| Topic: |
Science > Physics |
| User: |
"Jean" |
| Date: |
28 Feb 2005 06:26:05 AM |
| Object: |
Something Crazy...! |
This question poped up in my mind while I was riding a bike over a
speed breaker..
Consider two points A and B lying on a horizontal plane...Its a real
plane on planet earth where there is friction.To ride a bike from A to
B you have to spend some X litres of fuel.
Now place a wooden board of sufficient length with one end
placed at A and other end held high above the midpoint O of the
linesegment AB at point P. Adjust the height of the tip of the board OP
so that if you ride a bike from A to P it only takes less than X
litres of fuel.
Do you think that OP can be made greater than zero in such a case ?
Then ofcourse you can save fuel..! (by placing a planck sloping down)
(The point O need not be necessarily at the centre of the linesegment.)
Anything wrong with this kind of thinking ?
. P .
. | .
. | .
. | .
. | .
. | .
. | .
A---------------------------------------B
O
.
|
|
| User: "Uncle Al" |
|
| Title: Re: Something Crazy...! |
28 Feb 2005 02:38:26 PM |
|
|
Jean wrote:
This question poped up in my mind while I was riding a bike over a
speed breaker..
Consider two points A and B lying on a horizontal plane...Its a real
plane on planet earth where there is friction.To ride a bike from A to
B you have to spend some X litres of fuel.
Obviously not a spherical homogenous isotropic cow. Is it a Euclidean
plane or a curved "plane" of invariant gravity potential?
Now place a wooden board of sufficient length with one end
placed at A and other end held high above the midpoint O of the
linesegment AB at point P. Adjust the height of the tip of the board OP
so that if you ride a bike from A to P it only takes less than X
litres of fuel.
Do you think that OP can be made greater than zero in such a case ?
Then ofcourse you can save fuel..! (by placing a planck sloping down)
(The point O need not be necessarily at the centre of the linesegment.)
Anything wrong with this kind of thinking ?
. P .
. | .
. | .
. | .
. | .
. | .
. | .
A---------------------------------------B
O
Gravitation is a conservative field. The value of any path integral
(energy used to get from here to there) only depends on the start and
the finish. The intervening path is irrelevant. In the real world,
the minimum action path is the most efficient one. If there is
topography in the way, adjust accordingly.
If A is above B, make the curve a brachistochrone and all intermediate
starting points give you the same total transit time. If you tunnel
and evacuate rather than bridge, the coast from A to B can be a free
ride with a properly shaped chord (less friction and Coriolis losses).
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf
.
|
|
|
|
| User: "Maarten van Reeuwijk" |
|
| Title: Re: Something Crazy...! |
28 Feb 2005 07:57:18 AM |
|
|
Jean wrote:
This question poped up in my mind while I was riding a bike over a
speed breaker..
Consider two points A and B lying on a horizontal plane...Its a real
plane on planet earth where there is friction.To ride a bike from A to
B you have to spend some X litres of fuel.
Now place a wooden board of sufficient length with one end
placed at A and other end held high above the midpoint O of the
linesegment AB at point P. Adjust the height of the tip of the board OP
so that if you ride a bike from A to P it only takes less than X
litres of fuel.
Do you think that OP can be made greater than zero in such a case ?
Then ofcourse you can save fuel..! (by placing a planck sloping down)
(The point O need not be necessarily at the centre of the linesegment.)
Anything wrong with this kind of thinking ?
Nope nothing wrong with it, but if you would add the fuel needed to get from
O to P I reckon you will find you actually need more fuel than before.
Furthermore I would think it could be quite painful if you lose your
balance halfway the trip :)
--
===================================================================
Maarten van Reeuwijk Thermal and Fluids Sciences
Phd student dept. of Multiscale Physics
www.ws.tn.tudelft.nl Delft University of Technology
.
|
|
|
|
| User: "mysterious_man" |
|
| Title: Re: Something Crazy...! |
28 Feb 2005 09:04:25 AM |
|
|
OK let us imagine you will will do what you said.
let Energy you normally consume from A to B is X
let Energy you will consume from A to P =k*X where k smaller than 1 and
you will then go down from PB by only gravitation
this energy is divided to two parts
1- The energy waste in friction = [wight (w) * friction factor (a) *
cos(s)]*AP length
where s is the angle between AP and earth = AO/Cos(s)
then
The energy waste in friction = wight (w) * friction factor (a) *AO
length
2- Energy you will put in the earth gravitational field = Weight * OP
length .... this part is what will be used at the rest of journey till
you reach B
Then we have
k*X= w*a*AO + w*OP
recall that X=wight (w) * friction factor (a)*AB length
k*(w*a*AB)=w*a*AO + w*OP
W*OP = w*a*(k*AB-AO)
to reach the end you have to have
W*OP> w*a*OB
then you have to have
w*a*(k*AB-AO) > w*a*OB
k*AB-AO> OB
k*AB>AO+OB
k*AB>AB
k>1
and this contradict our asumption in the beginning that k<1 (the
condition to save fuel)
Then you will not save any Fuel
Regards
.
|
|
|
| User: "Troels Forchhammer" |
|
| Title: Re: Something Crazy...! |
28 Feb 2005 09:26:35 AM |
|
|
In message <1109603065.343344.274010@o13g2000cwo.googlegroups.com>,
mysterious_man <ahmedkq@gmail.com> enriched us with:
OK let us imagine you will will do what you said.
<snip>
Then you will not save any Fuel
In a real setup, wouldn't it depend on the efficiency of the engine in
different situations?
If the efficiency of overcoming the graviational field is better than
that of overcoming the road friction, it might be possible to save fuel.
Let the slope PB be such that the friction is just overcome and the bike
continues with a constant speed (switch off engine -- no energy spent),
and let the slope AP be such that the efficiency of overcoming both
friction and gravitation is maximised, then it is possible, I think,
that the total energy spent (only spent on the distance AP) is less than
what would be spent if |OP| = 0
--
Troels Forchhammer
Valid e-mail is t.forch(a)email.dk
If no thought
your mind does visit,
make your speech
not too explicit.
- Piet Hein, /The Case for Obscurity/
.
|
|
|
| User: "CWatters" |
|
| Title: Re: Something Crazy...! |
01 Mar 2005 04:29:07 AM |
|
|
"Troels Forchhammer" <Troels@ThisIsFake.invalid> wrote in message
news:LKGUd.39051$k4.761645@news1.nokia.com...
In message <1109603065.343344.274010@o13g2000cwo.googlegroups.com>,
mysterious_man <ahmedkq@gmail.com> enriched us with:
OK let us imagine you will will do what you said.
<snip>
Then you will not save any Fuel
In a real setup, wouldn't it depend on the efficiency of the engine in
different situations?
Possibly.
Also don't forget that drag is proportional to a speed^3 so a constant speed
is better than a varying speed. If you have a fixed time to get there.
.
|
|
|
|
|
|
|
Related Articles |
|
|
