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All Springer/NP/PCP Air Gun Discussion General > "Bob and Lloyds Workshop"

External Ballistics of Pellets by Ballistician Miles Morris

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rsterne:
A couple of things I will try and explain.... First, Timo is correct, when you use the Kolbe Drag Calculator, at subsonic velocities the Meplat diameter has little effect on the drag.... I always wondered about that, but since it, and the nearly identical drag calculator on the JBM website, had the same conclusions, I assumed that was correct.... Interestingly , the JBM calculator will not allow you to input a Meplat larger than 30% of the caliber (a restriction the Kolbe calculator does not have, but should)…. They are both based on the math of Robert McCoy, from his "McDrag" software, and Miles kindly explained to me that McDrag was developed for calculating the drag of artillery shells, none of which have much of a Meplat…. Therefore, using them for the large Meplats typical of airgun slugs will produce flawed results.... Miles is a contemporary of McCoy, and with over 40 years of employment studying Exterior Ballistics for the UK Government, we would be well advised to heed his advice.... Large Meplats will increase the drag, particularly if the edge between the Meplat and the Ogive is sharp.... A surprisingly small radius there reduces the drag a lot....  8)

As to the concept that diabolo pellets are not "drag stabilized", but instead stabilized by lift forces, acting through the CP, and creating a "moment" about the CG that corrects the flight path, I freely admit that was not something I was familiar with, nor had I even considered it.... I have always assumed it was the drag being behind the CG the made the pellet "straighten out and fly right" (apologies to Nat King Cole)…. Miles correctly points out that with a Wadcutter, where a large part of the drag is on the front, will not have the CP much, if at all, aft of the CG, so the concept that the drag, which is almost exactly on the centerline and acts parallel to it, produces enough moment about the CG to "steer" the pellet straight makes no sense.... I got it wrong, and I apologize for perpetuating the myth....  :-[

The key for me, in understanding what Miles was saying about pellet stability, was to ignore the shape of the pellet and think about it acting like the tail of an aircraft.... If it is yawed to the line of flight, it produces lift, which acts "normal to" (ie at 90 deg.) to the centerline of the pellet.... That lift acts through the CP.... If the CP is behind the CG, then that provides a correcting moment which tends to reduce the yaw.... After oscillating from side to side, and assuming the pellet also has dynamic stability, the yaw reduces and the pellet flies straight, or nearly so.... Yes, the pellet isn't shaped very efficiently to be considered a wing, but the lift is a "vector sum" of all the side forces on the pellet (positive and negative), and those forces will always be away from the line of flight because the yaw is creating an "angle of attack" for the pellet as a whole.... By definition, the CP is the point through which the sum of the lift forces act.... Since that is behind the CG that causes a moment, or "torque" if you like, about the CG.... and that moment reduces the yaw angle.... which is the definition of aerodynamic stability (yaw is reduced in flight instead of increased)…. The flare at the rear of the pellet is the main contributor for moving the CP aft, hence why you would consider a pellet to be "flare stabilized"....

With a slug, the CP is forward of the CG, so the slug is unstable, and without spin the yaw would increase until it tumbles.... That is why a slug requires gyroscopic stability, because its aerodynamic stability is negative....

I would like to thank Miles for explaining the various types of stability, and for correcting my erroneous use of the term "drag stabilized".... I got it right when I said that there is a correcting moment because of the CP being behind the CG.... What I didn't realize is that it was actually a lift force, acting at right angles to the line of flight (ie "normal to" ) that created this moment, not the drag force acting parallel to it....

Bob

rsterne:
By MJP (Marko)….

Ok my mistake interpreting your picture on my mobile.
Well I used air friction as my native language is not English. Drag would have been a better word but it slipped my mind at the time of writing.
I see now where that lift comes from, but do you call it lift if the pellet is at its opposite oscillating position nose pointing downward.
As with that is the nominal flight model if there is no spin stabilization the pellet is jawing in a circular manner in flight wagging it's tail as the lift goes from up down side to side with wind and as the lifting force changes.
Oscillating wobling, I don't know the term in English.
As the high and low pressure areas change as the orientation is bound to change with the lift vector.
Lift pushes the skirt up and the high and low pressure areas follows the motion accordingly now the lift vector is pointing down and so on.

Marko

rsterne:
By WhatUPSbox (Stan)….


--- Quote from: ballisticboy on February 26, 2020, 09:57:53 AM ---
It has been shown in wind tunnel tests that the axial force does not change in magnitude until large angles of yaw are obtained so any change in drag at low yaw angles is caused by the tiny component of normal force in the drag direction.

--- End quote ---

Do you have any links or references to pellet tests with varied yaw angles? I've found wind tunnel and CFD results for pellets but they are all aligned with the flow.

rsterne:

--- Quote ---do you call it lift if the pellet is at its opposite oscillating position nose pointing downward.
--- End quote ---

Yes, it's just lift in the downwards direction.... It could just as easily be to the side, or on any angle in between, since the pellet can be yawed in any direction.... as it would be if it left the muzzle crooked.... In fact, since the pellet is spinning, and hence seeing precession and nutation (wobbling), the lift vector is always changing.... What is important is that since the CP is behind the CG, it is always trying to reduce the yaw at that instant.... which is what we call aerodynamic stability....

It's a slightly difficult concept to grasp, but once the lightbulb goes on, it makes perfect sense....  8)

Think about a football (pointed elliptical) shape, with an internal weight inside the nose, so that the CG is well forward of the CP.... It would tend to fly straight, even without spin.... Now move the internal weight to the back, so that the CG is behind the CP.... It will tend to swap ends and fly backwards, right?.... Now spin it fast enough so that it has gyroscopic stability.... Even with the weight in the back, it will remain flying point forward.... Normal footballs (not talking a soccer ball, sorry non-North Americans) have the CG at the center, and because of their shape and speed, the CP is slightly forward of that.... so unless you spin them, they tend to tumble.... Give them even a relatively slow spin rate, and then they fly straight....

Bob

Thank you for your patience while I combined Miles' threads on Stabilty…. It will be much easier to find them as a single "sticky"....
It is the plan for Miles to add additional topics in this thread to make it a valuable archive on External Ballistics.... Stay Tuned !!!!

Bob

johnnyfoos:
Thanks to ALL !

Yes my head did feel this some, but
I do understand.

SO-
"and Other Stability Topics"
I didn't see anything about the old round ball, ?
I was looking for anything to explane why they work so good,
{enough for what I use them for at least}
I know why they fly so much farther than the pellets
but
 a slightly difficult concept to grasp
is why almost no one likes them,
I do and use them and hit what I'm shooting at.
Just
sayn
$0.02

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