>> That's apparently the Milner-Hindley type inference algorithm. But 
>> whatever.
> 
> That's what the file name says :D

I believe the correct response is "that's what SHE said!"

And besides, I named the file. (The website does some JavaScript 
trickery to make it maximally awkward to copy the image file. But they 
didn't bargin for the PrtSrc key...)

Post a reply to this message

Kevin Wampler wrote:

> I suppose I normally view distance in Euclidean space from the same 
> definition that applies to non-Euclidean spaces, rather than the 
> sqrt(dx^2 + dy^2) form, so I didn't really consider this.  You're right 
> though, if you're starting from the pythorgean theorem view of distance 
> it does bear some thinking about how it generalizes to the non-Euclidean 
> space.
> 
> 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.

So how *do* you compute the distance between two points in a non-Euclid 
space anyway?

For that matter, is there a way to unambiguously refer to a specific 
point in such a space?

(Normally you would of course just use Cartesian coordinates, but it is 
not clear to me that this works any more once you remove the parallel 
postulate.)

Post a reply to this message

>> Interesting fact: In elliptic geometry, pi is less than arcsine 1.
> 
> It's less than arcsine 1 where you're sitting right now. That's why they 
> say gravity bends space-time.

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...

Post a reply to this message

> Erm... 1.6L means that the engine block has a displacement of 1.6L, while 
> 2.3L means that the displacement is 2.3L - i.e., the cylinders are 
> physically bigger.

It used to be like that, if you bought a "one point six" it meant the engine 
displacement was roughly 1600 cc, but nowadays car makers like to keep the 
"one point six" naming convention but actually have a standard engine 
displacement across all models.  A bit like how AMD called their processor 
an XP2400, but it wasn't 2400 MHz.  If I'd bought the "1.6" version of my 
car it would have exactly the same engine as the "2.0" version, displacement 
1998cc.

> The Real WTF of course is that displacement is not directly related to 
> power output in the first place...

There are a vast number of things that significantly affect power output 
apart from displacement.  A useful quantity is "horsepower per litre" to 
compare engines.  Really efficient road-car engines can get up to 100 
HP/litre, racing engines over 300 hp/litre.

Post a reply to this message

scott wrote:
>> Erm... 1.6L means that the engine block has a displacement of 1.6L, 
>> while 2.3L means that the displacement is 2.3L - i.e., the cylinders 
>> are physically bigger.
> 
> It used to be like that, if you bought a "one point six" it meant the 
> engine displacement was roughly 1600 cc, but nowadays car makers like to 
> keep the "one point six" naming convention but actually have a standard 
> engine displacement across all models.  A bit like how AMD called their 
> processor an XP2400, but it wasn't 2400 MHz.  If I'd bought the "1.6" 
> version of my car it would have exactly the same engine as the "2.0" 
> version, displacement 1998cc.

Sure, but AMD don't actually call it the XP 2.4GHz. That would be false 
advertising - as would claiming that an engine has a displacement of X 
when it's actually Y.

>> The Real WTF of course is that displacement is not directly related to 
>> power output in the first place...
> 
> There are a vast number of things that significantly affect power output 
> apart from displacement.  A useful quantity is "horsepower per litre" to 
> compare engines.  Really efficient road-car engines can get up to 100 
> HP/litre, racing engines over 300 hp/litre.

Or just HP if you want to know how powerful it is, 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.)

Post a reply to this message

> Sure, but AMD don't actually call it the XP 2.4GHz. That would be false 
> advertising - as would claiming that an engine has a displacement of X 
> when it's actually Y.

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).

> Or just HP if you want to know how powerful it is,

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.

> 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.)

Didn't the UK car tax depend on the displacement of your engine?  Also lots 
of racing formulas have limits on the engine displacement (eg 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.

Post a reply to this message

scott wrote:
>> Sure, but AMD don't actually call it the XP 2.4GHz. That would be 
>> false advertising - as would claiming that an engine has a 
>> displacement of X when it's actually Y.
> 
> 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).

