Yes, I've gone quiet - I'm following along... and doing some background work. Almost have a high speed strobe and photo/acoustic-trigger built! I'm hoping to be able to provide some classic "lead-glans-penetrating-pumpkin" shots for the gallery. Should be able to get nice attitude-on-impact shots as well (provided I can hit the target). Projectile shape is slow due to a lack of either tools or slinging space depending on where I am. I'm away until the 2nd, but might be able to convince my "almost as crazy as me" family to assist in some sling performance evaluation while I'm visiting. Northern Alberta (prairie) is good sling country. Might finally be able to recover some projectiles!

And what about our "ball series" experiments? Surely some of you guys have some tennis/golf/base/softballs?

Hey and didn't we have some stop-motion pictures promised? David_T mentioned them a while back.

Matthias

ROUGH PROJECTILES

Although it´s somewhat incredible, the rugosity of the projectile has to do with the range, in the way of the golf balls, extending the reach, although not as much as in them because golf balls have less density and are affected in greater measure by this effect. Let us consider first a stone spherical projectile.

Re = Air density * Velocity * Diameter/air viscosity

Considering always the same projectile  Re= K1 * V

On the other hand :

Drag force Fd = Cd/2 *  air density * cross section * V^2  (CD = drag coefficient)

For the same projectile: Fd = K2 * CD * V^2

The drag force will vary then with the speed of the projectile, first by itself and secondly by its dependency of CD that varies with Re, that varies as well with V. The relation of CD with Re comes given from experimental form by the curves of Achenbach for spheres:



The upper curve, corresponding to smooth spheres, has an almost constant value around 0,5  until arriving at the point in which the speed of the projectile causes a turbulent air flow, falling drastically the CD. Nevertheless, the required speed for this it is higer than the maximum one that can reach a slinger, reason why hardly we will enter this favorable zone.

Nevertheless, if the sphere is rough, we see that the corresponding curve provides lower values of CD, now in the margin of speeds of the slinger. For that reason the air drag force will be smaller and greater the range. The curve shown corresponds to a projectile of rugosity K/D = 0,01250, wich expresses the ratio between the depth of the holes and the diameter of the projectile. Thus, for a projectile diameter of 4 cm the holes would be of 0,5 mm. A projectile like this is easy to make striking a smooth-stone around all their surface with another stone, or with a rounded hammer.

In order to calculate the increase of range of this rough projectil vs a smooth or polished one we will have to make approximated calculations, since the speed of the projectile will be changing as it goes being restrained by the air, and therefore will be changing its CD. In the picture I have selected two zones that corresponds to the variation of speed for projectiles thrown with two initial speeds: 55,55 and 120 m/s, that are the speeds of launching of the considered average slinger and of a recordman.
I have used the Simulator to get in both cases an aproach to the end speed of the projectile, that could be of about 25 m/s and 65 m/s respectively. As it is  very awkward to evaluate the effect of the changing Cd, I have taken an average Cd for each zone, as it is indicated in the figure. For a projectile of 100 gr. the calculated values of the range are:

Speed.......................55,55...........120 m/s
CD (Smooth) ........... 0,5............... 0,47
CD (rough)............... 0,272............0.37
Range (smooth )......167............... 353 ms
Range (rough )........ 208............... 409

We see that for the average slinger the increase of range with rough projectile is of 25%. The recordman, nevertheless, is penalized by the high end speed of the projectile, that does not take advantage of the zone of lower Cd.

The following calcualtions will be with lead projectiles, that surely also are influenced by this rugosity effect  (I progress little by little, but soon I´ll discover the carefully kept secret of Jurek... but I shall not disclose it   )

Quote:


Hondero,

Ohh no! It isn't truth. I have just tried to share it all time. But maybe... a bit clumsily

After your last lecture, I should try dimpled glandes again.

Jurek

GLANDES

Let us consider finally the famous effect of the shape and performances of glandes. The more trustworthy data on drag coefficients I´ve found are from H. Rouse (1946), and come expressed in the following curve:





The ellipsoid of the curve has a ratio between axes smaller than the typical glandes, whose average ratio could be 1:2.4, been the most fat of them about 1:2. Also the glandes have the ends more pointed and are more aerodynamic, reason why the values calculated here would be the minimal corresponding to a glans.

