negative drag

"... and it has a fiberglass engine and it runs on water, man!"

Quoted message said:

On Thu, 13 Dec 2007 17:56:16 -0800 (PST), peter <[email hidden]>
wrote:

[snip]

Quoted message said:

Now does this make any practical sense? No.

[snip]

Dear Peter,

You're getting closer.

No, I'm continuing to say exactly what I did in my original post since
that was correct. Note that in that post I also indicated that the
effect would be too small to be practical and that a passive fairing
makes much more sense if the goal is to reduce the effects of wind
resistance.

Quoted message said:

You can extract useful energy by sticking a propeller into an
airstream to use onboard, just as you can extract useful energy
through a generator's roller to run a light.

You cannot, however, extract energy that is useful for propelling the
vehicle forward _faster_ because you lose more than you gain.

The obvious difference here, as compared to turning on the generator,
is that no additional drag is created by placing the propeller into a
part of the airstream that would otherwise generate just as much drag
by hitting the cyclist directly. Look at the example I gave in the
previous post where the propeller is a slightly modified fairing shape
and may actually have less air resistance than the cyclist alone. In
that case there's a slight gain even if the energy extracted from the
wind is thrown away - and a slightly larger gain if it's used to aid
the propulsion of the cycle.

But, as I've said all along, I don't think the magnitude of the gain
in practice would be sufficient to justify the added weight,
bulkiness, and complex mechanism. Nevertheless, it is in no way a
perpetual motion machine (of either the first or second kinds) and
there is no physics principle that prohibits obtaining small
mechanical benefits by utilizing part of the wind energy that would
otherwise be wasted upon hitting the cyclist.

Tim McNamara said:

"... and it has a fiberglass engine and it runs on water, man!"

What are you talking about?

--
Tom Sherman - Holstein-Friesland Bovinia
"Localized intense suction such as tornadoes is created when temperature
differences are high enough between meeting air masses, and can impart
excessive energy onto a cyclist." - Randy Schlitter

On Dec 13, 8:18 pm, Tom Sherman <[email hidden]>

Quoted message said:

Peter Rathman said:

...
My car has a coefficient of drag of 0.35, and it has a much more
streamlined shape than a regular upright cyclist. Where did your
factor of 10 (implying a Cd of 0.1) come from? Figures I've seen for
normal cyclists have been more around 0.6 or 0.7....

Here is what a bicycle with a coefficient of drag of slightly less than
0.1 looks like:
<http://www.ent.ohiou.edu/~et181/hpv/Andrea_64.7mph.jpg>.

Agreed, and clearly for that kind of cycle adding any additional
external apparatus would add considerable extra drag since the shape
has already been optimized for minimum Cd. But the proposal in the
original post included illustrations that made it clear it was for a
regular upright cyclist - not even one in the drops or aero-bar
positions.

peter said:

For example, the object we put out in front of the cyclist could be in
the shape of an aerodynamic nose cone. Let's say a fairing of that
type cuts his wind resistance by 20%. Now we add some bearings and
little fins to the nose cone so it'll start rotating in the wind. The
fins will obviously add back some air resistance, but by keeping them
small we can make sure that the overall result is still no worse than
the unfaired cyclist. Any energy we can extract from the spinning
cone and use for propulsion is now a net plus if we're only interested
in power needed to overcome air resistance.

No. Starting with your initial nose cone, the cyclist is putting a
certain amount of power into the system. Once you add the fins, you
start transferring additional momentum from the air into spinning the
fairing. Recall that aerodynamic drag is a vector quantity, not a
scalar. Adding rotational drag to a body will not decrease drag in
the axial direction. In order for this additional rotation to
decrease the total power requirement from the cyclist, more power
needs to be extracted from the rotating fairing than is put into it.
This is simply not possible.

Quoted post said:

On Dec 14, 2:49 am, "Leo Lichtman" <[email hidden]>

Quoted message said:

I sat down and designed a propeller that would increase the speed of a
bicycle with NO INCREASE IN POWER INPUT. I wound up with a propeller that
had no moving parts, and whose blades were shaped like a fairing.

Me to.

A slight spiral shape should generate centrifugal force depending on
the speed and drag. Then have a recumbent slide down the vacuum in the
center of a vortex. It's that what Victor Schauberger calls light air.

But to smoothly pedal the air up to speed the bike would become much
to long.

