Try a "continuity" argument: A pushes on the (now CYLINDRICAL, with axis
vertical) block (silo), from the South, with 10 units of force. B initially
pushes from the North with 10 units. Result, 0 net force on the block. But
now let B move off to the East somewhat (to his left) and push, again (and
always) with force 10 units. Net force then has small components to the West
and North. Now let B move farther to his left. Larger components to West and
North. By the time B has moved around to the Southeast, the net force will
have large components to the North and considerable to the West. If B moves
into A's postion, the net force will be 20 units to the North. By
continuity, the net force increases continuously from 0 to 20. So at some
point that force will start exceeding 10 units (and stay that way).

John

--
John T Lowry, PhD
Flight Physics
5217 Old Spicewood Springs Rd, #312
Austin, Texas 78731
(512) 231-9391


"'Vejita' S. Cousin" wrote in message
...
In article ,
Casey Wilson wrote:
(James L. Freeman) wrote in message
.com...
Can someone offer a non-mathematical EXPLANATION (as opposed to
DESCRIPTION) of why the speed of headwind and crosswind components of
a wind add up to more than the speed of the wind?

I'll give it a go (use to tutor math in college but that was a while
ago ^_^). This works best with pictures but here's teh basic outline.
Imgine you have a block on the floor. Two guys (A and B) are going to
push on the block. Since we're doing this wihtout pictures let's imgine
you're looking at the block from teh top down and it can go
North/south/east/west over teh floor.

1. A pushes on the south side of the block with 5 units (of whatever), B
pushes on the south side of the block with 5 units of force. The result
the block moves to the north with 10 units of force.

2. A pushes on teh south side of the block with 5 units, B pushes on the
north side of the block with 5 units. Result, teh block doesn't move at
all. But Both A & B are pushing with 5 units.

3. A pushes on the south side of teh block, B pushes on the east side f
teh block. Result is the block moves north-east.

That sounds ok right? But wait a mintue, in example 3 if only A was
pushing then the block would move north and only north. And if only B was
pushing the block would move east and only east. The block moves
north-east because both are pushing.
In example 2 the block didn't move at all, because A and B are pushing
in opposite directions with equal force.

But What if A pushing on the south side of rh block with 10 units and B
pushes on teh north side with 8 units? Well the block would move north,
at 2 units ofr force.
From the blocks POV having A push from teh south at 10 & B push from
teh north at 8, is THE SAME THING as just having someone push at 2 units
of force.

This is know as vector addition. You need to take teh scaler (number
of units of push) and the vector (direction) into account to do vector
addition.
So if I told you that A was pushing at 10 units and B was pushing at 10
units, and asked what direction is the block moving what would you say?
Well you 'should' say "I don't kow." Because you don't know what
direction A and B are pushing.

The above examples are easy because A nd B are pushing in opposite
direttions. It's a little harder to think of it when A and B push between
0-180 degrees. The math is easy (sin/cos stuff or use a cross wind
diagram). It's the same thing thou.

Let's say you want to land on runway 36 (to make life easy). The wind
is 045 @ 20. Well just like teh block having the win at 045 @ 20, is the
same as having two winds that are pushing the plane at the same time.
One wind is coming from 360 and the other from 090, the end result is a
single wind from 045 (yes I know wind doesn't work like that work with me
here).
The reason we 'spilt the wind up' is because the 'peice' of wind coming
from 360 doesn't concern us, but that peice from 090 does, as it'll blow
us off course when landing.
So it's the reverse of the block examples, we have one force at some
odd angle, and we spilt it into two force: head wind and cross wind.
Because these forces have strength (number of units) and direction (in
this case 045) we can't just add/subtract like number.

Just like the block example above where the block was moving forward at
2 units, wind acts the same. Landing on 360 with a wind from 360 @ 10 is
all head wind, 015 @ 10 a little cross wind, 080 @ 10 almost all cross
wind.
So the cross wind component varies with direction, and you can't just
add/subtract the units to get there. Now find any url about trig and look
up sin and/or cos and this will make a lot more sense (I hope). But you
asked why and not how to calculate it

This stuff is actually pretty easy to do if you have a scienctific
calculator. Sorry the above is so long ...