Sorry Christopher, but you're wrong. (I don't like having to say that - it's not personal) In your analogy, you've not only moved the hand to 4:30 but you've also moved the clockface and the mechanisim so that 12:00 is at the 4:30 position. The clock still chimes at midnight even though it's lopsided on the mantlepiece. If you twist both the crank and the cylinder position 7 degrees in the same direction they "fire" at the 120 degree interval in relation to the other two cylinders.
Hahhh! We had four cylinder compounds with cylinders in line on 3'6" gauge. (Aa Class) Imagine setting the internal valve gears on that. (watchmakers were mentioned) The next batch (Ab) had just two simple cylinders.
The entire clock _is_ being rotated for the centre cylinder. It stays in it's proper position for the two outside cylinders. Picture three clocks, one in front of the other on the mantlepiece. The center one is tilted 7 degrees and then the main shafts welded together. They still chime at the same time at midnight even though the hand of the center one leads the other two by seven degrees.
You turn the _clock_ around the hand's axis until the 4:30 had position matches 4 o'clock. What you appear to be missing is not only can you move the hand (crank) on the shaft, the clock face around relative to the mechanism, but you can also turn the clock around it's central axis. Turning the cylinder and the crank the same degree is like tilting the clock - you don't change the time by doing so.
No, it's not. You're forgetting the mechanical relationship between the crank and the cylinder.
Because if the inside crank is at half past four instead of 4 o'clock, the piston has to fire at [crank time] 4.30, not 4.
If you got one revolution per 12 hours, you would get the beats at midday, 2pm, 4.30pm, 6pm, 8pm, and 10.30pm.
Unless the length of either the inside cylinder's piston rod or connecting rod changed dynamically during its stroke.
It's more like a clock that chimes every two hours, chiming at 4.30 instead of 4, and 10.30 instead of 10.
But you can only take the clock analogy so far because it gives (almost) continuous motion while the pistons give one stroke in each direction per revolution.
The beats correspond to the extreme positions of the piston inside the cylinder. Which correspond with the crank position.
No, you don't.
Because the outside cylinders are horizontal. They stay at 12 o'clock and 8 o'clock. While you move the 4 o'clock position to their 4.30 for the inside cylinder.
Which means that its beat comes at 4.30 their time (and the listener's) not 4.00.
No, it's not. It is like only moving the 4 o'clock to 4.30 and leaving the others where they are.
I think I see your problem - 4:30 is the time on the dial, not on the crank. If you place TDC of the piston at 4:30 instead of 4:00 of the other two then you _advance_ the crank by 30 minutes and all three reach TDC at the same moment, in spite of two saying
4:00 and one saying 4:30.
OK, we revolve two of the cranks to 8:00/2:00 and 12:00/6:00
Nahh, that gets too complicated :-)
The analogy works fine for the crank.
Which corresponds with the crank position in relation to the cylinder. It has nothing to do with the absolute position of the crank.
err ...
Sure.
No, I moved the relative position of the center crank _and_ the relative position of the center cylinder.
There are three hands on the same clock shaft - we're moving one of them (the center crank) forward by half an hour and giving the dial for that hand a twist by 30 minutes so that it will show 4:00 at 4:00 even though the hand is displaced by 30 minutes. (rather like moving the gate over a foot because your wife keeps driving there when she backs the car out ;-)
Not really, all my three cylinder locos are driven by little electric motors so they run quite smoothly whatever the time happens to be.
It does. The firing time comes from the relationship between the cylinder and it's crank, not from the relationship between the cranks themselves.
No. What I've told you is that the center clock is tilted by 30 minutes so that at
4:00 it's hand is at 4:30 compared to the other two clocks but it is pointing to 4:00 on it's own face.
Look at the problem from the other end - the center cylinder valve gear in the Gresley system has it's valve timing derived from the two external valve gears. The only timing you can derive using rocking levers is 12:00, 4:00, 8:00 and the three intermediate times. If the valve timing was 7 degrees out the loco would internally haemorrhage at high cut-offs with one cylinder driving forward and another driving backwards for 7 degrees of each stroke. OUCH. With wear in the derived motion pins, the opening and the closing of the valve got later and later while the valve motion took up the slack after each change of direction, so that 7 degrees would extend considerably further and the haemorrhaging would become steadily worse!
