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Pellet Spin Damping

Discussion in 'Anything Airgun Related' started by Ballisticboy, Aug 4, 2014.

  1. Ballisticboy

    Ballisticboy Posting Addict

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    This is one which is only going to be of interest to real tech heads wanting to try to understand pellets so be warned.
    Some time ago one of the members of a US forum published some data on measured twist rates on pellets at different ranges. He did it by marking the front of some pellets with a felt tip I think and then firing them through two paper screens set up at different ranges. The screens were always the same distance apart and the pellets left marks on the paper from which he could measure what angle the pellet had turned through between the two screens. From these measurements he could then work out the twist rate at the different ranges. The screens were set up at 2, 225, 300 450 and 600 feet away from the gun. The gun was a BSA (I think, it certainly had a BSA barrel) firing 0.25 JSB pellets at 890 ft/sec. There were chronographs at the muzzle and at the end of the range. In a fit of enthusiasm I foolishly volunteered to work out spin damping coefficients from his data. This is a copy of the report I made on that forum.
    The measured twist rates were as below.
    2 ft = 1 rev per 18.9 inches ie., 1:18.9 (assumed to equal rifling twist rate of the BSA 0.25 cal barrel).
    So:
    2 feet = 1: 18.9
    225 feet/ 75 yards = 1:15.9
    300 feet/ 100 yards = 1:14.9
    450 feet/ 150 yards = 1:13.2
    600 feet/ 200 yards = 1:12.8
    The measured pellet speeds were 890 ft/sec at the first point and 506 ft/sec at the end point. The pellets were 0.25 JSB King. To obtain the moments of inertia and the pellet weight I have a small computer program into which I can put the internal and external shape. If the predicted weight is about right then the moments of inertia should be pretty close. The estimated weight was 25.32 grains (actual 25.39 grains) so the estimated spin inertia of .0696 grm cm[SUP]2[/SUP] should not be too far out.
    The next problem is to establish the actual pellet spin rate at each point. This can only be done if we know the pellet speed at each point. To get the speed I took a standard domed pellet drag coefficient curve which was used in a data pack for a six degree of freedom trajectory model. This was calibrated to match the measured figures. The resulting drag coefficients are rather on the low side but match the measured velocity drop over the 200 yards range.
    [​IMG]

    Once I had a drag curve I could then get estimates of the pellet speed at each point and from that the estimated spin rates from the data.

