside of Bluetooth range for student experiments like launching it up with a slingshot. It also makes using it on the Zero-G flight easier because you don't need to bring a computer or use a smart phone.

Launching a wireless accelerometer/altimeter with a rubber band

My fourth experiment is a pendulum using PASCO's wireless rotary motion sensor. The pendulum is constructed from the rod and masses that come with the pendulum accessory The rotary sensor can measure the position and velocity of the pendulum versus time. Using the rigid rod instead of a string keeps the pendulum from swinging out of plane. The data can be used to find the period during the Martian and lunar parabolas and the high-g experienced when the plane pulls up. In free fall it will not oscillate but rotate in a circle with a period dependent on how hard you push it. However, there might be some surprises about its behavior in free fall. Pendulums have been flown by teachers on past Zero-G flights. Below is Tony Fleury's pendulum experiment he flew on a Zero-G teacher flight in 2009. It is intended for classroom use. Students can measure the periods from the video of the spring/mass and the pendulum using a stopwatch. The acceleration is measured by a PASCO PASPort accelerometer and displayed in m/s2 on a PASCO Spark Science Learning System.

The wireless rotary motion sensor with the pendulum accessory can be mounted with the plane of rotation at an angle to the vertical. This simulates reduced gravity in the classroom. Students can experiment like Tony without having to fly on the Zero-G plane.

Students can collect data at various angles and find the relationship between the angle and period. They can try and create a system that will have the same period as the one on the Zero-G plane for the reduced g-levels. Below is some sample data. The incline is the angle from the vertical.


Zero-g Flight

My colleagues suggested more experiments, but I knew that conducting all of them on one Zero-G flight would be difficult. They will have to wait for future flights. On 11/17/21 I boarded my flight to Ft. Lauderdale, connecting through Atlanta. It took all day, but it was good to fly again. I received my third Pfizer COVID vaccine shot 3 weeks before, so I felt safe on the crowded flights. I met with Deb Houts the next day to discuss experiments, plan the teacher flight program, and walk-through G-Force One. One of the first things I learned is that Friday's flight would be different than a normal Zero-G flight. Academic and commercial research experiments were onboard. Instead of the usual 15 parabolas, they were going to fly 30! I had prepared myself for 15 and was confident I would not have much motion sickness. The good news was I would have more time to conduct my experiments and to enjoy the experience of floating. The bad news was I would have more time to get motion sickness. In addition to the researchers would be 11 intrepid adventurers who signed up for Zero-G's new Astronaut Experience Program (AE). The main attraction for them was the 30-parabola flight. At $10,500 it is only $2300 more than the 15-parabola flight. That is a savings of almost $200 per parabola! Deb approved my experiments except for the pendulum. It needs to be mounted to the side of the plane, requiring a high-g test and more paperwork. We hope to have that done by the time teachers start flying. She also said any PASCO sensor must be checked for electronic interference. The accelerometer/altimeter was given a pass because I was going to use it in remote logging mode. The walk-through of the plane was very exciting. The researchers were configuring their experiments and the Zero-G personnel were getting the plane ready. It had flown in the morning for the 4th time that week. Boeing was conducting missile tests in the Gulf of Mexico requiring the Zero-G flights to take off at 7:00 AM. I needed to be at the executive jet terminal at 5:30 AM the next day. I was still on West Coast time, so I decided to go to bed early.

Looking aft on the G-Force One 727-200. My Kundt's tube is in then lower left. Next to it is a glove box for experiments in dexterity for the Astronaut Experience participants.

Zero-G shuttled the AE participants to the hangar after meeting in the executive jet lobby. We got into our jumpsuits, got a preflight briefing, and were supposed to have a breakfast of bagels and juice. Unfortunately, the delivery person got stuck in traffic. This was the first of several bagel-related incidents that would occur this morning. The preflight briefing was given by our flight coach, Dr. C. Marsh Cuttino. Marsh works part-time for Zero-G and conducts medical space research with his company, Orbital Medicine. Marsh has flown many Zero-G and NASA parabolic flights so we listened attentively. I had a chance to chat with a few of the AE participants before boarding the plane. Two came from Germany and one ran a Virginia distillery. He wanted some video of his bourbon floating. He also brought along a small bottle for each participant.

