Need Help Finding Ballistic Formulas

[pbft]

I'm looking for the accepted formula for calculating BC from velocity at the muzzle and at a set distance. I've found various on-line tools, but I'd like to do the math myself.

Here's a typical case I'd like to be able to calculate:

Muzzle Velocity: 1021 fps
Velocity at 50 yards: 795 fps
BC = ?

If I have the correct formula, I should also be able to solve for velocity at any distance given BC and muzzle velocity.

I've worked with the Sellier & Bellot formula. I've found the GA curve CD data and I've tried to use that to back into the published data from the HAM pellet tests - no luck.

[PikeP]

(0.003594 * Distance between velocity recordings) / ( SQRT(Velocity 1) - SQRT(Velocity 2))/2

= .024

[pbft]

(0.003594 * Distance between velocity recordings) / ( SQRT(Velocity 1) - SQRT(Velocity 2))/2

= .024

Thanks - that gives a reasonable number with distance in yards and velocity in FPS. Does the 0.003594 value take into account the GA drag model or is it just a combination of unit conversion and air density?

[rsterne]

I also would be interested in the source of that formula, and what the constant contains.... 

According to Chairgun, the BC (G1) is 0.0334.... and the BC (GA) is 0.0337.... Even using the antiquated constant drag model (Cd = 0.22), the BC would be 0.0274.... This assumes the testing was done at ICAO conditions....

The use of a constant confuses me, because the drag of any projectile is not a simple curve, but increases many-fold in the transonic region....

Bob

[larspawn]

Following.  Wondering if it is altitude dependent because how would you know air density?

[rsterne]

Yes, the air density is important in determining the BC at standard conditions....

Bob

[pbft]

Thanks, Bob - I'm hoping that your interest scares up the details on this. My understanding of BC is this:

• BC is the ratio of the drag of given projectile to a 'standard' projectile of the same profile (actually, the reciprocal of the ratio so that larger is better)
• G tables contain the CD of each of several typical profiles at different velocities

Therefore, in order to calculate BC from change in velocity, you'd have to integrate CD from the correct G table across the range of velocities in question.

I found a table of CD values for the diabolo  profile (the GA curve, as opposed to G1 or G7 that are more commonly used). I built a spreadsheet that calculated velocity loss in 1 foot increments using the appropriate CD values from the GA table for the velocity at each increment. I can fudge it to get a near-perfect match to chrony data, but I end up with a BC value that doesn't match anything.

The formula that PikeP provided gives a great match for BC to what HAM calculates, but it doesn't appear to take into account the GA curve.

[pbft]

I can't seem to embed images in my posts, but I'll try as an attachment. Here's what I'm trying to do:

Prepare a performance summary for each pellet of interest showing it's performance in each of my rifles. I'd like to use my own test data if available, third-party test data next, or manufacturer's data if that's all that I have. I calculate a trajectory based on muzzle velocity and ballistic coefficient, then use that to see where I should zero my scope for that pellet.

[rsterne]

Generally you don't bother integrating the Cd values for the G1 model (or whatever you choose).... you just use the Cd for the average velocity range to match the range you used....

The key is calculating the Cd, which can either be done using F=ma, or there is an alternate formula using the natural log LN, they seem to produce identical results.... WATCH YOUR UNITS.... and don't forget to use your local air density during the time of test.... It is better to work in  Mach Number (corrected for your temperature, of course).... because then if will be accurate at ICAO conditions (or shooting conditions, as Mach depends on temperature).... Note the SoS does not depend on altitude and air density, only on temperature....

Variables include initial and final velocity, distance between, frontal area of projectile, mass of projectile, and air density.... and I say again, WATCH YOUR UNITS....

Bob

[subscriber]

Hi pbft,

Just to make things more complicated, BC depends on the pressure at which pellets are launched, and the abruptness of that launch.  This is because a higher peak pressure balloons a pellet skirt more than a gentle launch down a long barrel, even if the same muzzle velocity is reached.

A "tight" barrel will result in the pellet having less frontal area, effectively raising its sectional density and thus BC; all else being equal, compared to a barrel that is "loose".  If the barrel is choked, then it is the choke diameter that matters here, rather than the breech (or un-fired pellet).

This current thread, from this post (including the one quoted inside it) discuss pellet distortion affecting BC:  https://www.gatewaytoairguns.org/GTA/index.php?topic=174899.msg155974749#msg155974749
There have been previous threads that addressed that particular topic, but I would have to dig to find them.

My advice is to shoot your preferred pellets from your guns.  To measure the velocity at a number of discreet ranges - the more, the better.  To capture actual pellet drop at the same time; and to use the combined data to interpolate and extrapolate pellet drop and energy, for the rest of the range intervals you care about.

There seems to be so many opinions about which BC models are better for pellets.  There seems to be some agreement in that diabolo pellets don't obey existing drag models very well; and that velocity ranges make a huge difference to the effective BC.   Another common opinion seems to be that Chairgun is pretty good.  Or perhaps it was some other software .

The point of ballistic tables is to get you on paper, rather than to enable you to shoot rats in they eye, at any range from 2 to 75 yards.  If only something would precisely calculate the right number of clicks for you...

[PikeP]

FWIW the source of the formula I provided is from Pyramid Air... that is not to say it's credible...

[rsterne]

That explains it, Matt.... Their BC calculations are base on an antiquated constant BC model.... Think of the G1 drag curve as a straight line, and you get the idea.... It works OK up to about 800 fps, starts diverging quite a bit at 900, and is useless at over 1000 fps.... 

Bob

[PikeP]

Good to know. I shoot between 850-900 primarily which explains why it always worked for me. That is to say within reason...being that the Ballistic Coefficient of a projectile is not static through-out its range so trying to formulate such in a simple fashion would be quite the challenge that someone greater than I would have to be up for. I can see using multiple bc's if shooting at a particularly long range, but for the most part a static bc that is within reason will 'get ya there', or at least me. Shooting beyond 100 yards I certainly would opt to use at least 2 bc's, one to get it to 100~, and one beyond. The ballistic software I have worked on a bit will likely integrate a multi bc function in the far future much like sterlok currently has, but as I only shoot under 100 I lack much interest pursuing it for now, nor have I ever even pondered setting up to look at the bc of my projectiles between 100-150yd.

My ballistic software uses an adjusted bc which takes into account air density and temp ect...

[Tygon]

just do the shooting for yourself.  no better way to do it.

some say it takes too much time.  well, how much time have you spent trying they way you are now?  like others said, the burst of air in a short barrel compared to a long barrel..etc..
i use several ballistic calculator apps to get close, but adjustments are always made when i do the true shooting for myself.  you need to also learn how to adjust in the field.  all my guns including a gauntlet, compatto, and fx wildcat shoot high when the temps rise and sun is beating on the gun.  so at that point all numbers are off.