Halloween Science: How Do Broomsticks Fly?
Just in time for Halloween, Ask Science looks at just what kind of science would be involved in a flying broomstick, and what forces would govern such a flight.
Lee Falin, PhD
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Halloween Science: How Do Broomsticks Fly?
A few weeks ago, my family and I visited a castle where they filmed part of the first Harry Potter film. Despite the rich history of the castle, one of the biggest draws for visitors with young children is the daily broomstick flying lessons. My youngest daughter was quite excited about this, until about 5 minutes into the lesson when she realized the brooms didn’t actually fly. (A fact which I’m pretty sure we explained to her beforehand).
That experience made me wonder though, just what kind of science would be involved in a flying broomstick? What forces would govern such a flight? So just in time for Halloween, let’s take a look at the science of flying broomsticks.
Up!
Let’s start with the basics: getting that broomstick to hover off the ground with nobody on top of it.
Now if you remember from our discussion of Newton’s Laws, the First Law of Motion says that unless an outside force acts on our broomstick, it isn’t going to move anywhere. So in order for our broomstick to hover off of the ground, we need to apply an upward force, which we’ll call thrust. But how much thrust do we need?
The Gravity of the Situation
Well, as you probably know, the thing that keeps me, you, brooms, and witches from just flying off into the sky, is gravity.
Assuming we’re flying our brooms on Earth, the Earth’s gravity accelerates objects towards its center at 9.8 m/s².
Newton’s Second Law of Motion tells us the force that gravity applies to our broomstick is equal to the mass of the broomstick, multiplied by the gravitational acceleration. Amazon tells me that a traditional witch’s broom has a mass of about 1 kilogram. So we have:
Force of Gravity = 1 kg * 9.8 m/s² = 9.8 Newtons
This means the force of gravity acting on the broomstick is 9.8 Newtons.
We Have Liftoff
So imagine for a minute that you have a tug-of-war game going on with a bunch of kids, who for some reason have exactly the same amount of strength and tug-of-war skill.
If we have an equal number of kids on each side of the rope, the amount of force trying to move the rope on each side will be equal. As you might imagine, this means that the rope won’t move. Now if we add one extra kid to the left side of the rope, the rope will start moving to the left. If we add two extra kids to the left side of the rope, the rope will move left even faster. The same principle applies to lifting our broomstick off the ground.
If we ignore things like the viscosity of the air, we can determine that in order for lift off to happen, our magical broom needs to exert more than 9.8 Newtons of thrust.
If we want it to sit stationary, the broom needs to exert the same amount of force as the gravity pulling down on it (9.8 Newtons), and to descend we need to exert less than 9.8 Newtons of thrust.
How fast the broomstick moves up or down will depend on how much more (or less) the force is.
Something’s Wrong with My Broom
So now comes the uncomfortable part of the lesson where I have to admit that broomsticks don’t actually fly. If you’re like my daughter, you might be ready to cry at this point, but perhaps I can distract you with a brief discussion of how other things generate thrust.
If you blow up a balloon, and then let the air out of it, thrust is generated by the air flying out of the back of the balloon. Newton’s Third Law of Motion tells us that when the air is pushed out of the balloon with a certain amount of force, the balloon is propelled in the opposite direction with the same amount of force.
Rockets use the same technique, but instead of just releasing air, they burn rocket fuel which generates exhaust gas which is pushed out of the bottom of the rocket, causing the rocket to move in the opposite direction. Another fancier method of producing thrust is by using electrostatic charges to propel a stream of charged ions out of the engine.
Whatever method is used to produce thrust, be it air, chemical reactions, ions, or magic, the result is the same: an equal amount of force in the opposite direction. If that force is enough to overcome the force of gravity, then we have liftoff.
If you want the broomstick to fly with you on it, just add your own mass to the equation:
Force = (Your Mass + Mass of Broomstick) * 9.8 m/s²
So if your mass is 99 kg, and the broomstick has a mass of 1 kg, you need 980 Newtons of thrust in order to counteract the force that gravity exerts on you and your broomstick.
Conclusion
So now, not only do you know a little more about Newton’s Laws of Motion, you also know just how much magical force you need in order to make a broomstick fly.
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Broom image, myfreeweb at Flickr. CC BY 2.0. Rocket image courtesy of Shutterstock.
