General Trajectory Calculators
Calculates the trajectory from bullet BC and firearm info.
Inputs include muzzle velocity, sight heights, chronograph distance,
ballistic coefficient, drag function, line of sight and cant angles and
atmospheric conditions. Output options include variable ranges and choice
of units for windage and drop (inches, MOA, and mils). Calculations are
performed assuming the bullet is a point mass. Elevation and azimuth are
iteratively corrected to ensure a correct zero.
- Trajectory -- Drift
This is almost exactly like the
Trajectory calculator above, but
it includes inputs for barrel twist, twist direction and bullet length.
These values are used to calculate spin drift using an approximation
developed by Bryan Litz and published in his book,
Applied Ballistics for Long Range Shooting.
The stability factor is calculated using the Miller stability formula.
When using the bullet library, you must still input the bullet length
because it is not in the library.
- Trajectory -- Simplified
Many people don't use all the terms in the trajectory calculation page listed
above, so this program uses the default values for inputs not set by the user.
The calculation is done with the same program as the trajectory page
- Modified Point Mass Trajectory
Calculates a trajectory from bullet dimensions. This type of trajectory
provides a good estimate for things like spin drift and stability.
I have also added coriolis effects. It has a considerable number of
inputs, so beware. This online calculation replaces my previously available
Range cards calculate bullet drop for atmospheric conditions that are different
than the zero conditions. They do this by calculating a trajectory at the zero
conditions and then applying the elevation angle at zero to different atmospheric
conditions. For more information see this topic.
All of these calculators find the muzzle velocity at the shooting temperature by
using linear interpolation given two muzzle velocities and two temperatures.
All of these calculators include spin drift as an option.
- Trajectory Cards
A range card for multiple temperatures and altitudes. The output is a matrix
of values for bullet drop and windage as a function of temperature and altitude
- Trajectory μCards
A small range card. Most of the inputs are the same as the large
trajectory card, but it also includes target direction and speed. Cant is not
included, because it makes the target lead pretty complicated (if not useless).
Output includes only the notes that you enter and the table. The table is
similar to the old card -- drop, windage and lead in two units.
- Trajectory μCards Wind Only
A small range card with three columns of wind values only -- no drop or target
lead. This card does not include drift in the wind values.
- Trajectory μCards - Constant Drop
A small range card but with regular drop intervals. It does this by finding ranges
for which the drop is an even multiple of the desired values (e.g. every minute
of angle). This causes the ranges to be irregular. The windage is displayed for the
range and input wind speed.
- Maximum Distance
Calculates the maximum range a bullet can travel given the
muzzle velocity, ballistic coefficient, weight and atmospheric
Ballistic Coefficient Calculation and Conversion
- Ballistic Coefficients (Time)
Calculates the ballistic coefficient for a near velocity,
time of flight, atmospheric conditions and drag function.
- Ballistic Coefficients (Velocity)
Calculates the ballistic coefficient for near and far
velocities, atmospheric conditions and drag function.
- Bullet Drag and Twist
Calculates the bullet CD, and CD components, BC required twist and
stability for input twist. Inputs required are the bullet measurements
including nose length, total length, boattail length, meplat diameter,
base diameter, caliber, weight, atmospheric conditions and drag function.
This algorithm is based on the McDrag work done by Robert McCoy.
- Drag Function Conversion
Converts a single ballistic coefficient for one drag function to a ballistic
coefficient for another drag function. Also calculates the sectional
density and form factors.
- Drag Function Array Conversion
Converts an array of ballistic coefficients to available drag functions
and recommends a single BC and drag function to use. This is most commonly
used to convert multiple BCs to the best single BC.
Power Factor and Recoil
- Power Factor
Calculates the power factor and checks divisions for IDPA,
IPSC, TSA, USPSA and SASS. Output shows whether or not the division
is made (green/red) and by how much in percent.
Calculates the free recoil energy and velocity using firearm
weight, charge weight, bullet weight and firearm velocity.
Calculates the Miller stability factor. This formula was derived
by Don Miller and published in Precision Shooting. This formula
is much better than the antiquated Greenhill's formula. Stability
value should be in the range of 1.3 to 2.0 to ensure bullet stability.
Don Miller and Dave Brennan (editor of
Precision Shooting) have also
been kind enough to let me host his stability paper on my
exterior ballistics bibliograpy page.
The paper is titled
A New Rule for Estimating Rifling Twist An Aid to Choosing Bullets and Rifles.