Top dead centre

[Propellor]

It is said that the speed of a piston will be zero twice per Rev. Seems logical. One moment it is whizzing upwards, next moment whizzing downwards. So at some point it must have been travelling at zero speed. That point is tdc and bdc. Again, all seems logical.

But hang on. Tdc and bdc are defined by a line. At zero degrees. A line that has no width. So if we keep zooming in, so to speak, to check the piston speed as the crank moves ever closer to zero degrees, it never actually seems to exist at zero degrees for any time. So that's a bit strange. If there's no time, then how can it happen? How can the piston speed ever be zero? And the other strange thing is, it seems that this is independent of rpm. There's no doubt that the piston speed increases with rpm, but the infinitely thin line defining tdc and therefore zero piston speed is just as infinitely thin at high rpm as it is at low rpm.

So, just how long is a piston at tdc? How long is it travelling at zero speed?
Conundrum.

[Andy M]

How perfect and slack free are the components movements? How good is your measuring equipment?

This is the difference between engineering and geometric theory.

The piston will be stationary for the time it takes to take up the lash in various bearings and switch the likes of the con rod from its compressed to over compressed or tensioned length.

Andy

[Propellor]

How perfect and slack free are the components movements? How good is your measuring equipment?

This is the difference between engineering and geometric theory.

The piston will be stationary for the time it takes to take up the lash in various bearings and switch the likes of the con rod from its compressed to over compressed or tensioned length.

Andy

Hi Andy

I'm thinking geometric theory (or as best I know it!). We can come to the real world later.

Cheers.

Andy.

[Propellor]

It seems to apply to the max piston velocity too. In fact any piston speed relating to the corresponding angle of crank rotation. The line defining the angular position itself doesn't have any width. It seems weird. It tells you what the piston speed will be, but the piston seems to "linger" at that speed for no amount of time.

I suppose what I'm indirectly saying is that a sinusoidal curve has absolutely no straight bits on it. The position occurs, but the amount of time spent at it is zero!

I'm definitely no mathematician (in case you hadn't guessed), but zero seems every bit as weird as infinity.

It seems to apply to everything. How wide is the line that defines (say) a 100 metre position? Zero width. So, regardless of how fast I ride past that marker, I spend zero time at that position! This is how it seems.

[Andy M]

Zero by definition isn't there. The mathematicians don't have to worry beyond this.

What engineers call zero is the end of the measuring tool. Even when a comparative measure comes out at zero you just know a finer tool will eventually show a difference.

Andy

[Propellor]

Zero by definition isn't there. The mathematicians don't have to worry beyond this.

What engineers call zero is the end of the measuring tool. Even when a comparative measure comes out at zero you just know a finer tool will eventually show a difference.

Andy

The mathematicians might not worry but what about head scratchers like me?    Lol.

I understand what you mean re the more practical angle (pun). But when you dig a bit all sorts of weird things happen
 
I used to love geometry, even as a kid. Never questioned it though.

[guest564]

What engineers call zero is the end of the measuring tool.
Andy

I would dispute that. Many tools, such as the dial gauge you would use to find TDC, have zero in the centre. An engineer understands that zero is not measurable and will apply a tolerance to measurements. i.e. zero +/-n or x cm +/ y cm.
The piston speed reduction causes another issue. Measuring at TDC is quite difficult because there is very little change in displacement against angle, the conventional method is to measure the angle at a fixed displacement either side of TDC and then determine TDC from there.

[Andy M]

A dial gauge is a type of comparator. It is not an absolute scale.

As a distance tool the negative is just the start of distance in another direction. 2 mm from here describes a sphere. Minus 2 mm on the DTI is telling you the direction along the plunger plus mechanical movement, so describes a very thin  banana/ lens shaped zone 2mm of plunger extension from the point that was set at zero.

Its like zero degrees on temperature. Celsius has an arbitrary zero and hence negatives to give direction towards less molecular level activity. Kelvin has the actual end of the scale at zero.

Andy

[Propellor]

A dial gauge is a type of comparator. It is not an absolute scale.