Dr. C. Marsh Cuttino, second from left, advises us not to try and swim while floating

We boarded the plane after going through the mini-TSA screening in the hanger. There were 44 seats in the back of G-Force One full of AE participants, researchers, and Zero-G personnel. Deb Houts was serving as flight director. I thought I had a great post-teaching job! The bagels and juice finally arrived. I grabbed what I thought was a cheese bagel, but it turned out to be cinnamon. That would haunt me later.

Although our final destination was back to the Ft. Lauderdale airport, I wouldn't have boarded any other private jet on the tarmac regardless of where it was going.

Our flight path took us over the Gulf of Mexico. The plane would do 5 parabolas, turn around, do 5 more and repeat until we reached 30. Here is an animation of the flight path from Flight Tracker. In addition to location data, Flight Tracker also posts direction, speed, altitude, and climb rate data for flights.

The AE participants were led to the front of the plane just before reaching the starting point for parabolic flight. It was a little cramped because they were trying something new. A green screen had been taped to the front bulkhead and draped around the sides, taking up a lot of volume. Further limiting our space was the restriction on going near the research experiments. It is hard to keep from colliding with the experiments when you are floating. The green screen would be used to take pictures of us floating so background graphics could be inserted. Personally, I can't think of anything I would rather have in the background than the bulkhead with the Zero-G logo on it. They took the green screen down after everyone had their turn and we had a lot more room to float.

I predict this will be the last time they use a green screen on a Zero-G flight

For the first parabola they flew the plane so that it had a downward acceleration of about 6.1 m/s2. The people are still pulled to the floor by the Earth's gravitational force. However, the normal force is less than mg because they are accelerating. A quick free body diagram of a passenger with up as positive gives N - mg = ma. Using a = -6.1 m/s2 and g = 9.8 m/s2, N = m*(9.8 N/kg - 6.1 m/s2) = m*(3.7m/s2). The normal force is equal to what it would be for the passenger if they were at rest on the surface of Mars where g = 3.72 N/kg. They flew one more Martian gravity parabola followed by two lunar gravity parabolas. The gravitational field strength on the surface of the Moon is 1.62 N/kg. The plane had to fly with a downward acceleration of about 8.2 m/s2. Doing reduced gravity parabolas helps passengers adjust before going zero-g. The 15 parabola flights only get one Martian and lunar parabola. I alternated between taking video of the Kundt's tube (more on this later) and hopping around. Some did 1-arm pushups and other feats of strength. The lunar gravity was especially fun. I envy future tourists traveling to the Moon.

Between parabolas the plane (hopefully) causes an upward acceleration to reduce and then change direction of the downward vertical velocity. This upward acceleration is about 7.8 m/s2. This creates a normal force about 1.8 times what the passenger would feel if they were at rest on the surface of the Earth. On our fifth parabola the plane caused a downward acceleration of 9.8 m/s2. A free body diagram shows the normal force is equal to zero. Normalforcelessness at last! It is amazing to feel the transition from laying on the floor accelerating upward at 7.8 m/s2 to downward at 9.8 m/s2. As this change was ending, I could feel myself slowly rise out of the padding. Once complete, a slight push sent me floating toward the ceiling. Is it still the ceiling? There is no up or down now. I had spent my whole life feeling the gradient of normal force equal to my weight at my feet and decreasing to zero at the top of my head. That gradient is gone in free fall. There is only a gravitational force acting on me pulling equally on every neutron and proton in my body so it cannot be felt. I was accustomed to where my internal organs hang in my abdominal cavity. In free fall they shifted toward my neck and stayed there. My head looked and felt puffy as my heart kept pumping blood as if it had to work against gravity. After about 22 seconds this ends and you are pressed to the floor, feeling much heavier than normal. The transition was more abrupt than usual to extend free fall for the experiments. If you were unprepared, you could find yourself falling more than a few feet and/or landing on someone. Everyone aboard had been vaccinated or had a recent negative test for COVID. We were required to wear masks but they can be a problem if you are sick. We were advised to take them off if we felt even mildly nauseous. Most participants had their masks off after a few parabolas. Below are clips from some of the zero-g parabolas. Look for my encounter with the floating bagel.