    [TABLE]
    [TR]
    [TD="class: xl63"]Range[/TD]
    [TD="class: xl63"]Speed[/TD]
    [TD="class: xl63"]Spin[/TD]
    [/TR]
    [TR]
    [TD="class: xl63"]Yards[/TD]
    [TD="class: xl63"]ft/sec[/TD]
    [TD="class: xl63"]Rev/sec[/TD]
    [/TR]
    [TR]
    [TD="class: xl63, align: right"]0.667[/TD]
    [TD="class: xl63, align: right"]890.1[/TD]
    [TD="class: xl63, align: right"]565.1[/TD]
    [/TR]
    [TR]
    [TD="class: xl63, align: right"]75[/TD]
    [TD="class: xl63, align: right"]706.1[/TD]
    [TD="class: xl63, align: right"]532.9[/TD]
    [/TR]
    [TR]
    [TD="class: xl63, align: right"]100[/TD]
    [TD="class: xl63, align: right"]660.3[/TD]
    [TD="class: xl63, align: right"]531.8[/TD]
    [/TR]
    [TR]
    [TD="class: xl63, align: right"]150[/TD]
    [TD="class: xl63, align: right"]578.1[/TD]
    [TD="class: xl63, align: right"]525.5[/TD]
    [/TR]
    [TR]
    [TD="class: xl63, align: right"]200[/TD]
    [TD="class: xl63, align: right"]506.3[/TD]
    [TD="class: xl63, align: right"]474.7[/TD]
    [/TR]
    [/TABLE]
    The numbers are not an exact match at start and finish but are close enough. Now it was a case of putting values of spin damping coefficients (Clp) to match the measured spin rates at each range. To get an exact match the coefficients needed to be as below.
    [TABLE]
    [TR]
    [TD="class: xl65"]Mach[/TD]
    [TD="class: xl65"]Clp[/TD]
    [/TR]
    [TR]
    [TD="class: xl65, align: right"]0[/TD]
    [TD="class: xl65, align: right"]-0.0485[/TD]
    [/TR]
    [TR]
    [TD="class: xl65, align: right"]0.517[/TD]
    [TD="class: xl65, align: right"]-0.0485[/TD]
    [/TR]
    [TR]
    [TD="class: xl65, align: right"]0.518[/TD]
    [TD="class: xl65, align: right"]-0.0055[/TD]
    [/TR]
    [TR]
    [TD="class: xl65, align: right"]0.59[/TD]
    [TD="class: xl65, align: right"]-0.0055[/TD]
    [/TR]
    [TR]
    [TD="class: xl65, align: right"]0.591[/TD]
    [TD="class: xl65, align: right"]-0.0001[/TD]
    [/TR]
    [TR]
    [TD="class: xl65, align: right"]0.632[/TD]
    [TD="class: xl65, align: right"]-0.0001[/TD]
    [/TR]
    [TR]
    [TD="class: xl65, align: right"]0.635[/TD]
    [TD="class: xl65, align: right"]-0.017[/TD]
    [/TR]
    [TR]
    [TD="class: xl65, align: right"]1[/TD]
    [TD="class: xl65, align: right"]-0.017[/TD]
    [/TR]
    [/TABLE]
    The values are jumping around far too much to be satisfactory so I took a typical spin damping coefficient/Mach number curve for a small calibre projectile and calibrated it to obtain a best fit. The values I obtained are here.

    [TABLE]
    [TR]
    [TD="class: xl65"]Mach[/TD]
    [TD="class: xl65"]Clp[/TD]
    [/TR]
    [TR]
    [TD="class: xl65, align: right"]0[/TD]
    [TD="class: xl65, align: right"]-0.0171[/TD]
    [/TR]
    [TR]
    [TD="class: xl65, align: right"]0.6[/TD]
    [TD="class: xl65, align: right"]-0.0159[/TD]
    [/TR]
    [TR]
    [TD="class: xl65, align: right"]0.8[/TD]
    [TD="class: xl65, align: right"]-0.015[/TD]
    [/TR]
    [TR]
    [TD="class: xl65, align: right"]1[/TD]
    [TD="class: xl65, align: right"]-0.0135[/TD]
    [/TR]
    [/TABLE]
    These values of Clp are about half of what you would expect for a bullet. This is probably due to the pellet shape compared to a bullet.
    One criticism of the method so far is that if the drag law is wrong the estimated spin rates will be wrong in the intermediate positions. To look at this effect I took a constant drag coefficient (equivalent to a constant BC) and repeated the exercise. Sure enough the estimated speeds and spin rates were different as you can see here. Again the numbers are not exact matches but it will make little difference to the final result.

