Drag coefficient of a sphere (shot)

[HogBiologist]

I found the range for th drag coefficient for a sphere (.07 - .5) and a calculator for the Drag coeff and found a #7 HW to have a Cd (drag co) of Cd=.127

Now that I have a range and a possible exact measure I can plug it into a Ballistic Coefficient equation.

In reply to:
The ballistic coefficient (BC) of a projectile is a measure of its ability to overcome air resistance in flight. It is given by the mass of the object divided by the diameter squared that it presents to the airflow divided by a dimensionless constant i that relates to the shape. It is inversely proportional to the deceleration—a high number indicates a low amount of deceleration, so a bullet with a high BC will travel further than one with a low BC. Since dense materials give more mass for a given volume or cross-section, bullets often employ lead in their construction.

Ballistic coefficient has units of lb/in² or kg/m².

The formula for calculating the ballistic coefficient is as follows:

(1)C = SD / i = w / id2

where:

C = ballistic coefficient
SD = sectional density
i = form factor
w = weight of object, lb or kg
d = diameter of the object, in or m

Alternately:

C = M / CdA

where:

C = ballistic coefficient
M = Mass
A = cross-sectional area
Cd = Cd factor

(quoted material from Wikipedia online encyclopedia)

I used the above equation that is bolded for my calculation. I had to get the weight in Lbs from grains to get the correct BC.

I located a calculator online that will allow you to enter a list of bullets OR use your own dimensions. Here is the link: http://www.norma.cc/htm_files/javapagee.htm
Use the define your own bullet and enter the weight of the #7 HW in grains (1.96) and the Ballistic coefficients.

I did three tests (one for high, low, and calculated Cd)

Here are the results:


For Cd=.5 the BC=.07 and the equation in norma computed a speed of 922 fps and 4 ft/lbs energy at 100 yds

For Cd=.127 the BC=.28 and the equation in norma computed a speed of 1152 fps and 6 ft/lbs energy at 100 yds

For Cd=.07 the (Ballistic Coefficient)BC=.51 and the equation in norma computed a speed of 1214 fps and 7 ft/lbs of energy at 100 yds


This means that at Standard Atmospheric Pressure the speed of a #7 HW pellet (With a MV of 1301 fps) at 100yds can range from 1214 fps down to 922 fps but most likely has a speed of 1152 fps.

This is good because a #7 HW weighing 1.96 grains only needs to travel at 607 fps to have 1.6 ft/lbs of energy. This program showed that the energy can range from 4 to 7 ft/lbs of energy at 100 yds.
_________________________
Endurance is nothing more than a lack of alternatives!

[HogBiologist]

I am in no way condoning 100 Yard shots. I just quickly copied and posted an old PM from the NWTF site. Considering the message board over there is going the way of the Do Do Bird. I may sit down and try doing the lead in a week or two.

[DirtNap647]

lol you lost me,  but  great info...I think lol

[Cut N Run]

First, let me say that all my life I am a C math student...some things I just don't get numbers-wise.  You can run, but you can't hide.  I understand the formula here, I just can't plug the numbers in and make them work out right to answer my questions.  Regardless, By the numbers and by my own experience, those Hevi #7s are definitely some seriously bad news for turkeys.

Thank you for posting this.  Physics is not my favorite subject, but I love seeing the way things perform on paper in addition to real life.

Here's the questions I have;

How would those numbers be calculated for half that distance (50 yards instead of 100 yards) downrange (hunting range)?  Since the muzzle velocity is where the energy of the shot charge (pellet speed) will always be greatest and the shot progressively loses energy/velocity with drag (time and distance), is there a sliding scale to calculate ft/lbs along the entire flight path? 


A lot of Hevi shot pellets are not perfectly spherical in shape either, so the variance in calculations depends on drag of the shape of each individual pellet, but we won't go there.

I'm glad there won't be a test on any of this.  All you really need to know is that HTL shot really slams a turkey.  They may be pricey, but for no more than I shoot during turkey season, I love how effective that Hevi shot is.  I can only imagine how awesome these same numbers would look with TSS.

Jim

[HogBiologist]

It is easy to find the KE of all shot types/sizes at various speeds. I have done that already. The unknown is deceleration. I had found that a perfect sphere could have a range of drag coefficients. I ran the high and low in the formula an got a range of speeds. I had to do 100 yds because that is the shortest distance the calculator woul do. I was big into fed HW #7 when I did these calculations. I used that material (15 g/cc density) information for the calculations. This was done several years ago, but I may try to run the formulas for lead soon. Right now I am in the process of moving and turkey season opens next weekend.

[Cut N Run]

Thanks for the reply.  Good luck this season.

One of my best friends lives in N.W. Arkansas and he's fired up for turkey season.  He'll be crossing over to enjoy some Missouri turkey hunting too.

Jim

[Rapscallion Vermilion]

Fun calculations, thanks for posting this.   I thought the Cd of small spheres (2.5 mm, as small as a #7 shot) well below sound speed (~ Mach 0.5) was well established to be around 0.4 to 0.5, based on experiments.  [Miller & Bailey, 1979]  For higher velocities, closer to the sounds speed, it goes up.   One reason shooting high velocity loads doesn't buy you a lot at longer ranges.

[Strick9]

Hog,

Great work brother! Inquiring minds want to know!!

The main reason I keep running the Fed HW 7s isn't for the Turkeys , its what they can do to a yote at 75 as he is sneaking in.

[HogBiologist]

I really didn't worry about hevishot velocities, since most everyone was worried about the fed HW 7's killing abilities out past 40. If you don't kill with the Federal HW #7's it is the fault of the shooter, not the shell.

Also, I always hear about "pellets in the head and neck".  The entire head and neck are not the vitals. The Central Nervous System (CNS, spine and skull) is the lethal area. I don't count flesh wounds to the neck. I only count direct bone shots. I boiled down a turkey neck after I  it one year. I reconstructed it and put it on a copy machine. Now I have a perfect target for practice. That is why when I post pellet counts I give #'s in the 10 and hits to the CNS.

[HogBiologist]

I was in a hurry last night, could a moderator move this to the turkey gun section please.

[outdoors]

      

[HogBiologist]

Between Reynolds numbers, drag coefficients, drag force, etc.; my head is swimming. I should have it all figured out in a week or 2. From what I have learned so far, in a sphere the math is as follows.

First you get the Mach number and Reynolds Number

Those numbers helps you get drag coefficient (Cd)

Cd is used to get ballistic coefficient (Bc)

Bc can be plugged in to a calculator to get deceleration of pellets over distance from a shotgun.

I already have Kenetic energy of various materials at various speeds.