Hmm, probably.

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.)

>> Or just HP if you want to know how powerful it is,
> 
> 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.

Or that, yes.

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...

>> I never did understand 
>> the fascination with displacement. (Other than that I guess you can 
>> unambiguously measure it.)
> 
> Didn't the UK car tax depend on the displacement of your engine?

Ah yes, if your car is 1.1L or less, you get cheaper car tax.

Presumably the government chose this value since all 1.1L cars known to 
man are actually 1103 cc, not 1100 cc. Hence, approximately 0.1% of the 
population qualify for this.

In any case, given that this is supposedly a "green tax", taxing based 
on emissions or fuel efficiency would seem far more logical. But then, 
the entire concept that you can make people abandon their cars just by 
making it too expensive is laughable. You make people use alternatives 
by making the alternatives ACTUALLY ****ING WORK, not just by taxing 
them off the road. But then, the former costs money, while the latter 
generates money under the pretenses of giving a **** about green, so...

> Also 
> lots of racing formulas have limits on the engine displacement (eg 
> 2400cc for F1 currently).

Yes. Presumably so that to make the car go faster, you have to actually 
*work at it* rather than just make it burn petrol faster. ;-)

Post a reply to this message

Stephen wrote:
> Eero Ahonen wrote:
> 
>>  - still having
>> 150bhp/320Nm (upgradeable to 175bhp/370Nm with just a software) with
> 
> Let’s have an argument about the difference between hp and bhp, please. :-P
> 

Bhp is a more defined unit than hp - bhp is the actual power that comes
out of the engine (and goes to the gearbox).

Well, actually bhp should be "braked" from the car itself - and they
will be, after I'll upgrade the software.

-Aero

Post a reply to this message

scott wrote:
> 
> Aren't all cars upgradeable with just software nowadays?  

Yes. Actually even my '89 9000 has upgraded software.

> In my car the
> "1.6L", "1.8L", "2.0L" and "2.3L" versions all actually have exactly the
> same engine.  

No, they are not :). The very basic engine (=the block itself) is the
same, yes.

> You are just choosing whether you want the 116, 143, 177
> or 204 BHP software installed when you buy it :-)  

Nope. The 123d has two turbochargers. The 120d has a bigger
turbocharger, different injectors, IIRC different crankshaft and some
other differencies compared to 118d. 118d and 116d may possibly be the
same engine, I haven't found theier differencies, but I'd guess that
they too have different turbos.

Yes, 1-series was one of the possibilities I though about, so I did a
little digging :p.

> I heard some people
> got up to 265 BHP out of that engine, but to me that seems really stupid
> as all the other components will not have been reliability tested at
> that power level.

I'd say that if it's done correctly, the reliability shouldn't be a
major problem on that engine (especially 123d). But the software I
referred to is a official software (by Hirch), so it won't trash the
warranty of the car.

-Aero

Post a reply to this message

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...

And probably by a lightly loaded large commercial jet, for that matter.

-- 
Darren New, San Diego CA, USA (PST)
   Forget "focus follows mouse." When do
   I get "focus follows gaze"?

Post a reply to this message

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"?

Post a reply to this message

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"?

Post a reply to this message

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

Post a reply to this message

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

Post a reply to this message

"Invisible" <voi### [at] devnull> 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

Post a reply to this message

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

Post a reply to this message

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.

Post a reply to this message

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.

Post a reply to this message

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*

Post a reply to this message

>> 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*

Post a reply to this message

On Wed, 13 Jan 2010 19:35:00 +0000, Orchid XP v8 wrote:

> 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.

