Transport Capacity and Dispatch Interval
In the planning of roller coasters and other transportation systems, transport capacity and dispatch interval are critical factors. Spike coasters achieve high capacity even with smaller vehicles due to integrated distance control. This article explores the technical details and considerations involved in the design and optimization of these rides.
Capacity
Transport capacity, expressed in persons per hour (pph), is one of the key criteria for roller coasters and other transportation systems. It is calculated based on the number of passengers or seats per vehicle (seats) and the number of vehicle dispatches per hour (dispatches):
Capacity = Seats × Dispatches
rom the number of dispatches per hour, the dispatch interval in seconds can be calculated as follows:
Dispatch Interval = 3600 / Dispatches or conversely:
Dispatches = 3600 / Dispatch Interval
Thus, the capacity can be expressed as:
Capacity = Seats × 3600 / Dispatch Interval
Example:
Vehicle with 10 seats: Seats = 10
Dispatch Interval = 20 s (i.e., 3600/20 = 180 dispatches per hour)
Capacity = 10 × 3600/20 = 1800 pph
Therefore, the capacity increases with more seats per vehicle and shorter dispatch intervals. Often, it is desirable to keep the number of seats per vehicle low, making the dispatch interval the crucial component. Reasons for using smaller vehicles with fewer seats instead of large trains include:
• More interesting layouts with tighter radii
• Lighter support structures with fewer columns
• Greater spectator appeal through more frequent vehicle movements
• Shorter and lighter mechanical installations (transfer tables, special mechanical effects)
• Better interaction opportunities for passengers
The last point, in particular, has led to the use of 2-seater vehicles in Spike Racing. This maximizes the ratio between drivers who can actively control the speed and passive passengers.
2-seat Spike Racing car with interactive driver control
Block Sections vs. Distance Control
The reduction of the dispatch interval required for high capacity is limited in traditional roller coasters by the need to divide the track into block sections for safety reasons. These block sections must be separated by safety brakes to ensure that only one vehicle is in a safety block at any time, allowing it to be stopped in time if the next block is unexpectedly not clear. The safety brakes are positioned so that a stopped vehicle can always proceed to the station without additional assistance after releasing the brake. Thus, block boundaries are always located at the high points of the ride. The ride elements between blocks determine the block length and block clearance time, which in turn sets the minimum dispatch interval. Conversely, the required capacity limits the possible duration of continuous ride elements.
In Spike coasters, safety brakes are built into the vehicles and activated via distance control in emergencies. Block sections or track-integrated safety brakes are therefore not necessary, allowing for unrestricted ride element duration and dispatch interval. This enables very high throughput even with two-seater vehicles, as demonstrated in the following diagram:
In practice, the minimum dispatch interval, and thus the achievable capacity on Spike, is only limited by the required safety distance between two vehicles and the dispatching time at the station.
Safety Distance
To determine the required safety distance between two Spike vehicles, it is assumed that a defective vehicle could stop abruptly without delay. The distance to the following vehicle must then be sufficient for it to come to a complete stop safely ("brick wall" criterion).
The pure braking time (t) depends on the deceleration (a) and the current speed (v):
t = v/a
Example:
Speed: 80 km/h = 22 m/s
Deceleration: 1.2 g = 12 m/s²
Braking time: t = (22/12) s = 1.89 s
For a downhill section, the slope-induced acceleration (a_hill) due to the slope angle α must also be considered (with g = gravitational acceleration = 9.81 m/s²):
a_hill = sin(α) × g
Example:
Slope angle: 40°
Slope-induced acceleration: a_hill = sin(40°) × g = 0.64 g = 6.3 m/s²
The deceleration generated by the braking force is reduced by the slope-induced acceleration, so the braking time (t) for a downhill section is:
t = v/(a - a_hill)
Example:
Speed: 80 km/h = 22 m/s
Deceleration: 1.2 g = 12 m/s²
Slope angle: 40°
Braking time: t = (22 m/s) / ((1.2 - 0.64) × g) = (22 m/s) / ((1.2 - 0.64) × 9.81 m/s²) = 4 s
Additionally, the reaction time of the control system and braking mechanism, as well as an extra safety buffer, must be considered. The practical safety buffer can be accurately determined for each layout through simulation but will not exceed about 7 seconds for Spike. With such a set dispatch interval, even with only two seats per vehicle, a capacity of over 1000 pph can be achieved.
If the interactive control feature in Spike Racing is to be used, the adjustable time difference in the control system between the fastest and slowest driver must be added to the minimum dispatch interval. If this difference is, for example, 3 seconds, the previously mentioned minimum dispatch interval would increase to 10 seconds, resulting in a capacity of 720 pph. Greater ranges of interaction would further reduce capacity unless synchronization points are included in the layout design where the gap between fast and slow vehicles is reset to the original dispatch interval.
Station Dispatching
The usual station setup, where vehicles stop in a fixed position for boarding and disembarking, should be replaced with a more space-efficient and robust continuous station handling (Omnimover) system when dispatch intervals are under 20 seconds. In this system, boarding and disembarking occur in vehicles moving slowly through the station. According to EN 13814 and ASTM standards, speeds of up to 0.5 m/s are permissible; higher speeds require a conveyor belt to double the boarding speed. Comfort considerations or certification body requirements may necessitate this earlier, e.g., at 0.4 m/s.
The possible dispatch intervals (t) with a continuous station depend on the vehicle speed (v) and the vehicle length plus safety distance (l):
t = l/v
Example:
Speed: v = 0.4 m/s
Vehicle length including safety distance: l = 4m
Possible dispatch interval: t = 4m / 0.4m/s = 10 s
Number of Required Vehicles
Once the desired capacity and dispatch interval (t) are determined, the required number (A) of vehicles can be calculated from the cycle time (T = ride time + station time):
A = T / t
Example:
Dispatch interval: t = 10 s
Cycle time: T = 70 s
Number of vehicles: A = 70 s / 10 s = 7
Thus, the desired ride time or track length and capacity are the key parameters for budgeting the ride.
