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

April 19 2017 at 10:51 AM

Crosman Forum Member

...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?

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Phil
Crosman Forum Member
208.87.234.201

# Yes, indeed!

April 19 2017, 12:15 PM

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.

 This message has been edited by Duane35 from IP address 208.87.234.201 on Apr 19, 2017 12:26 PM

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Steve in NC
Crosman Forum Member
162.198.201.47

# Could you whip out a quick sketch of your test rig, please?

April 19 2017, 2:37 PM
 I'm having trouble visualizing it -- especially how a 4" link worked with a 4" pivot arm.
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Phil
Crosman Forum Member
76.120.212.220

# Now, Steve! Just say B.S.! Call me out when in error!

April 19 2017, 3:11 PM
 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.☺
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Steve in NC
Crosman Forum Member
162.198.201.47

# LOL! Okay, then. Consider this significant difference between your test and actual...

April 19 2017, 4:28 PM

...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.

 This message has been edited by pneuguy from IP address 162.198.201.47 on Apr 19, 2017 4:30 PM

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Phil
Crosman Forum Member
76.120.212.220

# That hurts, Steve!

April 19 2017, 6:31 PM
 If you're implying I am incorrect in logic, that's fine. Certainly can handle that. If you are implying that this test never happened, well, that just hurts. 😢 You are correct. The force in a pumper isn't there until near closed. However, the experiment was to only show how a longer link reduces load compared to a shorter link. That's it. Simply that. All because of the angle. Only that. Reduced effort was witnessed all through the curve of the lever, not just 90 degrees where, of course, the heavy load was causing the input force of the lever to put force on the side wall being so high up in the stroke (where it is never seen in a pumper). The family and I are off to N.C. (Raleigh area) tomorrow. When we return, the jig is being reassembled, dam it! You!
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Steve in NC
Crosman Forum Member
162.198.201.47

# Ouch! What we have is a failure to communicate -- mine!

April 19 2017, 6:35 PM
 I certainly never meant to imply you didn't do the test, but only to wonder how helpful it is when applied to pumper physics. Speaking of communication, I'm thinking it might still be helpful to have that sketch.
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Phil
Crosman Forum Member
76.120.212.220

# I know, Steve. Just fooling around with ya'!

April 19 2017, 6:46 PM
 Pretty certain you mean well. No harm. Seriously, we are going out of town for a few days. A move may be in the works for me/us. Ugh. Not AGAIN! Every five years it seems. Ho hum. For now, this evening anyway, got to figure out PB video posting, or may switch to the site you use to image host. Hate PB with a passion.
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Steve in NC
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162.198.201.47

# *Whew!* Glad we're on the same page after all, as I figured but was...

April 19 2017, 6:57 PM
 ...unwilling to assume. As for PB, the day is long gone when used them (as I once did) for everything. Now I avoid them like Yersinia Pertis.
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CO222
Crosman Forum Member
27.252.177.19

# I think we've been talking about different things

April 19 2017, 4:50 PM
 I've been concerned with the effect of the B/L ratio per your nomenclature: http://www.network54.com/Forum/275684/message/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. -
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Steve in NC
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162.198.201.47

# I've adopted your definitions of A = pivot-to-pivot distance on pump arm and...

April 19 2017, 4:57 PM
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CO222
Crosman Forum Member
27.252.177.19

# In that case the reasoning in #2 is not true

April 19 2017, 6:12 PM
 "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.-
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Steve in NC
Crosman Forum Member
162.198.201.47

# Stipulation #1 makes it true. To keep a constant stroke while increasing the B/A ratio...

April 19 2017, 6:28 PM

...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.

 This message has been edited by pneuguy from IP address 162.198.201.47 on Apr 20, 2017 10:48 AM

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CO222
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27.252.177.19

# Why limit the possibilities by keeping B+A constant?

April 20 2017, 4:43 PM
 I agree that the 5.0 ratio in my analysis results in an impractically long airgun. But there are plenty of ratios say from ~1.0 to 2.0 that still result in a practical length. I disagree that we should prioritise fixing B+A length over stroke length and bore diameter. When I designed my pump I had certain tube stock that could not readily change diameter, and I wanted a certain swept volume output, so stroke length was fixed. However it was quite practical to give or take an inch or two from the airgun's length, so the B+A value was given flexibility. One thing remains constant: there's no fair comparison when you have so many variables. To make it a fair comparison of one imposed parameter, it's unfair on the others, and vice versa.-
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Steve in NC
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# For much the same reason that stroke volume should be kept constant if...

April 20 2017, 6:15 PM

...comparisons of pumping effort are to be meaningful.

For example, if the B/A ratio is increased from 1.1 to 2.0, total closed-arm length of the 2.0 linkage must increase by 53% if stroke length is to remain constant. Of what use would a pumping-effort comparison be when the 1.1 action could have been scaled up to the same length and stroke volume but with a 53% longer stroke and therefore smaller piston-head area and proportionally smaller P x A pumping force at any given pressure?

Meanwhile, I appreciate what practical limits on available design choices (e.g., available tubing dimensions) imply for construction projects, but didn't this discussion begin as a theoretical exercise?

 This message has been edited by pneuguy from IP address 162.198.201.47 on Apr 20, 2017 6:16 PM

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Steve in NC
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# For example, with 392-ish parameters of A + B = 8.5", stroke volume =3.5c.i...

April 19 2017, 5:11 PM

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

 This message has been edited by pneuguy from IP address 162.198.201.47 on Apr 19, 2017 11:21 PM

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Phil
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# In the graph...

April 28 2017, 11:41 AM
 Is it determining that the bore I.D. will need to increase to 1.2" in order to accommodate the same sweep volume as the .6" bore and 8.5" stroke of the Benji? Seems very accurate.
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Steve in NC
Crosman Forum Member
162.198.201.47

# Yup -- except that real Benjis have a ~1.125:1 ratio, a 7.5" stroke, and a ~0.77" bore.

April 28 2017, 6:59 PM
 The B=A 1:1 ratio is only a theoretical limit, as I think you've already commented elsewhere.
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