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Ballistic Coefficient Calculator

Table of contents

What is ballistics?What is ballistic coefficient?How to calculate ballistic coefficient using this calculator?Using the ballistic coefficient calculatorApplications of ballistic coefficientFAQs

The ballistic coefficient calculator will assist you in calculating the ballistic coefficient of a projectile. A projectile can be any object, such as a ball, a flying disk, or a bullet shot from a gun. The ballistic coefficient of a projectile depends on factors such as its mass and cross-sectional area. Along with various parameters like time of flight, height, range, and trajectory), this parameter is used in physics to estimate the behavior of projectile mid-air in the field, known as the external ballistics.

The parameter also has significance in the area of space vehicle re-entry, therefore is considered important while designing these systems. Read on to understand how to calculate the ballistic coefficient.

🔎 You may also be interested in checking our time of flight calculator to evaluate the flight duration during a projectile motion.

What is ballistics?

Before we understand the ballistic coefficient, let us have a look at ballistics as a field. Depending on what a projectile faces, there are three types of subfields in the area of ballistics, which are:

  • Internal ballistics — This field covers the time when a bullet is inside a muzzle, i.e., the propulsion phase of a projectile.
  • External ballistics — Once the bullet or a projectile leaves the launcher, its interaction midair against various forces of nature, such as gravitation or air resistance, and throughout its trajectory.
  • Terminal ballistics — Once the projectile reaches towards its end of the trajectory, it most likely collides with an object, say a bullet piercing a target or a ball hitting a wall. The interaction between the projectile and its target as well as the effect on both object is covered by terminal ballistics.

🔎 You can quickly find the range of the shot with our projectile range calculator.

What is ballistic coefficient?

The ballistic coefficient falls under the premise of external ballistics and is regarded as the property of an object to overcome air resistance while traveling. For a projectile weighing m kg and having drag coefficient C, the ballistic coefficient B can be written as:

B = m / (C × A)

where A is the area of cross-section of the projectile. The ballistic coefficient is measured in the units kg/m² or lbs/in². There are 7 different mathematical models for ballistics named G1 to G7. The G1 model is the most popular and is used for the flat base and ogive nose projectiles. The ballistic coefficient related to the G1 model is also known as the G1 ballistic coefficient.

How to calculate ballistic coefficient using this calculator?

Follow the steps below to calculate the ballistic coefficient:

  • Step 1: Enter the mass of the projectile, m.
  • Step 2: Insert the area of cross-section, A.
  • Step 3: Fill in the drag coefficient, C.
  • Step 4: The calculator will then return the ballistic coefficient.

🙋 Omni's drag equation calculator will help you check how the shape of an object influences the drag force.

Using the ballistic coefficient calculator

Estimate the ballistic coefficient for a round projectile weighing 50 grams and having a diameter of 13 mm. Take the drag coefficient as 0.51.

To prepare for the input, first, let's calculate the area of the cross-section, considering a circular cross-section. We can calculate the area as:

A = π × D²/ 4 = π × 13²/4 = 132.73 mm²

You can either use the formula above or try our dedicated area of circle calculator. Now, let's find out the value of the coefficient.

  • Step 1: Enter the projectile's mass, m = 50 g.

  • Step 2: Insert the area of the cross-section, A = 132.73 mm².

  • Step 3: Fill in the drag coefficient, C = 0.51.

  • Step 4: The ballistic coefficient for the projectile is:

    B = m / (C × A) = 738.645 kg/m² = 1.0506 lbs/in²

The ballistic coefficient for the projectile is 1.0506 lbs/in². The bullet is one of the low-drag projectiles. The higher the value of the ballistic coefficient, the lower the negative acceleration.

Applications of ballistic coefficient

Did you know?

  • For a reentry vehicle from space, we would desire to have a low coefficient so that it can decelerate quickly, causing a softer impact with the ground.

  • However, reentry projectiles like Intercontinental Ballistic Missiles (ICBM) or long-range ammunition rounds are designed with higher ballistic coefficient to ensure the least interference of crosswinds and reach the target quickly with higher kinetic energy.

  • The low Earth orbit (LEO) satellite EYESAT-I has a ballistic coefficient of about 0.072 lbs/in². EYESAT-I is a cubical amateur satellite weighing about 11.8 kg. Whereas a 0.50 caliber low drag bullet has a ballistic coefficient of 1.062 lbs/in².

FAQs

What is ballistic coefficient?

The ballistic coefficient is the property of a projectile to withstand air resistance mid-flight.

How do I calculate ballistic coefficient?

To calculate the ballistic coefficient:

  1. Multiply the drag coefficient C of the projectile with its area of cross-section A.

  2. Find the inverse of the product.

  3. Multiply the mass m with the inverse.

    B = m / (C × A)

What are the units for ballistic coefficient?

Ballistic coefficients are measured in the units — lbs/in² or kg/m².

Should ballistic coefficient be high or low?

The ballistic coefficients for satellites are designed to be very low to slow it down and cause minimal damage while reentering the atmosphere. On the other hand, the coefficient for a bullet is kept high to ensure minimal interference from the atmosphere.

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