Some New Airgun Slug Drag Models by Miles Morris
HAM Technical Editor Bob Sterne continues working on slug ballistics. So this latest post is of great interest as he summarizes some new airgun slug drag models being proposed by Miles Morris.
For those unfamiliar with Miles, here’s a short summary of his impressive biography. He’s a Brit who qualified with a degree in aerodynamics and worked in the aircraft industry on Harriers and Hawks. On leaving the aircraft industry he joined the MOD (U.K. Ministry of Defence) working in the gun external ballistics department.
He has spent the best part of 40 years working on projectile external ballistics design, testing, modeling and theory. He became the recognized MOD expert on the subject of external ballistic data. He dealt with all calibers and speeds of projectiles from 1 meter caliber down to particle sized fragments from war heads with projectile speeds from 90m/s up to 10000m/s.
Miles is also an airgunner! He began looking at pellets back in the late eighties and worked with the late Gerald Cardew on new pellet designs. He also advised on Cardew’s book “From Trigger to Target” (and is credited for his work in the Acknowledgements page of that classic publication).
Take it away Bob…
Here’s The Problem
Miles Morris has been working on trying to calculate the Drag Coefficients for typical airgun slugs for a while now. It appears that neither the GA or G1 drag models are a particularly good fit. So some new airgun slug drag models are clearly needed…
The slugs most commonly being designed and produced for airguns are based on a cylindrical body. They have a tangent ogive nose, ending in a relatively large meplat (flat), often with a hollowpoint.
By comparison, the GA drag model is for typical round-nosed diabolo airgun pellets, and the G1 drag model is for a spitzer bullet that comes to a point (no meplat), as below:
Miles started out with slug designs that were 1.25 calibers long, with a cylindrical body that is 0.50 calibers long, and a tangent ogive nose that is 0.75 calibers long. He used several different meplat diameters. The slugs are much more similar to what we use, and look like this:
Miles used some wind tunnel results to develop these airgun slug drag models. He considers this data a “starting point” and not a final solution.
In particular, he mentioned that there is no yaw component included in the drag, it assumes that the slug is exiting the muzzle perfectly. Note that the calculations done using these models are not suitable for slugs with a boattail base.
How These Drag Models Differ
Existing drag calculators like the Kolbe or JBM Calculators, often use the “McDrag” program. This was developed by Robert McCoy during his time at the U.S. Army’s Aberdeen Proving Grounds.
Miles is a contemporary of Robert, and they shared some ideas back in the 1970s. McDrag was not designed for large meplats, and in fact the JBM version will not accept a meplat of over 35% of the caliber for that reason.
There are not actually any standard drag models that closely resemble the airgun slugs we predominantly use today, so Miles had a go at calculating what the Drag Coefficient (Cd) was for several meplat sizes at various velocities. They are plotted below against the mach number, where Mach 1 is the Speed of Sound.
Here is that chart:
There are three important things to note.
First of all there is virtually no difference in the drag between a 25% meplat and a 50% one.
Secondly, the drag for a 75% meplat is roughly double that of the slimmer two designs.
Thirdly, above Mach 0.9 (about 1000 FPS) the drag increases rapidly, as the blunt nose doesn’t work well close to the speed of sound!
The green line represents an average of the other three. It is also very close to the results for a slug with a 65% meplat. When plotted along with the G1 and GA drag models, we can see how they compare:
Currently, by far the majority of swaged slugs are around the 50-60% Meplat range. That also applies to some of the heavier (for caliber) cast slugs.
Most relatively short cast slugs are in the 65-75% range, and almost none are over that. Therefore the 50-75% range covers almost all airgun slugs except rather specialized (semi-pointed) ones.
Using the “average” drag model (the green line on the charts) should work, and those slugs with smaller meplats would simply have a better (higher) BC, which those with larger meplats would have a lower BC, just as they should.
Below Mach 0.8, this new average drag model is very close to the existing G1 and GA drag models. The big difference is that from Mach 0.8 to 0.9 (about 900-1000 FPS) the drag doesn’t increase as rapidly, and then above Mach 0.9 it increases so rapidly that it has more drag than the G1 (pointed) bullet by the time it reaches Mach 1.
Why does this matter, and why is it relevant?
If we measure how the velocity of our typical airgun slug decreases, starting at a muzzle velocity of about 900 FPS, and use the G1 model to calculate the Ballistics Coefficient, we will get a result that is reasonably realistic.
However, if we look at the same slug at closer to 1000 FPS, we may find it has significantly less drag than the G1 model (it doesn’t slow down as rapidly).
If we then calculate the BC using the G1 model, we will get a BC (G1) that is much greater. If we then use that BC to determine how the slug will continue to decelerate once it drops below 850 FPS, we may be fooling ourselves.
This may help to explain the very high BCs claimed by some of the manufacturers of airgun slugs. Compared to the G1 model, our typical airgun slugs may well slow down less from 1000 FPS to 800-900 FPS, and then may slow down faster below that.
How accurate are these new preliminary new airgun slug drag models? Only proper testing of a lot of different slugs, at a lot of different velocities, and then calculating the actual Cd at various mach numbers will confirm or refute this data.
Until then, this remains something to discuss, and a way to possibly explain why our slug ballistics may not match what we expect if we use the G1 model to calculate their remaining velocity, energy and trajectory. The quest continues…
Recent HAM readers can catch-up on all Bob Sterne’s Technical Airgun posts by following this link.