I'll leave you to figure the implications and the logical conclusion.
So explain it instead of asserting it. With emphasis on the fact that the cylinder fires at the extreme positions of the crank, and that
4.30 is the extreme position.
And I've already explained why the clock analogy was only useful for illustrating the rotational position of the cranks, because you have forgotten that the pistons have a fore-and-aft movement not the continuous circular movement of a clock.
Greg, I don't have any reference to hand - everything is packed away in preparation for moving - but I'm reasonably certain that the Aa didn't have valve gear between the frames, only the connecting rods. If memory serves me right a common valve chest served both high and low-pressure cylinders. But when I've unpacked I'll check on this.
1480 Class balanced compound Atlantics built by Baldwin, IIRC.
I'm certain that these also had didn't have any valve gear between the frames. From memory they had Walschaerts valve gear mounted backwards, and a rocker arm driving the valve in a common valve chest for both HP & LP cylinders.
Your clock analogy is fine for comparing the relative positions of the cranks, but you are now confusing the clock with absolute time. BTW there were single handed clocks before someone thought to add the minutes hand. On a clock the time is calculated in relation to the vertical 12 o'clock position, but in the locomotive situation actual indicated time relates to TDC/BDC of each piston which relates to crank position. Your 4:30 is the relationship between the three cranks, but it is not the relationship between all three pistons reaching TDC/BDC. The center cylinder _timing_ relationship is changed by the 30 minutes because the cylinder has been moved around the crank/hand axis by 30 minutes.
I thought we were taking that as read. TDC is when the crank or hand is precisely aligned with the piston/crank center line. The center line is not parallel in one of the three cylinders and therefore that cylinder would have an odd timing if the three cranks were equidistantly spaced. That inequallity is corrected by twisting the crank to match the angular difference of the center cylinder.
No, I am not. You're the one who took the analogy to places it was never meant for.
The extreme left/right positions of the piston, the point at which it fires (forgetting about lead), correspond to the extreme positions of the crank.
Mechanically it can't be anything else.
Which means that if the cranks are set at 12 o'clock, 4.30 and 8 o'clock, then the pistons also fire at those positions (and at those positions plus 6 hours because they are double acting).
Which means you get exhaust beats corresponding to the piston strokes
TDC describes the crank position corresponding to the extremes of the piston travel.
No, I am not. You're the one who took the analogy to places it was never meant for.
The extreme left/right positions of the piston, the point at which it fires (forgetting about lead), correspond to the extreme positions of the crank.
Mechanically it can't be anything else.
Which means that if the cranks are set at 12 o'clock, 4.30 and 8 o'clock, then the pistons also fire at those positions (and at those positions plus 6 hours because they are double acting).
Which means you get exhaust beats corresponding to the piston strokes.
At 12, 4.30 and 8 (also the corresponding reverse strokes of the double acting pistons).
TDC describes the crank position corresponding to the extremes of the piston travel.
Except that you claimed it gave an exhaust beat at 4 o'clock, not
4.30.
Explain how mechanically this is possible.
that cylinder would have
difference of the center
Which isn't what we are talking about. We are talking about the 4.30 exhaust beat which you claim happens at 4 o'clock.
Which is mechanically impossible.
the Gresley system
timing you can derive
If the valve timing
with one cylinder
valve got later and
direction, so that 7
steadily worse!
Except that this is not what happens. See below.
The outside cylinders and their valves are horizontal. The inside cylinder isn't, although the valves are.
You are partly right in that the timing of the outside valves is at 12 o'clock and 8 o'clock, hence (all things being equal) you might expect the inside valve spindle to be at 4 o'clock.
But I'll leave you to figure out what happens if you move the valves further along the valve spindle with respect to the steam ports to compensate for the angle.
Which is why the inside valve's timing is at 4.30 not 4'oclock. Matching the crank's position.
And why you get the inside cylinder's exhaust beat "off centre" between the beats for the outside cylinders.
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