Shot cycle Dynamics in 3 Spring-Piston Airguns Chap 4

APOLOGY.-
The editor wishes to apologize to the readers for the delay in publishing this chapter.
The editor takes full responsibility for this delay, in no way was this the Author's fault.
So, let's get back to business:

​LGU/LGV power plant swap: How does changing power plants affect performance and does a longer offset transfer port make a difference?

This adventure was initiated by Yogi's (of GTA fame) question about how transfer port (TP) geometry affects the performance of spring piston air rifles. Most break-barrel and some underlever (HW 77-97 series) air rifles have the TP located above the center of the compression tube, whereas the newer underlevers (TX200, LGU) have a TP that is centered on the compression tube. Jim Tyler has written several articles in Airgun World Magazine where he varied the TP diameter and length in the same rifle, but to our knowledge, no one has done a detailed comparison of central and non-central TPs. Hector realized that the Walther LGU and LGV were nearly identical except for the TP geometry, so he suggested we compare these two rifles more closely to try to answer Yogi’s question. In this chapter, I swapped the piston, mainspring, and trigger group between the LGU and LGV. In principle, using the LGU power plant in the LGV, and vice versa, should help isolate the effects of the TP geometry. Ideally, everything except the TP geometry should remain the same when the swap is made. So if one takes the power plant from the LGU and puts it in the LGV, the main difference will be that the LGU spring is pushing air through a longer, offset TP compared to when it was in the original LGU compression tube. The same is true when the LGV power plant is placed inside the LGU. Does the LGV power plant do better when it’s pushing air through the short, centered TP in the LGU? Unfortunately, other things also change when the swap is made. For example, the fit of the piston seal in the compression tube is slightly different. Ideally one would take the same rifle and move the TP around, as Mr. Tyler did with TP length and diameter, but this would be very difficult and would involve building a highly specialized rifle.
​ 
Figure 1 looks at the accuracy of the LGU before and after swapping its power plant with the LGV. Accuracy is better and velocity is about 20 fps lower before the swap. The standard deviation in muzzle velocity is nearly identical, suggesting that the consistency of the power plant does not depend on which rifle uses that power plant. 

Fig. 4.1 LGU accuracy based on 10-shot groups from the bench at 20 yards before a) and after b) the swap with LGV piston, spring and trigger group.

​Figure 2 shows the accuracy of the LGV before and after swapping its power plant with the LGU. The LGU gained about 20 fps with the LGV power plant but the LGV dropped by more than 66 fps with the same batch of QYS Dome pellets when it used the LGU power plant! This suggests that the LGV was better tuned for its power plant and is more sensitive to power plant changes than the LGU. Overall, accuracy was better before the swap, but the first three groups with JSB Exact 4.53 mm after the swap sure look good!

Fig. 4.2 LGV accuracy based on 10-shot groups from the bench at 20 yards before a) and after b) the swap with LGU piston, spring and trigger group.

​Now let’s take a look at the efficiencies of the two rifles before and after the swap, as shown in Fig. 3. The efficiency of the LGU dropped dramatically with the LGV power plant. Cocking work increased by about 22% but the muzzle energy increased only by about 5%. The efficiency of the LGV also dropped when using the LGU power plant, but not by as much. Even with the LGU power plant, the efficiency of the LGV was still pretty good, especially with the JSB pellets. It’s interesting that the most efficient pellet depends on the power plant. I would have naively expected that it just depends on the pellet friction in the bore, but it’s clear that with its original power plant, the LGV was slightly more efficient with QYS Dome pellets, but with the LGU power plant, the LGV was significantly more efficient with JSB 4.53mm pellets. The LGU’s greater efficiency loss in using a borrowed power plant could be due to the TP, but there may be other reasons. For example, this could also happen if the LGU piston seal is a bit undersized compared to the LGV piston seal. In that case, the LGU piston seal would slide with very low friction in the LGV compression chamber whereas the larger LGV piston seal would be a tighter fit in the LGU compression chamber, which would then encounter more friction and produce lower muzzle velocities. I didn’t notice much of a difference in piston seal friction when inserting the pistons, but if I were to do this experiment again, I would have kept the piston seals on the original rifles, that is, put the LGV piston seal on the LGU piston when inserting the LGU piston into the LGV and put the LGU piston seal on the LGV piston when inserting the LGV piston into the LGU. 

Fig. 4.3 Cocking work and efficiency of LGU and LGV with original and swapped internal parts.

