GTA
All Springer/NP/PCP Air Gun Discussion General => Machine Shop Talk & AG Parts Machining => Topic started by: HappyHunter on January 06, 2019, 11:40:12 AM
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Hello folks,
Without giving away too much detail at this point in the game, lets just say that I’m in the middle of designing a gargantuan, completely custom SSP rifle that will use a hammer-less, blow-open valve design instead of the usual knock-open type valves normally found in 13xx/2289 etc type guns.
I’ve got the logistics mostly sorted out & drawn up on the computer, but I can’t decide on what size of final valve volume I want to go with. I currently have the final valve volume drawn up as 5.025cc @ 2500psi, but can safely hog it out to 5.83cc which drops the final pressure to around 2160psi (13.75% difference).
Looking for power, not efficiency, so what would you guys go with….smaller volume/higher pressure or a slightly larger volume/lower pressure?
I’m (quite obviously) no engineer in any way, shape or form, but from a performance point of view (fps/fpe), my gut says it *shouldn’t* make much of a difference. Only advantage (if you can call it that) I can see with the larger valve/lower pressure configuration is less stress/force exerted on pump arm pivot points, end forces, cocking, etc….
Anyways, thank you for your time & I look forward to your advice/suggestions.
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Many variables of course, barrel length, hammer spring needed, dwell time, and more. My inclination is more pressure, less volume, because of my experience with increased volume FTP valve, but that is limited experience.
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Without giving away too much detail at this point in the game, lets just say that I’m in the middle of designing a gargantuan, completely custom SSP rifle
Without overstating the case, you want us to design the important bits for you, without reciprocating by sharing your design or intent?.... I sincerely hope you reconsider, and use the Forum for its intended purpose, not as a research facility to be tapped into as a one-way street.... particularly if your purpose is for commercial gain.... JMO....
Having said that, dump valves should be proportioned to the barrel volume, regardless of the pressure used.... If you make the valve more than 50% of the barrel volume, the gains in power are small, but the amount of air used is huge.... Consider this chart....
(http://i378.photobucket.com/albums/oo221/rsterne/Millenium%20Pumper/DumpValves_zps8ff30e30.jpg) (http://s378.photobucket.com/user/rsterne/media/Millenium%20Pumper/DumpValves_zps8ff30e30.jpg.html)
That should give you all you need to know....
Bob
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Many variables of course, barrel length, hammer spring needed, dwell time, and more.
Barrel length - 24” (23.6” actually)
Hammer spring - none (no hammer)
Dwell time - however long it takes to load the next pellet & close the bolt… ;) ;D
Thanks, Craig
Ya, I have a few bottle-fed & PCP rifles now so starting to get a grasp on how to tune them efficiently, but this time around it’s going to be a Single Stroke Pneumatic & a dump valve (every shot completely empties the valve). No check valve or anything, just cram as much air as possible into the reservoir with one stroke then send it all down the pipe as quick as possible when you squeeze the trigger… ;). Never played with a dump valve before so not sure if same principals apply.
Technically, I suppose it’s more of a reservoir than a conventional valve, but whatever you want to call it, I will most likely end up just making one in each size & post what the results are when the time comes.
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Without overstating the case, you want us to design the important bits for you, without reciprocating by sharing your design or intent?.... I sincerely hope you reconsider, and use the Forum for its intended purpose, not as a research facility to be tapped into as a one-way street.... particularly if your purpose is for commercial gain.... JMO....
:o
WHOA!…slow down, Sherriff! Was not the case at all…not even remotely.
I know this is going to come across the wrong way…not my intent, but whatever….but with all due respect, I don’t recall ever asking you or anyone else to design anything, Bob. I was simply just trying to eliminate making an extra part if at all possible by asking what method is better. Pump arm geometry & trigger mechanism was a lot more challenging for me than boring two different sized holes through some 6061 hex bar. Not a big deal. Like I stated in my reply to CraigH - I will just make two separate reservoirs & see which one works better, if in fact there is any difference. My bad for trying to take a lazy shortcut.
Commercial gun? Seriously?
