Bunker-to-Bunker Kill Corridors

6. Bunker to bunker kill corridors

Once players leave the start box and reach bunkers, many engagements occur between two relatively fixed positions. A bunker to bunker kill corridor is the clear line of sight region through which a paintball can travel from one player's position to the other without being blocked by bunkers or the ground.

This section treats these interactions as a timing and geometry problem, with three main ingredients:

1. The other player's movement from their own starting position to their bunker. 2. The line of sight distance between the two bunker positions once both players are established. 3. The relationship between exposure time, human reaction, and ball flight time at that distance.

All distances in the timing formulas are consistently tied to:

The path length from the other player's starting position to their ending bunker (for player travel time). The straight line distance from the shooting player's barrel position to the other player's position (for ball travel time).

6.1 Geometry and line of sight distance

On a tournament style field, the surface can be described with a 2D coordinate system:

x axis: downfield (from one start box toward the other). y axis: sideways (left–right).

Each grid square is 10 ft by 10 ft, so coordinates in squares can be converted to feet.

6.1.1 Coordinates in squares

Let each bunker or position be given grid coordinates in squares:

Shooting player's bunker: (x1, y1). Other player's bunker (ending position after their run): (x2, y2).

The differences in squares are:

Δx_squares = |x2 − x1|. Δy_squares = |y2 − y1|.

Converted to feet:

Δx = 10 × Δx_squares (feet). Δy = 10 × Δy_squares (feet).

The straight line distance between the bunker positions is:

d_LOS = sqrt[(Δx)^2 + (Δy)^2].

Here, d_LOS is the line of sight distance in feet between typical head or marker positions at the two bunkers. When both players are established in those bunkers, this is the distance a paintball travels from one player's barrel to the other player's head or marker region, assuming a clear path.

6.1.2 Path length from the other player's starting position

Independently of the shooter's position, the other player moves from their own starting position to their bunker along some ground path.

Let L_run be the length of that path in feet, measured from the other player's start box to their ending bunker.

The average and fast player models yield travel times:

Average model: t_player,avg = L_run / 15. Fast model: t_player,fast = L_run / 20.

These expressions describe how long it takes the other player to move from their starting position to the bunker that defines one end of the kill corridor.

Once the other player reaches that bunker, the relevant distance for paintball flight between the two players is d_LOS as defined above.

6.2 Ball travel time across a bunker to bunker corridor

At a nominal marker velocity of 300 ft/s (ignoring drag), the time for a paintball to travel from the shooting player's barrel to the other player's bunker position is:

t_ball(d_LOS) = d_LOS / 300.

For typical bunker to bunker separations, this gives approximate flight times such as:

20 ft → t_ball = 20 / 300 ≈ 0.067 s. 30 ft → t_ball = 30 / 300 = 0.10 s. 40 ft → t_ball = 40 / 300 ≈ 0.133 s. 60 ft → t_ball = 60 / 300 = 0.20 s.

At these distances, air drag has limited impact on flight time; the constant speed model provides a useful lower bound. Actual flight times will be equal to or slightly longer than these values.

In this framework:

The other player's starting position to bunker motion is characterized by L_run and the corresponding travel time. Once both players are established in bunkers, the bunker to bunker interaction is characterized by d_LOS and the corresponding ball flight time.

6.3 Exposure time and the reaction chain

When players engage from bunkers, they often perform brief exposures from behind cover. In timing terms, three elements interact:

1. Exposure duration: how long part of the target (mask, marker, upper body) is visible in the kill corridor. 2. Human response time: how long it takes an opponent to detect the exposure, decide to act, and move their finger and marker. 3. Ball flight time: how long the paintball takes to cross the corridor once fired.

The probability of a hit during a single exposure is constrained by how these intervals overlap.

6.3.1 Approximate human response components

For a player who is not pre committed to a particular shot and responds in a purely reactive way:

Visual reaction: time to notice the exposure and initiate a response is commonly around 0.20–0.30 s, often summarized as roughly 0.25 s. Motor initiation and movement: additional time for the finger and marker to move and complete a trigger pull may be on the order of 0.05–0.10 s, depending on the task and individual.

If a player begins from a neutral ready position (not already firing or fully committed), a simple modeling range for the combined decision and movement portion is:

t_decision+movement ≈ 0.30–0.35 s.

6.3.2 Combining response and ball flight

The total delay from the start of an unexpected exposure to the arrival of a paintball at the target region can be modeled as:

t_total,reactive(d_LOS) ≈ t_decision+movement + t_ball(d_LOS).

For a 40 ft corridor:

t_ball(40) = 40 / 300 ≈ 0.133 s. t_decision+movement ≈ 0.30–0.35 s.