​Another possibly important factor in the swap is that the LGV uses an anti-bounce piston (ABP), which we expect to increase muzzle energy by about 10% (see Chapter 2). Maybe the ABP is working better in its original home, the LGV, than in its new host, the LGU? To get a better idea of how the rifles are recoiling, which also could give some clues about how the ABP is working, I measured the recoil traces of both rifles before and after the power plant swap, as shown in Fig. 4. The recoil of the LGU gets significantly stronger with the more powerful LGV spring, as can be seen by the position, velocity and acceleration plots in Fig. 4a). The second dip in the acceleration is clearly deeper with the LGV spring. On the other hand, the first positive peak in the acceleration is a little bit smaller with the LGV spring. Maybe the ABP is moderating the abrupt slowdown of the piston before it starts heading backward? These strong changes in recoil result in a small increase in the muzzle velocity. Unlike the LGU, the LGV shows very small changes in recoil (Fig. 4b) that are accompanied by a much larger decrease in muzzle velocity. There is hardly any difference between the original and swapped power plants in the first few oscillations of the LGV’s acceleration despite the fact that the muzzle velocity drops by 66 fps when the power plant is swapped.

Fig. 4.4 Recoil traces showing the position, velocity, and acceleration of the sled-mounted rifles over 250 ms for the a) LGU (AADF) and b) LGV (JSB Exact) with original (blue traces) and swapped (red traces) piston, mainspring, and trigger group.

​Figure 5 zooms in on the early parts of the recoil traces for the LGU (Fig. 5a) and the LGV (Fig. 5b). Also shown in the velocity vs time plots are the light gate traces, which show when the pellet exits the muzzle. The timescale for the recoil plots was shifted to align the pellet exit times for the original and swapped components. It’s surprising how little the recoil changes when power plants are swapped, suggesting that the dominant factor in recoil is not the power plant, but the rest of the rifle!? It looks to me like the LGU recoil remains distinct from the LGV recoil regardless of which power plant it uses. This is especially puzzling since the LGV power plant uses an ABP and the LGU power plant doesn’t. For example, the shoulder just before the first peak in the LGU velocity (see black arrow in Fig. 5a) occurs with both power plants. Also, the distinctive flattening at the top of the first velocity peak for the LGV (see black arrow in Fig. 5b) occurs with both power plants. The LGU power plant does appear to enhance this flattening, so maybe this is where the ABP makes a difference? Furthermore, the LGU spring is nearly dry with a very light coating of Superlube whereas the LGV mainspring has a heavy coating of tar. This doesn’t show up very strongly in the recoil traces. Part of this apparent insensitivity in recoil to the power plant is due to the far greater total weight of the LGU rifle, which simply rescales the vertical axes in the recoil plots; it’s harder to get a heavier rifle moving. The LGU will always be heavier than the LGV, regardless of power plant! However, the qualitative shape of the recoil traces seems to not depend much on the power plant and this is perhaps where we’re seeing the TP geometry making its biggest impact? Of course, all this analysis has to be taken with a grain of salt since the rifle is moving forward in the sled given the huge forces pulling on the Velcro strap at the piston bounce, as Steve in NC pointed out in the Airgun Warriors thread.

Fig. 4.5 Recoil traces showing the position, velocity, and acceleration of the sled-mounted rifle over 50 ms for the a) LGU (AADF) and b) LGV (JSB Exact) with original (blue traces) and swapped (red traces) piston, mainspring, and trigger group. Pellet exit times are marked by vertical black lines. Black arrows show distinctive features in the velocity traces.

In the final two figures we look at the recoil energy for the LGU (Fig 4.6) and LGV (Fig. 4.7). Since we know how the entire rifle moves during recoil, we can determine its kinetic energy as a function of time or position. This is important and interesting since the movement of the rifle can affect the POI. There are three ways to determine recoil kinetic energy of the moving rifle and sled. The easiest way is to use the formula E=½ mv^2, where E is the kinetic energy (the energy of motion), m is the mass of the rifle and sled added (since they’re moving together) and v is the velocity of the rifle and sled. Figure 4.6a) shows the kinetic energy of the rifle and sled system as a function of time. Note that this energy is always positive; whenever you square a real (positive or negative) number like velocity you get a positive answer. The kinetic energy oscillates just like the velocity. As the rifle recoils backward, the peak energy absorbed by the rifle occurs at around 0.007 s, which corresponds to a sled position of -3.6mm according position vs time plot at the top of Fig. 4.5a). This peak energy is 2.4 J (1.8 ft lbs) for the original innards and 3.0 J (2.2 ft lbs) for the swapped LGV innards. I placed red and blue dots to mark these positions. The second way to determine the recoil energy is to use the instantaneous power at time t, P(t), which is just the product of the force and velocity at that time. One can then just integrate the power from the starting time to time t to get the energy expended in recoil during that time window. Although I don’t plot the result, it looks exactly like the plot in Fig. 4.6a). The third way to get the recoil energy is to plot the force F as a function of position x, F(x), and then integrate that force from the starting position to some position x to get the energy expended to get to x. The integral along x is bit trickier since the dx intervals vary (remember that we record with a constant time interval between points, but the distance between the positions of neighboring points will vary as v varies). I used this method to determine recoil energy vs position by plotting the force as a function of position x (not time!), as shown in Fig. 4.6 b) and d) integrating the force over position, as shown in Fig. 4.6 c) and e). In Fig. 4.6 b) and d), the plot retraces itself as the rifle moves back and forth in position. Using this technique we see that the peak recoil energy occurs when the sled position around -3.6 mm, as can be seen in Fig. 4.6 c) and e).  I placed red and blue dots to mark these positions. I'm very relieved to see that the positions and times of these peaks, as well as the peak values agree pretty well using the three methods. Newton was right! The further oscillations in energy appear to be pretty consistent when comparing E(t) and E(x). The recoil energy peaks about 0.003s before the pellet leaves the barrel. So this peak recoil energy could have a big impact on accuracy, as the rifle reaches its maximum kinetic energy right before the pellet leaves the barrel.  The more the rifle moves before the pellet leaves the barrel, the harder it will be to stack pellets on top of each other! In Fig. 4.6 one can see that the peak recoil energy increases by about 25% when the LGV spring is used in the LGU. Unfortunately, this strong (25%) increase in peak recoil energy is accompanied by a very weak (5%) increase in muzzle energy.