That's why one would use a propeller I think. Or a rotating cone. :-)

I doubt efficiently gearing windmills to the wheels a bit.

It would be better to use the wind to further enhance the air flow.

http://gabydewilde.googlepages.com/negative-drag
gabydewilde - negative drag

But where is this magical vortex coming from? Generating a vortex
from an axial flow consumes so much energy that the aeronautics
industry has spent decades developing wing tips specifically not to
create them. There are some very good fundamental reasons why
mainstream aerodynamic vehicle design has been focused on transferring
the minimum possible amount of momentum to the air. If your own study
of fluid dynamics had extended past reading crackpot theories on the
internet, it might be more clear to you.

<[email hidden]> wrote in message
news:[email hidden]...
: On Dec 13, 10:21 pm, "[email hidden]" <[email hidden]> wrote:
: > On Dec 14, 2:49 am, "Leo Lichtman" <[email hidden]>
: > wrote:
: >
: > > I sat down and designed a propeller that would increase the speed of a
: > > bicycle with NO INCREASE IN POWER INPUT. I wound up with a propeller
that
: > > had no moving parts, and whose blades were shaped like a fairing.
: >
: > Me to.

I sat down and designed a bicycle with no propeller.
I wound up with pedals that increased the speed by
pushing on them.

On Dec 14, 12:35 am, Tom Sherman <[email hidden]>

Quoted message said:

Tim McNamara said:

"... and it has a fiberglass engine and it runs on water, man!"

What are you talking about?

--
Tom Sherman - Holstein-Friesland Bovinia
"Localized intense suction such as tornadoes is created when temperature
differences are high enough between meeting air masses, and can impart
excessive energy onto a cyclist." - Randy Schlitter

I believe he's suggesting that our friend Gaby might be developing her
theories with some kind of herbal assistance.

Quoted message said:

peter said:

For example, the object we put out in front of the cyclist could be in
the shape of an aerodynamic nose cone. Let's say a fairing of that
type cuts his wind resistance by 20%. Now we add some bearings and
little fins to the nose cone so it'll start rotating in the wind. The
fins will obviously add back some air resistance, but by keeping them
small we can make sure that the overall result is still no worse than
the unfaired cyclist. Any energy we can extract from the spinning
cone and use for propulsion is now a net plus if we're only interested
in power needed to overcome air resistance.

No. Starting with your initial nose cone, the cyclist is putting a
certain amount of power into the system.

But we're *not* starting with an initial nose cone - we're starting
with a regular upright cyclist. We're then adding a reasonably
aerodynamic windmill right in front of him that consists of a nose
cone shape with fins along the side so it spins when in the wind. The
combination of original rider/bike plus the added windmill can be made
to have the same, or even slightly less, air resistance than the rider/
bike had. Therefore adding the windmill didn't add any extra drag.
But it does allow you to extract some small amount of power from the
wind - power that was wasted before in creating extra turbulence as
the wind hit the decidedly non-aerodynamic rider. Not enough to be at
all practical, but enough to show that in principle some energy can be
extracted.

Note that I had already explicitly said before that the windmill is
not as aerodynamic as the plain unfinned nose cone - but that's not
the comparison since we never actually have the unfinned nose cone.
We start with the plain rider/bike and we add the finned nose cone as
the windmill element.

Quoted message said:

Once you add the fins, you
start transferring additional momentum from the air into spinning the
fairing. Recall that aerodynamic drag is a vector quantity, not a
scalar. Adding rotational drag to a body will not decrease drag in
the axial direction. In order for this additional rotation to
decrease the total power requirement from the cyclist, more power
needs to be extracted from the rotating fairing than is put into it.
This is simply not possible.

peter said:

Quoted message said:

On Dec 13, 8:56 pm, peter <[email hidden]> wrote:

Quoted message said:

Quoted message said:

For example, the object we put out in front of the cyclist could be in
the shape of an aerodynamic nose cone. Let's say a fairing of that
type cuts his wind resistance by 20%. Now we add some bearings and
little fins to the nose cone so it'll start rotating in the wind. The
fins will obviously add back some air resistance, but by keeping them
small we can make sure that the overall result is still no worse than
the unfaired cyclist. Any energy we can extract from the spinning
cone and use for propulsion is now a net plus if we're only interested
in power needed to overcome air resistance.

Quoted message said:

No. Starting with your initial nose cone, the cyclist is putting a
certain amount of power into the system.

