The question of how high a bullet will travel when fired straight into the air is a classic physics problem involving a complex interplay of forces. The initial muzzle velocity provides the upward energy, but forces immediately begin to work against it the moment the bullet leaves the barrel. Understanding the bullet’s journey requires separating the theoretical possibilities from the harsh realities imposed by the atmosphere. Examining the idealized scenario first provides a baseline for the maximum potential altitude before introducing the factors that limit that reach and determine the bullet’s eventual return speed.
Calculating the Theoretical Maximum Altitude
To establish the absolute ceiling a bullet could reach, physicists first consider a theoretical scenario: firing the bullet in a complete vacuum where no air exists. In this idealized environment, the only force acting against the bullet’s upward momentum is the constant pull of Earth’s gravity. The calculation relies on kinetic energy being converted into gravitational potential energy. The maximum height is determined solely by the bullet’s initial velocity and the acceleration due to gravity. The formula simplifies to the muzzle velocity squared divided by twice the gravitational constant.
For a common 9mm handgun round leaving the barrel at approximately 1,250 feet per second, this suggests a theoretical altitude of around 7,360 meters, or about 4.5 miles. For a high-powered rifle round, such as a 5.56mm NATO cartridge, the theoretical height increases dramatically. Calculations for these faster rounds can yield vacuum altitudes exceeding 40,000 meters (over 25 miles high). While these numbers establish the maximum potential based on initial energy, they represent a condition that does not exist on Earth.
Factors That Limit Ascent
In the real world, the theoretical maximum altitude is never achieved because the bullet must travel through the Earth’s atmosphere. The dominant factor limiting the bullet’s ascent is air resistance, or drag. This force acts opposite the direction of motion, rapidly stripping the bullet of its velocity immediately after it exits the muzzle.
The bullet’s shape and weight, measured by its ballistic coefficient, determine how quickly it slows down. A sleek, high-mass rifle bullet maintains its speed longer than a short, light pistol bullet, but both are slowed significantly by the dense air near the ground. Because the drag force increases exponentially with velocity, the bullet loses upward speed much faster than gravity alone dictates.
As a result, the actual peak height, or apogee, is drastically reduced. A rifle round that might theoretically reach over 25 miles in a vacuum may only climb to an actual height of around 3,000 meters, or about 10,000 feet, in the atmosphere. The combination of drag and gravity causes the bullet to run out of upward momentum and begin its descent much sooner.
The Danger of the Falling Projectile
Once the bullet reaches its maximum altitude and begins to fall, its downward speed is governed by the atmosphere, not its initial muzzle velocity. The falling projectile accelerates due to gravity until the force of air resistance balances the force of gravity, a point known as terminal velocity. Unlike the stabilized, nose-first trajectory during ascent, a bullet fired straight up typically begins to tumble or fall sideways upon descent.
This tumbling significantly increases the bullet’s surface area exposed to the air, which increases the drag and lowers its terminal velocity. For most common rifle and pistol calibers, the terminal velocity of a falling bullet ranges between 150 and 300 feet per second.
Although this downward speed is only a small fraction of the muzzle velocity, it is more than enough to cause serious injury or death. Falling bullets traveling at speeds as low as 150 feet per second (45 meters per second) possess sufficient energy to penetrate human skin. Furthermore, speeds around 200 feet per second (60 meters per second) can penetrate the skull, which is why firing firearms into the air presents a serious, indiscriminate public safety hazard.