Holy &^^&, I’m just a hillbilly living out in the sticks that likes to play with airguns who, I thought, asked a simple question….have to remember not to do that again. I have a 7x12 mini lathe & a home-brewed milling attachment. Airguns & machining are just a hobby, nothing more… ::)
As for “sharing my design” - I haven’t even finished drawing the "dang" thing all out on the computer yet, let alone dimension it. Good chance I won’t be starting to make chips for at least a few months. I have no problem whatsoever sharing the design before actually building anything, & I most certainly will, ONCE I’ve double/triple checked my final drawings to the best of my abilities. My apologies for not being quite as confident in my abilities as you are with yours, I was just trying to dot my ‘I’s & cross my T’s so I could at least post something worth reading, unlike the quick downward spiral of this thread.
Friendly forum, huh?….that’s debatable
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You DID notice that regardless of your motive, and the way you worded your first post, I still answered your question didn't you?.... ::)
If you are interested in sharing and I completely misinterpreted your statement, I apologize.... I have little use for people that take and don't give back....
Bob
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Does seem to be some tightly knotted knickers about, laugh it off and don't worry about it Todd, this @$%^ is supposed to be fun and if it ain't fun...stuff it. ;)
With a fixed volume of air available from a single pump, I would prefer low volume high pressure. You're blowing the valve open and higher initial pressure will see faster valve opening times to full flow.
What are you leaning towards as far as valve design? Crosman 140/1400, Sharp, GC2, Paradigm or? If you haven't looked these up, you should.
Still in the design phase, pay attention to things like dead volume created by the valve when it opens, transfer porting volumes and forces on the trigger and pumping bits.
Feel free to shoot me a pm or email and we can bounce some ideas around.
Regards,
Al
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Todd,
For an SSP, better efficiency means more power. Higher pressure, smaller reservoir designs are more efficient, because relative to barrel volume, they produce a larger expansion ratio.
In any event, for each foot.pound pellet energy, you will need about 16.5 CCs of air, starting from one atmosphere. If you end up compressing that to 0.1 CC at 170 atmospheres per ft.lb, that should be plenty efficient, assuming the air can flow freely into a barrel with a 10 to 15 CC volume.
If your reservoir holds 5.83 CC at that pressure, it has the potential to impart 60 ft.lb to the projectile; assuming a barrel long enough for the caliber. Certainly, 5.83 CCs at 2500 PSI suggests a swept volume of about one liter. That is a monster!
Based on Bob'd experience and thus assuming the barrel volume is at least twice that of the reservoir, your 24" barrel in .22 caliber should work nicely. If it were .25 caliber, you should get more power out of it than the same length barrel in .22; due to the larger expansion ratio.
A 60 ft.lb SSP is going to have quite a long heavy cocking stroke. Some would say it can't be done. In any event, the trick with high volume to high pressure in an SSP seems to be cocking linkage geometry. User rgb1 made a custom 20 ft.lb SSP rifle. Here is a link to whet your appetite: https://www.gatewaytoairguns.org/GTA/index.php?topic=138392.msg1389301#msg1389301 (https://www.gatewaytoairguns.org/GTA/index.php?topic=138392.msg1389301#msg1389301)
rgb1's hammerless valve design: https://www.gatewaytoairguns.org/GTA/index.php?topic=94054.msg883576#msg883576 (https://www.gatewaytoairguns.org/GTA/index.php?topic=94054.msg883576#msg883576)
Rgb1's cocking linkage is similar to that used in the SSP pistol I got last week:
I bought a Baikal SSP air pistol precisely because its cocking linkage works brilliantly. None of that typical SSP cocking effort, that starts off soft and then spikes drastically near the end, only to have the cocking arm (or barrel) snap shut violently.
Rather, the mechanism has a continuously varying sliding fulcrum, that results in the compression piston sweeping fast initially, while the pressure is very low, then slowing down exponentially while tracking and thereby nulling out the effect of the air pressure building up. This results in a cocking force that is higher earlier, and lower later, than one would predict. Also, the harsh snapping shut, as conventional SSP toggles go over center is completely absent. If you want to know more, my impressions of the Baikal can be found here: https://www.gatewaytoairguns.org/GTA/index.php?topic=153027.msg155683138#msg155683138 (https://www.gatewaytoairguns.org/GTA/index.php?topic=153027.msg155683138#msg155683138)
If you want to cut to the user manual to get some idea of the guts of the mechanism, look here:
https://www.krale.shop/media/blfa_files/Baikal_MP-46M_manual_EN.pdf (https://www.krale.shop/media/blfa_files/Baikal_MP-46M_manual_EN.pdf)
If you would like some more pictures of the mechanism in various stages of travel, I can provides those too. I think my hard copy user manual may have more sectioned images of the assembly too.