But we're *not* starting with an initial nose cone - we're starting
with a regular upright cyclist. We're then adding a reasonably
aerodynamic windmill right in front of him that consists of a nose
cone shape with fins along the side so it spins when in the wind. The
combination of original rider/bike plus the added windmill can be made
to have the same, or even slightly less, air resistance than the rider/
bike had. Therefore adding the windmill didn't add any extra drag.
But it does allow you to extract some small amount of power from the
wind - power that was wasted before in creating extra turbulence as
the wind hit the decidedly non-aerodynamic rider. Not enough to be at
all practical, but enough to show that in principle some energy can be
extracted.

Note that I had already explicitly said before that the windmill is
not as aerodynamic as the plain unfinned nose cone - but that's not
the comparison since we never actually have the unfinned nose cone.
We start with the plain rider/bike and we add the finned nose cone as
the windmill element.

Quoted message said:

Once you add the fins, you
start transferring additional momentum from the air into spinning the
fairing. Recall that aerodynamic drag is a vector quantity, not a
scalar. Adding rotational drag to a body will not decrease drag in
the axial direction. In order for this additional rotation to
decrease the total power requirement from the cyclist, more power
needs to be extracted from the rotating fairing than is put into it.
This is simply not possible.

You can't suggest a nose cone, and then say it was never there. Sure,
some finned, spinning, nose cone contraption might be more areodynamic
than the cyclist alone, but it's physically impossible for it the
system to be as efficient as the un-finned, non-spinning fairing. So
why make it spin and try to get the energy back out that you put into
it to make it spin in the first place?

a reasonably aerodynamic windmill?

that's the point where creative writing enters from, well, use the
lift-stage center.
like magic tricks, right? gues which shell hides the pea? say look
over there at the naked cheerleader.. why there's the pea under shell
one.

distract the reader then write "reasonably aerodynamic windmill cited
by Pieere La Fountainblue, Academy la Marseille Vol 36 Letters

Quoted message said:

You can't suggest a nose cone, and then say it was never there. Sure,
some finned, spinning, nose cone contraption might be more areodynamic
than the cyclist alone, but it's physically impossible for it the
system to be as efficient as the un-finned, non-spinning fairing.

I can accept a closed body being more efficient as just a propeller.
Still you are arguing about using only the drag. Sailing does not work
like that.

Here you have a picture again. I think you missed it before.

http://i.treehugger.com/images/2007-2-21/Windmill-Sailboat.jpg

The faster you go the more the wind turns into your face so one might
as well put the propeller at the front.

This is why it must spin.

Quoted message said:

So
why make it spin and try to get the energy back out that you put into
it to make it spin in the first place?

I'm hoping the wind can buy us a sucking vortex.

I've made a new thread for the vortex cone here.
http://groups.google.com/group/rec.bicycles.tech/browse_frm/thread/921e418d6cffd70d

More rotary "excuses".

Enjoy.

:-)

who? said:

peter said:

Quoted message said:

On Dec 13, 8:56 pm, peter <[email hidden]> wrote:
> For example, the object we put out in front of the cyclist could be in
> the shape of an aerodynamic nose cone. Let's say a fairing of that
> type cuts his wind resistance by 20%. Now we add some bearings and
> little fins to the nose cone so it'll start rotating in the wind. The
> fins will obviously add back some air resistance, but by keeping them
> small we can make sure that the overall result is still no worse than
> the unfaired cyclist. Any energy we can extract from the spinning
> cone and use for propulsion is now a net plus if we're only interested
> in power needed to overcome air resistance.
No. Starting with your initial nose cone, the cyclist is putting a
certain amount of power into the system.

But we're *not* starting with an initial nose cone - we're starting
with a regular upright cyclist. We're then adding a reasonably
aerodynamic windmill right in front of him that consists of a nose
cone shape with fins along the side so it spins when in the wind. The
combination of original rider/bike plus the added windmill can be made
to have the same, or even slightly less, air resistance than the rider/
bike had. Therefore adding the windmill didn't add any extra drag.
But it does allow you to extract some small amount of power from the
wind - power that was wasted before in creating extra turbulence as
the wind hit the decidedly non-aerodynamic rider. Not enough to be at
all practical, but enough to show that in principle some energy can be
extracted.

Note that I had already explicitly said before that the windmill is
not as aerodynamic as the plain unfinned nose cone - but that's not
the comparison since we never actually have the unfinned nose cone.
We start with the plain rider/bike and we add the finned nose cone as
the windmill element.

