A Modest Proposal: I think the recent discussion of pump link length...

...and its effect on pumping effort is very interesting and possibly of importance to optimum pumper design, but variations in design assumptions between different simulations are making the results hard to understand and relate one to another.

So I suggest we standardize assumptions, and start again. Specifically, peak pumping effort numbers are only comparable if we choose in advance...

1. Overall A + B linkage length, because practical pump arm length (and therefore pumping leverage) is related to this sum. Stated differently, because you can theoretically make pumping effort as low as you like if you don't care how long the gun, and therefore the pump lever get, overall length needs to be held constant to make the various results comparable.

2. Total stroke volume. Comparisons of pumping effort are impossible unless the same amount of air is being compressed. Since different B/A ratios result in different stroke lengths, to make comparison of effort meaningful, ratios with shorter strokes should be evaluated against a larger pump bore area to keep volume constant.

3. Full-open pump arm angle. We've seen simulations starting with 90, 120, and 135 degrees. Let's pick one and stick to it.

Any other parameters come to mind? Any preferences for specific design numbers?

The diminished reduction is so slight.

Approximate figures here:

UNIT A pump arm with 2" pivot distance and a toggle 2.75" long @ 90 degrees open lever will yield 2.75" stroke.

UNIT B pump arm with the same 2" pivot distance and toggle 3.5" long at 90 degrees open lever will yield about 2 5/8" stroke.

Minimal reduction in sweep volume, yes, for the exampled layout (more reduction the longer the link is). However, if we were to use the above examples and fatten the tube enough where their sweep were equivalent, say it is UNIT B we do this with.

Yes, there will be the values that will never disappear, pressure multiplied by surface area of the piston, the longer link and its reduced angle of attack to move the piston does reduce the effort in comparison.

Back to that test sled mentioned earlier. It is, or was, (may assemble it again and do a video) like so:

Lever is 24" long, pivot 4" test load of 500lbs. Link #1 4" long link, #2 8" long link. The test conducted with the lever itself set to 90 degrees.

Using a heavy pull spring scale and a ratchet system to move the lever, Link #2 was greatly easier to move the load exhibiting much less weight on the scale (effort to us).

The test itself was not used to measure build pressure of a tube/vessel, but rather to experiment with what ME was gained by the longer link in any given position moving a fixed amount of weight.

Did not believe a difference would be noted at all, as the assumption has historically been that our levers fall into one of the three classes of levers. They do not, as I, II, and III levers have a fixed MA. Our levers and their toggle arrangement throw another element of MA into the mix.

While studying efficient and easy levers on the physics forum (do believe you are on there Steve?) someone proposed the longer link theorem. After looking deeper, and learning the math to better ease my mind, it was decided to just build a test jig.

I was sold for my particular project, that is near completion now.

I'm having trouble visualizing it -- especially how a 4" link worked with a 4" pivot arm.

You're right. Just got home and dug out my pieces parts. Thinking to myself, "What does he mean he can't visualize it?".

You bet. Me neither. My lever pivot holes are roughly 3" to 3 1/8" center to center. The short link is in fact 4" - not the hole spacing too.

Was sitting in the office earlier, bored, typing that up not having access to things here at home.

You're right. At 90 degrees THAT would be difficult.☺

...pumps. In your rig there's a large angle between the link and the axis of the "tube" and direction of the 500# load. This angle is (much) worse in the case of the short link than the long link, which in the former case is placing a side load on the "piston" that's (much) larger than the load itself. Consequently a large part of the resistance you felt at the lever in the short-link case was probably caused by friction between piston and tube.

But in an actual pumper, by contrast, pressure and force don't become significant until late in the stroke when the lever is far past vertical and the link, no matter what the B/A ratio, is nearly parallel to the tube, making the contribution to total effort that comes from side loading and friction relatively minor even for short links.

To cut to the chase, and unless I'm still failing to visualize it (very possible), I guess I'm saying your whole test was B.S.

...and its effect on pumping effort is very interesting and possibly of importance to optimum pumper design, but variations in design assumptions between different simulations are making the results hard to understand and relate one to another.

So I suggest we standardize assumptions, and start again. Specifically, peak pumping effort numbers are only comparable if we choose in advance...

1. Overall A + B linkage length, because practical pump arm length (and therefore pumping leverage) is related to this sum. Stated differently, because you can theoretically make pumping effort as low as you like if you don't care how long the gun, and therefore the pump lever get, overall length needs to be held constant to make the various results comparable.

2. Total stroke volume. Comparisons of pumping effort are impossible unless the same amount of air is being compressed. Since different B/A ratios result in different stroke lengths, to make comparison of effort meaningful, ratios with shorter strokes should be evaluated against a larger pump bore area to keep volume constant.

3. Full-open pump arm angle. We've seen simulations starting with 90, 120, and 135 degrees. Let's pick one and stick to it.

Any other parameters come to mind? Any preferences for specific design numbers?

I've been concerned with the effect of the B/L ratio per your nomenclature:
http://www.network54.com/Forum/275684/m ... 1492380784
not the B/A ratio (which does change as B/L changes, but it's determined by B/L and the intended stroke length)

Every one of my graphed examples covering B/L ratios from 1.333 to 5.0 shares the same precisely 150 mm stroke (therefore same volume).
If I'm analysing a ratio that doesn't give the correct stroke then I simply scale the overall lengths so that it does.

I also keep the same point of effort, which is set at 400 mm, and same arc of 135 degrees - covering points #1 & #3.

...B = link length, as per your photo.

...and its effect on pumping effort is very interesting and possibly of importance to optimum pumper design, but variations in design assumptions between different simulations are making the results hard to understand and relate one to another.

So I suggest we standardize assumptions, and start again. Specifically, peak pumping effort numbers are only comparable if we choose in advance...

1. Overall A + B linkage length, because practical pump arm length (and therefore pumping leverage) is related to this sum. Stated differently, because you can theoretically make pumping effort as low as you like if you don't care how long the gun, and therefore the pump lever get, overall length needs to be held constant to make the various results comparable.

2. Total stroke volume. Comparisons of pumping effort are impossible unless the same amount of air is being compressed. Since different B/A ratios result in different stroke lengths, to make comparison of effort meaningful, ratios with shorter strokes should be evaluated against a larger pump bore area to keep volume constant.

3. Full-open pump arm angle. We've seen simulations starting with 90, 120, and 135 degrees. Let's pick one and stick to it.

Any other parameters come to mind? Any preferences for specific design numbers?

...and arm open angle = 120^o, then stroke length and bore I.D. for B/A ratios from 1 to 5 would look like this...

...B = link length, as per your photo.

"Since different B/A ratios result in different stroke lengths"

The stroke length can be the same for any practical ratio. See my post above.

The stroke length only changes if you want it to change.

...the total length must increase. Contrarywise, if B/A is increased while holding B+A constant, which is necessary if pumping efforts are to be comparable, stroke must decrease -- as graphed below. Agreed?



If so, I'd be happy to move forward and further discuss the significance of that fact as it affects practical tradeoffs in optimizing pump geometry.