PCP Airgun Internal Ballistics
This article is a transition from Bob’s series on PCPs to this next series on Ballistics. The science of Ballistics is divided into three parts, Internal Ballistics, External and Terminal.
Internal Ballistics is what happens to the pellet inside the barrel. External is what happens during the flight to the target. Terminal Ballistics is what happens when the bullet hits the target.
In this article, Bob will deal with Internal Ballistics, as they apply to a PCP.
Internal Ballistics – Force Causes Acceleration
The basis of Internal Ballistics is that the pellet starts at rest. when the gun is fired, the base of the pellet is acted on by air pressure creating a force to accelerate it.
As it travels down the barrel, the rifling causes the pellet to spin, at a rate determined by the twist rate of the rifling.
The larger the caliber, the greater the area for the air to push against, so the greater the force. On the other hand, the bullet is heavier, and greater force is required to accelerate it.
Air is released from a valve, usually for a specific time we call the “dwell”. During that time, nearly the full air pressure is available to accelerate the pellet.
After the valve closes, the air trapped in the barrel between the valve and the pellet expands. We can model what is happening and graph it like this. (Modeling spreadsheet by courtesy of Lloyd Sikes):
Look at the plot of the air pressure (in psi) inside the barrel (blue line). You will see that while the valve is open, the pressure only drops slightly as the air in the reservoir/plenum expands into the barrel.
In this model, the valve closes when the pellet has only moved about 4 Inches down the barrel. After that, the air trapped in that first 4 Inches expands and the pressure in the barrel drops until the pellet reaches the muzzle.
The pressure inside the barrel when the pellet reaches the muzzle is called the “residual muzzle pressure”. It is that pressure which causes the report (muzzle blast).
The air pressure causes the pellet to accelerate. The velocity (in fps) as it moves along the barrel is the green line. The energy of the pellet (in FPE) is the red line. Note that most of the velocity gain occurs early in the barrel, when the pressure is the highest, and so is the acceleration.
More Dwell = More Power and More Noise
If the graph above, we showed the valve only open for a short time. Surely if you kept the valve open until the pellet reached the muzzle you would get more power, right?
While that is true, what you really get a LOT more of is noise. Consider the chart below:
This chart is essentially three of the above sets of graphs, where the only thing changed is how long the valve is open.
The red lines are for the valve being open for 1 millisecond (0.001 sec.). The green lines are with the valve open for 2 mSec., and the purple lines with it open for 3 mSec. The solid lines are the air pressure (psi), the dashed lines the velocity (fps), and the dotted lines the energy (FPE).
First, notice how little difference there is between the velocity and energy achieved between a dwell of 2 mSec. and one of 3 mSec.
With a dwell of 2 mSec. the valve is closing when the pellet is about halfway to the muzzle. That extra 1 mSec. of dwell buys hardly any increase in velocity, and only about 1 FPE in energy. Now look at the pressure curves!
Why all the Noise?
With a dwell of 3 mSec. the valve is open until the pellet leaves the muzzle. The pressure drops about 200 psi, and that is how much air is used from the reservoir.
Reduce the dwell to 2 mSec. and the pressure only drops about 100 psi, meaning only half the air is used to produce nearly as much power.
Reduce the dwell to 1 mSec. and we use only about 30 psi to produce 25 FPE, compared to 200 psi to get 36 FPE.
We are getting over 2/3rds the power from about 1/6th the air, or roughly 4 times the efficiency.
Where is all the extra energy going? Look at the residual muzzle pressure.
With 1 mSec. dwell, it is about 300 psi. At 2 mSec. it increases to over 900 psi. With 3 mSec. of dwell, the residual pressure is about 1800 psi.
That means that the report will have 6 times the energy, in other words the gun will be LOUD.
Keeping the valve open after the pellet has traveled more than half the length of the barrel wastes air. PERIOD. The gain in velocity might be 2-3%, but the air used doubles. In addition to wasting a lot of air, the gun gets LOUD. It’s pretty obvious that is not the way to tune a PCP.
It is pretty easy to understand how a regulated PCP maintains a constant velocity – because the pressure is constant.
Unregulated PCPs aren’t really all that much of a mystery when you look at the Internal Ballistics. Consider the model below of a Discovery at three pressures representing the beginning, middle and end of the shot string:
The red lines are a model of what happens at 2000 psi. The green lines are for 1700 psi, and the purple lines are for 1200 psi.
The solid lines are the pressure, dashed are again the velocity and dotted are the energy.
Note that the highest velocity and energy occur in the middle of the shot string, at about 1700 psi. As you would expect, they drop a bit at the end of the string at 1200 psi.
However, they are also lower at the beginning of the string at 2000 psi. What is causing that?
The key is that the dwell of the valve is less at 2000 psi, and increases slightly with every shot as the pressure drops. This happens automatically, and is called “self-regulation”.
The hammer strike is constant. However, the higher the pressure in the reservoir, the more force holding the poppet closed, so the harder it is for the hammer to knock the valve open.
Constant Hammer Strike but Variable Dwell?
At 2000 psi, so much hammer energy is used just cracking the valve off of its seat, there is not a lot left to create dwell. Consequently the valve might close when the pellet has only moved 3 Inches or so.
Drop the pressure to 1700 psi and the valve is easier to open, so more hammer energy is available to create dwell. The valve might stay open until the pellet has moved 4-5 Inches. At the end of the shot string, at 1200 psi, the valve is much easier to open, and the hammer can now keep the valve open while the pellet moves maybe 8 Inches.
If you look at the pressure curves, you will see something interesting…
As the pressure in the reservoir drops, and the dwell increases, the residual muzzle pressure rises.
That is why unregulated PCPs get louder towards the end of the shot string. It is also why they are slightly more efficient at the beginning of a shot string, when the pressure is the highest.
Does Spinning the Pellet use up Energy?
The obvious answer is yes, but a lot less than you might think.
Accelerating the pellet down the bore takes a lot of force. Spinning it up, even though the RPM may be quite high, takes very little.
The rifling lands are at a very shallow angle to the bore, only about 2-3 degrees. As the pellet accelerates down the barrel, the lands bite into the pellet, and as it builds velocity, it also picks up spin.
You can calculate the amount of energy that takes, but I won’t bore you with it. Sufficient to say it is such a small percentage you can virtually ignore the velocity difference from faster twist rates. A much greater loss is the friction of the pellet against the barrel.
Diabolo (waisted) pellets are designed for the skirt to expand to create a seal, and that increases the friction a bit, but it is still small compared to the friction of a pellet, which has much more contact area with the rifling.
The greatest frictional losses in an airgun occur with a pellet that is oversize. The lesson here is to size pellets to match your barrel.
Next month I will start on the complex topic of External Ballistics. Hang on, it will be quite a ride!