Re: Speed of light cycling

dkahn400 said:

AndyC said:

I'm so sad.
The first thought I had when I read this message header was that it
would be impossible as it would mean the up/forward sroke of the
pedal would need exceed the speed of light...

I suppose it could be down a hill so freewheeling though ;o)

Cycling at the speed of light the top of the wheel would be travelling
at twice the speed of light. Does this mean the theoretical maximum
speed of a wheeled vehicle is only half the speed of light? And does it
matter that the wheels are no longer round?

No, they're all travelling no faster than the speed of light - it depends
on where the observer is. An observer on the bike would see the
ground moving backwards at c (the speed of light) and the top of
the whee moving forward at c. An observer on the ground would see
the bike moving forward at c but the wheels would be infinitely distorted
because the bottom would be stationary and the top would only apparently
be moving at c in the forward direction - but then you'd have to take
into account the change in the biker and ground-based observer's clock,
too. Travelling at c is a problem because singularities happen there,
it's better to think of it as travelling nearly at c. Well, to be
honest, it's better not to think of it at all because if you do so
too hard you brain turns into a Escher painting.

--
Trevor Barton

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

Quoted message said:

in message <[email hidden]>, LSMike

(') said:

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

Quoted message said:

in message <[email hidden]>,

Quoted message said:

Helicopters can fly at at most not quite half the speed of sound for
exactly this reason.

Not quite, I think the record is some 400km/hour (that's gone up since
I
last read). I thought the main limiting factor was the reducing lift
from the retreating blades.

The speed of sound is 1,237Km/h.

Depends on the conditions, surely?

Quoted message said:

The limiting factor is putting the tips
of your rotor blades through mach 1, because the stresses involved
would break them.

I rather think it's much more complex than this. I'm sure it's possible to
make rotor blades that can go faster than the speed of sound since under
certain conditions the tips of some aircraft propellers will go supersonic.
IANAE but I seem to remember that there are all kinds of aerodynamic
disadvantages to having part of a wing (i.e. rotor blade) super sonic and
part not.

Quoted message said:

You do need to adjust the pitch of the retreating
blades, because going relatively slower they need to have courser
pitch.

IIRC here is the problem. Low blade airspeed and coarse pitch on the
retreating blade = stall over some of the inner (and thus slower moving)
part of the blade. The faster you go the further out the stalled section
moves. Hence I still believe this is the limiting factor.

Quoted message said:

But if the advancing blades could exceed the speed of sound
without difficulty, then there would be no problem in spinning the
rotor so the advancing blades were running at (say) mach 5, the craft
was doing mach 3, and the retreating blades would still be doing mach 1
relative to the air. The reason you can't do this is as I stated.

--
[email hidden] (Simon Brooke) http://www.jasmine.org.uk/~simon/
Wannabe a Web designer?
<URL:http://userfriendly.org/cartoons/archives/97dec/19971206.html>

dkahn400 said:

AndyC said:

I'm so sad.
The first thought I had when I read this message header was that it
would be impossible as it would mean the up/forward sroke of the
pedal would need exceed the speed of light...

I suppose it could be down a hill so freewheeling though ;o)

Cycling at the speed of light the top of the wheel would be travelling
at twice the speed of light.

No it wouldn't. You're assuming that you can calculate relative velocities
through simple addition (e.g. person on road side sees rider is going at speed
0.5 relative to ground; top of wheel is going at speed 0.5 relative to rider,
therefore top of wheel is going at speed 1 relative to person on road side).
This assumes that distance and time measured by the rider are the same as
those measured by the person on the ground. This isn't the case. If you move
quickly, space and time are distorted in a way described by Einstein's theory
of relativity, which has its centenary this year, see
http://www.einsteinyear.org/facts/special_relativity

Quoted message said:

Does this mean the theoretical maximum
speed of a wheeled vehicle is only half the speed of light? And does it
matter that the wheels are no longer round?

Phil Barker said:

dkahn400 wrote:

Quoted message said:

Quoted message said:

Cycling at the speed of light the top of the wheel would be
travelling at twice the speed of light.

No it wouldn't. You're assuming that you can calculate relative
velocities through simple addition (e.g. person on road side sees
rider is going at speed 0.5 relative to ground; top of wheel is going
at speed 0.5 relative to rider, therefore top of wheel is going at
speed 1 relative to person on road side). This assumes that distance
and time measured by the rider are the same as those measured by the
person on the ground. This isn't the case. If you move quickly, space
and time are distorted in a way described by Einstein's theory of
relativity, which has its centenary this year, see
http://www.einsteinyear.org/facts/special_relativity

Yes, I believe you are correct. The out-of-roundness of the wheels is
also associated with this, I believe, so that the closer you get to the
speed of light the more the bicycle is shortened and the more closely
all parts of it appear to an observer to be moving at the same speed.
It would not appear distorted to the rider though. I'm happy to be
further corrected on any of this by someone who really knows what
(s)he's talking about. I sympathise with the quote from Chaim Weizmann
after he'd made an Atlantic crossing of several days with Einstein.
"Einstein explained his theory to me every day and on my arrival I was
fully convinced that he understood it."

--
Dave...

dkahn400 said:

I sympathise with the quote from Chaim Weizmann
after he'd made an Atlantic crossing of several days with Einstein.
"Einstein explained his theory to me every day and on my arrival I was
fully convinced that he understood it."

I though the quote was going to be "Einstein explained his theory to me
every day and on my arrival I was fully convinced that time dilation had
occurred on a transatlantic crossing ..."

--
Trevor Barton

Trevor Barton said:

dkahn400 said:

I sympathise with the quote from Chaim Weizmann
after he'd made an Atlantic crossing of several days with
Einstein. "Einstein explained his theory to me every day and
on my arrival I was fully convinced that he understood it."

I though the quote was going to be "Einstein explained his theory
to me every day and on my arrival I was fully convinced that time
dilation had occurred on a transatlantic crossing ..."

Unlikely. He was a brilliant chemist in his own right, as well as later
becoming the first president of Israel.

--
Dave...