Fig. 4.6 Recoil energy of LGU with original (blue) and swapped (red) internals: a) recoil energy vs time and pellet exit traces, b) and d) force vs position, and c) and e) recoil energy vs position. The peak recoil energies are indicated red and blue solid circles and are the same whether one uses kinetic energy in a) or integrates force in c) and e).

​In Figure 4.7 I do the same recoil energy analysis for the LGV with its original and LGU innards. In this case, “original” means the ABP piston, which certainly is not a standard piston in the LGV, but it’s what the LGV had when I got it. Again, the three techniques for obtaining recoil energy produce the same results. The time (Fig. 4.7a) and position (Fig. 4.7 c and e) of the recoil energy peak are 0.006s and -4.0 mm, respectively. These are very similar to the values obtained for the LGU and are consistent with the position of the sled at that time (Fig. 4.5b). In this case however, the original and swapped innards produced almost exactly the same peak recoil energy of around 3.5 J (2.6 ft lbs).  This is surprising since the original ABP in the LGV produces about 19% more muzzle energy compared to the LGU piston and spring in the LGV. So for the same peak recoil energy, the ABP in the LGV produces about 19% more muzzle energy. Unfortunately, the ABP doesn’t produce a similar enhancement in the LGU, but this isn’t surprising since the ABP needs to be specially tuned for each rifle. The peak recoil energy is higher in the LGV (2.6 ft-lbs) compared to the LGU (2.2 and 1.8 ft-lbs), which is due to the lighter mass of the LGV. There’s another very interesting and possibly important difference between the LGU and LGV recoil energy traces. In the LGV, the pellet exits a bit later and the recoil energy peak occurs a bit earlier, so at the time of the pellet exit the LGV is moving less than the LGU. If the pellet were to leave another millisecond or so later, the LGV would actually be at rest at the moment that the pellet leaves the barrel. Unfortunately, all the motion before the pellet leaves the barrel could disrupt the aim, so there may not be much of an advantage in having the rifle stationary at the moment the pellet leaves the barrel. You really would want the rifle to not move at all from the trigger pull to the pellet exit, not just during the pellet exit.

Fig. 4.7 Recoil energy of LGV with original (blue) and swapped (red) internals: a) recoil energy vs time and pellet exit traces, b) and d) force vs position, and c) and e) recoil energy vs position. The peak recoil energies are indicated red and blue solid circles and are the same whether one uses kinetic energy in a) or integrates force in c) and e).

​The main conclusion of this first swap test is that it may be too soon to make any strong conclusions. It is clear that the LGV is just as efficient as the LGU, so any arguments about the inefficiency of long, non-central TPs doesn’t apply here. There also was a strong asymmetry in the muzzle energy gain and loss when power plants were switched. The LGU gained much less than the LGV lost when the power plants were switched. Maybe the ABP was optimized for the LGV and didn’t produce the same degree of improvement in the LGU? It also is clear that the distinctive recoil traces of the two rifles was maintained even after the power plants were switched, which suggests that the rifle itself (maybe the TP geometry) is more important than the actual power plant in determining how the rifle recoils. It’s also interesting that the peak recoil energy significantly increased in the LGU when using the more powerful LGV spring and ABP, but that the increase in muzzle energy was very weak.
​On the other hand, the ABP in the LGV produced the nearly the same peak recoil energy as the LGU piston and spring, but with a much higher muzzle velocity.