|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.
|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
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.
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.
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.
|Graduate students from the University of Missouri prepare their condensation experiment for flight as their professor supervises.|
|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.
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.