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A new topic, Elevation, has been added. It shows the differences in trajectories when zeroing at different atmospheric conditions and how to calculate a trajectory for different atmospheric conditions.

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JBM - Calculations - MPM Terms

Input Data

Altitude: Used in estimating the atmospheric conditions. This value is not used unless the Standard Conditions at Altitude checkbox is checked.
Axial Moment of Inertia: The moment of inertia about the centerline axis of the bullet.
Azimuth: The horizontal (side to side) angle the barrel makes with the line of sight. This value is not generally known and can be ignored if the "Azimuth Correction for zero range" option is checked.
Azimuth Correction: If checked, the azimuth is changed to make the bullet cross the line of sight at the zero range -- zero windage at the zero range.
Barrel Twist: The twist rate (inches per turn) of the barrel. This value is used to calculate stability. It should not be confused with the required twist calculated by Bullet Drag.
Base Diameter: The diameter of the base of the bullet. For boattails, this is smaller than the caliber.
Boattail Length: The length of the boattail from the rear of the bearing surface to the base of the bullet. It is zero for flat base bullets.
Bullet Specific Gravity: The density of the bullet, relative to the density of water (1.0). 10.7 is a commonly used value for jacketed bullets.
Bullet Weight: The weight of the bullet.
Caliber: Diameter of the bullet's bearing surface (that part that contacts the rifling of the barrel), measured in inches.
Cant Angle: The angle of the tilt of the firearm to the right or left from vertical. Positive angles are to the right.
Chronograph Distance: The distance from the muzzle of the firearm to the chronograph used for muzzle velocity measurements. If the muzzle velocity is estimated, enter 0.0 for this value -- no correction.
Core Depth: Distance from the tip of the bullet to the top of the lead (or other material) core.
Core Specific Gravity: Specific gravity of the bullet core
Corrected Pressure: Check this box if the pressure entered is a corrected station pressure. If it is an absolute pressure, leave this unchecked.
Direction: Firing direction in degrees. This is the compass direction the firearm is pointing. North is 0° East is 90°, South 180° and West is 270°.
Drag Function: The drag function to use to calculate the ballistic coefficients. Most commercial bullets use the G1, but for some long range bullets, the G7 or G8 is typically a better choice. Some military bullets fit the G5 and G6 functions better than the G1. The GL is for high drag bullets and won't really fit anything that Bullet Drag can calculate coefficients for. GI is the Ingall's drag function and is thrown in for fun. This value is only used for calculating the ballistic coefficient.
Drop and Windage units: Sets the units used to display the drop and windage values in the calculated data. There are two inputs, one for the first column of drop, windage and lead and one for the second column of each. The first column is a linear measurement. The second is an angular measurement.
Elevation: The vertical angle the barrel makes with the line of sight. This value is not generally known and can be ignored if the "Elevation Correction for zero range" option is checked.
Elevation Correction: Or Drop correction, causes the elevation to be raised as required to cause the bullet to cross the line of sight at the zero range. Without this box checked, the zero range is ignored.
Include Coefficients: If checked, the ballistic coefficients used to calculate the trajectory are included in the output
Jacket Length
Include Coriolis Effects: If checked, the coriolis effects are included in the trajectory calculation
Include Magnus Effects: If checked, the magnus effects are included in the trajectory calculation
Include Trajectory: If checked, a trajectory is calculated and included in the output
Jacket Length: This value is the length of the jacketed portion of the bullet. This will typically be equal to the length of the bullet, but for those bullets with a lead tip, this value will be less than the total length. NOTE: if you have a jacket length less than the total length, the program sets the core depth to zero.
Jacket Specific Gravity: Specific gravity of the bullet jacket.
LOS Angle: The angle between the line of sight and the ground.
Maximum Range: The maximum displayed range.
Meplat Diameter: The diameter of the flat portion of the tip of the nose of the bullet. For some bullets, the meplat diameter is zero (or very close).
Minimum Range: The minimum displayed range. Data is calculated from the muzzle the maximum range, but may be displayed from the minimum to the maximum range. (e.g. with a minimum of 990, maximum range of 1010 and a range increment of 10 you would see data 990, 1000, 1010 yards).
Muzzle Velocity: The velocity of the bullet as either (1) measured at some distance from the muzzle or (2) as estimated from reloading data. The on-line ballistics page can correct for the distance to chronograph. (The velocity lost traveling to the chronograph.)
Nose Length: The length of the nose from the front of the bearing surface to the tip.
Ogive Radius: The radius of the nose ogive. For conical bullets, this value is not used since the ogive radius is essentially infinite.
Pressure: The barometric pressure. It may be corrected or uncorrected depending on the state of the "Corrected Pressure" checkbox.
Range Increment: the increment used in displaying the calculated data.
Ranges in Meters: When checked, all ranges entered (minimum, maximum, increment and zero) are in meters.
Relative Humidity: Relative humidity (percent)
Rotating Band Diameter: The diameter of the rotating band, if any. Most small arms bullets do not have rotating bands (although the rear of the bearing surface may be 1/10000's larger than the caliber, Bullet Drag Calculations do consider this a rotating band) and therefore the rotating band diameter is equal to the caliber.
Sight Height: The height of the sight (or scope) above or below from the centerline of the barrel. This is required because the bullet starts at a drop of -[Sight Height].
Sight Offset: The offset of the sight (or scope) to the left or right of the centerline of the barrel.
SPINNER CLα, CMα and CLp: This program has two methods for calculating CLα, CMα and CLp, GE's SPINNER program or Bob McCoy's INTLIFT and McDrag program. If checked (default), SPINNER is used, if not, McCoy's INTLIFT and McDrag are used.
Standard Conditions at Altitude: When checked, the temperature, pressure and humidity for standard atmospheric conditions at the entered altitude (always 0% at standard conditions) are entered in the calculation. The standard used is the ICAO standard atmosphere.
Temperature: The measured or estimated air temperature.
Total Length: The total length of the bullet from the base to the meplat.
Transverse Moment of Inertia: The moment of inertia about an axis perpendicular to the bullet centerline, through the center of gravity.
Twist Direction: The direction of barrel twist when looking down the barrel from the chamber to the muzzle. A clockwise twist it "Right", a counterclockwise twist is "Left".
Vital Zone Radius: Radius of the vital zone for which the maximum point blank range is calculated. The vital zone is defined as the area from one radius below the line of sight to one radius above the line of sight.
Wind Angle: Angle of the wind direction. A wind blowing downrange has an angle of zero, a wind blowing to the shooter's right has an angle of 90, a headwind, an angle of 180 and a wind blowing to the shooter's left has an angle of 270 degrees.
Wind Speed: The speed of the wind.
Zero Height: The height of the zero point at the zero range.
Zero Offset: The lateral displacement the zero point at the zero range.
Zero Range: The range at which you wish the bullet to cross the line of sight.

