Why Don’t We All Get A Balloon, And Then We Can Fly Into The Sky?

A couple of weeks ago, I was at a birthday party for one of my son’s friends. It was a great day, at a little park a half hour drive north and east of where I live, situated on a tributary of the Ohio River. The kids all had squirt guns and the like, and got each other soaked down while the adults sat back and watched and took pictures and were grateful that they brought extra clothes and towels. There were balloons as well, because there were kids.

One child was super excited about the balloons. They were your ordinary latex kind, that you blow up with your own lungs, but he was bouncing them around and laughing. “Why don’t we all get a balloon?” he asked excitedly. “And then we can fly into the sky!”

So, yeah. It wasn’t my son that asked it. But it’s the kind of question he could have asked, so I’ll answer it.

How does a balloon float?

The same way a boat does.

Care to elaborate?

Of course.

It’s tempting to say that things float because they’re light, but that’s not quite accurate. For example, an oil tanker floats but it is not light – they can carry anywhere from 1,500 to 550,000 deadweight tons, depending on size. No. Floating has everything to do with the mass of the object, and the fluid that surrounds it. See, all objects placed into a fluid displace some of the fluid (put a rock in a cup of water to see for yourself). If the mass of the fluid you displace is greater than your mass, you float. And air, for these purposes, can be considered a fluid.

But let’s look at some math, since the University of Chicago was kind enough to put together a document (Lighter Than Air: Why Do Balloons Float?) that explains all of this in some detail. There are two forces in play, the downward force (which is the pull of gravity) and the upward force (which is how much the fluid resists the downward force). The downward force (Fg) is the mass of the object (M) x gravitational strength (g), which is also how you calculate “weight” in physics. Weight, after all, is mass times gravity (which is why you weigh less on the moon, even though you retain the same mass). Upward force (Fb) is the mass of the fluid displaced (m) x gravitational strength (g).

Once you have Fg and Fb, you can calculate life=t. All that is is Fb – Fg. If the result is positive (meaning Fb is larger than Fg), you are sinking. If the result is negative (meaning Fb is larger than Fg), you are rising. And if the result is 0 (meaning the two forces are equal), you are floating immobile in midfluid.

Uhm. Okay.

Let’s do an actual example, shall we?

Yeah. Lets.

After consulting Google, I found an estimate that the average-sized party balloon masses 1.7 grams, and several notes that they can weigh more depending on the actual size, thickness, etc, etc. This will be important, momentarily.

Now, the density of air at sea level is about 0.0012 grams per cubic centimeter. So, if you inflate your hypothetical average-sized party balloon to a diameter of 1 foot (0.3048 meters, which means 30.48 centimeters), you get a sphere (for the sake of not making me crazy) containing 14,826.7 cubic centimeters of air. The inflated balloon weighs a total of (14,826.7 x 0.0012) + 1.7 = roughly 19.5 grams, and displaces 17.8 grams of air. So, it sinks. If you inflate the balloon to 2 feet in diameter (60.96 centimeters), you get a balloon containing 116,613 cubic centimeters of air. It weighs 141.6 grams, and displaces 139.9 grams of air.

Clearly, both balloons sink. And, in a vacuum, both would sink at the same rate because they have the same lift (-1.7).

But they don’t fall at the same speed. Not the ones I’ve played with, anyway.

Nope. Because we live in an atmosphere. And atmospheres create air resistance. I won’t go into the math there, because it made my head hurt a little, but it works like this: an object produces drag (a resistance to acceleration) based on the cross-section of the object perpendicular to the direction of movement. As the cross-section gets larger, the power needed to overcome the drag increases. How much? Well, it’s based on the cube of the cross-section. If you double it, you need 8 times as much power. If you triple it, you need 27 times as much power. And so on.

For the balloon, acceleration is down towards the ground and the cross-section is the diameter of the balloon. Doubling the diameter of the balloon means you would need 8 times the power to make it fall at the same speed as the smaller balloon. Since gravity (roughly) stays the same, that means you would expect to see it fall 8 times as slowly.

