Like I said, I like the "constant power" idea because it is simple, and I can understand it.... and its even pretty easy to build into a spreadsheet.... Throw in Thermodynamics and that mystical "k" factor, and I'm totally lost.... not so much on the math, but the validity/applicability of the whole concept.... Bob
The simple concept: maximum possible velocity is the SOS flow rate + the expansion rate. The maximum expansion rate also happens to be near the SOS.So "about 2xSOS" for a maximum velocity estimate. That sorta lines up with the Fanno realtions.I tried to do a spreadsheet starting with that simple concept. To see if I could do a simpler spreadsheet and model any specific dump chamber airgun.I played all day with it to model the flow+expansion as two distinct regimes, subsonic and supersonic, and hopefully get an accurate result.No good results.I still need to deal with the amount of expansion to accurately model a specific airgun. We need to take into account k, SOS, temperature, and changes to each along the way.It just won't work without them. And as I add them into the "simpler" spreadsheet, it starts to look just as hairy as my old spreadsheet.I sent rsterne a copy of the simpler spreadsheet. And I think it shows the concept of using a "hard" dividing line between subsonic and supersonic. That concept helps with a simple explanation of the maximum possible velocity predicted by Fanno relations, but it does not help when modeling an actual airgun.I'll stick with my older, more complex, spreadsheet for now. That was a mind boggling exercise in itself. The thought of trying to recreate it scares me.
Quote from: jhm757 on March 02, 2017, 12:21:31 PMWow! Reading this is giving me brain pain!I don't have a clue! Wish I did but I don't!Jim - jhm757I enjoy the information and occasionally after reading several times it begins to make some sense but the physics has always made my brain hurt and my eyes cross I am also married to an RN so I am frequently in way over my head when I sit and listen to her conversations with other nurses and doctors so I am getting used to having a puzzled expression on my face and a dull ache behind my eyes
Wow! Reading this is giving me brain pain!I don't have a clue! Wish I did but I don't!Jim - jhm757
Even with a conventional valve arrangement, with a 180* turn to the airflow, I was able to exceed 1700 fps at 2900 psi with a .25 cal airgun by simply using a very light projectile.... yet the speed of sound at 3000 psi is only 1360 fps....
After doing a lot of perusing, I think the instantaneous pressure behind a super-light-for-caliber projectile theory has merit:Think of the air rushing in behind the pellet as a coil spring. The closer the coils, the higher the pressure.Now, as the column of air collides with your stationary light-weight pellet, the "coils of the spring" in the region of contact get stacked closer together. This represents a sub-volume of pressurized air that has been forced to be at a higher pressure than the average pressure in the rest of the column due to the change in flow velocity.That high pressure region has limited volume; thus it has limited total energy. However, its fraction of energy is enough to accelerate the light pellet to higher than expected velocities (based on the average pressure in the air column). While the light pellet does not exceed the velocity of sound in the temporary high pressure air column front, it exceeds the speed of sound in air at 3000 PSI.A train that crashes at 10 MPH can still squish a pallet of toothpaste tubes so abruptly that toothpaste flies out radially at more than 10 MPH. The toothpaste comes nowhere close to absorbing all the train's energy; just like your light pellet absorbs only a fraction of the energy contained in the initial air volume at 3000 PSI.The more familiar model is that a pellet launched by means of only 1000 PSI air produces way more pressure than that, should it impact something rigid close to the muzzle. The air column running into the back of a rigid pellet in the chamber is no different; except that it is the air smacking into the pellet at the speed of sound, rather than the pellet smacking the target that produces the pressure spike that launches your light hyper velocity pellet.
The pellet moves before the air can start moving.
If you read the thread I linked above...