# Phil, here's that math you asked for: The maximum theoretical muzzle energy of an SSP...

Joined: November 28th, 2002, 6:26 pm
Ambient pressure of 1 bar and volumes in cubic inches are assumed. 1 bar corresponds to an elevation of no more than 300 feet above sea level and a temperature of no more than 64F. Higher elevation or temperature will reduce available energy.

ME = 3.02 Vs (1 - (Vv / (Vv + Vb))^0.4)

Where:
ME = muzzle energy in fpe assuming zero airflow and frictional losses
Vs = Pump Stroke volume in in^3
Vv = Valve volume in in^3
Vb = Bore volume in in^3

For example...

Vs = 1.7ci = 28cc
Vv = 0.01ci = 0.16cc
Vb = 0.394ci (16" of .177" barrel)

ME = 3.02*1.7(1 - (.01/(.01 + .394))^.4)) = 5.13(1 - .228) = 4fpe

In my experience, it's very rare for a practical airgun to realize better than 2/3rds of this theoretical figure. So for this combination, I'd realistically expect no more than about 2.7fpe.

Steve
Last edited by pneuguy on January 16th, 2011, 2:57 am, edited 1 time in total.

Joined: April 1st, 2009, 3:18 am

"Well, I thought it was a rabbit but it turned out to be Bear Grylls in a rabbit hide."

Joined: November 28th, 2002, 6:26 pm
...only applies to conventional SSPs where all energy is stored in the charge. Air-conserving and displacer-piston powerplants (like the Paradigm) are different cats.

Steve

Joined: June 5th, 2006, 12:49 am
Ambient pressure of 1 bar and volumes in cubic inches are assumed. 1 bar corresponds to an elevation of no more than 300 feet above sea level and a temperature of no more than 64F. Higher elevation or temperature will reduce available energy.

ME = 3.02 Vs (1 - (Vv / (Vv + Vb))^0.4)

Where:
ME = muzzle energy in fpe assuming zero airflow and frictional losses
Vs = Pump Stroke volume in in^3
Vv = Valve volume in in^3
Vb = Bore volume in in^3

For example...

Vs = 1.7ci = 28cc
Vv = 0.01ci = 0.16cc
Vb = 0.394ci (16" of .177" barrel)

ME = 3.02*1.7(1 - (.01/(.01 + .394))^.4)) = 5.13(1 - .228) = 4fpe

In my experience, it's very rare for a practical airgun to realize better than 2/3rds of this theoretical figure. So for this combination, I'd realistically expect no more than about 2.7fpe.

Steve
Scarily close to the 400fps I didn't expect to be exceeded with these pellets!

Still it's an inspiring and thought provoking build.

Joined: April 1st, 2009, 3:18 am
...only applies to conventional SSPs where all energy is stored in the charge. Air-conserving and displacer-piston powerplants (like the Paradigm) are different cats.

Steve
I am amazed with that Webley rifle. After more inspection of the scematic (still cannot find the gun for sale any place) the spring mentioned is a series of disk springs. Unless there is some magical properties to disk springs, it, or they rather, befuddle me. Disk springs don't actually work like a coil at all (more like reeds). If a scoil spring was used, the springer effect makes sense; then again, wouldn't compression of the spring be equal to built pressure in the reservoir? With that, how does it produce so much power. After comunicating with Mr. Allen, he stated that the gun was designed to create more power, but due to UK restrictions it was tuned down to 11.5 ft-lbs. Just gotta know how it works! All that talk about using ..."Formula One technology..." is moot, really. A red herring.

"Well, I thought it was a rabbit but it turned out to be Bear Grylls in a rabbit hide."

Joined: April 12th, 2002, 5:26 am
I think I read that somewhere recently.

Joined: June 5th, 2006, 12:49 am

Joined: January 17th, 2010, 12:03 am
I am amazed with that Webley rifle. After more inspection of the scematic (still cannot find the gun for sale any place) the spring mentioned is a series of disk springs. Unless there is some magical properties to disk springs, it, or they rather, befuddle me. Disk springs don't actually work like a coil at all (more like reeds). If a scoil spring was used, the springer effect makes sense; then again, wouldn't compression of the spring be equal to built pressure in the reservoir? With that, how does it produce so much power. After comunicating with Mr. Allen, he stated that the gun was designed to create more power, but due to UK restrictions it was tuned down to 11.5 ft-lbs. Just gotta know how it works! All that talk about using ..."Formula One technology..." is moot, really. A red herring.

"Well, I thought it was a rabbit but it turned out to be Bear Grylls in a rabbit hide."

Feb. 2010 and I still have not seen any for sale. Anyone know whats up or if it is for sale where??

Rich

Joined: November 28th, 2002, 6:26 pm
I am amazed with that Webley rifle. After more inspection of the scematic (still cannot find the gun for sale any place) the spring mentioned is a series of disk springs. Unless there is some magical properties to disk springs, it, or they rather, befuddle me. Disk springs don't actually work like a coil at all (more like reeds). If a scoil spring was used, the springer effect makes sense; then again, wouldn't compression of the spring be equal to built pressure in the reservoir? With that, how does it produce so much power. After comunicating with Mr. Allen, he stated that the gun was designed to create more power, but due to UK restrictions it was tuned down to 11.5 ft-lbs. Just gotta know how it works! All that talk about using ..."Formula One technology..." is moot, really. A red herring.

"Well, I thought it was a rabbit but it turned out to be Bear Grylls in a rabbit hide."

...about them. Disk springs (a.k.a., spring washers) are simply the preferred (i.e., cheaper) way to make a spring that has high force (e.g., 100s of lbs) but limited movement (e.g., .01"s), whereas coil springs are much better when larger motions are involved.

The Paradigm could have used a coil, but Webley chose disks because the total movement of the Paradigm piston is probably less than 0.1".

It's not so much the the spring that makes the Paradigm different from a springer, but the fact that, in a springer, it's the piston that moves the air.

In the Paradigm, it's the air that moves the piston.

Steve

Joined: November 28th, 2002, 6:26 pm
I am amazed with that Webley rifle. After more inspection of the scematic (still cannot find the gun for sale any place) the spring mentioned is a series of disk springs. Unless there is some magical properties to disk springs, it, or they rather, befuddle me. Disk springs don't actually work like a coil at all (more like reeds). If a scoil spring was used, the springer effect makes sense; then again, wouldn't compression of the spring be equal to built pressure in the reservoir? With that, how does it produce so much power. After comunicating with Mr. Allen, he stated that the gun was designed to create more power, but due to UK restrictions it was tuned down to 11.5 ft-lbs. Just gotta know how it works! All that talk about using ..."Formula One technology..." is moot, really. A red herring.

"Well, I thought it was a rabbit but it turned out to be Bear Grylls in a rabbit hide."

...from several years ago.

http://www.network54.com/Forum/275684/m ... ressure---

When the gun is cocked and the pump arm closes to the point where the charge pressure rises high enough to overcome the preload force of the spring, then the charge stops compressing and the stack of disks spring begins compressing.

Thus, at the end of the stroke, the total energy input during the stroke is shared between charge and spring.

When the gun is fired, the pressure of the charge is initially maintained almost constant as the piston is driven forward by the force of the spring until the energy of the spring is exhausted. Only then does the piston stop and the charge begin to expand and pressure start to fall like in a normal SSP.

Steve
Last edited by pneuguy on January 16th, 2011, 3:17 pm, edited 1 time in total.