Description:
The TKPH (Ton Kilometre Per Hour) or TMPH (Ton Mile Per Hour) is an expression of the working capacity of a tyre. The TKPH (TMPH) is a function of the maximum allowed internal operating temperature of a tyre.
Calculation:
These values reflect the specific requirements on site and can be obtained by using the following formula:
*formula
Basic site TKPH = Qm * Vm
Where:
Qm = Average load per tyre
Vm = Average cycle speed, in km per hour
To obtain the average load per tyre:
Average load per tyre(Qm) = (Qc + Qv)/2
Where:
Qc = is the load per tyre in ton (TKPH) on a laden vehicle.
Qv = is the load per tyre in ton (TKPH) on an unladen vehicle.
Example:
1.- To calculate the final full weight, one needs certain inputs such as the truck payload, empty weight, full weight, and number of tyres. These parameters can typically be found in the product specification sheet of the truck.
*formula
Final Full Weight1 = (Full Weight1 - Empty Weight1)/(Full Weight1 - Empty Weight1 + Full Weight2 - Empty Weight2 ) * Truck Payload * 1000 + Empty Weight1
Final Full Weight2 = (Full Weight2 - Empty Weight2)/(Full Weight1 - Empty Weight1 + Full Weight2 - Empty Weight2 ) * Truck Payload * 1000 + Empty Weight2
Truck Payload(t) = 225.5
╔═════════════════════════════════════════╦═════════╦═════════╗
║ ║ Axle 1 ║ Axle 2 ║
╠═════════════════════════════════════════╬═════════╬═════════╣
║ Empty Weight (kg) ║ 69763 ║ 81239 ║
║ Full Weight (kg) ║ 122359 ║ 254129 ║
║ Number of tyres ║ 2 ║ 4 ║
║ Final Full Weight (kg) ║ 122359 ║254129 ║
2.- To calculate the Empty load per tyre:
*formula
Empty load per tyre1 = Empty Weight1 / 1000 / number of tyres1
Empty load per tyre2 = Empty Weight2 / 1000 / number of tyres2
║ Empty load per tyre (t) ║ 34.9 ║ 20.3 ║
3.- To calculate the Full load per tyre:
*formula
Full load per tyre1 = Final Full Weight1 / 1000 / number of tyres1
Full load per tyre2 = Final Full Weight2 / 1000 / number of tyres2
║ Full load per tyre (t) ║ 61.2 ║ 63.5 ║
4.- To calculate the Average load per tyre:
*formula
Average load per tyre1 = (Empty load per tyre1 + Full load per tyre1) / 2
Average load per tyre2 = (Empty load per tyre2 + Full load per tyre2) / 2
║ Average load per tyre (t) ║ 48.0 ║ 41.9 ║
5.- Average speed: This value comes from the cycle distance divided by the cycle time, in this example, there is a cycle distance of 2005 Km and an 11.67 min cycle time.
║ Average speed (km/h) ║ 10.3 ║ ║
6.- Now, the basic site TKPH can be calculated:
*formula
Basic TKPH = Average load per tyre * Average speed
║ Basic TKPH ║ 495.4 ║ 432.3 ║
7.- K1 and K2 coefficients:
K1: Michelin recommends that the K1 coefficient be applied to the basic TKPH for cycle distances exceeding 5 km. To compensate for this, the site TKPH must be adjusted by application of the K1 coefficient. Based on the cycle distance, use the K1 coefficient from the table in the reference section.
*formula
K1 = This value comes from the K1 coefficient table (See references below)
K2: In the calculation of the tyre TKPH a standard ambient temperature of 38°C is used. This means that for a given speed when the ambient temperature deviates above or below 38°C so will the tyres TKPH. To compensate for this the site TKPH must be adjusted by application of the K2 coefficient. The table in references or the following formulas can be applied:
*formula
if Ambient Temperature < Reference Temperature:
K2 = ((Average speed + 0.25*(Ambient temperature - Reference temperature)) / Average speed)
else:
K2 = ((Average speed + 0.40*(Ambient temperature - Reference temperature)) / Average speed)
║ Michelin
║ Ambient Temperature (c) ║ 32 ║ ║
║ Reference Temperature (c) ║ 38.0 ║ ║
║ K1 for return distance > 5km ║ 1.0 ║ ║
║ K2 = (Vm + 0.25(TA-TR))/Vm ║ 0.855 ║ ║
8.- Real site TKPH (Michelin)
*formula
Real site TKPH = basic site TKPH * K1 * K2
║ Michelin
║ Real site TKPH ║ 423.3 ║ 369.5 ║
9. Real site TKPH (Bridgestone)
Bridgestone calculates their TKPH based on the following points
- Base temperature is 38 °C.
- Maximum one-way distance is 16km (32 km return trip)
- If the cycle distance is less than 5km ((loaded and empty trip)) then the TKPH value can be increased by 12%.
*formula
Real site TKPH = Average speed * Average load per tyre
║ BridgeStone
║ Real site TKPH ║ 495.4 ║ 432.3 ║
╚═════════════════════════════════════════╩═════════╩═════════╝
The same haulage results were observed in Haul Infinity for real site TKPH.
Tyre TKPH and Site TKPH
Whenever the site TKPH 423 rises above the tyre tkph (Setup Task > Operating Conditions), Haul Infinity will implement a TKPH delay in the cycle time for the tyres to cool down. For example, let's consider a tyre tkph of 200. Then, the new cycle time is 21.24min (this cycle time is purely calculated on tkph).
*formula
Tkph Delay(min) = New Cycle Time - Old Cycle Time
Tkph Delay(min) = 21.24 - 11.67 = 9.58
*pseudocode
if real site TKPH > tyre TKPH:
Tkph delay increases
else:
Tkph delay equals to 0.0
References:
1. Michelin K1 Coefficients
2. Michelin K2 Coefficients
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