Ball Flight: Time, Drop, and "Can the Ball Physically Get There?"

1. Ball flight: time, drop, and "can the ball physically get there?"

This section describes the basic flight of a .68 caliber paintball fired at 300 feet per second (fps), focusing on three neutral questions: How long it takes to reach a given distance. How far it falls under gravity during that time. When there is, or is not, a physically possible path from the marker to a given point in space.

Unless otherwise stated: Muzzle speed is taken as 300 ft/s (approximately 91.44 m/s). Gravity is modeled as g ≈ 9.81 m/s^2. The initial model is ideal: no wind and no air drag, followed by a short descriptive discussion of real world drag.

Distance definition (reference frame) In all formulas, the distance d is the straight line distance from the shooting player’s barrel position at the moment of the shot to the point in space where the paintball reaches the other player: For a stationary opponent, this is simply the fixed distance between the two players. For a moving opponent, the relevant distance is from the shooter’s barrel to the opponent’s ending position at the moment of impact (their position after they have moved).

The geometry required to determine that ending position and its distance from the shooter is handled in the moving player sections. The ball flight formulas below apply once that distance d is known.

3.1 Time of flight

3.1.1 Basic formula If a paintball leaves the barrel at 300 ft/s and air drag is ignored, the time to travel a horizontal distance d_feet (in feet) is: t_ball(d) = d_feet / 300 seconds.

This is simply the relationship time = distance ÷ speed with speed fixed at 300 ft/s.

The distance d_feet must always be interpreted as the straight line distance from the shooter’s barrel to the opponent’s position at impact, as defined in the reference frame above.

3.1.2 Example times for common distances For typical paintball distances in the ideal no drag model: 30 ft → t = 30 / 300 = 0.10 s. 45 ft → t = 45 / 300 = 0.15 s. 60 ft → t = 60 / 300 = 0.20 s. 90 ft → t = 90 / 300 = 0.30 s. 120 ft → t = 120 / 300 = 0.40 s. 150 ft → t = 150 / 300 = 0.50 s.

On a typical 150 ft long field, a full cross field shot from one backline to the opposite backline therefore corresponds to about half a second of flight time in this ideal model.

3.1.3 Interpretation and air drag In real conditions, a paintball slows down as it travels because of air resistance. This has two main effects relative to the ideal 300 ft/s constant speed assumption: The true time of flight is slightly longer than d / 300 for the same distance d. The ideal values from the simple formula are therefore lower bounds on the time.

A straightforward interpretation is: For any distance d, the ideal model gives the fastest possible arrival time at 300 ft/s. Real paintballs at field velocities will arrive later than or equal to this ideal time, never earlier.

3.1.4 Intuitive sense of time scales The times involved in ball flight are all well under a second: Around 0.10–0.20 s for typical short to medium distances of 30–60 ft. About 0.50 s even for a full 150 ft cross field shot.

In the frame of the game, ball flight is therefore extremely quick compared with the time it takes players to move between bunkers, which is measured in whole seconds. At the same time, small timing differences of a few hundredths of a second can still matter when comparing exposure windows, human reaction, and ball flight.

3.2 Gravity drop (ideal, level shot, no drag)

3.2.1 Model and equations To describe how far the ball falls under gravity while it travels forward, a simple projectile model is used with these assumptions: The ball is fired perfectly level, so the initial vertical velocity component is zero. The horizontal speed is 300 ft/s, which corresponds to approximately 91.44 m/s. Gravity acts downward with acceleration g ≈ 9.81 m/s^2. Air drag is ignored in this ideal model.

Using SI units for the underlying equations: Let d be the horizontal distance in meters. Let v = 91.44 m/s be the muzzle speed. Let t be the time in seconds. Let y be the vertical drop in meters.

The motion can then be described by: 1. Horizontal motion: t = d / v. 2. Vertical motion: y = 0.5 * g * t^2.

To apply these equations to field distances: Convert distance in feet to meters using 1 ft ≈ 0.3048 m. Compute t = d / v using the distance in meters. Compute y = 0.5 * g * t^2 to obtain the vertical drop in meters. Convert the resulting drop back to feet or inches if desired for field intuition.

Again, the horizontal distance d is always measured from the barrel to the opponent’s position at impact.

3.2.2 Ideal gravity drop table Using the model above and a level shot with no drag, the following approximate horizontal distances, times, and vertical drops are obtained:

30 ft: t ≈ 0.10 s, drop ≈ 0.049 m ≈ 0.16 ft ≈ 1.9 in. 60 ft: t ≈ 0.20 s, drop ≈ 0.196 m ≈ 0.64 ft ≈ 7.7 in. 90 ft: t ≈ 0.30 s, drop ≈ 0.441 m ≈ 1.45 ft ≈ 17.4 in. 120 ft: t ≈ 0.40 s, drop ≈ 0.785 m ≈ 2.58 ft ≈ 30.9 in. 150 ft: t ≈ 0.50 s, drop ≈ 1.23 m ≈ 4.02 ft ≈ 48.3 in.

