Is Force Created in a Compression Linear?

[SpiralGroove]

Questions:
Trying to increase the force created (SSG) by a compression spring of fixed length.  If compressing further by 3/8" reduces spring travel by the same 3/8" length:

1) Has total force been changed?

2) If yes, which way ... more or less?

3) How is a break-even point calculated?

Thanks,
Kirk

[rsterne]

Compressing the spring 3/8" increases the force by 3/8" x the spring rate in lb.in.... If the spring rate is 20 lb/in, it takes (0.375 x 20) = 7.5 lbs. more to compress that spring.... If you are talking about the preload in an SSG  being increased by 3/8" (shortening the overall length of the SSG by 3/8"), it takes 7.5 lbs more force before the spring compresses at all....

If increasing the preload on the SSG spring ALSO increases the gap between the front of the guide and the hammer by 3/8", then the hammer can be drawn back an additional 3/8" before it contacts the guide and starts to compress the spring.... It then takes an additional 7.5 lbs of force before you start compressing the spring.... HOWEVER, at full cock, in this case (only) the maximum cocking force would remain the same....

To make this clearer, let's say you have 1" of hammer travel available from touching the valve stem to catching on the sear.... With no gap (and no preload), it would take (1" x 20 lb/in) = 20 lbs. to pull the hammer back to engage the sear.... If you have 1/8" of gap, and 1/8" of preload, the hammer would slide back the first 1/8", and it would take (0.125 x 20) = 2.5 lbs. to pull it back any further (the spring preload), but it would still take 20 lbs. to engage the sear.... If you increase the preload from 1/8" to 1/2", and the gap to 1/2", the hammer would slide back 1/2", and then it would take (0.5 x 20) = 10 lbs. to pull it back any further, but still only 20 lbs. to engage the sear....

On the other hand, if you increase the preload from 1/8" to 1/2", and then move the SSG forward to reduce the gap to the original 1/8".... the hammer would slide back the first 1/8", then take (0.5 x 20) = 10 lbs. to pull it back any further, and (0.5 + 0.875) x 20 = 1.375 x 20 = 27.5 lbs. to engage the sear....

The total force at sear engagement is the preload force PLUS the (spring rate) times the (hammer travel minus the gap)....

Bob

[SpiralGroove]

Thanks Bob

In my case (RAW HM1000x SSG) I intend to increase pre-load, while retaining my original gap.
This will give me more power (roughly 920 fps) in my lower powered SSG for 18.13 JSB's, while keeping it's 1/8" gap, but also give me more power while shooting 25.39 JSB's as I reduce the gap to 0".

What is the max recommend gap?
What is the min. allowable gap?

- I've found my current 1/8" gap setting (low powered SSG) to give 18.13 pellets a velocity range of about 880 fps the 940 fps as the gap is reduced go 0".

- With the same SSG, I've found my current 1/8" gap setting to give 25.39 pellets a velocity range of about 860 fps to 895 fps as the gap is reduced.

Right now getting about 160 shots with 18.13 pellets using a 480cc bottle with a set-point of 117 bar.
Hopefully, with a bit more pre-load ... I can get my 18.13's up to 920 with a 1/8" gap and reduce gap slightly with 25.39's to get their velocity of to 910+.

God only knows what this will do to my ES ?

Kirk
   

[Hack21]

Kirk,

The equation for energy stored in a spring is (k*x^2)/2 where k is the spring rate and x is the distance compressed.  So for example, a 10lbf/in 2" free length spring compressed 1" and then allowed to expand back to the original 2" length would release (10*1*1)/2= 5in*lb of energy. If that same spring had 0.25" of preload and was then compressed an additional inch it would release (10*1.25*1.25)/2 - (10*.25*.25)/2 = 7.5in*lb.  You simply subtract the portion of spring energy that cannot be released due to the mechanism limiting the travel. So adding 0.25" of preload and retaining the same amount of relative travel would increase hammer energy by 50% in this example.

I think part of what makes an SSG work so well is that the spring stoping device has mass. When the hammer rebounds off of the valve it finds a static SSG mechanism that will require energy to accelerate/displace. With this said, the lightest cocking force requirement and resulting force at the sear will be with minimal gap/maximum relative travel and that is what I would target. A long soft spring with lots of preload and the minimal gap makes sense to me. The heavier the SSG mechanism the greater the the amount of spring energy/force that will be required but it should also resist hammer bounce better. 

Hopefully this is helpful. Best of luck.

[SpiralGroove]

Thanks Everybody ,
Surprising to see that 1/8" increase in pre-load, keeping gap constant yields ... +80 fps increase using 18.13 JSB's.  Each different pellet weight really needs its own SSG.

I think I've decided to simply go with 3 different SSG's as they can be changed out in my RAW in about 2 min.
1) 18.13 JSB @ 920
2) 25.39 JSB @ 900
3) One using slugs of my choice

If I decide to increase my FPE I will likely change my set-point to 125/130 bar instead of 117.

[rsterne]

I try and keep my gap at 1/16"-1/8", but don't usually find any problem up to 1/4" or so.... ES is more a function of where you tune a regulated gun, ie how near to the knee.... Detuned it below the knee and the ES tends to widen significantly....

Bob