Output Data

Atmospheric Density: The calculated density of the air.
Azimuth: The angle that the barrel makes with the line of sight in a horizontal direction -- positive to the shooter's right. This is the "lead" angle in minutes of angle for the selected zero range.
BC: The ballistic coefficient calculated using the drag function you selected.
CD: Drag coefficient.
CD_&alpha²: Drag coefficient, second derivative.
C_{l_α}: Lift coefficient
C_{l_ρ}: Spin damping moment coefficient
C_{m_α}: Pitching moment coefficient.
C_{yp_α}: Magnus force coefficient
C_{np_α}: Magnus moment coefficient
Drop: The distance above or below the line of sight. Listed in either inches, minutes of angle or mils (6400 mils per 360 degrees or 3.375 mils per MOA). Drop is positive above the line of sight and negative below the line of sight.
Elevation: The angle that the barrel makes with the line of sight in a vertical direction. This is the "holdover" angle in minutes of angle for the selected zero range.
Energy: Kinetic energy of the bullet. The kinetic energy is a measure of the maximum amount of work (force time distance) an object can do. [It is also a measure of the work done by the firearm/case/primer/powder on the bullet.]
FF: The form factor for the bullet. This is a ratio of the actual CD of the bullet to that of the CD of the "standard" bullet for the selected drag function.
Mach Number: Mach number for the given velocity and atmospheric conditions.
Maximum Point Blank Range: Maximum range for which the bullet does not go above or below the maximum point blank range radius.
Maximum Point Blank Range Zero: Zero range to achieve the maximum point blank range.
Range: Distance from the shooter along the line of sight.
Range at Max. Height: This is the range at which the bullet reaches its maximum height in the vital zone when doing the maximum point blank range calculation. This is NOT the maximum height of the bullet for the trajectory calculation.
Sectional Density: Bullet sectional density
Stability: Stability factor for the bullet at the given velocity/range. It should be greater than 1.0 to ensure stability.
Speed of Sound: The calculated speed of sound.
Time: The time of flight of bullet in seconds.
Velocity: The speed of the bullet in feet per second.
Windage: The distance to the right or left of the line of sight. Windage is positive to the shooters right and negative to the shooters left.

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