Quoted message said:

Once you add the fins, you
start transferring additional momentum from the air into spinning the
fairing. Recall that aerodynamic drag is a vector quantity, not a
scalar. Adding rotational drag to a body will not decrease drag in
the axial direction. In order for this additional rotation to
decrease the total power requirement from the cyclist, more power
needs to be extracted from the rotating fairing than is put into it.
This is simply not possible.

You can't suggest a nose cone, and then say it was never there. Sure,
some finned, spinning, nose cone contraption might be more areodynamic
than the cyclist alone, but it's physically impossible for it the
system to be as efficient as the un-finned, non-spinning fairing. So
why make it spin and try to get the energy back out that you put into
it to make it spin in the first place?

With the proper lighting, a spinning nose cone would look really cool at
night.

--
Tom Sherman - Holstein-Friesland Bovinia
"Localized intense suction such as tornadoes is created when temperature
differences are high enough between meeting air masses, and can impart
excessive energy onto a cyclist." - Randy Schlitter

On Dec 15, 3:49 am, Tom Sherman <[email hidden]>

Quoted message said:

who? said:

peter said:

On Dec 14, 5:55 am, [email hidden] wrote:

Quoted message said:

Quoted message said:

> On Dec 13, 8:56 pm, peter <[email hidden]> wrote:
>> For example, the object we put out in front of the cyclist could be in
>> the shape of an aerodynamic nose cone. Let's say a fairing of that
>> type cuts his wind resistance by 20%. Now we add some bearings and
>> little fins to the nose cone so it'll start rotating in the wind. The
>> fins will obviously add back some air resistance, but by keeping them
>> small we can make sure that the overall result is still no worse than
>> the unfaired cyclist. Any energy we can extract from the spinning
>> cone and use for propulsion is now a net plus if we're only interested
>> in power needed to overcome air resistance.
> No. Starting with your initial nose cone, the cyclist is putting a
> certain amount of power into the system.
But we're *not* starting with an initial nose cone - we're starting
with a regular upright cyclist. We're then adding a reasonably
aerodynamic windmill right in front of him that consists of a nose
cone shape with fins along the side so it spins when in the wind. The
combination of original rider/bike plus the added windmill can be made
to have the same, or even slightly less, air resistance than the rider/
bike had. Therefore adding the windmill didn't add any extra drag.
But it does allow you to extract some small amount of power from the
wind - power that was wasted before in creating extra turbulence as
the wind hit the decidedly non-aerodynamic rider. Not enough to be at
all practical, but enough to show that in principle some energy can be
extracted.

Quoted message said:

Quoted message said:

Note that I had already explicitly said before that the windmill is
not as aerodynamic as the plain unfinned nose cone - but that's not
the comparison since we never actually have the unfinned nose cone.
We start with the plain rider/bike and we add the finned nose cone as
the windmill element.

Quoted message said:

Quoted message said:

> Once you add the fins, you
> start transferring additional momentum from the air into spinning the
> fairing. Recall that aerodynamic drag is a vector quantity, not a
> scalar. Adding rotational drag to a body will not decrease drag in
> the axial direction. In order for this additional rotation to
> decrease the total power requirement from the cyclist, more power
> needs to be extracted from the rotating fairing than is put into it.
> This is simply not possible.

Quoted message said:

You can't suggest a nose cone, and then say it was never there. Sure,
some finned, spinning, nose cone contraption might be more areodynamic
than the cyclist alone, but it's physically impossible for it the
system to be as efficient as the un-finned, non-spinning fairing. So
why make it spin and try to get the energy back out that you put into
it to make it spin in the first place?

With the proper lighting, a spinning nose cone would look really cool at
night.

You get extra points for this Tom.

lol

"Vince Morgan" <vinharAtHereoptusnet.com.au> wrote in message
news:[email hidden]...

Quoted message said:

"CWatters" <[email hidden]> wrote in message
news:[email hidden]...

Quoted message said:

"Elmo" <[email hidden]> wrote in message
news:[email hidden]...

Quoted message said:

Of course what would really happen is that the wind would initially

blow

Quoted message said:

Quoted message said:

you backwards slightly, the backwards motion causing the fan to rotate
backwards which would cause you to go backwards faster, causing the

fan

Quoted message said:

Quoted message said:

Quoted message said:

to rotate faster and so on. The effect would snowball until you were
going backwards at the speed of sound.

elmo

One of these can sail dead into wind....

http://i.treehugger.com/images/2007-2-21/Windmill-Sailboat.jpg

It can? How is that possible?
Vince

Why is it impossible? What physical laws does it break?