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Baikal MP-46M assembly section view, from the user manual.
Todd, I have captured a series of images of the air charging system, with the cocking handle in a progression of states. Also, both orthogonal and "quartering" views, so one can judge (or measure the lever angles) views, and see the piston position at that cocking lever angle.
These are saved in a word document (and perhaps a PDF). If you want to see this document (there are 25 images), let me know. I am not going to post them to this thread, unless requested.
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It looks like Elvis has left the building. Perhaps he has been put off by what was perceived as unearned hostility, or other cannibalistic tendencies.
More likely, Todd has realized the ambitious magnitude of his project, as inferred by the values of air volume at pressure he provided. Thus, he does not need any more help (or abuse), as he has quietly decided to "re-scope" the project (down to zero). Therefore has nothing more to share. Not even, that has given up.
Todd, your GTA profile shows that you have been browsing the forum. So, why have you gone quiet on this project? Who is right; Bob or me?
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subscriber, Todd and I have apologized via PMs, and all is good.... it was merely an misunderstanding.... ::)
Bob
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I would prefer low volume high pressure. You're blowing the valve open and higher initial pressure will see faster valve opening times to full flow.
If power is the object this is the right answer.
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subscriber, Todd and I have apologized via PMs, and all is good.... it was merely an misunderstanding.... ::)
Good to hear, Bob.
My problem is that Todd waved some bacon in front of my nose with this thread, and now I can't stop thinking about it. :)
I sent him an email via GTA offering images I took of the charging mechanism of my 46M SSP pistol. He may have all he needs; and the thread by rgb1 certainly contains even better info than my pictures. But, what frustrates me is that I have heard not so much as a "no thank you" from Todd; hence my impertinent post above...
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OK, c’mon guys, can we please just all get along without the false accusations & conspiracy theories? I’m usually a pretty easy going, fun-lovin’, polite guy who likes to joke around & all, but enough is enough already.
Nope, Elvis has in fact NOT left the building. Or giving up on this project either. Or rethinking any aspect of it other than maybe my choice to post the original question to begin with… ;) ;D
Yes it’s true, I have quickly checked this thread a few times this week while at work (break/lunch time)…on my I-phone. No way am I typing out a lengthy reply on that thing. It would take me all afternoon! :o. I admit, at the very least I should have taken the time to quickly thank you & Al for the wealth of information you both provided, for which I am immensely grateful…honest & truly I am. Haven’t even had time to check out the links you supplied, but I will over the weekend. Thank you both again!
I work outdoors framing custom homes for a living from 7am - 5pm (winter hrs) in sub-zero weather (-18*C yesterday, -27*C wind-chill), so by the time I get home & have a hot shower, cram a hot meal down my gullet & stoke the fire up I’m lucky if my weary old bones are still awake by 8pm (no joke!). Weekends are about the only time I can devote any amount of spare time & attention to “me time” & even if I do manage to sneak in a few hours of play time, unfortunately there’s no guarantee that I’ll get to spend it doing airgun stuff. So as harsh as it may sound to some, if MY sporadic schedule to work on MY personal project isn’t up to anyone’s standards here, then I honestly don’t know what to say…I guess tune back in when I present the finished project.
So, I’m going to step away for a bit, let everyone get their ruffled feathers preened & back in place (myself included) & in my next post (whenever that may be) I’m gonna attempt to start somewhat fresh & try to get back (& stay) on topic without all the drama & salvage what little dignity I & this thread might possibly have left. Despite the horribly negative start, I DON”T have any hard feelings towards anyone here & I DO welcome any input, suggestions, questions & even criticism (within reason) that anyone feels like sharing as the build progresses. That’s how we learn right? But rest assured…I am NOT playing this “Judge Judy” game anymore….I hate that show! LOL
Despite not being anywhere near ready to present a completed project design yet, I will however try to appease the impatient here & leave you with a few basic preliminary design specs off the top of my head to mull over in the meantime. TRY to remember that I’m just in the early planning stages…nothing is carved in stone!