So, getting back to the wish to “fly into the sky”…

Sure. See, to make a balloon fly, you need something less dense than room-temperature air. That’s why hydrogen and helium are so popular. They’re gaseous at “room temperature”, and they weigh far, far less. Hydrogen weighs 0.000089 grams per cubic centimeter, and helium weighs 0.00018 grams per cubic centimeter. So, looking at the two balloons from the earlier example, we get the following information:

  • The 1 foot balloon weighs 3 grams if you fill it with hydrogen, and 4.4 grams if you fill it with helium. It displaces 17.8 grams of air.
  • The 2 foot balloon weighs 12 grams if you fill it with hydrogen, and 23 grams if you fill it with helium. It displaces 139.9 grams of air.

Regardless of which gas you fill the balloon with, it weighs less than the gas it displaces. So it has positive lift and it goes up. In fact, it could even lift additional weight – the 2 foot balloon filled with hydrogen would have neutral buoyancy with a 127.9 gram weight attached to it, so you could attach two Hershey’s chocolate bars (1.55 oz, or 44 grams each) to the balloon and still watch it go skyward.

Heating the air will also work, as gasses become less dense with heat. Sadly, I don’t have a good equation (that I understand) to show how much you’d have to heat the air to make it lift.

How many balloons would I need to fly to the sky, then?

Well, that’s more or less easy. How much do you weigh, and what gas are you using? I’ll illustrate with my son. He weighs around 60 pounds right now. That’s 27.2155 kilograms, or 27,215.5 grams. Looking at the two foot balloons, the lift for the hydrogen balloon is 127.9 grams per balloon and the lift for the helium balloon is 116.9 grams. So, it would take 27,215.5/127.9 = 213 2 foot hydrogen balloons to give him neutral buoyancy. 233 2 foot helium balloons would be required to achieve the same effect. You’d need another 18 hydrogen (20 helium) balloons to offset the weight of his clothes (maybe more if he’s planning on flying high). And I have no idea how many balloons would be required to offset the weight of the lines he’s holding on to or the harnesses to keep the balloons attached to him. And, of course, he’d need more to actually go up.

By contrast, I weight 316 pounds. So I’d need 1,121 hydrogen balloons or 1,227 helium balloons to achieve the same effect. That’s 37,553.5 cubic feet of hydrogen balloons, or a sphere roughly 42 feet in diameter. Oh, and it could explode.

Don’t do this at home.

No kidding.

You’d think so, but at least one person did.  Larry Waters used 45 8-foot weather balloons filled with helium to lift himself, his lawn chair, his parachute, his pellet gun (so he could pop balloons and descend), his CB radio, his camera, and sandwiches and beer to a height of 16,000 feet.  He flew for 45 minutes, and got fined $1,500 by the FAA after an appeal.  But, because he was a trained pilot and lucky, he didn’t die.

Can They Hear Me In China?

“BOO!” my son yells, leaping out from a shrub.  And then he dissolves into a fit of laughter.

This is a game he likes to play, whenever he gets the chance.  As soon as we’d parked and he got out of the car, he ran up the sidewalk towards the front door of our condo.  And then he ducked back behind the hedge, lurking.  The game, now, is for me to walk towards the door.  Then he’ll jump out and shout “boo” and try to make me jump.

“Did you know I was there, daddy?” he asks.

Of course I did, I think.  You hide in the same place every time.  “Kind of,” I tell him.  “I guessed where you were.”

He blows that off.  “I was loud, wasn’t I?”

“Yes, you were,” I answer, unlocking the door.

“Was I loud enough for them to hear me in China?”

How Do We Hear?

Obviously, we hear with our ears.


Sound waves, which are really just pressure waves in the atmosphere, strike the outer ear and are channeled into the ear canal.  These pressure waves vibrate the eardrum, which in turn vibrates the bones of the inner ear (the malleus, the incus, and the stapes), amplifying the vibrations and transmitting them into the inner ear (or cochlea).  Hairs in the cochlea are stimulated by these vibrations, creating an electrical signal that transmits along the auditory nerve to the brain.

Yes, this is terribly simplified.

How Loud Are You?

Strictly speaking, “loud” is a matter of perception – the same pressure wave can result in different experiences of “loudness”.  However, this perception is tied to the intensity of the pressure wave, just as the perceived pitch of a sound is tied to the frequency of the wave.