A sailing boat can tack upwind. There is little difference. Think about two
sailing boats on opposite tacks towing the same barge. The sail boats go
back and forth but the barge can be towed directly up wind. Look down on a
windmill from above and you see one blade going left to right and the other
right to left.

I believe there was a you tube clip somewhere on the web once.

More examples and some discussion..
http://www.boatdesign.net/forums/showthread.php?t=14182

On Dec 15, 3:47 pm, "CWatters" <[email hidden]>

Quoted message said:

"Vince Morgan" <vinharAtHereoptusnet.com.au> wrote in message
news:[email hidden]...

Quoted message said:

"CWatters" <[email hidden]> wrote in message
news:[email hidden]...

Quoted message said:

"Elmo" <[email hidden]> wrote in message
news:[email hidden]...
> Of course what would really happen is that the wind would initially

blow

Quoted message said:

> you backwards slightly, the backwards motion causing the fan to rotate
> backwards which would cause you to go backwards faster, causing the

fan

Quoted message said:

Quoted message said:

> to rotate faster and so on. The effect would snowball until you were
> going backwards at the speed of sound.

Quoted message said:

Quoted message said:

> elmo

Quoted message said:

Quoted message said:

One of these can sail dead into wind....

Quoted message said:

Quoted message said:

http://i.treehugger.com/images/2007-2-21/Windmill-Sailboat.jpg

Quoted message said:

It can? How is that possible?
Vince

Why is it impossible? What physical laws does it break?

A sailing boat can tack upwind. There is little difference. Think about two
sailing boats on opposite tacks towing the same barge. The sail boats go
back and forth but the barge can be towed directly up wind. Look down on a
windmill from above and you see one blade going left to right and the other
right to left.

I believe there was a you tube clip somewhere on the web once.

More examples and some discussion..http://www.boatdesign.net/forums/showthread.php?t=14182

Hey hello,

That's a great topic Colin. There is so much to learn here. I bet you
will be crying from laughter when you figure out this negative drag
topic. :-)

I mean, almost everyone else is looking for excuses not to look? And
not looking equals not knowing. No matter how often one self proclaims
being an expert. At best they are experts at finding excuses not to
investigate things.

Down the wind the vehicle has contact with 2 mediums. We should
picture the vehicle as traveling inside the wind using the relatively
moving road as it's propulsion to be able to move down the wind
faster. Or move relative to the medium it sits in.

A poster in the topic above suggest the combination of going faster as
the wind and going directly up the wind. Apparently there are even a
lot of fly-cycles today. I've seen so much propeller driven crafts by
now I'm starting to think it would not require any extra parts to do a
little bit of both. One could both go twice as fast as the wind and
sail straight up the wind using the same rig.

I have a good idea how this guy's special windmill works.

http://www.sailwings.net
Peter Worsley - Wingsailing
http://www.sailwings.net/markone.html
Peter Worsley - Wingsailing Mark 1
http://www.sailwings.net/marktwo.html
Peter Worsley - Wingsailing
http://www.sailwings.net/tldescribed.html
Peter Worsley - Wingsailing
http://www.sailwings.net/wingelec.html
Peter Worsley - Wingsail/Electric
http://www.sailwings.net/article.html
Peter Worsley - Wingsailing

Nice stuff he has.

As a hint all I needed was to know we missed something rather foolish
while deploying the windmill in our imaginations. :-)

But.......

....... if you can sail 45 degrees up the wind faster as you can sail
down it. Then why would we put the windmill straight up the wind! The
thing can stand under an angle and tack the blade up wind half a
rotation then have it capture the full wind over the other half. The
wind is still coming from straight ahead but it's pushing against the
side of the boat now!

This is how the blades stand while sailing up the wind.
http://i.treehugger.com/images/2007-2-21/Windmill-Sailboat.jpg

It's not facing forwards as that would subtract the wind force from
the kinetic energy.

I had already half figured this out with the vortex recumbent cone.

http://gabydewilde.googlepages.com/vortex-recumbent
gabydewilde - vortex recumbent

use side wind rather then drag.