Dual arm pump mechanism
Breech - 1.25” 6061-T6 aluminum hex bar
No real “valve” to speak of…air reservoir is part of breech
Pump tube - 2”o/d x 1.76” i/d (.120” wall) 4130 CrMoly tubing…..2400psi MSWP @ 4:1 safety factor
Max pump stroke - 21.328” x 1.76” i/d = 850.26cc
Final reservoir volume (main reservoir incl all air passages then bolt volume subtracted) = 5.03cc (roughly 1/3 barrel volume)
Total swept volume (855.29cc) compressed into 5.03cc = 2499.55psi final pressure (3.84:1 safety)
5.83cc = 2158.52psi final pressure (4.45:1 safety)
You all are a hardcore bunch here, I’ll give you that.. ;D....not even 6:30 in the morning & I’m ready for a whiskey already! :o ;D ;D
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Thanks for the detail, Todd. Looks like you have a solid working plan.
You could have appeased the impatient (me) with, "I'll be back..."
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I will be interested in what kind of lever system you are planning for the pump.... You have a 1.76" ID tube, which has an area of 2.43 sq.in.... At 2500 psi, that will require a force of 6079 lbs. on the piston.... I'm glad I'm not leaning on the end of that pump lever.... :o
To put that in context, my Millenium Pumper, at 1800 psi, had a maximum force on the piston of 784 lbs.... I could pump it to 2000 psi, which required 871 lbs.... but that last 200 psi was hard enough I tuned it for 1800 instead.... I was using the Steroid linkage for a Benji 392 from Mac1.... Even with twice as long a pump arm, I can't imagine a pumper that requires nearly 4 times the force mine did.... even if you do only have to do it once....
Bob
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Even with twice as long a pump arm, I can't imagine a pumper that requires nearly 4 times the force mine did.... even if you do only have to do it once.
Not all levers are equal. Force can be reduced by making the lever longer on one side of the fulcrum, or shorter on the other. Also; one should not assume that the lever has a fixed fulcrum position through the piston stroke...
Simple SSPs, such as the Beeman P17 and Daisy 753 have very spiky cocking effort, despite their meager power: Very soft through 3/4 of the stroke, and then the lever snaps shut harshly around 95% lever travel, as the linkage goes over center; just after peaking at what feels like "too much".
Peak force is what makes it hard to cock, and what breaks parts (potentially). What matters for SSP performance is average force applied over sufficient distance to store enough energy to be useful. The trick is to speed up the piston travel when the air is still at low pressure. Then to slow it down and increase leverage, to dull the exponential spike in effort that would otherwise be required.
It is this characteristic of an air-spring, to have an exponential spring rate, that is the challenge. Simple sine wave toggle operated SSP piston motion helps reduce the peak force, but is not enough for anything larger than short range paper punchers or "toy" BB guns.
Todd sent me some info via PM about his linkage design. However, let's allow him to reveal that in his own time. It is not a Daisy-type toggle...
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Force can be reduced by making the lever longer on one side of the fulcrum, or shorter on the other...
Max pump stroke - 21.328”
I'll be interested in seeing how he reconciles those two statements.... ;)
Bob
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Good afternoon, fellas!
Ahhh…now this is the type of civilized conversation and/or debate I was hoping to see :). Nothing wrong with having a difference of opinion or POV, in fact I think it can only help by exploring all possible scenarios, ideas & POV’s.
Now, before we all get into “shop talk”, I believe I should make a bit of a disclaimer at the very beginning so we can at least all start out on the same page:
1) First off - I’m not even going to pretend that I’m half as smart as you guys ‘cause I know for a fact that I’m not. If at any point during the journey I come across as argumentative or seems like I’m challenging a statement you have made, I can assure you that I am not. If I ask you to clarify something or show me how you reached a particular conclusion, please don’t get offended, I am most certainly not doubting you….it will be because I myself don’t understand & I just want to learn so I don’t keep making the same mistakes or asking the same questions over & over. “Because I said so” is a completely useless answer that teaches us nothing, IMO.
2) My calculations or method of doing things are definitely NOT to be viewed as “The” way. Quite possibly could even be the wrong way! I will explain my thought process on how I reached a particular conclusion & if it happens to be correct, then “WooHoo!…Hero biscuit to Todd for figuring it out on his own”! But if I am wrong …& let's be honest, I will be sooner or later (& likely more than once)…. by all means, somebody PLEASE jump in & correct me so we can all learn….just don’t beat me over the head with a 2x4 while your doing it! ;) ;D
3) At this point, NOTHING is carved in stone! Although my drawings are not completely finished yet, there is enough relevant info that I think(?) you can see what I’m shooting for (no pun intended ;)). I needed an initial, working “base point” to start from, so I will be making numerous tweaks/changes to them as needed as we progress.
