Schoolyard Science #5: Coriolis, Down the Drain

During our visit to Quito Ecuador, we spent an afternoon visiting the equator and its adventures in physics.  See how the  water goes down the drain differently (circularly), even though the three basins are only about six feet apart.

North Hemisphere (above).

Southern Hemisphere (above)

On the equator (below)

This proves the Coriolis effect that you've heard before.  Right?

Are you now a true believer?

Don't be.

Apparently it's a trick.

The Coriolis forces can only kick in over long distances.  Think hurricane.

The good folks at National Geographic tell us "Despite the popular urban legend, you cannot observe the Coriolis effect by watching a toilet flush or a swimming pool drain. The movement of fluids in these basins is dependent on manufacturer’s design (toilet) or outside forces such as a strong breeze or movement of swimmers (pool)."  (Or in our video cases shown above, the water for the north and south examples wasn't perfectly still, as it was in the "test" performed directly on the line.)

Oh well.  Don't you just hate a spoiler?  Anyway, We enjoyed watching the sink drain. ;-)

For a full explanation, see Wikipedia here.  And here's a summary:

"As the Earth turns around its axis, everything attached to it, including the atmosphere, turns with it (imperceptibly to our senses). An object that is moving without being dragged along with the surface rotation or atmosphere such as an object in ballistic flight or an independent air mass within the atmosphere, travels in a straight motion over the turning Earth. From our rotating perspective on the planet, the direction of motion of an object in ballistic flight changes as it moves, bending in the opposite direction to our actual motion. When viewed from a stationary point in space directly above the north pole, any land feature in the Northern Hemisphere turns anticlockwise—and, fixing our gaze on that location, any other location in that hemisphere rotates around it the same way. The traced ground path of a freely moving body in ballistic flight traveling from one point to another therefore bends the opposite way, clockwise, which is conventionally labeled as "right," where it will be if the direction of motion is considered "ahead," and "down" is defined naturally."

Here's more from the Wikipedia killjoys:

"Contrary to popular misconception, water rotation in home bathrooms under normal circumstances is not related to the Coriolis effect or to the rotation of the Earth, and no consistent difference in rotation direction between toilet drainage in the Northern and Southern Hemispheres can be observed.[49][50][51][52] The formation of a vortex over the plug hole may be explained by the conservation of angular momentum: The radius of rotation decreases as water approaches the plug hole, so the rate of rotation increases, for the same reason that an ice skater's rate of spin increases as they pull their arms in. Any rotation around the plug hole that is initially present accelerates as water moves inward."

Life was more fun in the days of a flat earth. ;-(

Schoolyard Science #4: Getting into hot water.

More on living at Bogota's very high altitude (8,300 feet above sea level)

Next demonstration.
We ran a little experiment and boiled water.  (We did not watch it boil.)
The theory says that the lower atmospheric pressure will allow water to boil at a lower temperature (less atmospheric pressure making it easier for low energy molecules to escape the pot...another way to say "boiling";  lower temperature=less molecular kinetic energy)

Here's the result.
The water boiled at 199 F; not the 212 F that we observe at sea level.

Checking our handy copy of the steam-water equilibrium graph (Which I've been waiting to use since my last thermodynamics class in college! See diagram to the right.), we see that a temperature of 199F has its boiling pressure at about 11.45 psi, which turns out to be about 77% of the pressure at sea level.

And we remember from an earlier posting that the predicted air pressure in Bogota's altitude is 11.5 psi, 77% of the air pressure at sea level.

Hurrah! Thermodynamics is safe for another day! (Whew!)

That's it for today, kids!
You can try this at home.

#4

(On a personal note, only after about two months living at 8,600 ft. did I finally reach a point of sleeping through the night without waking up at least once feeling out of breath.  In general we don't huff and puff as we used to.  So, we've gotten used to the thin air.)

Schoolyard Science #3. Take Off!

  

Okay class, We're revisiting  altitude and atmosphere...

Quick review:
Bogota is one of the highest cities in the world  (Denver's at 5,300 ft.  Bogota's at 8,300 ft / 2,500 meters.) Check out the graph from Wikipedia...
Bogota has about 77% of the air that Miami has.

[Special Shout Out to Buck Buchanan, ace instructor at Airbus.  Thanks, Buck!
Any errors in this blogpost are mine. Buck did not check my final posting.]

We've been on a couple of airplane flights between Bogota and cities along the coast, and we made some interesting observations.
First a little background music...
When a jet plane accelerates to take off, it grabs air from in front of the engines, and shoves it out the exhaust at very high speeds.  (There's other stuff going on too, but that's the big idea.)  The accelerated air causes the plane to move forward. (No.  The exhausting air doesn't "push" on the static outside air.  See me after class if you have questions about this.)
The plane builds up speed, and when it reaches 150 knots, the pilot tips the plane up and the plane takes off.  The pilots call this speed "VR".  At sea level, this acceleration takes about 30 seconds to get from zero speed to 150 knots (VR).  Here a sketch from Wikipedia.

So what's this got to do with Bogota?

Here's a photo of a timer I used to record how long it took to get airborne from an airport near sea level.

That's cool. About 33 seconds to take off at sea level. 

Yawn.

Ok Class. But what happens if the air is less dense, say if you landed in Bogota and your now going to take off?
- Does it take longer to accelerate to 150 knots? Less time?
- Do you accelerate faster because there's less wind resistance (the air is thinner.)?
- Do you need a longer runway or a shorter runway?  (Said another way...Will you run into the nursery school that's at the end of the runway? Ugh...)
- Is 150 knots the speed you need? More or less?