Well, the others had good ideas as well - grip seems an important thing, 
too - power on a ice vs. power on pavement end up with two vastly 
different results.. :-)

Or was that sarcasm? ;-)

Jim

Post a reply to this message

>> Finally, somebody correctly identifies the issue... sheesh.
> 
> Well, the others had good ideas as well - grip seems an important thing, 
> too - power on a ice vs. power on pavement end up with two vastly 
> different results.. :-)
> 
> Or was that sarcasm? ;-)

Power is nothing without control, 'tis true. But most cars (and animals) 
don't really have much of a problem with traction. The glaringly obvious 
thing about fast animals (including the cheetah) is that they weigh 
approximately nothing. Hell, fast cars tend to have the exact same 
property! Except they're made of metal, which is strong, but quite heavy.

Of course, a cheetah can out-accelerate most cars, but has limited top 
speed and severely limited endurance. But then again, if it doesn't kill 
something in 90 seconds or so, the animal it's chasing won't give it 
enough food to be worth continuing the chase anyway.

I gather the cheetah is limited primarily by overheating. Then again, it 
leaves in a freakin' desert wilderness, after all...

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

Post a reply to this message

Eero Ahonen wrote:
> Stephen wrote:
>> Eero Ahonen wrote:
>>
>>>  - still having
>>> 150bhp/320Nm (upgradeable to 175bhp/370Nm with just a software) with
>> Let’s have an argument about the difference between hp and bhp, please. :-P
>>
> 
> Bhp is a more defined unit than hp - bhp is the actual power that comes
> out of the engine (and goes to the gearbox).
> 
> Well, actually bhp should be "braked" from the car itself - and they
> will be, after I'll upgrade the software.
> 
> -Aero

Do you call that an argument? LOL

 From my memory of mechanics at school, hp was more an advertising unit ;)
Bloody farmers couldn’t tell an erg from an egg :-)


-- 

Best Regards,
	Stephen

Post a reply to this message

scott wrote:
> Didn't the UK car tax depend on the displacement of your engine?

I don't know about the UK, but the USA both taxes and bases some
insurance off of displacement.

Post a reply to this message

On Wed, 13 Jan 2010 20:33:02 +0000, Orchid XP v8 wrote:

> Power is nothing without control, 'tis true. But most cars (and animals)
> don't really have much of a problem with traction. The glaringly obvious
> thing about fast animals (including the cheetah) is that they weigh
> approximately nothing. Hell, fast cars tend to have the exact same
> property! Except they're made of metal, which is strong, but quite
> heavy.

True - though many newer cars are lighter than older counterparts, what 
with using machined aluminium, carbon fibre, and other such composites 
(many of which come from the aerospace industry where high strength and 
low weight are absolutely necessary features), there's no doubt they 
still weigh more than the average cheetah. :-)

> Of course, a cheetah can out-accelerate most cars, but has limited top
> speed and severely limited endurance. But then again, if it doesn't kill
> something in 90 seconds or so, the animal it's chasing won't give it
> enough food to be worth continuing the chase anyway.

Yep, and often they'll abandon the chase when it becomes apparent that 
nothing useful comes from it.

> I gather the cheetah is limited primarily by overheating. Then again, it
> leaves in a freakin' desert wilderness, after all...

True. :-)

Post a reply to this message

Orchid XP v8 wrote:
> 
> Power is nothing without control, 'tis true. But most cars (and animals)
> don't really have much of a problem with traction. The glaringly obvious
> thing about fast animals (including the cheetah) is that they weigh
> approximately nothing. Hell, fast cars tend to have the exact same
> property! Except they're made of metal, which is strong, but quite heavy.
> 

Have you ever actually driven anything more powerful than the 1.6i? With
the traditional 1-wheel drive grip practically somewhere around 150hp
starts to make an effect (depending on the car, of course), even on
clean asphalt. Around 250-300hp you'll really start missing 4wd when
accelerating from standing position. Remember that the cheetah can take
practically ~full power to its legs right from the start (and to the
ground also). On nature films I've never seen a cheetah to "sping the
feet". Now, if the cheetah would be on clear ice, it would be a bit
different...

Yes. Even when you have the power-to-weight -ratio, to accelerate a car
like a cheetah you'll need enormous traction, an amount that actually is
incredible.

-Aero

Post a reply to this message

Eero Ahonen wrote:
> Now, if the cheetah would be on clear ice, it would be a bit
> different...

