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Author Topic: My confusion with BC formulae... Help?  (Read 116 times)

poorman plinker

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My confusion with BC formulae... Help?
« on: August 16, 2017, 10:37:52 AM »
Here is what I am trying to sort out... Too many formulae, not enough grey matter.
Anyone have an idea of how to organize these into a logical order???

Some require knowing the BC of Df to get the factors for the formulae that come before. I am looking for a way to use a hand calculator and not just load info into on-line programs.

I know:
BC = SD/FF
SD = W / d ^2
FF = Cd/Cg
Cg = G coefficcient off of charts

So I  still need to determine Cd and Drag force

What I do not know:

for Cd
Cd = 2/n*sqrt(4n-L/n)
Where:
Cd= Coefficient of drag (dimensionless)
n = ogive in caliber for bullets
L = Pellet length (inch)
********************
Cd = 8/SD*v^2*(Pi*d^2)
Where:
Cd = Drag coefficient (dimensionless)
SD =  Sectional Density (dimensionless)
v= Projectile velocity at range (FPS)
Pi = 3.14159
d = Diameter of projectile (inches)
****************************
Cd = Df / .5 *(a* Ad* v^2) or
Cd = 2*Df/a*Ad*v^2
Where:
Cd = Drag coefficient (dimensionless)
Df = Drag Force (ftlb)
a = Reference Area (ft^2)
Ad = Density of the air (lb/ft^3)
v = Velocity with respect to the object and fluid (FPS)
*********************************
    c d = 2 F d/ ρ u 2 A
where:
 F d  is the drag force, which is by definition the force component in the direction of the flow velocity,[6]
    ρ  is the mass density of the fluid,[7]
    u  is the flow speed of the object relative to the fluid,
    A is the reference area.

For Df
Df = v^3
Where:
Df = Resistance (FPS)
v = Velocity (FPS)
*******************
Df = m(v1-v2/t1-t2)
Where:
Df = Force of resistance (FPS)
m = Mass
v1-v2 = Reduction in velocity (FPS)
t1-t2 = Time over which the reduction was measured
***************************
Df = (1/2 Ad*v^2)*a*(Fc *Rn)
Where:
Df = Drag Force (ft-lb)
Ad = Air Density  (lb/ft^3)
a = Reference Area (ft^2)
v = Flow speed of the object relative to the fluid medium (FPS)
Fc = Form coefficient of the Reynolds number (dimensionless)
Rn = Reynolds number (dimensionless)
************************
Df = (1/2 *Ad*v^2)*a*Cd
Where:
Df = Drag Force (ft-lb)
Ad = Air Density (lb/ft^3)
a = Reference Area (ft^2)
v = Speed of the object relative to the fluid medium (FPS)
Cd = Drag coefficient (dimensionless)
***************************
Df =  Cd*(v*a*Ad*u)
Where:
Df = Drag Force (ft-lb)
Cd = Drag coefficient (dimensionless)
v = Flow speed of the object relative to the fluid medium (FPS)
a = Reference Area (ft^2)
Ad = Air Density (lb/^3)
u = kinematic viscosity of air (ft^2/s)
********************************
Fd = cd 1/2 ρ v2 A
where
Fd = drag force (N)
cd = drag coefficient
ρ = density of fluid (1.2 kg/m3 for air at NTP)
v = flow velocity (m/s)
A = characteristic frontal area of the body  (m2)
************************************
D = qCdA = qCdPi R
q = dynamic pressure filb
Cd drag coef
a reference area sq ft
Pi = 3.14139
R = radius cross section
q= 1/2pv^2
  p = air density lbsec^2/ft^4
v = flow velocity ft/sec




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poorman plinker

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Re: My confusion with BC formulae... Help?
« Reply #1 on: August 16, 2017, 12:12:42 PM »
Perhaps to answer my own question...
Cd = (2*Df) / (Ad*v^2*Fa)
where
Df = m*a
m =  gr / 225120
a = (v1-v2)(inch/sec) / t (sec)
t = Inch distance/(v1-v2/2) (inch/sec)
Ad = air density (gr/in^2)
v = v1-v2/2 (inch/sec)
Fa = a= Pi*r^2 (in^2)
inch Distance of chronos

FF = Cd/Cg
Cg (inch / gr) = G model coefficient at mach # off of charts

SD = W / d ^2 (grain / inch)

BC = SD/FF
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rsterne

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Re: My confusion with BC formulae... Help?
« Reply #2 on: August 16, 2017, 01:14:20 PM »
Your second post is basically correct, but watch the units.... Below are the conventions used for calculating the Df and Cd....

Distances are in feet
Frontal Area is in ft^2 = in^2 / 144
Velocities are in feet/sec
Time is in seconds
Acceleration is in feet/sec^2
Drag Force is in lbs.
Mass is in slugs = lbs / 32.174 = grains / 225218 .... (your 225120 is close enough)
Air Density is in slugs/ft^3 = lb/ft^3 / 32.174 .... (you can look up air density in lb/ft^3 for your altitude, barometric pressure, and humidity)

Cd is a dimensionless number, as is the Cg, so therefore FF is also dimensionless....

SD is calculated from (grains / 7000) / cal^2.... where in this case the weight in grains is converted to lbs., and the caliber is in inches.... The units are "sort of" psi, but since the factor PI/4 is not used, the SD in ballistics is considered dimensionless.... so the BC ends up dimensionless also....

HTHs....

Bob

« Last Edit: August 16, 2017, 01:16:45 PM by rsterne »
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poorman plinker

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Re: My confusion with BC formulae... Help?
« Reply #3 on: August 18, 2017, 10:11:22 AM »
As always, thanks for the feedback... I will adjust the units accordingly.

HTHs?
 8)
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rsterne

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Re: My confusion with BC formulae... Help?
« Reply #4 on: August 18, 2017, 01:03:02 PM »
HTH = Hope That Helps !

Bob
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