Now lets pretend the drag is side wind. :P

I conclude there are 2 mediums in contact with the vehicle but those 2
have 2 directions each. This gives us 4 directions to work in rather
then just having drag.

^_^

http://gabydewilde.googlepages.com/negative-drag
gabydewilde - negative drag

http://www.wrh.noaa.gov/forecast/MapClick.php?site=pqr&smap=1&textField1=45.50583&textField2=-122.70194

"CWatters" <[email hidden]> wrote in message
news:[email hidden]...

Quoted message said:

"Vince Morgan" <vinharAtHereoptusnet.com.au> wrote in message

Quoted message said:

It can? How is that possible?
Vince

Why is it impossible? What physical laws does it break?

A sailing boat can tack upwind. There is little difference. Think about

two

Quoted message said:

sailing boats on opposite tacks towing the same barge. The sail boats go
back and forth but the barge can be towed directly up wind. Look down on

a

Quoted message said:

windmill from above and you see one blade going left to right and the

other

Quoted message said:

right to left.

I believe there was a you tube clip somewhere on the web once.

More examples and some discussion..
http://www.boatdesign.net/forums/showthread.php?t=14182

I won't go into the laws of science, which I mistakenly did in another group
recently.
However, as a thought experiment alone it has problems. Consider the
following.
I'll use a land vehical rather than a boat as an example so as to eliminate
some complexity.

I take a test vehical and mount upon it a wind turbine (as seen in the
video) facing directly into the wind. However, when I get to my test
location, there is no wind. Then I think for a moment. What is the wind
anyway? I soon realize that if I am moving into what is otherwise still air
I have the exact equivalence of wind.
Armed with my new realization I give my test bed a hard push, it finds
itself now apparently in wind, so it accelerates away from me. As it
accelerates there appears to be more wind, so it continues to accelerate.
The wheels I used have very good high speed bearings that offer very little
resistance to motion so the vehical just keeps accelerating until the tips
of the turbine blades hit Mach1?
Vince

"Vince Morgan" <vinharAtHereoptusnet.com.au> wrote in message
news:[email hidden]...

Quoted message said:

"CWatters" <[email hidden]> wrote in message
news:[email hidden]...
I take a test vehical and mount upon it a wind turbine (as seen in the
video) facing directly into the wind. However, when I get to my test
location, there is no wind. Then I think for a moment. What is the wind
anyway? I soon realize that if I am moving into what is otherwise still

air

Quoted message said:

I have the exact equivalence of wind.
Armed with my new realization I give my test bed a hard push, it finds
itself now apparently in wind, so it accelerates away from me. As it
accelerates there appears to be more wind, so it continues to accelerate.
The wheels I used have very good high speed bearings that offer very

little

Quoted message said:

resistance to motion so the vehical just keeps accelerating until the tips
of the turbine blades hit Mach1?
Vince

There is a difference. In one there is no relative movement between air and
land.

Sailing boats also experience "apparent wind" and can sail faster than the
real wind.

raise the jibs'l Mr Morgan

II. The relationship between an object's mass m, its acceleration a,
and the applied force F is F = ma. Acceleration and force are vectors
(as indicated by their symbols being displayed in slant bold font); in
this law the direction of the force vector is the same as the
direction of the acceleration vector.
This (preceeding) is the most powerful of Newton's three Laws, because
it allows quantitative calculations of dynamics: how do velocities
change when forces are applied. Notice the fundamental difference
between Newton's 2nd Law and the dynamics of Aristotle: according to
Newton, a force causes only a change in velocity (an acceleration); it
does not maintain the velocity as Aristotle held.
This is sometimes summarized by saying that under Newton, F = ma, but
under Aristotle F = mv, where v is the velocity. Thus, according to
Aristotle there is only a velocity if there is a force, but according
to Newton an object with a certain velocity maintains that velocity
unless a force acts on it to cause an acceleration (that is, a change
in the velocity). As we have noted earlier in conjunction with the
discussion of Galileo, Aristotle's view seems to be more in accord
with common sense, but that is because of a failure to appreciate the
role played by frictional forces. Once account is taken of all forces
acting in a given situation it is the dynamics of Galileo and Newton,
not of Aristotle, that are found to be in accord with the
observations.

III. For every action there is an equal and opposite reaction.
unless a force acts on it to cause an acceleration (that is, a change
in the velocity), as above to the extant of law lll
Otherwise, chaos
The overall theory, an expanding universe will collapse.