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Re: [Phys-l] Coriolis effect puzzlement



On 12/03/2011 06:16 AM, Philip Keller wrote:

One of the first things I show students when we get to circular
motion is an Interactive Physics simulation of a racecar going around
a track. I just use it to show the direction of the velocity and
acceleration vectors. The car is held to the circular path by a rope
and after a couple of laps, I have the rope break. It was my
intention to show that without the centripetal force, the car goes in
a straight line. But the first time I ran it, I admit that I was
surprised to see the car move off in a straight line, but also rotate
-- it was actually a very realistic view of a car "spining out". But
I wasn't expecting it and I thought "What makes the car start to
rotate?". Then I realized that the car didn't START to rotate -- it
was already "rotating" as it circled the track, just like the moon.
In fact, observers in the center of the track would never see the
dark side of the car. You can even time the rotations after the rope
breaks and see that the period matches the period of the circular
motion.

That's a nice example.

Continuing that line of thought, let's replace the car with an airplane.
Note the contrast:
-- In the car you have only one directional control ... namely
the steering wheel.
-- In the airplane, you have separate control of which way you
are /pointing/ and which way you are /traveling/ ... namely
the rudder and the bank angle (respectively).

Terminology: The word "heading" properly refers to the direction
you are pointing, not the direction you are traveling. Non-experts
abuse the terminology by saying things like "I'm heading to the
store" when they really mean "I'm going to the store." You can
appreciate the distinction in the following example: Crabs are
famous for moving sideways. This crab is /heading/ north but
/traveling/ eastward:


/\
( / @ @ ()
\ __| |__ /
-/ " \-
/-| |-\
west / /-\ /-\ \ ========> east
/ /-`---'-\ \
/ \


Note: To see ASCII art properly, you need a fixed-width font.
Set your mail-reader accordingly ... or go to the archive and
look at it using your web browser.
https://carnot.physics.buffalo.edu/archives/2011/12_2011/threads.html

Moving from terminology to real, practical physics, consider
what happens when an airplane begins a turn. This is actually
two maneuvers in one:
-- At the beginning of the turn, you need to do something to
establish a rate of change of heading i.e. establish a yaw
rate. This requires using the rudder to provide a transient
torque.
-- All during the turn, you need a rate of change of direction
of travel, i.e. a rate of change of the momentum vector.
This requires a steady sideways force, which normally comes
from banking the entire aircraft. So to start a turn, you
need to roll into a bank.

In contrast to a normal turn, there are some maneuvers that
require a change in heading *without* any change in direction
of travel. An example occurs right after liftoff during a
crosswind takeoff.

I guarantee you that student pilots were not born knowing about
the spin/orbit distinction, i.e. the distinction between the
heading and the direction of travel. Indeed, even in a roomful
of flight instructors I commonly get pushback when I mention
that in a crosswind takeoff, right after liftoff, you want a
pure yaw and you should *not* be coordinating the ailerons
with the rudder.

It is "mostly" true that techniques you learn in one airplane
can be used in another, but sometimes the details differ.
Consider these two airplanes:


/\
| |
| |
_____________/ \______________
/ MMMM \
| MMMM |
=======-------. .--------=======
||||
||
||
||
||
.---||---.
| |
'---<>---'

/\
|MM|
| |
_____________/ \______________
/M | | M\
|M | | M|
=======-------. .--------=======
||||
||
||
||
||
.---||---.
| MM |
'---<>---'


The letter "M" denotes mass.

The first airplane has lots of mass concentrated near the
center, while the second has lots of mass at the extremities.
They have the same total mass, but the second airplane has
a greater moment of inertia, and therefore requires you to
apply more rudder at the beginning of a turn.

This is an interesting way of driving home the distinction
between mass and moment of inertia. It is slightly more
complicated -- but arguably more interesting -- compared
to the notorious race between the ball, solid cylinder,
and hollow cylinder.

Nitpickers note: I am quite aware that yaw-axis
inertia is not the only reason why the rudder is
involved in a turn. There are also various types
of adverse yaw, but that's not what we are discussing
today.

==================

Getting back to the nominal topic, namely Coriolis:

1) As always: The Coriolis effect exists when you are using
a rotating reference frame and not otherwise.

2) Therefore it is always a Bad Idea to say that such-and-such
physical situation demonstrates the Coriolis effect, because
you can analyze the situation using any reference frame you
like. Some people may choose a rotating reference frame but
others may choose differently.

If you want to be really professional about it, you can analyze
the system one way and then re-analyze it the other way. The
physics will be the same, but the words we use to model it
will be different.