These values correspond to a ball fired level from a fixed height, with no drag, and give the vertical distance the ball has fallen below the barrel’s height by the time it has traveled each stated horizontal distance.

3.2.3 Physical interpretation For a level shot in the ideal model: At 30 ft, the ball has dropped only about 2 inches. At 60 ft, the drop is roughly 8 inches. At 90 ft, the drop is about 1.5 ft. At 120 ft, the drop is about 2.6 ft. At 150 ft, the drop is a little over 4 ft.

Consequences of these idealized values include: At short ranges, the ball’s path is nearly straight relative to the barrel line, with only slight sag. At long ranges, a perfectly level barrel would result in the ball reaching the downfield distance several feet below a same height target. To hit a target at the same height at 120–150 ft, the barrel must be angled upward so the ball follows an arc that climbs above the initial muzzle line before falling back down to the target height.

3.2.4 Real paintballs and additional drop Real .68 caliber paintballs are relatively light and relatively large in diameter. They experience substantial air resistance as they travel. As a result: The ball slows down in flight, so the actual time of flight is longer than predicted by the ideal constant 300 ft/s model. Gravity therefore acts for a longer time, producing more vertical drop than the ideal values in the table. At longer distances (on the order of 100–150 ft and beyond), actual drop can be several feet greater than the ideal predictions, especially when wind, variable paint quality, or small differences in barrel angle are present.

This behavior is consistent with the general idea of an effective range where: Hits and breaks are reasonably reliable over tens of meters (roughly 75–150 ft) under typical field conditions. Very long lob shots beyond this range are geometrically possible but tend to be much less consistent in both accuracy and impact, due to increased time of flight, extra drop, and greater sensitivity to dispersion.

3.2.5 Measuring drop in controlled tests (descriptive) Real world gravity drop for a given marker–paint–velocity combination is often characterized in controlled tests: Markers are chronographed to a set velocity (for example, around 280–300 ft/s) according to local field rules. The marker is supported so that its height and angle remain fixed, typically with the barrel approximately level. Targets such as boards or paper are placed at known distances from the muzzle (for example, 30, 60, 90, 120, and 150 ft), measured along the ground with a tape or measuring wheel. Groups of shots are fired at a reference aim point marked at the same height as the barrel or at a clearly recorded reference height on each target. The average vertical offset of the impact group below the aim point is measured for each distance.

The observed offsets at each distance provide an empirical drop curve that can be compared with the ideal table: At short distances around 30–60 ft, measured drops may be relatively close to the ideal 2–8 inch range. At longer distances around 90–150 ft, measured drops typically exceed the 1.5–4 ft ideal values due to drag, paint variability, and small deviations from a perfectly level barrel.

Any such testing remains subject to standard paintball safety practices, including eye and face protection, the use of approved masks, adherence to local velocity limits, and compliance with field rules.

3.2.6 Intuitive picture of the trajectory In simple terms, a paintball in flight: Moves forward at high speed along an approximate horizontal direction. Simultaneously falls downward under gravity.

The combined motion produces a curved path: At short times, such as around 0.1 s, the ball has not had much time to fall, so the actual trajectory lies only slightly below a straight horizontal line. At longer times, such as around 0.5 s for a full 150 ft shot, gravity has acted for much longer, so the ball has fallen several feet.

At typical game distances: Close shots behave almost like straight lines, with only modest sag relative to the line of aim. Cross field shots behave more like arcs, particularly when the barrel is tilted upward so that the ball rises above the initial muzzle line and then drops significantly before reaching the target distance.

3.3 Summary (easy version)

Core relationships Time of flight (ideal): t_ball(d) = d_feet / 300, where d_feet is the straight line distance from the shooter’s barrel to the opponent’s position at impact. Gravity drop (ideal, level barrel): 30 ft → about 2 inches of drop. 60 ft → about 8 inches of drop. 90 ft → about 1.5 ft of drop. 120 ft → about 2.6 ft of drop. 150 ft → a little over 4 ft of drop.

Key interpretations Even a full length 150 ft shot has an ideal flight time of about 0.5 s. At short ranges of a few tens of feet, the paintball path is nearly straight, with only modest sag under gravity. At longer ranges around 100–150 ft, the ball must follow a clear arc to reach a same height point. A perfectly level barrel would cause the ball to pass several feet below that point. Real world drop is greater than the ideal values because drag slows the ball and increases its time in the air, especially at longer distances.

Geometric viewpoint Every question of whether the ball can physically reach a given point in space reduces to geometry and physics: The distance from the shooter to the opponent’s position at impact, defined as the straight line separation between the barrel and that impact position. The time required for the ball to cover that distance at its actual speed. The amount of vertical drop under gravity during that time. Whether the resulting curved path intersects the ground, bunkers, or any other obstacle before reaching the intended point.

Within these constraints, all shots and trajectories on the field take place. The ball flight model provides a neutral, physics based foundation for later discussions of effective range, long shots, arcs, and the interaction between ball flight and player movement.