Here's the answer, from a recent take off from Bogota's airport.

Whoa!
Taking off in Bogota takes about 40% more time than in Miami! (46sec/33sec = 140%).
It's true, because the planes in Bogota accelerate more slowly than they do in Miami...even when the engines are running at the same speed.  (We checked :-)  Two engine aircraft always set their throttles to the same value for take-off*.  That way the engines are most efficient and operate most cost-effectively.)

But wait.  Does more time needed to take off mean planes require more distance to take off?  After all, they're moving more slowly, right?   The pilots of the plane told me that take off speed was about the same for Miami and Bogota (150 knots). (Yes.  I asked them. And you can check it out here.)

For any former high school physics students, here your challenge question:
Assume that:
1. The take off speed for an airplane is the same at any altitude.
2. And at a higher runway altitude it takes 46 seconds to reach take off speed, and at sea level it takes 30 seconds to reach that speed.
3. Acceleration from break release through take off is constant.

Tell us:
- How long is the takeoff distance in Bogota compared to Miami? Show your work.
Post your answers on this blog. :-)  It's okay to show off.
(Hint: Use a graph of velocity vs. time.)

Bonus question.
Now, Why does the plane accelerate more slowly?  Show your thinking. :-)
Hint: F=ma.
First think about the mass of the air that's going into the engine.
Assume that the air accelerates from zero at the engine intake to some exhaust velocity. (It doesn't matter what the actual velocity is.)
Assume that the engine's rotation speed is the same in both scenarios.  (It is.)
Next make a simplifying assumption about the mass of the fuel that's added to the engine.
Compare this generated force (which is now acting on the mass of the airplane) with the acceleration of the plane in the two altitude scenarios.  Go ahead, you can do it.

Your answer won't come out exactly, because there are other factors that affect the take off time, buot I think you'll be impressed at how close you'll get.  Good luck!

Schoolyard Science #2: Celestial observations from the equator

Hi Class!  This is the next in our series of Schoolyard Science from South America.

We all have heard that the earth rotates on its axis, and that the axis of rotation is tilted relative to the axis of the earth's orbit around the sun.  Right?  Remember that?


It just so happens that on December 21st, we were exactly on the equator in the Galapagos Islands of Ecuador at exactly noon. With a clear view of the sun and horizon.  (We were on a ship.)

So we used that as a chance to check on the tilt angle of the earth.  (There are many other ways to do check, but this one is very straightforward.)

The textbooks say that the earth's north pole is tilted 23.5 degrees away from the sun on the day of the winter solstice. (See diagram above.)

At noon, with the sun at its highest point in the sky for that day, we measured the angle between the horizon and the sun.  We measured about 67.5 degrees.  (3/4 of the angle between the horizon and straight up). You don't need a sextant to estimate this value.  You can use your arm, hand and fingers and come pretty close.  See here.)

The angular width of the sun as seen from the earth is about 1/2 degree, so our measurement was really someplace between 67.0 and 68.0 degrees.

Straight overhead - angle from the horizon = angle from straight overhead.
Our numbers:  90 degrees - 67.5 degrees = 22.5 degrees.  with a half degree on either side.
Textbooks:  90 degrees - 66.5 degrees = 23.5 degrees.

So we were off by 1/2 to 1.5 degrees.  I'll take that result, given my measuring instrument was fairly primitive.

So, the science textbooks pass this test. :-)

You can try something like this at home, but you'll have to adjust for your latitude.  our being on the equator simplified the situation for us.
Cheers!

For more Schoolyard Science, see this blog post on altitude.

For more on our travels, visit here.  Thanks!

Schoolyard Science #1: Atmospheric Pressure. You can try this at home.

  

Okay class,
Today's lesson is altitude and atmosphere...
Air gets 'thinner' as altitude increases, right?

Bogota is one of the highest cities in the world  (Denver's at 5,300 ft.  Bogota's at 8,300 ft / 2,500 meters.) Check out the graph from Wikipedia...
Bogota has about 77% of the air that Miami has.

When we first got here, we were huffing and puffing.  Climbing a stair was challenging.

Luke pointed out that soda pop was really fizzy.

#1.
I went on flight from high Bogota (8,300 ft) to the coast (0 ft).  I started with a plastic water bottle filled with air.  (Now class, Keep in mind that this air is at Bogota's lower pressure.)

When the plane landed near the coast (altitude ~0 ft), this is what the bottle looked like (below). Crushed.
The more dense air at the coast (outside the bottle) squeezed the less dense air inside the bottle until the air inside and outside were at the same pressure.  (When the pressures were different from each other, the walls would be moved by the difference.  And, they were!)

This is the same sort of thing that happens to your ear drums when your ears 'pop' in a plane or tall elevator.  A pressure difference builds up across your eardrum, and your eardrum bends, until either:
1) you clear your ears and relieve the pressure difference (which usually happens naturally when you yawn), or
2) Your eardrums explode.

But is this case, we just measured the volumes of air that were in the bottle before and after the compression. Without compression...600 ml.  With compression...about 440 ml.
Ratio With/Without = 440/600 = 73%.  Which isn't too far away from the prediction of 77%

(Bonus question:  How can you measure the 440 ml volume of the compressed bottle?
Post your answer on this blog below.)