How One Pellet Factor Can Affect Your Group Size

Discussion in 'General Airgun Chat' started by Ballisticboy, Mar 23, 2019.

  1. Ballisticboy

    Ballisticboy Active Member

    Joined:
    Jan 4, 2019
    Messages:
    74
    Location:
    Maidstone
    This is one which may be of interest to some or not. Just seeing how it goes.

    There are dozens of things which will affect group size, probably the biggest effect being you. However, after your pellet has left the gun there are a whole new set of things which will affect the group size over which you have little or no control. The biggest is probably wind; your pellets are highly vulnerable to the slightest wind. Another variable which people worry about is velocity changes though at most of the ranges we are shooting the effects are fairly minimal. If you are attempting to fire a 155mm shell 60km then changes in muzzle velocity have a major effect but not really at 40 yards. One thing which does have a large say in your group size which most people may not be aware of is the aerodynamic overturning moment normally written down as Cma.

    Cma is involved in both aerodynamic and gyroscopic stability and a lot of other ballistic behaviour characteristics. Amongst those are how pellets react to yaw and yaw rates as they leave the gun barrel. It is an important little devil.

    Cma is just the shortened way of saying C M alpha where alpha is the angle of yaw. The coefficient Cma dictates the size of the aerodynamic overturning moment about the projectile centre of gravity as alpha varies. The aerodynamic overturning moment is just the product of the aerodynamic normal force on the pellet multiplied by the distance between the centre of gravity and the centre of pressure.

    All projectiles have a value of Cma; the problem with diabolo pellets is that it tends to be very small. To show you the effect of Cma on your group size compare two pellets. The two pellets are identical in every way except Cma on one is the computed normal value for a pellet and on the other it is three times as big. Please don’t ask how you can find a pellet with a big Cma, I don’t know of any.

    Each of the two pellets has been fired in the same windless conditions and each of them miraculously leaves the gun with the same Muzzle velocity and the same yawing rate, caused by a very small pellet centre of gravity offset. The initial yaw rate does not have to be caused by the offset centre of gravity it is just an easy one to model. The diagram below shows the group size in inches you could expect to obtain with the two pellets.

    CmaGroup.jpg

    Before you get excited remember this pellet does not exist. The point of the diagram is to show the importance of Cma to group size. It also smooths out the flight path of the pellet as the maximum yaw angle will be much smaller even though the initial yaw rate was the same. This relationship has been known for years but knowing it and getting a large value of Cma are two different things.

    One way of getting a much larger Cma is to go from a diabolo to a bullet type shape. Unfortunately in air rifles the bullet shaped pellet weight tends to get very high and the barrel twist rate is too low for gyroscopic stability to be easily obtained. One of the favourite ways to reduce the weight is to have a hole in the back or the front of the bullet but, if the hole is in the back it reduces Cma making it little better than a diabolo, or if the hole is in the front you are immediately creating a high drag losing one of the advantages for a bullet shape and you may need a higher twist rate for gyroscopic stability.

    Another way to obtain a higher value of Cma is to use a very long Diabolo shape. Unfortunately, you would need to use something other than lead in the flare, the pellet drag would probably increase and you would end up with a very long pellet which would not fit in any magazines.

    In the end using a modified bullet type shape, designed specifically for air guns, using a mixture of materials seems the only way to go to get a significant increase in Cma along with a stable pellet. Such a round will be much more expensive to make and buy so it will be up manufacturers to decide if shooters are likely to buy one should it be made and sold.

    But at least you now have another excuse for when you miss that vital shot.
     
  2. MikeSeago

    MikeSeago Sloth like member

    Joined:
    Nov 22, 2014
    Messages:
    226
    Location:
    Norwich
    Would the Cma be higher for the old sabot pellets you used to be able to buy back in the 80’s as these were basically bullet shaped with a plastic sleeve.
     
  3. Tone

    Tone Active Member

    Joined:
    Apr 29, 2010
    Messages:
    765
    Location:
    Bristol
    Club:
    Bristol Aero & Nomads
    But at least you now have another excuse for when you miss that vital shot.

    Ballisticboy, Today at 3:30


    Good stuff thanks, so if you got the target down others are struggling with you could you say 'thats down to my Cma being larger than the average guys'? :eek::D
     
    Waldo and MickyFinn like this.
  4. C.Eaton

    C.Eaton Confirmed Anschutz Nut...