At the beginning of the video above you can see me hard at work on the Kundt's tube. It was a distracting work environment to say the least. It was attached to the floor with Velcro, and I wedged the frequency generator between the padding. The Kundt's tube stayed in place, but people kept kicking it and landing on it. This pulled the wires off the speaker. Reattaching them would sometimes send me floating toward the ceiling, unable to adjust the frequency or take video. Before the flight I thought about soldering the wires to the speaker. I am glad I didn't because the wires might have broken. Deb and I decided that the Kundt's tube should be mounted to the wall next time, so it is easier to see and reach. It also will keep people from landing on it when the plane pulls up.

When I was a teacher my students would sometimes be climbing the walls but not literally!


 Zero-g Experimental Results

The results from the Kundt's tube experiment were fascinating. Below is what it looks like in 1g at the PASCO office building. The video first shows it resonating at the fundamental frequency and then at the first overtone of the 0.92 m long tube.

Students can measure the wavelength of the standing wave using the tube dimensions knowing there is a node at each end. Multiply it by the frequency to find the speed of sound in the tube. Notice the other patterns in the tube. The Styrofoam pellets form walls in the wave pattern. They are tallest at the anti-node. It was her curiosity about what would happen to these walls in reduced gravity and free fall that motivated Deb to want to fly a Kundt's tube. The cause of these structures is not easy to explain, even Kundt couldn't. The best explanation I found was a 1932 paper titled "On the Groupings and General Behavior of Solid Particles Under the Influence of Air Vibrations in Tubes" by Edward Andrade. I recommend reading the summary and inspecting the pictures at the end. A pdf of the paper will download if you click on this link. Apparently the eight-shilling price has been waived! The short answer is that vortices form around spheres in a vibrating fluid. The vortices act to repel other spheres. However, they cause an attraction if they get very close. The spheres forming walls are close enough to feel the attraction, but they repel the spheres in the adjacent walls. There also are small air currents flowing longitudinally in the Kundt's tube. These distribute the spheres along the tube and cause some spheres to change walls. You can see these phenomena in the closeup slo-mo video below.

The main question Deb had was "what will the walls look like in reduced gravity and free fall?" An obvious guess was that they will become taller because the disturbing forces from the wave interference can lift them higher. This guess was confirmed by their appearance during the Martian gravity parabolas. I wish I would have marked the tube for comparison height measurements, but they certainly look taller.

The walls were even higher during the lunar gravity parabola, some of the spheres can be seen bouncing off the top of the tube.

I was very curious to see what would happen in free fall. I suspected they would get even taller and be symmetrical. Walls might fill the tube as a thin cylinder. That is what happened, but I was still surprised by what I saw.

The Styrofoam spheres were forming cylinders but near the nodes. In 1 g and reduced g trials the standing wave pattern remained with little going on near the nodes. The walls were always tallest at the anti-node. What was going on? At the anti-node the disturbance from the wave interference was enough to disrupt wall formation. Perhaps gravity is needed to keep the spheres close enough so the attractive force is a factor. Without it, the disruption from the wave interference is able to keep them apart. The only way to tell there was resonance was the formation of the cylinders near the nodes and the increase in sound volume. The small amount of disturbance near the nodes was enough to form the cylindrical walls but not enough to immediately disrupt them. This is certainly not Nobel-prize worthy, but it was exhilarating to discover something that has never been observed before. Unfortunately, I don't I have more video with wider angle shots, slo-mo, and higher resonant frequencies. I had enough trouble getting these shots. This video shows what often happened after the tube was running and I tried to get a video.