Ok, now that that jibber-jabber is out of the way, let’s finally get down to business!
I will be interested in what kind of lever system you are planning for the pump.... You have a 1.76" ID tube, which has an area of 2.43 sq.in.... At 2500 psi, that will require a force of 6079 lbs. on the piston.... I'm glad I'm not leaning on the end of that pump lever.... :o
Yes, before I even started I knew going in that I was gonna be facing some pretty severe forces, but my eyes nearly fell out of my head when I punched in the #’s & it spit out 6075lbs back at me :o. Granted, that’s at the very end of the stroke, but it’s still there nonetheless. This fact alone is why I chose to go with a dual-arm pump configuration.
Force can be reduced by making the lever longer on one side of the fulcrum, or shorter on the other...
Max pump stroke - 21.328”
I'll be interested in seeing how he reconciles those two statements.... ;)
Bob
I have attached a few pics of my (preliminary) pump arm configuration…max stroke, half stroke & closed. Nothing original or groundbreaking, just my version of an already proven design. I have deleted the pump tube from the diagrams so you can see the piston movement, but everything else is drawn to scale & in their correct position.
As stated earlier, I needed a starting base point so the primary arms as drawn are 18” long from center of pivot point to the end, but I can make them up to 25” long for extra leverage if need be without interfering with anything. I may need a stepladder to cock it, but the option is there ;D. The smaller, darker link arms (for lack of a better word) or secondary arms if you will, are 12” c-t-c of pivot points. 4 link arms in total…1 above & 1 below each of the 2 primary arms. No science behind those measurements, just needed somewhere to start from.
Link arms are drawn as straight for now, but I believe(?) I may have to make them with a slight curve somewhere between pivot points so that once in closed position, primary & secondary arms are not in perfect alignment as they currently appear.
In the first pic, at max stroke the primary arms rotate 162.3* & give me 21.328” of tube volume which equates to 51.886ci or 850.255cc
In the second pic, the primary arms have only rotated 81* (half stroke) but the piston has already moved 19.188”, leaving 2.140” between piston/end cap faces. That 2.14” long x 1.76” i/d space equates to 5.206ci or 85.310cc. Add 5.03cc (final reservoir volume) to 85.310cc = 90.34cc total reservoir volume @ half-stroke.
So, 850.255cc tube volume + 5.03cc final reservoir volume = 855.285cc total swept volume compressed into 90.34cc = 139.17psi generated @ half-stroke? :o I must have missed something ‘cause that just doesn’t seem right at all, but I ran the #’s like 8 times now & keep getting the same results. Sure could use either a confirmation or correction here to ease my mind. Told ya I was going to make a mistake sooner or later…just didn’t think it would be this soon! :-[
Provided my calculations above are correct(?), that would mean I’m generating an additional 2360psi in that last 2.14” of piston movement & I have around 80* +/- of pump arm rotation to git-r-done.
When & how long/how much that peak in psi occurs can be manipulated by changing the distance between pivot centers on secondary link arms where they attach to the primary arms. I haven’t had a chance to mess with it yet, but I will be soon just to see where the “sweet spot” is & get back to you all.
Hopefully this all makes sense because I’m just about as confused as you can get right about now! I don’t know how Bob does this day in & day out…he can’t possibly be 100% human is all I can figure ;).
(http://i64.tinypic.com/4jt6hz.jpg)
(http://i66.tinypic.com/zj6lc5.jpg)
(http://i63.tinypic.com/11u9nk6.jpg)
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Thanks for the update, with clear diagrams, Todd
Your calculations look correct in principle: If you reduce the volume of air to 1/10th of its original volume; the pressure should be 10 times higher. Starting at an absolute pressure of 14.7 PSI (at sea level), such an excursion should take you to 147 PSI; or 132.3 PSI gauge pressure.
It is gauge pressure that you have to resist against the piston, and that actually drives the pellet, because one atmosphere is always pushing on the other side of the piston and against the front of the pellet. When you get to working pressures as high as 2500 PSI, the difference between gauge and absolute pressures represent noise and can be ignored, in my opinion.
The fact that you have "so much" volumetric compression in the first half of the handle stroke looks right: It is desirable, because you need the other half (or more) of the handle stroke to provide much greater force multiplication in the last portion of the piston travel. This is because every time you halve the air volume, the pressure doubles.