    Joined:
    Aug 9, 2011
    Messages:
    1,374
    Location:
    Hockley, UK
    Club:
    Springfield / TEGC
    One thing that immediately springs to mind is a bullet shaped pellet with say an aluminium core sheathed in lead, so that it weighs the same as say a .177 heavy ie. 10.34g?
    Forget about the difficulties of manufacture for a minute, would this theoretically get the cma in a better place?
     
    gdavison likes this.
  5. Ballisticboy

    Ballisticboy Active Member

    Joined:
    Jan 4, 2019
    Messages:
    74
    Location:
    Maidstone
    Cma would have been higher on the old sabot pellets which I think had some form of boat tail as well which would increase it further. Unfortunately everything else about the sabot pellet was wrong. According to calculations I carried out at the time the sub projectile as gyroscopically unstable with usual air gun twist rates. The designer seemed to have forgotten that sub calibre projectiles need higher twist rates than full bore ones of the same design. There was also the problem that the sub projectile was often not in the centre of the bore giving massive yaw rates and random lateral velocities to say nothing of the sabot separation problems. There are limits to what a large Cma can achieve.
    The problem with using a lead sheath bullet style would be the transverse compared to the axial moments of inertia which would not be favourable. A .177 10 grain version of the pellet in my avatar was made and fired. The plastic could be replaced with aluminium but the weight would increase and there seems little point since the plastic was not in contact with the barrel
     
  6. C.Eaton

    C.Eaton Confirmed Anschutz Nut...

    Joined:
    Aug 9, 2011
    Messages:
    1,374
    Location:
    Hockley, UK
    Club:
    Springfield / TEGC
    Ok again thinking theoretically, how about a spun moulded lead bullet that was completely enclosed but had a hollow core to keep weight down?
    Or alternatively moulded solid but then carefully drilled out at the back then plugged?
     
  7. dave croucher

    dave croucher FT, the sport where simple becomes complicated

    Joined:
    Aug 27, 2009
    Messages:
    540
    Location:
    dartford
    Tried this when i was 16 with home made LEM Spitzers and an ASI Statical semi recoiless. Dunno about the ballistic properties but they made BIG dents in the brother's tonka toys!
     
  8. terryn

    terryn Active Member

    Joined:
    Oct 26, 2016
    Messages:
    114
    Location:
    ASHFORD KENT
    Club:
    Kent Woodsmen
    You mean you were really once 16,were'nt always old then.
     
  9. C.Eaton

    C.Eaton Confirmed Anschutz Nut...

    Joined:
    Aug 9, 2011
    Messages:
    1,374
    Location:
    Hockley, UK
    Club:
    Springfield / TEGC
    Why am I not surprised, then I was shooting up my brother's Action men figures with a Webley Junior pistol and that didn't end well for them either...:D
     
  10. Ballisticboy

    Ballisticboy Active Member

    Joined:
    Jan 4, 2019
    Messages:
    74
    Location:
    Maidstone
    Any projectile which has lead or any other relatively high density material over its full length will have a high value for the transverse moment of inertia which, when combined with relatively high values of Cma, will need a higher twist rate for gyroscopic stability than is normal in an air gun. The only way to improve the stability with a fixed twist rate will be to reduce the value of Cma which negates much of the point of using a bullet type shape and will still not work very well due to the high inertia.
     
  11. Adam

    Adam Well-Known Member

    Joined:
    Jan 5, 2009
    Messages:
    1,056
    Location:
    Leeds
    Club:
    Redfearns & the UBC
    What would be the "optimum" twist rate for the theoretical super pellet in your avatar? And what would it be for the usual JSB suspects? Assuming .177 12 ft.lbs
     
  12. Ballisticboy

    Ballisticboy Active Member

    Joined:
    Jan 4, 2019
    Messages:
    74
    Location:
    Maidstone
    The pellet in the avatar was specifically designed to use the usual air gun twist rate of around one turn in sixteen inches. It would be somewhat different now if I were to try it again.
    In previous work I have done on twist rates the same twist rates are about right for the JSB family. BARREL TWIST RATES
     
    Last edited: Mar 26, 2019
    Adam and C.Eaton like this.

Share This Page

  1. This site uses cookies to help personalise content, tailor your experience and to keep you logged in if you register.
    By continuing to use this site, you are consenting to our use of cookies.
    Dismiss Notice