This gives a total interval of approximately:

t_total,reactive(40) ≈ 0.30–0.35 + 0.133 ≈ 0.43–0.48 s.

This means that, for a player who only begins reacting when an exposure appears, a typical total time from exposure onset to a ball arriving in that corridor is on the order of 0.4–0.5 seconds for a 40 ft bunker to bunker distance.

If an exposure at that distance lasts significantly less than this interval, a hit occurring purely from such a neutral, reactive process within that same exposure is constrained by the limited time overlap.

6.3.3 Anticipation and pre aim

Human responses are not always purely reactive. In many interactions, a player may:

Already be aiming at a specific bunker edge or gap. Be mentally prepared to initiate a shot as soon as any motion is detected there.

In such prepared states:

The visual decision component can be shorter, because the potential target location is already known. The effective response may approach a simpler "go" signal, reducing total reaction time.

In that case, the relevant delay from actual trigger initiation to ball arrival is closer to:

t_prepared(d_LOS) ≈ t_motor + t_ball(d_LOS),

where t_motor represents the finger and marker movement time (for example, about 0.05–0.10 s).

For a 40 ft corridor:

t_motor ≈ 0.05–0.10 s. t_ball(40) ≈ 0.133 s.

So the total prepared response interval is roughly:

t_prepared(40) ≈ 0.18–0.23 s.

These values are illustrative and depend on individual physiology, equipment ergonomics, and specific circumstances. They show that pre aiming and anticipation can substantially reduce the interval between the onset of exposure and the arrival of paint in the corridor compared with a fully neutral, reactive response.

6.4 Neutral corridor analysis

A bunker to bunker kill corridor can therefore be described by four measured or modeled quantities:

1. Other player's path length from starting position to bunker: L_run in feet, describing the route from their start box to the bunker that defines one end of the corridor. Travel time from their own starting position: Average model: t_player,avg = L_run / 15. Fast model: t_player,fast = L_run / 20.

2. Line of sight distance between bunkers: d_LOS = sqrt[(Δx)^2 + (Δy)^2] in feet, where Δx and Δy are differences in feet between the shooting player's bunker and the other player's bunker. Ball flight time from the shooting player's barrel to the other player's bunker position: t_ball(d_LOS) = d_LOS / 300.

3. Exposure duration: The time interval during which some part of the other player's target region (mask, marker, upper body) remains within the kill corridor and not fully hidden by the bunker. This can be described as a time window T_exposure in seconds (for example, 0.2 s, 0.3 s, 0.5 s), derived from observation or video analysis.

4. Response profile of the shooting player: A reactive profile, with a total response time approximately t_total,reactive ≈ t_decision+movement + t_ball(d_LOS), where t_decision+movement may be modeled around 0.30–0.35 s. A prepared profile, with a shorter effective delay t_prepared ≈ t_motor + t_ball(d_LOS), where t_motor may be modeled around 0.05–0.10 s.

From these quantities, several descriptive statements can be made:

For a given corridor distance d_LOS, paintball flight times are on the order of a few tenths of a second or less. Reactive human response times plus flight time are typically in the range of several tenths of a second, often exceeding 0.4 s for medium length corridors. Exposures shorter than the total reaction plus flight interval for a neutral response present limited time for a hit within that single exposure when no anticipation is involved. Pre aimed and anticipated exposures, by contrast, may fit within much shorter windows, especially at shorter distances, because the human decision component is reduced.

These relationships do not prescribe specific tactics. They simply describe how distances, starting positions, exposure durations, and reaction characteristics interact to define whether a hit in a given exchange is physically feasible within a single exposure window.

6.5 Simplified descriptive summary

In simplified terms:

The other player begins at their own starting position and travels along a path of length L_run to a bunker. The travel time from their start to that bunker depends on their speed model (15 ft/s or 20 ft/s). The shooting player occupies a different bunker. The straight line distance between typical head or marker positions at the two bunkers is d_LOS. A paintball fired at 300 ft/s from the shooting player's position takes d_LOS / 300 seconds to reach the other player's bunker. When the other player briefly exposes part of their body into that line of sight, this exposure has a duration T_exposure. A purely reactive response from the other bunker involves: Time to notice the exposure and decide to fire. Time for finger and marker movement and ball flight across d_LOS. A prepared or anticipated response reduces some of the decision time and can occur within shorter exposure periods.

The result is a geometric and temporal description of bunker to bunker kill corridors:

The starting position and path of the other player determine when they arrive at their bunker. The relative distance between the two bunker positions determines how quickly paintballs can travel between them. The timing of exposures and the human response characteristics determine when hits are physically possible within those corridors, without reference to any specific tactical choices.