A wave

Using the above image of a wave, the intensity is how high the peaks and how low the valley is – the higher the peak, the more intense the wave.  Another way to think of intensity is how much energy the wave carries – the taller the wave, the more energy (just like how bigger ocean waves hit harder than small ones).  Frequency, on the other hand, is how fast the wave moves – the closer together the peaks, the faster the wave moves and the higher the frequency.  Generally speaking, we perceive intensity as loudness (because the pressure wave hits the ear harder) and we perceive frequency as pitch (because the pressure wave stimulates the bones in the ear faster).

“Loudness” is measured in decibels (dB), because one decibel is the “just noticeable difference” in sound intensity for the human ear – assuming the pressure wave generated is in the 1,000 Hertz (Hz) to 5,000 Hz range we are best at hearing.  Every 10 dB represents multiplying the intensity of the pressure wave by 10 – that is, a 10 dB sound is 10 times more intense than a 0 dB sound, a 40 dB sound is 10,000 times more intense than a 0 dB sound, and a 100 dB sound is 10,000,000,000 times more intense than a 0 dB sound.

We generally can’t hear anything below 0 dB, and normally speak in the 60 to 65 dB range.  A jackhammer 50 feet away is about 95 dB, a power mower 3 feet away is around 107 dB, and loudness causes pain starting around 125 dB.  Sounds at 140 dB and greater can cause permanent damage with even short exposure.

How Far Away Can We Hear?

This gets tricky, because the answer is “no further than when the perceived volume falls to 0 dB”.  Tricky, because sound obeys the inverse square law which states that for any source power P generated at the center of a sphere, the intensity of at the surface of that sphere is P/4πr2 (although a good approximation is P/r2, since the math gets easier).  According to Hyperphysics, r is pretty much always measured in meters for these purposes (because sound intensity is actually measured in watts per meter squared, so it keeps the units the same).

Since sound intensity can be transformed into decibels, it’s really not a stretch to directly apply the inverse square law to decibel measurements.  So, a 60 decibel conversation would be perceived as 60 decibels at 1 meter away, 60/(2*2) = 15 decibels at 2 meters, 60/(3*3) = 6.6 decibels at 3 meters, 60/(4-4) = 3.75 decibels at 4 meters, less than 1 decibel at 8 meters, and so on.  Realistically, at this point, it’s probably safe to call it “inaudible” (even though you could technically detect it).

How Loud Would You Have To Be For Someone To Hear You In China?

All right, here’s where the math gets… entertaining.  I live in Cincinnati, Ohio, which is (according to Google) 10,969 kilometers from Beijing.  Measuring along the curved surface of the Earth, that is.  But, to keep things simple, we’ll ignore that.  So, 10,909 kilometers is 10,909,000 meters.  To be heard in Beijing, we’d have to generate enough decibels to result in a greater than 0 dB sound 10,909,000 meters away.

For laughs, let’s aim for a 60 dB sound.  That way, our sound can be clearly understood.  The radius is 10,969,000.  So, the equation looks like this:  x/10,969,0002 = 60.  Solving for x gives us x = 60(10,969,0002), or x = 7,219,137,660,000,000 dB.  This is a nonsensical level of perceived volume, and would render you deaf in ludicrously tiny fractions of a second.

What could generate that?  Well, we’d have to reverse engineer the decibels into watts of power, which converts to 721913765999988 watts per meter, or about 721.9 terawatts of power.  Now, you can roughly convert watts to Joules per second, so that’s roughly the explosion of a 200 kiloton nuclear weapon.

Assuming I did my math correctly, which I’m not guaranteeing.  What I can guarantee is that there is no way you’d want to be standing anywhere near something loud enough in Cincinnati that you can hear it in China.

Why Does Oil Make A Rainbow?

It’s summer, and it’s just finished raining, and we’re walking across a parking lot on our way back to the car from running an errand. My son is, as five-year-olds are wont to do, taking the opportunity to jump in puddles and laugh as they splash. Suddenly, he stops. “Look!” he cries, pointing at the ground. “There’s a rainbow!”


I go and look. Sure enough, there’s a small puddle with a thin film of oil slicking the top. I nod at him, and looks at it again. “Why is there a rainbow on the ground?” he asks.

“There’s oil on the puddle.”

He looks at it for a moment, then looks up at me. “How does oil make a rainbow?”

Yeah. You’ve just stumped me son.

So, what’s up?


Specifically, PHYSICS!