Next time we fly it we will use a dedicated camera for the Kundt's tube and have some restraints for the experimenters to use while taking additional video. Mounting it to the wall will help get better video. The addition of a scale to the tube would allow for more quantitative measurements.

The Kundt's tube experiment yielded an interesting result for the speed of sound. The fundamental frequency was measured at 177 Hz. The wavelength is twice the tube length or 1.84 m. This gives a speed of sound equal to 177 Hz x 1.84 m = 326 m/s. What is interesting about that? The fundamental frequency measured at PASCO was 186 Hz. This gave a speed of sound of 342 m/s. Why the difference? I first thought it was the lower cabin pressure. Planes typically are pressurized to the equivalent of about 8000 ft. My college chemistry teacher would have been disappointed by my hypothesis because I am sure I learned that the speed of sound does not vary with pressure. It seems like it should because at zero pressure there is no speed of sound. Shouldn't it gradually get slower as the pressure is reduced? The answer is that the speed of sound gets smaller as pressure is reduced but it increases as density is reduced. These two factors cancel out. The difference was due to a difference in temperature. We can estimate the temperature from the speed of sound. The equation below solves for the speed of sound in air at a given temperature.

Solving for T given v = 326 m/s yields 8.7o C or 48o F. It was chilly on the plane, but our jumpsuits were warm and we were too exhilarated to notice. Students could calculate the cabin temperature using their teacher's onboard measurements with the Kundt's tube. It would be good to add a temperature measurement for comparison

The bottle of water worked as expected. I equalized the pressure with the valve and removed the tape over the holes. A few drops came out as I took the tape off but nothing after that. I enjoyed watching the spherical drops float away. I noticed the water sloshing in the half-filled bottle. It reminded me of a problem we had when I worked as an aerospace engineer. Rocket propellant on an orbiting satellite sloshes too, making it difficult to extract for a rocket thrust. There are several methods to control sloshing. These include spinning the satellite or accelerating it with compressed gas thrusters. It was fascinating to Observe this phenomenon first hand. The video below shows me doing the experiment and pondering the slosh. The closeup shots of the bottle are from the GoPro camera I Velcroed to my chest. I knew it would be useful to take hands-free video in free fall. The GoPro worked great when I tested it in my hotel room. I was disappointed about how shaky it was when I viewed it after the flight. In the hotel room gravity pulled on the camera keeping it stable. In free fall it tilted up and down from the slightest jostling. Most of the GoPro footage proved unwatchable. On a future flight I will mount it to the cabin wall so I can film experiments hands-free.

I was anxious to download the data from the wireless acceleration/altimeter. A downside to using the remote logging feature is you can't see the data display as it is collected. However, I couldn't have successfully monitored a computer during the flight without a lot of preparation. It turned out the data was all there. During remote logging setup, PASCO's SPARKvue software gives you an estimate of how long it can collect data based on the sample rate, the number of sensors activated and the sensor's internal memory. To increase the time I turned off the gyro and lowered the sample rate to 5 Hz. This gave me one hour that should measure most of the parabolas. Next time I will keep the gyro on to measure the pitch rate of the plane during a parabola. I activated the acceleration/altimeter after the first Martian parabola. It collected data for almost an hour, stopping during the 26th parabola. Below is the acceleration graph showing the resultant acceleration in m/s2 on the vertical axis and time in seconds on the horizontal axis.

Because I had the sensor in my pocket or floating in the cabin, I graphed the resultant acceleration. It is the vector sum of all 3 directions but is predominately from the vertical direction. There is some acceleration in other directions caused by the plane, my motion, and the accelerometer colliding with things. On future flights I will mount it to the wall. When the graph is at or near zero, the plane is in Martian or lunar gravity or free fall. The free fall parabolas are after the first 3. I measured the duration of a few, they are about 20 s each. They advertise 22 s or more, perhaps some of them were that long. The screenshot below shows a free fall with a steady reading. I used SPARKvue's delta tool to measure a duration of 19.6 s.


