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Invisible wrote:
> Space-time is an inhomogenous space anyway. I hear that gravity bends it
> with positive curvature, but the universe itself appears to have
> slightly negative curvature...
They're still arguing over whether it's positive or negative, or dark
energy, or what. There is, so far, no good way to measure the curvature of
really big areas of space.
--
Darren New, San Diego CA, USA (PST)
Forget "focus follows mouse." When do
I get "focus follows gaze"?
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Kevin Wampler wrote:
> That said, I'm not sure it's necessary to actually understand the proper
> definition of distance in order to talk about circles in other spaces --
> particularly if we limit ourselves to spherical and hyperbolic spaces
> which are more or less easy to visualize.
Actually, I was thinking of actual real space, where the same distances are
different depending who is measuring them. What's a circle for me isn't a
circle for you, so I find it hard to imagine a good definition for "pi"
under such circumstances.
--
Darren New, San Diego CA, USA (PST)
Forget "focus follows mouse." When do
I get "focus follows gaze"?
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scott wrote:
> Yeh, I doubt any car makers falsely advertise the displacement. But
> calling your car a "1.6 TDI" or whatever and it actually having a
> displacement of 2000cc is probably ok (even though 90% of people would
> assume the displacement was 1.6 litres).
The only manufacturer I actually know done this is Saab. After all, BMW
doesn't call eg. 116d a 1.6l - they just refer to 116d (I think the
first BMW with misleading model name was 318i somewhere at 90's running
with 2.0 engine). Saab's 1.8t is actually a 2-liter engine (pretty much
the same as 2.0t) - they say that 1.8t is just the model name, not the
engine. And all the manufacturers actually have theier engine specs
available, so they aren't actually hiding the truth.
> I doubt many people are actually interested in the maximum power their
> engine can develop at one particular engine speed. What's more useful
> is how quickly the car can accelerate, eg 40-70mph or 70-100mph times.
> This depends on how much power the engine can develop across a wider
> range of RPMs, and also the mass of the car.
Yep, the curve telling this is called torque curve, the higher and wider
it is, more practical the car and more easy the engine usually is.
Turbocharged engines manage to get high torque even at low rpm's, so
they tend to be easy and nice to drive, even while providing high
hp/liter -ratio and reasonable economy.
>> MPG if you want to know how efficient it is... I never did understand
>> the fascination with displacement. (Other than that I guess you can
>> unambiguously measure it.)
The displacement tells you roughly how much torque you'll get from the
engine. The basic feature for a naturally aspirated engine is somewhere
around 100Nm/l nowadays - charged ones get even to 200 and over it (eg.
Saab 9-3 1.9 TTiD - 1.9 liter engine and 400Nm of torque). That also
tells you the nature of the engine - do you need to rev it to make the
car accelerate, do you need to change the gear often etc.
> 2400cc for F1 currently). The HP/litre figure is also a good guide as
> to how well engineered and advanced the engine is. And of course higher
> displacement usually means a heavier engine, which is something you
> usually try to avoid.
Yes, and it also tells you if the engine is nasty to drive as a
daily-driver. Sure, you can get 200hp from naturally aspirated 2-liter
engine (Honda Civic Type-R), but you'll also *need* the 4+krpm revs to
make the car actually accelerate and to find that power. Hit in a
turbocharger or even couple of them, and you'll get the power even from
1500rpm's.
-Aero
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Invisible wrote:
>
> I'm pretty certain my car's engine *really is* 1.6L though. (The Haynes
> manual has different instructions depending on the size and/or year.)
>
Yes, yes it is (or at least only some cm3's away from it), though 1.6l
ain't an engine - it's a coffee mug :-P.
> I still find it quite impressive that a CAR, which is made of METAL and
> powered by EXPLODING PETROL, can apparently be out-accelerated by a
> cheetah, which is MADE OF MEAT. Then again, an adult cheetah probably
> weighs significantly less than an Audi TT...
It's the grip. That cheetah has incredible amount of grip on its feet
when it goes for a prey.
-Aero
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"Invisible" <voi### [at] dev null> wrote in message
news:4b4dd7fa$1@news.povray.org...
> I still find it quite impressive that a CAR, which is made of METAL and
> powered by EXPLODING PETROL, can apparently be out-accelerated by a
> cheetah, which is MADE OF MEAT. Then again, an adult cheetah probably
> weighs significantly less than an Audi TT...
Of course, it's not what they're made of, or their mass, or what their fuel
is, but the efficiency with which they convert their fuel to energy, and the
efficiency with which they translate that thermal energy into mechanical
energy. Hydraulic transfer systems can certainly be more efficient than
complex mechanical linkages.
Of course, there are cars that can out-accelerate a cheetah. But, those cars
have the same problem that the cheetah does... they need to stop and
re-fuel. I expect there's a greater need for cars that keep chugging along
without stopping, whatever speed they do it at and however long they take to
reach that speed. :-)
--
Jack
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On Wed, 13 Jan 2010 14:26:01 +0000, Invisible wrote:
> I still find it quite impressive that a CAR, which is made of METAL and
> powered by EXPLODING PETROL, can apparently be out-accelerated by a
> cheetah, which is MADE OF MEAT. Then again, an adult cheetah probably
> weighs significantly less than an Audi TT...
It's all about the power to weight ratio. :-)
Jim
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Darren New wrote:
> Actually, I was thinking of actual real space, where the same distances
> are different depending who is measuring them. What's a circle for me
> isn't a circle for you, so I find it hard to imagine a good definition
> for "pi" under such circumstances.
Do you mean as in special relativity? In such a case you'd probably
have to define a circle under the Minkowski metric, in which case it
won't look much like a circle. I *think* that in such a case all
circles end up having zero circumfrence, but I haven't actually worked
out the math so there's a good chance I'm wrong here.
Agreed that a pi-like constant really only makes sense in Euclidean
space though.
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Invisible wrote:
>
> So how *do* you compute the distance between two points in a non-Euclid
> space anyway?
Generally you start with a notion of something like a dot product
defined in the tangent spaces of your space and then write out an
integral to define the arc length of a curve. Then the distance between
two points can be defined to be the minimum length of any curve
connecting them.
> For that matter, is there a way to unambiguously refer to a specific
> point in such a space?
Depends on the space. A relatively general but computationally
cumbersome solution is to cover your space will small Cartesian patches
which connect together in a "nice" way. The you can define a point by
giving its Cartesian patch and its coordinates within that patch.
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Jim Henderson wrote:
> On Wed, 13 Jan 2010 14:26:01 +0000, Invisible wrote:
>
>> I still find it quite impressive that a CAR, which is made of METAL and
>> powered by EXPLODING PETROL, can apparently be out-accelerated by a
>> cheetah, which is MADE OF MEAT. Then again, an adult cheetah probably
>> weighs significantly less than an Audi TT...
>
> It's all about the power to weight ratio. :-)
Finally, somebody correctly identifies the issue... sheesh.
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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>> So how *do* you compute the distance between two points in a
>> non-Euclid space anyway?
>
> Generally you start with a notion of something like a dot product
> defined in the tangent spaces of your space and then write out an
> integral to define the arc length of a curve. Then the distance between
> two points can be defined to be the minimum length of any curve
> connecting them.
Any idea what the hell a tangent space is?
>> For that matter, is there a way to unambiguously refer to a specific
>> point in such a space?
>
> Depends on the space. A relatively general but computationally
> cumbersome solution is to cover your space will small Cartesian patches
> which connect together in a "nice" way. The you can define a point by
> giving its Cartesian patch and its coordinates within that patch.
Hmm, sounds like kind of a patchy solution...
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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