Could you… elaborate? Just a little?

It all starts with the nature of light, which as we all know is simultaneously a particle and a wave. Here’s how Professor Emeritis Dinesh O. Shah explains it in Scientific American:

Light reflects upward both from the top of the oil film and from the underlying interface between the oil and the water; the path length (the distance from the reflection to your eye) is slightly different depending on whether the returned light comes from the top or from the bottom of the oil film. If the difference in path length is an integral multiple of the wavelength of the light, rays reflected from the two locations will reinforce each other, a process called constructive interference. If, however, the rays reach your eye out of step, they will cancel each other out due to destructive interference.


Sunlight contains all the colors of the rainbow–the famous ROYGBIV (red, orange, yellow, green, blue, indigo, violet). Each color of light has a different wavelength. Hence, a given disparity in the path length will cause constructive interference of certain colors, whereas other colors will not be observed because of destructive interference. Because the oil film gradually thins from its center to its periphery, different bands of the oil slick produce different colors.

Constructive and destructive interference?

Think of the classic sine curve you had to draw (we all had to draw them) when you took algebra or pre-calculus in high school. The wavy line that looks kind of like a snake. That thing. It’s the most common way to represent a wave of any sort, with the height of the “hills” of the wave representing amplitude (how intense the wave is – brightness for light, loudness for sound, and so on) and how close together the “hills” are representing frequency of the wave (how energetic it is).

Now, think hard about that math class. Do you remember what happens if you add two sine waves together? It changes the nature of the wave. Two identical waves will end up dobuling the amplitude (making it brighter or louder), while two utterly opposite waves will flatten the wave into a line. Check out the image below, if that isn’t clear.


The amplitude of the light is how bright it is, so the areas of the puddle where the reflected light interferes constructively you can see it clearly while you can barely see it when the light interferes destructively. The colors shift because the frequency of the reflected light (which determines the color) vary with the thickness of the oil on the water and the angle at which the light hits your eye.


How Does Air Conditioning Work?

“The car is cold!” my son declares as he climbs in. “Good!”

It’s a hot day out, although not as hot as it’s been recently. Stil, the car’s pleasantly cool because I’d just parked it a few minutes ago so I could pick him up from Kindergarten, and the air conditioning had been running. “You’re right,” I agree.

“Why is it cold?” he asks.

“I had the air conditioning running,” I answer.

“Does it run all the time?” he asks, fastening his seatbelt.

“No,” I answer. “Only when I turn it on. You wouldn’t want it running in the winter, after all. When it’s cold out, you don’t want to make it colder.”

He nods at that, agreeing with the idea. “How does it make it cold?”

Uhm. “I… don’t know,” I answer, although I’ve got a vague idea in my head of how I think it works. Something to do with freon and fans, clearly. “I’ll have to find out.”

How do air conditioners work?

Air conditioners work, it turns out, for reasons very similar to the water cycle we all learned about as children. They have a liquid in them (the refrigerant) which absorbs heat from the environment (your house or car), evaporating into a gas in the process. This gas is warmer than it was as a liquid, but it’s still not hot. It gets hotter, though as it’s circulated into a compressor, a device designed to pressurize the gas back into a liquid. A side effect of this pressurization is heat (to see this yourself, try squeezing a rubber ball – the pressure generates heat).

The hot liquid is then passed into a condensor, where it goes through a radiator that allows the heat to dissipate. This works because, even if it’s really hot outside, the pressurized refridgerant is hotter. The cooler pressurized liquid is then passed through a narrow hole into the evaporator, where the pressure drops and the temperature drops along with it. Once it enters the evaporator, the whole cycle has started over.


This is an extremely simplified version of the process, of course. You can read a far more detailed explanation of air conditioning here.

Why does changing pressure make things hotter or colder?

According to Hyperphysics, heat is “energy in transit from a high temperature object to a lower temperature object. An object does not possess ‘heat’; the appropriate term for the microscopic energy in an object is internal energy. The internal energy may be increased by transferring energy to the object from a higher temperature (hotter) object – this is properly called heating.”

Internal energy is “defined as the energy associated with the random, disordered motion of molecules. It is separated in scale from the macroscopic ordered energy associated with moving objects; it refers to the invisible microscopic energy on the atomic and molecular scale.”

