# Cycle Time Calculation Guide

These notes are included as a reference for the cycle time calculations.

## Cycle Time

Cycle time is defined as the time for a truck to complete one return trip between any two points on the haul.

```TheoreticalTruckCycleTime = SpotAtLoader + TruckLoadTime + LoadedTravelTime + SpotAtDump + DumpTime + UnloadedTravelTime + TKPHDelay
TruckCycleTime = TheoreticalTruckCycleTime + Queue```

Loader Load Time is defined as the time taken to load one truck payload. This makes it equal to the total swing time plus any delays between loading, such as the truck spot time.

```LoaderLoadRate = TruckPayload / LoaderLoadTime

Truck Load Time is defined as the time taken to fill the truck, exclusive of truck spot time. It is assumed that the truck is backing up under a full bucket, which makes Truck Load Time exclude the first bucket swing.

```TruckLoadRate = TruckPayload / TruckCycleTime
TruckLoadTime = (NumBuckets – 1) * BucketCycleTime```

## Truck Matching

The Nominal Number of Trucks is calculated as the ratio of Final Loader Rate (after overrides) over Theoretical Truck Rate (excluding queue time).

`NominalNumTrucks = FinalLoaderRate / TheoreticalTruckRate`

This number is then rounded or replaced according to the Truck Matching Method and any truck number overrides.

## Truck Queue Time & Loader Hang Time

If the digger is over trucked, then there will be queue time.

`Queue = NumTrucks * LoaderLoadTime - TheoreticalTruckCycleTime`

If the digger is under trucked, then there will be loader idle time / hang time.

`LoaderIdleTime = TheoreticalTruckCycleTime - NumTrucks * LoaderLoadTime`

## TKPH Delay

TKPH delays are calculated from the axle weights and truck speeds according to the formulas available in Michelin and Bridgestone handbooks.

Note that Michelin provides a temperature coefficient for calculating TKPH at different temperatures. This coefficient can sometimes be negative if the average haul speed is below 5 kilometres per hour. Essentially this means that there are no TKPH delays.

## Calculation FAQ

### Why can't I have less than one truck when using theoretical truck matching?

Haul Infinity imposes a productivity cap on trucks such that a truck cannot be more productive than its loader. In other words, it cannot move more tonnes than are physically loaded into it.

A corollary of this decision is that there is a minimum of one truck per haul. If a loader were to load "half a truck", then the full truck would have a productivity greater than the loader.

### Why does truck load time exclude the first bucket pass?

Truck load time starts at the instant the first bucket is dumped into the truck and ends when the truck starts driving away. As such, it excludes the digger first pass delay and first bucket swing (these become part of the Queue Time).

### What does a negative Michelin TKPH value mean?

Michelin provides a temperature coefficient for calculating TKPH at different temperatures. This coefficient can sometimes be negative if the average haul speed is below 5 kilometres per hour. Essentially this means that there are no TKPH delays.

### Why is the loaded travel time the same regardless of payload?

Haul Infinity calculates travel time by applying the rimpull curve to the Axle Data full axle weight for loaded hauls, and the empty axle weight for unloaded hauls.

If you light-load or overload the truck payloads in the Trucks tab, this is used to calculate load times but does not influence the travel time.

If you need to calculate an exact travel time using a specific payload or if you need to model some amount of carryback material, alter or add a new truck with corrected axle data.

### How can my average speed be greater than my speed limit?

Exercise due caution with Operating Conditions! These change the truck travel times, and by extension they alter the truck speeds. It is possible to make a truck travel faster than the posted speed limit by reducing the travel time too much.

### Why is travel time / fuel burn the same on two different retard curves?

The difference in braking causes less than 0.01 minutes change in travel time, so it doesn't show up due to formatting. If you put an extremely weak retard curve in, then the travel time and fuel is affected.

### Does Haul Infinity calculate speed from the rimpull/retard curves or the acceleration settings?

Settings > Acceleration > caps the rimpull/retard force that a reasonable operator chooses to apply.

Settings > Traction > caps the rimpull/retard force that can be applied to the road.

Settings > Retarder > caps the maximum percentage of retard force that a reasonable operator chooses to apply.

Haul Infinity uses the rimpull/retard curve up to the first cap that it hits, for any instantaneous point in travel.

### How does Haul Infinity work out when to slow the truck down?

Every segment in the route has a max acceleration/deceleration based on the gradient, rolling resistance, retard settings, traction settings, acceleration settings, and retard curve.

Every segment in the route has a maximum exit speed based on road signs, cornering speed limits, and uphill/downhill speed limits.

Haul Infinity can then calculate, for any stop sign or slow point, how early it must start decelerating in order to reach it without violating any of the above constraints.

### How does Haul Infinity calculate the time/distance to reach top speed?

Top speed is context-dependent upon the current gradient, rolling resistance, road signage, turning speeds, ramp speeds, and safe braking distance.

Acceleration is context-dependent upon instantaneous velocity, rimpull/retard, rolling resistance, gradient, and traction.

Using the above, Haul Infinity integrates the velocity curve over the whole path.

### How is engine load calculated?

Engine Load is (actual acceleration * gross mass + total resistance) / available force. Available force is what we get from current velocity and rimpull.

### How is time/distance to reach engine load calculated?

Using the above, the engine load curve is calculated directly off the acceleration curve.

Example: As a truck climbs a ramp, its velocity drops, rimpull increases, and engine load increases in turn.