I must thank you for one of the most amusing mental images I've seen all week.

-- 
Darren New, San Diego CA, USA (PST)
   Forget "focus follows mouse." When do
   I get "focus follows gaze"?

Post a reply to this message

> Power is nothing without control, 'tis true. But most cars (and animals) 
> don't really have much of a problem with traction.

Have you seen cats on hardwood floors? (they slip a lot)

Or someone flooring it in a car from a standstill? (the wheels spin a lot)

I suspect the cheetah is so fast at accelerating because its claws can dig 
into the ground to get traction.

If you got a vehicle with spiked tyres and drove it on grass it would 
probably accelerate quicker too.  IIRC snow-mobiles have a similar drive 
system that digs into the ice and they can get phenomenal acceleration.

Post a reply to this message

> Nope. The 123d has two turbochargers. The 120d has a bigger
> turbocharger, different injectors, IIRC different crankshaft and some
> other differencies compared to 118d. 118d and 116d may possibly be the
> same engine, I haven't found theier differencies, but I'd guess that
> they too have different turbos.

I stand corrected! I assumed that as there seemed to be software upgrades 
available that the hardware was actually the same.

> I'd say that if it's done correctly, the reliability shouldn't be a
> major problem on that engine (especially 123d). But the software I
> referred to is a official software (by Hirch), so it won't trash the
> warranty of the car.

Yeh I saw that a lot of the more reputable companies will pay for anything 
if the OEM refuses to pay out.  It seems though that (at least for BMW) you 
do not automatically invalidate your warranty by changing the software, just 
that they reserve the right to refuse to pay out if they think it's because 
of you changing the software.

Post a reply to this message

scott wrote:
>> Power is nothing without control, 'tis true. But most cars (and 
>> animals) don't really have much of a problem with traction.
> 
> Have you seen cats on hardwood floors? (they slip a lot)

Or lino.

But then, domestic cats didn't evolve for that environment. There *are* 
in fact animals which regularly hunt on sheets of ice, and they have 
special adaptations to increase traction. (That said, none of them is 
anywhere near as fast as a cheetah. But you might argue that's due to 
lack of available fuel...)

> Or someone flooring it in a car from a standstill? (the wheels spin a lot)
> 
> I suspect the cheetah is so fast at accelerating because its claws can 
> dig into the ground to get traction.

And not because, oh, I don't know, it's 100x smaller mass has 
significantly lower inertia to overcome in the first place?

Post a reply to this message

> And not because, oh, I don't know, it's 100x smaller mass has 
> significantly lower inertia to overcome in the first place?

That's only important once you get up to a high enough speed that you can't 
overcome friction (about 10-20 mph in road cars, 60 mph in fast cars, up to 
100 mph in racing cars).  Before that coefficient of friction is the only 
thing that matters.

Post a reply to this message

scott wrote:
>> And not because, oh, I don't know, it's 100x smaller mass has 
>> significantly lower inertia to overcome in the first place?
> 
> That's only important once you get up to a high enough speed that you 
> can't overcome friction (about 10-20 mph in road cars, 60 mph in fast 
> cars, up to 100 mph in racing cars).  Before that coefficient of 
> friction is the only thing that matters.

My point being that a smaller mass requires a smaller force to 
accelerate it, and thus less traction.

A cheetah's legs don't need to generate 500 BPH to get it from 0 to 60 
in 4 seconds. Because a cheetah doesn't weigh a quarter of a ton...

Post a reply to this message

> My point being that a smaller mass requires a smaller force to accelerate 
> it, and thus less traction.

Actually exactly the same traction.  If you accelerate an object at 10 m/s^2 
then it will need a coeffcient of friction of about 1.0 no matter what the 
mass is.  This is the point I was trying to make.

