Contents
Form Factor
The Form Factor of a bullet is a value that is determined by comparison of the retardation of the bullet in question with the retardation of the standard projectile for which a particular Ballistic Retardation Table was made.
While the form factor of a bullet is best determined by experimental firing tests, a function exists that closely estimates the factor for pointed jacketed bullets from the shape of the bullet nose that is presented toward the ballistic wind.
Using a modified version of this function can be used to determine form factors for cast bullets.
That nose shape of a tangential ogive bullet may be defined and given a value by determining the Ogive Radius of the nose curve.
Use of the value of the Ogive Radius in a function will return a pointed bullet form factor value for the G1 Resistance Table as follows:
F = G1 Form Factor.
R = Ogive Radius in Nose diameters (Radius of the ogive in inches / base of the ogive in inches)
F = 2 / R * Square root of ( ( 4 * R - 1 ) / 7) (Basic function to determine the form factor of tangential ogive sharp pointed jacketed bullets)
( for use with the Average Ogive method outlined below, substituting 6.5 for the divisor 7 in the above equation works well)
A blunt or flat point on a bullet will greatly increase the value of the form factor and must be considered when the calculations are made.
The cross sectional area of the shoulder or driving band of cast bullets will also increase the form factor value.
The length of a cast bullet in proportion to it's length and attendant grease grooves and irregularities will increase the form factor value.
Each of these four aspects of the bullet will have a proportional influence on the form factor value.
The tip or meplate, whether it be round or flat, at cast bullet speeds may be represented as a hemisphere or, round nose, which has a calculated Ogive Radius of 0.50.
A method that seems to work well is to obtain an average Ogive value derived from the Ogive and the tip , this average being determined by the percentage of the cross-sectional area of each portion that is being presented toward the ballistic wind.
The form factor of the shoulder or driving band may be represented as having a form factor similar to a flat-faced wad-cutter bullet. This calculates out to a value of 2.3.
1. To determine the Average Ogive Radius AOR
2. Start by determining the total area of the bullet being presented to the wind.
BD = Shoulder or Driving Band Diameter
AB = Cross sectional area of the bullet
AB = BD * BD / 4 * Pi ( nose or ogive base diameter * nose or ogive base diameter / 4 * 3.141593 )
3. Determine the area of the meplate presented to the wind
TD = Diameter of the Tip or Meplate
AT = Cross sectional area of the Meplate
AT = TD * TD / 4 * Pi ( tip diameter * tip diameter / 4 * 3.141593 )
4. The total Nose area being presented to the wind
ND = Diameter of the Nose where it joins the bullet
AN = Cross sectional area of the Nose at the base of the ogive
AN = ND * ND / 4 * Pi ( nose diameter * nose diameter / 4 * 3.141593 )
5. The percentage of the Nose Ogive is found ( AN - AT ) / AB = PN ( [area of ogive base - area of tip] / area of bullet = percentage of ogive the ogive presented to the ballistic wind)
6. The Percentage of the Tip Ogive is found AT / AB = PT ( area of tip / area of base = percentage of the meplate or tip presented to the ballistic wind and has an ogive radius value of 0.5 )
7. The Percentage of the Shoulder Form Factor is found ( AB - AN ) / AB = PS ( [area of bullet - area of ogive base] / area of bullet )
8. An Average Ogive Radius value may now be determined.
AOR = Average Ogive Radius
PN = Percentage of ogive
R = Ogive Radius
PT = Percentage of meplate or tip
AOR = PN * R + PT * 0.50 ( average ogive radius presented to the ballistic wind )
9. An Initial Form Factor may now be calculated using the Average Ogive value and the function described above.
IF = Initial Form Factor
IF = 2 / R * Square Root of( ( 4 * AOR -1 ) / 6.5) ( basic form factor function altered for use with the Aerage Ogive Radius method )
Add the percentage value of the Shoulder Form Factor to the Initial Form Factor to find the Form Factor
IF2 = Form Factor of average ogive plus shoulder form factor
IF2 = IF + PS * 2.3
10. In order to bring the form factor into the realm of cast bullet reality it must now be reduced. Another physical characteristic that further affects the form factor is the length of the projectile. The Initial Form factor value needs to be decreased in proportion to the inverse of the square of the ratio of the diameter to the length of the bullet.
11. Bullet Length = BL, Bullet Diameter = BD
12. F, The final Form Factor, is now calculated by:
F = IF * ( 1 - BD * BD / BL / BL )
13. The Form Factor F is now ready to be used in the final Ballistic Coefficient Calculation
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