How Many Balloons Would it Take to Lift a Human?
Back in fifth grade, my teacher assigned the class a Genius Hour project, which always felt poorly named to me as we were given weeks to plan and create quite literally anything of our choice. I was working with a few of my friends in the class and after pitching ideas like building a car and making a house out of popsicle sticks, we decided that we wanted to make a rocket that could actually fly into space — quite the optimistic goal considering all we knew about physics at the time was that it sounded real similar to a Pokémon type. But, we were young, naive, and determined to make it work.
So, over the next few days, I began to assemble a makeshift rocket out of cardboard and another one of my friends went out to buy helium balloons — our chosen method of getting the rocket to fly up, up, and away. We were set on helium because a) we knew helium balloons rise, b) we didn’t know how to make an engine, and c) balloons aren’t too expensive. Unfortunately, we were very wrong about c). For a couple of 10-year-olds, our initial estimate of 50 helium balloons required turned out to be a little galaxy out of our budget, so we settled on buying 7 brave standard-sized balloons. As you might expect, our cardboard contraption didn’t float an inch above the ground and that was it for our project. My teacher expressed his disappointment in us, but I think it would’ve helped far more if he instead walked us through why our project failed and perhaps how many balloons we actually needed to get our little rocket off the ground and into the sky. I didn’t get that answer then, but now a decade later, I’ve realized I have the tools to find out for myself. So, let’s talk about lifting things with balloons. And since so much time has passed, instead of lifting some cardboard, let’s be more ambitious and try to make a human fly.
The science.
I know this premise might sound silly, but the idea of generating lift with balloons isn’t unheard of.
Blimps, zeppelins, and hot air balloons all use specific gases to provide lift, and while it’s not the same as attaching a bunch of helium balloons to a structure to make it float, many of the principles are similar. Balloonfliers, as I like to call these aircrafts, use “lighter-than-air” gases like helium which have densities lower than the atmosphere around them.
Rising and falling in these balloonfliers depends primarily on principles of density and buoyancy. Density is a measure of the amount of mass in a given volume and is determined mainly by molecular structures, temperatures, and containers for gases. Decreasing temperatures usually increases a substance’s density as its particles get closer together, and vice versa. However, you might know ice is an exception as it’s less dense than water—a result of the unique molecular structure of ice, stabilizing water molecules at larger distances from each other than observed in liquid water.
Bringing buoyancy into the equation, in a given fluid medium, an object or substance that is more dense than the medium will sink while something less dense will rise (depicted below). For example, the density of water is about 0.997 g/ml. If you add a block of ice with a slightly lower density at 0.917 g/ml, you will notice the ice floats in the water. The force that pushes the ice up within the water is called the buoyant force.
We can liken a balloonflier to this ice and water analogy. If the average density of the aircraft is less than the atmospheric density at a given elevation, the aircraft will rise and continue to float up into the air for as long as the relationship remains. Then, if the average density of the aircraft is changed to be heavier than the air around it, it will start to fall. This is how blimps and zeppelins work, and hot air balloons use heat to make the air inside the balloon more or less dense, giving the craft lift or letting it fall. There are also other principles at use, like the Archimedes’ principle which states that the upwards buoyant force exerted on an object is equal to the weight of the fluid it displaces, but the previously described ideas are the big ones to keep in mind.
Now, we can use these principles to try and figure out how how many helium balloons we need to lift a human.
How many balloons?
Our goal is to make the system of a human + the attached helium balloons less dense on average than the air around the human. However, dealing with density calculations for this system are a lot more complicated than doing the math with the lifting force of helium.
Helium has a density of 0.1786 g/L and under standard conditions, air has a density of 1.29 g/L, making helium a significantly lighter gas. Because of this density difference, helium has a lifting force of 1.0715 g/L, also considering some added weight from the balloon itself and whatever string is used to attach the balloons to the human. So, to find how many balloons we need to lift a human, we will need to a) settle on a weight for the human, b) figure out how much helium is needed to lift the weight of the human, c) figure out the volume of air that a balloon can hold, and d) use an approximate balloon volume to determine the number of balloons needed.
a) A quick google search told me the average human adult weight worldwide is 62 kg, or 62,000 g as we’ll be using grams in our calculations.
b) If the lifting force of helium is 1.0715 g/L and the human in question weighs 62,000 g, we need 62,000 ÷ 1.0715 = 57862.81 L of helium to take them off the ground.
c) The volume of air that a balloon can hold is tricky to estimate because you can technically overfill or underfill them and have them still keep their shape. So, to determine the volume for the calculations, we’re going to assume the balloons have a standard 11-inch diameter and they’re perfect spheres when filled with sufficient helium. Using the formula for the volume of a sphere; V = ⁴⁄₃ * π * r³, we get a volume of 11420.31 cm³, or 11.42031 L per balloon.
d) If we need a total of 57862.81 L of helium and each balloon can carry 11.42031 L of the gas, we need a total of 57862.81 ÷ 11.42031 = 5067 balloons to make the human fly.
Of course, that’s to make them just about lift off the ground. If we wanted the human to go further up faster, we’d have to add balloons to the number we got. But 5067 balloons is the magic number. Can you imagine that?
$$$.
Maybe if you put together a huge team of people, you could get these many balloons inflated with helium and ready to start lifting you into the air. But, how much would it cost?
It turns out, this question is still hard to answer. After an unreasonable amount of searching, I just about managed to find a shop that has a price on a helium-filled balloon of our needed dimensions, and it costs $5 per balloon which is also attached to a little weight to keep it grounded. So let’s kick it down to a generous $3 per helium balloon itself. So, for the 5067 balloons we need to pick up the human we’ve discussed, it would cost us a whopping total of $15,201.
So maybe this experiment is off the cards for a little genius hour experiment, but c’mon. Would you rather buy some lame old car thing or be able to momentarily float an incredible few centimetres off the ground? I think we all know the right answer.