I consider again the two slingers of reference and their 100 gr projectile.  We obtain the following values:

Initial speed......... 55.55......... 120 m/s
CD......................... 0,1.............0.06
Range.................... 300............1280 ms

The increases of range in relation to spherical smooth projectiles are 31 y 116 % respectively. We remember that the speed of 120 m/s of our recordman is a little excessive, reason why the probable reach (for 105 m/s) would be of 1010 m. Also we have to not forget that this range is for a perfect orientacion point-first of the projectile, what will not happen exactly in practice although we use special throwing tecniques. In regard to the effect of rugosity I have not found any data, but given their aerodynamic shape, the rugosity could not play an important role, since the trail left by the glans is enough narrow and it would not be reduced as much as for the spherical projectile.

And since we are speaking of glandes we can consider also the glandes of stone that have been used in different times and places, and the clay glandes too that comes from the warlike origin of the sling (Neolithic). The values of Cd are the same that for lead glandes and we considere also the same projectile weight of 100 g. and the two speeds of reference.

Speed...........55.55 m/s.............. 120 m/s
Stone............ 277 ms..................1072 ms
Clay...............267 ms.................. 997 ms

Surprising! There is no excessive difference between glandes of lead, stone or clay!

Arrived at this point it is the moment for summarizing and put together in a table the results of the different calculations made with projectiles of different density, rugosity and shape. The data are corrected for a max. initial speed of 105 m/s.



RANGES WITH PROJECTILE OF 100 GR.
ACCORDING TO DENSITY, RUGOSITY and SHAPE

Initial speed(m/s) ..................55.55..........105
Spherical smooth stone.................167.............319
Spherical rough stone...................208.............508
Spherical smooth lead...................229.............516
Spherical rough lead.....................267.............818
Elliptical lead (1:1.8 ) ..................300.............1010
Elliptical stone (1:1.8 ) ................277..............875
Elliptical clay (1:1.8 ) ..................267..............821


One first conclusion is the great importance of the characteristics of the projectile, that can triple the range for the same weight and are so  important as the power of the slinger.

Another observation is that glandes have an extraordinary performance, been their shape more important than the projectil density.

And a last one, among the many that can be done calculating ratios between the different modalities of projectile, is that the rough spherical lead projectiles can compete with glandes if these are thrown not well oriented point-first.

This takes us to the study of the throwing techniques and to the Yurek´s graphs to study the more suitable position. But that will be another day, after a rest of at least one month or so , when the secret to get the possible new Guiness record with lead (around 1000 m) will be eventually revealed  .

Let me commend all of you on this site- very informative. 

I have a question that you might be able to answer.  Doesn't a Glans shaped projectile need to spin in a fashion akin to a rifle projectile in order to fly true?  If it is not spinning along its long axis, the shape seems to ensure that it will spin along its short axis and the same force that aids in rifling would now cause it to veer- assuming a symmetrically weighted glans.

I'm not sure how the spin would be imparted, but if it exists it probably has to do withthe release from the pouch.  Are the pouches on ancient slings different for "bullets" than for balls?

Thanks,

Paul

Quote:


I use that method baseball step method. I call it the womens fast pitch softball throw. You get some longer ranges with it i believe.

i was bord during study hall today so i came up with a  formula to calculate the speed of the projectile( not to bad for a freshman algebra 1 student) and looking for insite if it is correct.  .  then multiply the lenth of the sling, Both sides including the pouch, by pi.  you then divide this number by the time the total time it takes for the sling to make a full rotation.  this should give you the feet per second for the stone.  i couldn't get outside to get an accurate reading ( Ohio rain in febuary, suposed to snow 6 inches tomarro) but my calculations for indoors is about 90 fps but keep in mind that i just started slinging about 3 days ago so i probubly can get much higher the longer the sling and fast the swinging

OK, How do you do a "Bernini"? ???