An important aspect of SSP design is the placement of the centers. Not only to proved the desired force multiplication, but to lock the linkage in the pressurized state at the end of the stroke. This is commonly done by making the linkage pivots "go over center". By making the "knee" go slightly beyond having all (3?) pivots in line, the high pressure air acts to keep the pump handle closed, rather than fling it back into your knuckles.
While the above aspect is important, I am of the opinion that commercial designs go overboard with how far their linkages go over center. The side effect is that the cocking force not only drops off a cliff, just after reaching its peak; it actually goes strongly negative. While this is "safe", it makes the handles slam shut in a way that shocks my hand, and I find highly objectionable. As examples of this "hand shock", I point to my Daisy Avanti 753; and the Beeman P17.
As everyone is able to deal with a spring air rifle that will spring back at you, if you don't complete the stroke and catch the piston at the sear, I don't get why SSP manufacturers don't just design their product to line up the linkage pivots, that capture the cocking handle with a latch? Perhaps it is because undoing the latch could result in the cocking lever flying open and hurting someone. In that case, design the linkage to go over center, but by a very small distance; or more exactly, a very small angle.
As this is your design, it is your preferences that matter. As long as you are aware of the consequences of each design decision in concert with the rest of the system. With a somewhat experimental design, I would be tempted to include adjustability, so you can make up your mind later. This could change the "feel" of using the system and potentially make it more user friendly:
Perhaps at least one of the cocking linkage centers (two because they are paired) can incorporate the ability to make small adjustments; via a lockable eccentric bushing. Now, perhaps your linkage geometry is not prone to abrupt peaking, followed by slamming shut. I have not analyzed it; nor do I have experience with that type of linkage.
Also, I suggest you make the effective compression volume adjustable. This will make life easier; should you decide the cocking effort needs to be reduced; or could be higher. Now, you could adjust the compression volume in a number of ways, but here is one way: The image below is of my Baikal MP-46M SSP pistol. It has the ability to adjust the piston's "TDC" distance from the "cylinder head" in 0.25 mm increments, via a little grub screw positioned in one of four windows in the threaded piston hinge base.
(https://www.gatewaytoairguns.org/GTA/index.php?action=dlattach;topic=153027.0;attach=256390;image)
(https://www.gatewaytoairguns.org/GTA/index.php?action=dlattach;topic=153027.0;attach=256503;image)
Carry on...
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Thank you for the info, Subscriber! You made some very good points that I will ponder & look into more closely for sure. Greatly appreciated! :)
Also, I suggest you make the effective compression volume adjustable. This will make life easier; should you decide the cocking effort needs to be reduced; or could be higher. Now, you could adjust the compression volume in a number of ways, but here is one way: The image below is of my Baikal MP-46M SSP pistol. It has the ability to adjust the piston's "TDC" distance from the "cylinder head" in 0.25 mm increments, via a little grub screw positioned in one of four windows in the threaded piston hinge base.
Interesting set-up 8)
My hillbilly way isn't near as elegant or effective... ;D.
Pump rod will be threaded through block that secondary link arms attach to & the end of rod is drilled/tapped for a 5/16-18 set screw held in place with red Loctite or retaining compound. Then I could just insert an Allen key in end of pump rod & adjust "piston TDC" as needed without tearing everything apart. Another set screw in bottom of block would lock rod in place.
If a full stroke & ~2500psi turns out to be too much for components...or me... I was thinking that I could simply place a "locking collar" of sorts on the pump rod (think drill bit collar/stop) that would limit how far I could open pump arms, thus reducing final pressure yet still be consistent.
Just thoughts right now though.
Thanks again! ;)
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Those approaches sound completely feasible, Todd.
Keep it simple...
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While Todd is on his way with a viable cocking mechanism, I thought those of you who are interested in SSPs that work really well, might be amused by the Solidworks model I just created of a Baikal MP-46M's mechanism:
https://www.gatewaytoairguns.org/GTA/index.php?topic=153475.msg155688851#msg155688851 (https://www.gatewaytoairguns.org/GTA/index.php?topic=153475.msg155688851#msg155688851)
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Did more detailed analysis and came to this conclusion:
The Baikal MP-46M's pumping sliding follower generates force multiplication geometry, that very nearly follows the inverse of the air pressure build-up, that would occur when its 49 CC air is compressed into (an assumed) 0.5 CC residual volume.
The link at the above quote will take you to all the good images, data and charts...