Now, let’s turn to the first law of thermodynamics, which states that “the change in internal energy of a system is equal to the heat added to the system minus the work done by the system.” Based on this, it makes sense that increasing pressure increases internal energy and decreasing pressure decreases internal energy. Why? Because when you increase pressure you’re adding energy (because work is being done to the system), and when you decrease pressure you’re removing energy (because the system is working at pushing outwards). The added energy when you increase the pressure increases the internal energy that can be transferred to other systems, increasing the heat. Likewise, the decreased energy when you reduce the pressure reduces the internal energy that can be transferred to other systems.

What’s a system? The thing in question. The refrigerant in the air conditioner, for example, is a system for this purpose. So is the air in your home, or your car.

So, why does an air conditioner work? Thermodynamics, and clever engineering.

Why Does The Sun Move So Slow?


I really wish I could remember what prompted this questions. I suspect it had to do with one of our conversations about time, and how “day” is from sunrise to sunset. There was probably something we were doing in the evening, something he was looking forward to doing, and the sun seemed to be just crawling through the sky. Whatever the reason, the question certainly seems to make sense. The sun takes all day to cross the sky, so it looks slow. It comes up gradually, takes four to six hours to reach noon, and then slowly sinks into the west.

Of course, appearances are deceiving.

How Fast Does The Sun Move Across The Sky?

This is actually sort of tricky, because the Sun isn’t actually moving around the Earth. To begin with, let’s refer back to the technical definition of sunrise and sunset:

Sunrise and sunset. For computational purposes, sunrise or sunset is defined to occur when the geometric zenith distance of center of the Sun is 90.8333 degrees. That is, the center of the Sun is geometrically 50 arcminutes below a horizontal plane. For an observer at sea level with a level, unobstructed horizon, under average atmospheric conditions, the upper limb of the Sun will then appear to be tangent to the horizon. The 50-arcminute geometric depression of the Sun’s center used for the computations is obtained by adding the average apparent radius of the Sun (16 arcminutes) to the average amount of atmospheric refraction at the horizon (34 arcminutes).

Now, an arcminute is 1/60th of a degree, so the day begins when the center of the sun is 5/6ths of a degree below the eastern horizon and ends when the center of the sun is 5/6ths of a degree below the western horizon. Assuming perfect viewing conditions, et cetera, et cetera. So, that means that the sun has to cover 181 2/3 degrees in a single day. Here in Cincinnati, sunrise on the day this article is published is(August 19, 2016) is 6:55 am, and sunset is 8:27 pm. So, it will require 13 hours and 33 minutes (813 minutes) to cover that distance. That works out to, let’s see… 181.6666 / 813 = 0.22345 degrees per minute, or 13.407 degrees per hour.

Now, let’s do some more math. Cincinnati is at 39.1031 degrees north. According to Ask Dr. Math, you “just multiply the equatorial circumference by the cosine of the latitude, and you will have the circumference at that latitude.” The equatorial circumference of the earth is 24,901 miles, so 24,901 * cos(39.1031) = 19323.48 miles. The Sun crosses 181.666/360 = 0.5046 of that distance in 813 minutes, so that’s 9751.197 miles in 813 minutes. That’s essentially 12 miles a minute or 719.65 miles an hour.

But that’s the speed at which the sun passes over the Earth at that latitude on August 19. It’s not how fast it appears to an observer on the ground! To an observer standing on the surface of the Earth, the distance to the horizon is approximately 2.9 miles. That means that my son, observing the motion of the Sun, is standing at the center of a perceptual circle with a circumference of 2(π)2.9 = 18.22 miles. Which means that he sees the Sun appear to take 813 minutes to cover 18.22 * 0.5046 = 9.19 miles. That works out to a perceived speed of 0.0113 miles per minute, or 0.678 miles an hour.

No wonder it looks so slow to him. When we’re out on walks, my son and I hit a pace almost four and a half times faster!

How Fast Does The Sun Move Through The Galaxy?

Of course, the speed of the sun gets even trickier. Because, although it doesn’t move through the sky (we move, creating the illusion), it still orbits Sagittarius A*, the supermassive black hole at the center of the Milky Way. This monster is some 26,000 light years from earth and weighs in at around 4,000,000 M☉. Our Sun travels in a roughly circular orbit around this distant behemoth at a speed between 217 amd 250 kilometers per second – let’s take the average of those five figures and call it 230.4 kilometers per second (143.16392 miles per second). That’s 829,440 kph (515,390.112 mph).