Post a reply to this message

scott wrote:
>> My point being that a smaller mass requires a smaller force to 
>> accelerate it, and thus less traction.
> 
> Actually exactly the same traction.  If you accelerate an object at 10 
> m/s^2 then it will need a coeffcient of friction of about 1.0 no matter 
> what the mass is.  This is the point I was trying to make.

So a force of 1N and a force of 1,000N both require the same amount of 
traction?

How does *that* work?!

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> So a force of 1N and a force of 1,000N both require the same amount of 
> traction?
>
> How does *that* work?!

If the 1000 N force is on an object weighing 1000 kg, and the 1 N force is 
on an object weighting 1 kg, then yes, they both require the same amount of 
friction and will result in the same acceleration.

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scott wrote:
>> So a force of 1N and a force of 1,000N both require the same amount of 
>> traction?
>>
>> How does *that* work?!
> 
> If the 1000 N force is on an object weighing 1000 kg, and the 1 N force 
> is on an object weighting 1 kg, then yes, they both require the same 
> amount of friction and will result in the same acceleration.

This must truly be the definition of "counter-intuitive". I cannot begin 
to imagine how this can be true. It is surely self-evident that applying 
a large force requires better grip than does applying a small force.

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>> If the 1000 N force is on an object weighing 1000 kg, and the 1 N force 
>> is on an object weighting 1 kg, then yes, they both require the same 
>> amount of friction and will result in the same acceleration.
>
> This must truly be the definition of "counter-intuitive". I cannot begin 
> to imagine how this can be true. It is surely self-evident that applying a 
> large force requires better grip than does applying a small force.

Not if the contact force is proportionally higher.

Press your thumb and finger together very lightly and see how much sideways 
force you need to slide them across each other.  Now press them together 
much harder and you'll find you need a much bigger sideways force to 
overcome the friction.

It's the same with a 1000 kg car and a 10 kg animal, because the car is 
pushing down on the road 100 times more than the animal it can generate 100 
times more forward force before slipping.

http://en.wikipedia.org/wiki/Friction

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>>> If the 1000 N force is on an object weighing 1000 kg, and the 1 N 
>>> force is on an object weighting 1 kg, then yes, they both require the 
>>> same amount of friction and will result in the same acceleration.
>>
>> This must truly be the definition of "counter-intuitive". I cannot 
>> begin to imagine how this can be true. It is surely self-evident that 
>> applying a large force requires better grip than does applying a small 
>> force.
> 
> Not if the contact force is proportionally higher.

I had assumed that the "amount of friction" already takes into account 
the contact force, along with the surface roughness, deformability and 
all the other things that affect friction.

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Stephen wrote:
> 
> Do you call that an argument? LOL

No, I call that a partly definition.

> From my memory of mechanics at school, hp was more an advertising unit ;)
> Bloody farmers couldn’t tell an erg from an egg :-)

Hp can be misleading, since it can mean lots of different hp's. It can
be either SAE or DIN and from the crankshaft or from the tires etc.

-Aero

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scott wrote:
>> So a force of 1N and a force of 1,000N both require the same amount of 
>> traction?
>>
>> How does *that* work?!
> 
> If the 1000 N force is on an object weighing 1000 kg, and the 1 N force 
> is on an object weighting 1 kg, then yes, they both require the same 
> amount of friction and will result in the same acceleration.

In other news, both feathers and hammers fall at the same speed in airless 
conditions.

-- 
Darren New, San Diego CA, USA (PST)
   Forget "focus follows mouse." When do
   I get "focus follows gaze"?

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Darren New wrote:

> In other news, both feathers and hammers fall at the same speed in 
> airless conditions.

Just once, I'd like to verify this experimentally...

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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Eero Ahonen wrote:
> Stephen wrote:
>> Do you call that an argument? LOL
> 
> No, I call that a partly definition.
> 

:D

>> From my memory of mechanics at school, hp was more an advertising unit ;)
>> Bloody farmers couldn’t tell an erg from an egg :-)
> 
> Hp can be misleading, since it can mean lots of different hp's. It can
> be either SAE or DIN and from the crankshaft or from the tires etc.
> 

Well I probably don’t think of hp as being anything as other than what 
non-technical people say. Who knows what work a horse can do nowadays? 
If the health and safety or animal welfare people allow it ;)

-- 

Best Regards,
	Stephen

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Orchid XP v8 wrote:
> Just once, I'd like to verify this experimentally...

http://www.youtube.com/watch?v=5C5_dOEyAfk

Of course, it wouldn't be *that* hard to do on earth.