As a distance tool the negative is just the start of distance in another direction. 2 mm from here describes a sphere. Minus 2 mm on the DTI is telling you the direction along the plunger plus mechanical movement, so describes a very thin  banana/ lens shaped zone 2mm of plunger extension from the point that was set at zero.

Its like zero degrees on temperature. Celsius has an arbitrary zero and hence negatives to give direction towards less molecular level activity. Kelvin has the actual end of the scale at zero.

Andy

I agree. In fact, when one thinks about it, there can't be such a thing as a negative value in anything other than a comparative sense. When it comes to absolute, there arent negatives. Are there? Does that mean that anything with a negative value is "only" a comparison?

With respect to my op, I had in mind the Euclidean version of a line. "Breadthless". Was it wrong of me to use the word zero to describe its width?

[Propellor]

What engineers call zero is the end of the measuring tool.
Andy

I would dispute that. Many tools, such as the dial gauge you would use to find TDC, have zero in the centre. An engineer understands that zero is not measurable and will apply a tolerance to measurements. i.e. zero +/-n or x cm +/ y cm.
The piston speed reduction causes another issue. Measuring at TDC is quite difficult because there is very little change in displacement against angle, the conventional method is to measure the angle at a fixed displacement either side of TDC and then determine TDC from there.

The dial gauge scenario is just as interesting and, to me, just as elusive. You can't (seem to) land bang on zero position, or any position denoted by a Euclidean line extending radially from the centre point, because the line doesn't seem to be there. By Euclidean definition it has no width. None. Mind you, the centre "point" doesn't cover any area. None. So that doesn't exist either. This is weird stuff. What were the ancient Greeks drinking? 

You can seem to go from one position to another ok, but as soon as you try to "stop" on the Euclidean line or point, it just keeps running away from you. The closer you get to it, on ever increasing magnification, the further it just moves away. To infinity? And yet you can cross it.

I need a beer.

[timbo]

Enjoying this thread. Its causing a bit of beard scratching though 

[guest564]

You guys must be mathematicians and not engineers, it reminds me of this joke:

A mathematician and an engineer agreed to take part in an experiment. They were both placed in a room and at the other end of the room was a beautiful woman lying naked on a bed. The experimenter said that every 30 seconds they would be allowed to travel half the distance between themselves and the bed. The mathematician stormed off exclaiming 'this is pointless', the engineer agreed to go ahead with the experiment. On the way out the mathematician explained to the engineer that he would never actually reach the woman to which the engineer replied 'So what, soon I'll be close enough for all practical purposes'.

[Propellor]

You guys must be mathematicians and not engineers, it reminds me of this joke:

A mathematician and an engineer agreed to take part in an experiment. They were both placed in a room and at the other end of the room was a beautiful woman lying naked on a bed. The experimenter said that every 30 seconds they would be allowed to travel half the distance between themselves and the bed. The mathematician stormed off exclaiming 'this is pointless', the engineer agreed to go ahead with the experiment. On the way out the mathematician explained to the engineer that he would never actually reach the woman to which the engineer replied 'So what, soon I'll be close enough for all practical purposes'.

Hee hee. Funny joke.

You never said that they were a male injuneer and maffimackikkiun. But I made the assumption they were. 

Ps. I already said I'm no mathematician. 

[Andy M]

The trouble is people have been brought up to expect " accuracy" in engineering. They think two parts toleranced to a gnats cock and meassured to half a cock hair five times during production are somehow better. When you tell they you've designed out the need to worry they get agitated and think you are pulling a fast one.

You have two eggs in a box and add another. How many eggs?  Mathematician says three. Production engineer says half a box full.

Andy
B Eng

[Propellor]

....... or any position denoted by a Euclidean line extending radially from the centre point......

When you think about it, a line extending radially from the centre point can't have any width anyway because the centre point doesn't have any area. For a line extending radially from the centre to have any width the centre point would need to have area. In other words another circle. But how would that micro circle be constructed? Ha ha.

It's madness and could never exist like that in the material world, but that's the principles upon which the machines we ride are based.

We know that shafts don't really rotate strictly about a centre point as defined by Euclid. But without Euclid I'm pretty sure we wouldn't be riding around on these machines today. We're taught this stuff at school so clearly somebody thinks the ideas or principles are pretty fundamental to our society.