Well, you do know the linear motion is only two directions, but you asked how we know when at some time (t) the speed=0, and the answer is simple, just look at the acceleration vector, it will point in the direction the body is going, it basically is forcasting for you a dx path for t+dt where dt is very small but not zero.
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Vertical motion (piston) converted to rotational motion (crankshaft). Seems you are going off in the weeds about your understanding the more the subject is discussed.
In that graph I posted of the sine wave that shows the piston vertical velocity, how do explain that sine wave curve going through the zero velocity axis at each TDC and BDC points?
Please excuse, the retarding acceleration vector one moment before had not the same direction as the movement. It already had the direction of the movement to come. But I never asked for the moment before or the moment after, as all is about just the moment of change of direction. Why don't you just tell me if it's still going upwards or already downwards or both or none at that point in time (when it must be moving with velocity=0)? Simple question, but not to be answered pointing to phase shift. The moment of shift of sign has the same problem as the moment of zero velocity.
Can't ride one pointing to the other and know the direction. But can't be without direction for one moment either when you need the movement to be riding.
Can't ride one pointing to the other and know the direction. But can't be without direction for one moment either when you need the movement to be riding.
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Not approaching zero, moving away from zero. Call one dorection +, and the 180 from that - if you like, the motion is to approach zero, 180, then move away from zero at each end of the stroke.
And no, your adding of those dx's will not equal zero, you need to take a diff, dx approasching TDC is neg, dx leaving TDC is pos, so your total dx = |-dx - +dx| = 2dx for any angle that is same on either side of zero deg (TDC).
V = distance/time. Distance can certainly be zero in many examples. Time doesn't stop ... distance traveled can.
Look again at that velocity sine wave curve I posted earlier. Velocity is zero at four points on the curve (two TDCs and two BDCs) ... how do explain that?
I said that the absolute dx is not zero and you are correct it will be sum of the 2 dx ... I also mentioned that the fact that absolute dx is not zero, will satisfy the math. However, that doesn't mean any progress has been made at the very top of the piston dx wise.
I explained it alredy.
Here, one last time.
Motion is a velocity vector, which has two components (I should say attributes) of speed and direction. Speed is a scalar #, direction can be described in any coord system of your choosing.
When speed (a scalar that is an attribute of the velocity vector) becomes zero, this observation alone does not tell us the body in motion has stopped moving, and in fact in this case the motion has not stopped. Why is that? Two way to know 100% for sure. You can see if an accelartion vector exists, or, look at any dt that spans the time where speed = 0. If the observation of that dt reveals a dx !=0 then 100% you know the motion has not stopped even though you also observed a point in time where speed became = 0.
We can also flip it around. To know when the object stopped take a look at dx for any dt !=0, and if dx=0 for any dt !=0 then we know 100% that the body in motion was not moving at all during that period in time.
Sorry, one part of the vid caught my attention......... and now this.... ha.
Time does stop, just make an observation of any function of time where you fix time, like t=5 or t=29.992, that's fixing time. If at time=14.2524242sec the speed is zero, ok, that only tells me what it looks like at some fixed point in time. Make your observations using dt.
Sine graph is of speed, or the velocity vector?
There is no "brief nano sec" when dt=0, which is the same thing as fixing time.
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V = zero when dx in dx/dt equals zero. dx equals zero for a very minuscule dt when the piston is at TDC and BDC. dt changes with the engine RPM. A piston is stopped longer at idle then when the engine is at 6000 RPM. Neverless, it always stops for some finite time at TDC and BDC.
No speed (velocity) means no movement by definition. At TDC and BDC the piston does not move for some measurable amount of time, even if in the nanoseconds realm.
There's even a dt even high engine RPM ... even if it was a billionth of nanosecond, it's a delta time. A ICE can't rev high enough to make dt hit zero, ever.
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100% false
If that were true then when does the piston "catch up" to the connection rod that is now some dx ahead of the wrist pin?
The part in orange, is true, BUT, that describes no motion for that dt. No motion has no speed for that same dt, etc.
If the piston stops for any dt, then the crank also stops rotating for that same dt? Hmmm, that would be interesting, and a lot of stopping.
Sorry, you do not understand the velocity vector.
Speed != Velocity
Speed is only the scalar that describes the magnitude of the velocity vector.
This is perhaps too technical for BITOG, but here goes:
see https://mathworld.wolfram.com/VelocityVector.html
Again, pistons move up and down, crank rotates. Two different motions, and obviously the crank keeps on trucking while the pistons stop at TDC and BDC.
There is no zero in the true sense of time as it marches on regardless of what happing in the world, expect on the Twilight Zone when all clocks and time actually stops. And therefore will always be a dt = t1 - t0 since you can measure time infinitely small.
We are taling about the motion of the piston.
If the piston stops for any dt, then the crank also stops rotating for that same dt? Hmmm, that would be interesting, and a lot of stopping.
You don't seem to truely understand how the desing of a piston engine really works (ref bold above). Obviously the crank can never stop when the piston stops at TDC or BDC. It's part of it's inherent design. For some reason you believe the motion of the piston somehow effects the motion of the crankshaft ... it doesn't. But the rotating crank and oscillating rod does effect the motion of the piston, which is a purely linear motion for all practical purposes inside the cylinder between TDC and BDC.
Well, the pistons do not stop. I already gave proof. The only way they stop MOVING is if dx=0 for any dt.
Show me any dt where dx=0 (with math), then you have proved me wrong.
until then, they do not stop moving.
Whaaaaa? They are physically tied with a hunk of metal, how could their motions ever decouple? Sorry, no, that's 100% bad info.
And in actual terms, the crank drives the pistons, so it is the crank that affects the motion of the pistons. Study prime drivers of motion, then you'll understand this.
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If there is no speed (velocity) there is also really no vector associated with that speed ... only what the vector was a infinitesimal time before V = 0. The length of a speed vector represents the speed magnitude ... and when speed goes to zero the vector disappears - poof, no vector.
For some reason you seem to believe nothing can stop inside an engine for any given dt. Do lifters stop in their bores as the cam rotates? Do pushrods, valves and rocker arms stop for some dt as they operate?
LoL ... what?
Not if it's an automatic and you slam it into R and floor it while moving forward ... seen it done before, lol.
Crank doesn't drive piston at TDC. If at TDC the crank pin were still moving upwards it would be before TDC. A contradiction.
If at TDC it were already moving downwards, then it would be after TDC. A contradiction.
It ain't moving upwards or downwards at TDC, therefore no jamming.
But that way you can get rid of all that rod and piston thingies Zeug. Just look at the crank pin. For some reason you can't even tell the crank pins direction of vertical movement for TDC. You just know that there has to be some to jam the rod & piston thingies. But won't ever know a direction.
If at TDC it were already moving downwards, then it would be after TDC. A contradiction.
It ain't moving upwards or downwards at TDC, therefore no jamming.
But that way you can get rid of all that rod and piston thingies Zeug. Just look at the crank pin. For some reason you can't even tell the crank pins direction of vertical movement for TDC. You just know that there has to be some to jam the rod & piston thingies. But won't ever know a direction.
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