Originally Posted by jstrong
This is somewhat of a "trick" question. Not because it is phrased in a
deliberately tricky way, but because people tend to have trouble
thinking about the operation of other vehicles apart from cars which
they know so well.
The heart of the confusion is simply these two important facts:
* cars propel themselves by pushing against the ground via friction
* airplanes propel themselves by pushing against the air
If you can let go of how cars operate and think about what an airplane
does, you'll be able to see the problem clearly.
One good way of tackling this problem is to find a good analogy. But
the analogy must be a valid one else you'll just get more confused.
For example, someone posted the analogy of running on a treadmill. Why
is that a bad analogy? Because one runs by pushing against the ground
via friction between their shoe and the ground. This is how a car
propels itself! It is not how an airplane propels itself, by pushing
against the air. Bad analogy.
Let's use this analogy. Instead of looking at the airplane, let's back
up and go into the airport. Suppose you're walking down to your gate
and pulling your carry-on bag behind you. It's a nice new bag with low
friction wheels. No problem! Up ahead you see one of those moving
walkways. You don't see anyone coming, so you decide to do a little
experiment. You go over to the walkway that is moving TOWARDS you and
place your bag on it. Meanwhile, you step off to the side of the
walkway, and still holding on to the handle of your bag, you continue
to walk along. In fact, you intentionally walk along at the same speed
that the moving walkway is going, just in the opposite direction.
Question: does the bag move or does it remain stationary as you keep
walking? Obviously it moves with you. So why does your bag move
forward when you are walking at the same speed of the conveyor going
in the opposite direction?
The answer to that question is also the answer to the
airplane-conveyor question. To complete the analogy, the pull of your
arm is analogous to the force of the airplane engines. The bag's
wheels are analogous to the airplane tires. Do the nice low-friction
wheels on your bag on the conveyor pull against you anymore than they
do when you're just pulling your bag along normally? No, they don't.
They are free-wheeling, after all. Meanwhile, you're pulling the bag
with the same force in both cases. So in both cases, the bag keeps
moving forward. Likewise with the airplane, the pull of the engines
doesn't change nor does the force on the airplane imparted by the
tires change no matter what the ground is doing underneath the tires.
You have the same force imbalance in either case, and since Force =
mass x accceleration, you have the same acceleration. Remember, we are
talking airplane engines which push against the AIR, not the ground.
The acceleration is with respect to the AIR, thus the airplane
develops a speed relative to the air and can eventually take off...
John Strong
Ph.D., biochemical engineering
M.S., chemical engineering
B.S., mechanical engineering