That sounds impressive, doesn’t it?

Here’s something to consider, though: the speed of light is 299,792,458 meters per second, or 299,792.458 kilometers per second. That means the Sun (and it’s attendant planets and dwarf planets and other detritus) are moving at 0.07685% of the speed of light. Remember that line above, the one that reads “this monster is some 26,000 light years from earth”? That means that our Sun orbits Sagittarius A* in a circle approximately 163,360 light years in circumference. As a result, it will take about 163.360/0.07685% = 212.5 million years to complete an orbit. (Actual calculations from real astronomers come in at between 225 and 250 million years, which makes sense – they have access to more accurate figures, and the sun would actually describe an ellipse instead of a circle.)

So, why is the sun moving so slow? It isn’t. It’s tearing through space at a pace five times faster than the New Horizons probe at it’s maximum velocity – the fastest ship ever built by humanity (although the Sun’s gravity had slowed it to ‘only’ 14 kilometers per second by the time it passed Pluto). We just don’t notice, because it’s a huge universe and we have a very small frame of reference.

Why doesn’t the sun melt?

This week, it seems, I’ll be writing about the sun. Why? Well, when we were walking home from preschool yesterday, I asked my son if he knew what day it was. “It’s the first day of summer!” he declared. And then he asked me a whole bunch of questions, one right after the other:

To be honest, I felt like I’d been hit by an avalanche of curiosity. But they’re all great questions.

What is melting?

Let’s start with the Dictionary.com, and a definition of melt that states:

  1. to become liquefied by warmth or heat, as ice, snow, butter, or metal.
  2. to become liquid; dissolve
  3. to pass, dwindle, or fade gradually (often followed by away)
  4. to pass, change, or blend gradually (often followed by into)
  5. to become softened in feeling by pity, sympathy, love, or the like
  6. Obsolete. to be subdued or overwhelmed by sorrow, dismay, etc.

From a more technical perspective, ‘melting’ is a first-order phase transition in which a material’s latent heat increases and it’s density or volume decreases sufficiently that it moves from the solid phase to the liquid phase.

Wait. Phases? Phase transitions? What now?

You’ve probably seen a diagram like this before:


That is a phase diagram for water, showing the different states (solid, liquid, or vapor) that water can be in based on temperature and pressure. Under one atmosphere of pressure (1 bar or 100 kPa), it is a solid at or below 0 degrees Celsius, a liquid between 0 and 100 degrees Celsius, and a vapor above 100 degrees Celsius. Phase is just the technical term for these states, and a phase transition is simply where the material changes (or makes a transition) from one phase to another.

While researching these phase changes, I ran into the terms “first-order phase transitions” and “second-order phase transitions” a lot. I’ll be honest and say I don’t fully understand them, because the best definitions all seem to involve a whole lot more physics than I understand. But here’s my best attempt at an explanation, after reading several articles and staring hard at Wikipedia:

  • A first-order phase transition is driven by heat, and the material transitions from one phase to another at a set rate based on the energy added to the system. Think of melting ice, or boiling water.
  • A second-order transition is also called a continuous phase transition, and appears to a uniform change across the material – imagine a block of ice instantly becoming water, for example.

The first-order phase changes

The first-order phase changes are the ones we’re all familiar with. There are a whole lot of other types of phase change, so have fun reading up on them some time.

Right. So what does all of this have to do with a star?

All of this is a long walk to the answer I originally gave my son, when he asked me why the sun didn’t melt. “The sun can’t melt,” I told him. “Melting is when a solid turns into a liquid, and the sun is made of gas and plasma. It’s way hotter than melting.” Which is more or less true, and also led to the next question he asked me. But we’ll handle that tomorrow.

What is a star?

I’ll be honest here. I thought the International Astronomical Union would have a formal definition of a star, much like they do for planet and dwarf planet and the like. But, if they do, I couldn’t find it. So, in brief, a star is “a luminous sphere of plasma held together by its own gravity”. It can’t melt, because “melt” is not a phase transition available to plasma. Anything in it that could have melted has already melted, then vaporized, then ionized around 4.6 billion years ago.