    [TABLE]
    [TR]
    [TD="class: xl65"]Range[/TD]
    [TD="class: xl65"]Speed[/TD]
    [TD="class: xl65"]Spin[/TD]
    [/TR]
    [TR]
    [TD="class: xl65"]Yards[/TD]
    [TD="class: xl65"]ft/sec[/TD]
    [TD="class: xl65"]Rev/sec[/TD]
    [/TR]
    [TR]
    [TD="class: xl65, align: right"]0.667[/TD]
    [TD="class: xl65, align: right"]890.7[/TD]
    [TD="class: xl65, align: right"]565.5[/TD]
    [/TR]
    [TR]
    [TD="class: xl65, align: right"]75[/TD]
    [TD="class: xl65, align: right"]720.8[/TD]
    [TD="class: xl65, align: right"]544[/TD]
    [/TR]
    [TR]
    [TD="class: xl65, align: right"]100[/TD]
    [TD="class: xl65, align: right"]671.3[/TD]
    [TD="class: xl65, align: right"]540.6[/TD]
    [/TR]
    [TR]
    [TD="class: xl65, align: right"]150[/TD]
    [TD="class: xl65, align: right"]582.3[/TD]
    [TD="class: xl65, align: right"]529.4[/TD]
    [/TR]
    [TR]
    [TD="class: xl65, align: right"]200[/TD]
    [TD="class: xl65, align: right"]505.2[/TD]
    [TD="class: xl65, align: right"]473.6[/TD]
    [/TR]
    [/TABLE]
    However, the estimated best fit spin rates remained almost exactly the same. The results for the two methods are summarised below.
    [​IMG]
    The loss in spin rate on the best fit curve can be seen to be pretty linear which throws up another possibility. By measuring spin rate as was done at different points and knowing our starting and finishing velocity we can estimate velocity at all the different points in between. The velocities obtained, using this method, are compared to the velocities from the estimated drag law below.
    [​IMG]
    Once we know our velocities and distances we can then, using the standard flat fire equations, estimate Cd and if wanted BC. (though why anyone would want BC once they have Cd is beyond me)
    I did this and obtained the Cd shown below.
    [​IMG]
    These Cds look not too bad except for the lowest speed one which is obviously wrong (unless the JSB had suddenly turned itself into a streamlined boat tailed projectile).
    In summary, the method of measuring spin shows potential for giving good usable data. The spin damping coefficients needed to match the spin rates are much lower than I expected and can probably be used for any round head diablo pellet. Gyroscopic stability factors increased (decreased?) from -1.7 at launch to -4.1 at 200 yards. (negative because the pellet is aerodynamically stable) This shows that as pellets travel down range they become more gyroscopically stable, not less as many think. Pellet instability at longer ranges is not due to a lack of spin stabilisation, probably just the opposite in fact.
    One thing to note is that the Clp values given are in European/modern US format not the old US format and use PD/2V for non-dimensional coefficients. I have never seen any spin damping data for pellets anywhere else so this data could be unique.
     
  2. Ganton Gunner

    Ganton Gunner Super Duper Moderator Staff Member Mod/Admin

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    do I get a prize for reading it all even if I got lost 1/2 way through
    p.s. good write up :up:
     
  3. Ballisticboy

    Ballisticboy Posting Addict

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    Well I did warn you at the start. :)
     
  4. Ganton Gunner

    Ganton Gunner Super Duper Moderator Staff Member Mod/Admin

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    yes but its like when you see a box saying don't open :rolleyes:
     
  5. Ballisticboy

    Ballisticboy Posting Addict

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    I know what you mean. I had a car years ago and when I looked under the dashboard there was a big red button with nothing telling you what it did.
     
  6. GPConway

    GPConway Busy Member

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    Maybe two reasons …
    a) BC is the intermediate coefficient that allows us to interpolate/extrapolate trajectory details for pellets with the same generic shape but with different masses and/or form factors,
    b) the instantaneous Cd value varies with velocity whereas the BC value does not (provided that the correct drag function is applied).

    Controversial or what? :D

    I've seen your "standard domed pellet drag coefficient curve" before (maybe on the same US forum as mentioned above) but it doesn't fit real-world range-velocity data very well. Could that be a significant source of error?

    George
     
  7. SteveO

    SteveO Top Poster

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    I'll leave this one to the egg heads!

    Good work though BB. :up:
     
  8. loki_79

    loki_79 Donator

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    Is there any significant reduction in spin rate due to penetration of the first sheet of paper?
     
  9. rabbitraider1

    rabbitraider1 Engaging Member

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    Please say you found out what it did, if not please tell me where I can find said car
     
  10. Ballisticboy

    Ballisticboy Posting Addict

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    Eventually found out it was a relay reset button. It was bright red and about 1 inch across. It was in a Rover SD1. Yes, I had to press it.
     

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