The highest readings occur when the plane is accelerating upward to change the direction of the vertical velocity. These peak at about 18 m/s2 or 1.8 g. We were advised to lay on our backs between free falls and focus on a spot on the ceiling to avoid nausea. I tried to do this every time. The seemingly impervious Zero-G staff walked around during the high g parts getting ready for the next parabola. I would glance around to see what they were doing and quickly found this to be a bad idea. Some of the AE participants sat up and even stood during the high g parts. The worst part for me was when the plane turned around after every 5 parabolas. On the graph the turnarounds show as an acceleration of 10 m/s2. It was very turbulent as the graph shows, especially the long one in the middle. I lay still on my back during those parts, anticipating my next chance to float.

During the reduced gravity parabolas, the acceleration values are not steady because I was jumping around and taking video of the Kundt's tube.  Zooming in and reading the graph where there is little movement shows they are reasonably close to the expected values of 3.7 m/s2 and 1.6 m/s2. You can download the SPARKvue data file by clicking this link. PASCO SPARKvue software is free for tablets and phones and can be downloaded here.


The altimeter data also was interesting. Below is a segment of altimeter measurements shown below the acceleration measurements for several free fall parabolas. The altitude in meters is graphed on the vertical axis and time in seconds on the horizontal.

The altimeter graph is zoomed in because the plane's pressurization system kept pressure constant in the cabin. The average was 2573 m or 8442 ft. The variations in cabin pressure resulted in changes to the altimeter reading of only ±5 m. The vertical axis is really showing pressure changes with some interesting trends. The pressure starts dropping at the start of each free-fall, then drops steeply followed by a slight increase before a rapid drop just as the plane starts to pull up. The overall drop can be explained by the fact that the air in the cabin is not accelerating relative to the inside of the plane. Without the walls, floor, or ceiling pushing on it, the pressure drops. I am not sure what causes the different drop rates, but it might have something to do with the pressure system adjusting to the increasing outside pressure as the plane loses altitude. The slight increase could be caused by me dropping to the floor at the end of free fall. The acceleration/altimeter was in my pocket and dropped almost 1 m. The highest pressure corresponds to when the plane has a large upward acceleration. The floor of the plane is pushing up on the cabin air and compressing it. There should be a gradient of pressure from the floor to the ceiling during the high g part. I will place acceleration/altimeters on the floor and ceiling for the next flight to see if it is measurable. There is a pressure drop followed by a rise before each free fall and a pressure drop at the start of each high-g part. My guess is the pressurization control system causes these changes. I will have to do some research on plane pressurization control systems.

The PASCO acceleration/altimeter and I are accelerating toward the ground at 9.8 m/s2 but it reads zero

PASCO's SPARKvue software has an analysis tool that integrates the acceleration data to find the vertical velocity of the plane. I normalized the values by subtracting 9.81 m/s2 from the data. There was a small drift that had to be subtracted too. I took one section of parabola and set the initial vertical velocity to zero and produced the graph below. If you want to see the details of these calculations, they are in the SPARKvue file I linked to above. The graph below shows the vertical velocity graph below the acceleration graph. Vertical velocity in m/s is on the vertical axis and time in seconds on the horizontal axis.

The graph shows that the plane is slowing down on the way up at the start of free fall. This is counter-intuitive for many people, including Miles O'Brien in the CNN video. It is not surprising because the word "fall" is almost always used to describe something that is heading toward the ground. That is a problem with the term free fall. Eventually the plane's vertical speed reaches zero and it starts speeding up on the way down. The 212 m/s change in velocity during the 20.8 s free fall period shown on the graph checks out. Accelerating at 9.81 m/s2 for 20.8 s would cause a 204 m/s change in vertical velocity.  If my analysis is correct, it reaches a maximum downward speed of 147 m/s after the first parabola on the graph. This is 327 mph! We were falling with style. Imagine the shock of students coming up with this value in class as they realize their teacher was hurtling toward the ground at 327 mph. It shocked me when I first calculated it. Below is a figure from the Zero-G website that shows that the plane free falling on the way up and down.