KEVOS® MAKEOS · Mechanics
Rail Width and Track Wheel Diameter for a Wheel Load
For a wheel load on a rail, how wide must the rail tread and head be, what is the smallest track wheel that will carry the load, and what load per unit length does the AREA formula allow for a steel wheel on a steel plate?
Rail and track wheel sizing by the formulas the handbook gives: tread width B = C ÷ (1250 D) and head width A = B + 5/8 in for a wheel load C and wheel diameter D (inches and pounds), the smallest safe wheel diameter D = C ÷ (A K) with the material factor K you enter, and the American Railway Engineering Association allowable load per inch of contact length p = (y.s. − 13,000) ÷ 20,000 × 600 d for steel cylinders up to 25 in diameter rolling on steel plates, worked in SI units with the head width you will use.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Load on one wheel C | kN | Load carried by one wheel. |
| Wheel diameter D | mm | Diameter of the track wheel. |
| Width of the rail head you will use | mm | Width of the head of the rail you intend to use. |
| Material factor K for the wheel | N/mm² | Factor for the wheel material from the handbook (given there in lb/in²; 1 lb/in² = 0.006895 N/mm²). |
| Yield strength of the steel (AREA formula) | MPa | Yield strength of the steel of the wheel or roller and plate, for the AREA formula. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Load on one wheel C
- What it is
- Vertical force carried by one track wheel onto the rail.
- Units and format
- Enter a number in kN: kilonewtons (1 kN = 1000 N). The form accepts 0.000001 kN to 100000 kN. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 44.48 kN as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The rail widths and the wheel diameter rise in proportion.
- Get it right
- Include the wheel’s share of the load, the trolley and any impact allowance you design for.
What this means: Wheel diameter D
- What it is
- Diameter of the track wheel at its tread.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 5000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 508 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger wheel needs a narrower tread and raises the AREA load.
- Get it right
- Measure across the tread, not the flange.
What this means: Width of the rail head you will use
- What it is
- Width across the head of the rail the wheel will run on.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 26.04 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A wider head lowers the smallest safe wheel diameter.
- Get it right
- Take it from the rail section you intend to use.
What this means: Material factor K for the wheel
- What it is
- Factor for the wheel material in the handbook smallest wheel formula.
- Units and format
- Enter a number in N/mm²: newtons per square millimetre (equal to MPa). The form accepts 0.000001 N/mm² to 100 N/mm². Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 4.137 N/mm² as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher factor allows a smaller wheel.
- Get it right
- The handbook gives ranges for steel castings and cast iron in lb/in²; 1 lb/in² = 0.006895 N/mm².
What this means: Yield strength of the steel (AREA formula)
- What it is
- Yield strength of the steel wheel or roller and plate for the AREA formula.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 3000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 220.6 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The allowable load per unit length rises with it above 13,000 lb/in².
- Get it right
- Use the lower yield strength of the wheel and the rail or plate.
Method and formulas
- Worked in inches and pounds: B = C ÷ (1250 D); A required = B + 5/8 in.
- Smallest safe wheel diameter D = C ÷ (A K), with A the head width you will use.
- AREA: p = (y.s. − 13,000) ÷ 20,000 × 600 d lb per inch of length, for d < 25 in and y.s. in lb/in²; contact length needed = C ÷ p.
- Results converted to SI (1 lb = 4.44822 N, 1 in = 25.4 mm).
- Example: the rail head must be at least 26.034 mm wide and the wheel at least 412.89 mm in diameter.
Limitations
- The tread and wheel formulas are empirical rules for cast wheels on rails; K depends on the wheel material and is entered by you.
- The AREA formula applies to steel cylinders rolling on steel plates with diameters below 25 in (635 mm).
- Check crane wheels and rails to the crane standard you design to as well.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size the rail head for a trolley or crane wheel
- Check that a track wheel is large enough for its load
- Find the contact length a steel roller needs on a plate
Who it is for
- Machine designers
- Materials handling engineers
- Structural designers
What you get
- Required tread and head widths of the rail
- Smallest wheel diameter for the head width used
- AREA allowable load per unit length and the contact length needed
- Whether the rail and wheel carry the load
Interpreting the result
- The AREA load corresponds to a contact (Hertz) stress of about 76,000 lb/in² for steel of 32,000 lb/in² yield strength, as the handbook notes.
- A wider head lowers the smallest safe wheel diameter.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 277–278. Topic reference; no source tables or recommended settings are reproduced.
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Open the Rail Width and Track Wheel Diameter for a Wheel Load calculator