-- 
Darren New, San Diego CA, USA (PST)
   Forget "focus follows mouse." When do
   I get "focus follows gaze"?

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>> Just once, I'd like to verify this experimentally...
> 
> http://www.youtube.com/watch?v=5C5_dOEyAfk

So much for "they did it on a soundstage and slowed it down". :-P

> Of course, it wouldn't be *that* hard to do on earth.

Yeah, because a high vacuum is easy to come by. Oh, wait...

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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Darren New wrote:
> Orchid XP v8 wrote:
>> Just once, I'd like to verify this experimentally...
> 
> http://www.youtube.com/watch?v=5C5_dOEyAfk
> 
> Of course, it wouldn't be *that* hard to do on earth.
> 

I've seen a demo of this in a few science museums.  It's pretty nifty, 
but in the vacuum they both fall fast enough that you don't really get 
to look at it for long.

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Orchid XP v8 wrote:
> Yeah, because a high vacuum is easy to come by. Oh, wait...

Well, yeah, it is.  It's called a bell jar.

http://www.youtube.com/watch?v=_XJcZ-KoL9o
(Note - the next video after the one I posted.)

You can go to edmond's scientific and buy bottles of vacuum for like a 
quarter each, too.  It's not like you need interstellar-space vacuum to 
prove the point.

-- 
Darren New, San Diego CA, USA (PST)
   Forget "focus follows mouse." When do
   I get "focus follows gaze"?

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>> Yeah, because a high vacuum is easy to come by. Oh, wait...
> 
> Well, yeah, it is.  It's called a bell jar.

You'd need a pretty damned big bell jar to drop an object any 
significant distance.

> You can go to edmond's scientific and buy bottles of vacuum for like a 
> quarter each, too.

Really?


The London Science Museum has a bell inside a jar with a vacuum pump. 
But last I checked, a pump powerful enough to create anything you could 
describe as "a vacuum" is an extremely expensive piece of scientific 
equipment.

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Stephen wrote:
> 
> Well I probably don’t think of hp as being anything as other than what
> non-technical people say. Who knows what work a horse can do nowadays?
> If the health and safety or animal welfare people allow it ;)
> 

In that, my friend, you are absolutely right.

-Aero

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Invisible wrote:
> You'd need a pretty damned big bell jar to drop an object any 
> significant distance.

Somewhat larger than the distance it takes to see a feather and a ball 
bearing falling at different speeds in atmosphere.

>> You can go to edmond's scientific and buy bottles of vacuum for like a 
>> quarter each, too.
> 
> Really?

Yes. Ever get blood drawn? How do you think that works?

> But last I checked, a pump powerful enough to create anything you could 
> describe as "a vacuum" is an extremely expensive piece of scientific 
> equipment.

http://www.google.com/products?q=vacuum+pumps+for+sale

Even the $25 pump gets you down to 29" of vacuum.

-- 
Darren New, San Diego CA, USA (PST)
   Forget "focus follows mouse." When do
   I get "focus follows gaze"?

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> Yes. Ever get blood drawn? How do you think that works?

Presumably they just use a syringe. I wasn't looking at the time; I was 
in far too much pain...

>> But last I checked, a pump powerful enough to create anything you 
>> could describe as "a vacuum" is an extremely expensive piece of 
>> scientific equipment.
> 
> http://www.google.com/products?q=vacuum+pumps+for+sale
> 
> Even the $25 pump gets you down to 29" of vacuum.

Interesting. I wonder what it costs to buy a large container than can 
withstand several thousand Newtons of force trying to crush it...

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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