A streetcar truck is the wheeled running-gear assembly beneath a car body. In a two-truck car, each truck can pivot relative to the body so its wheelsets can follow curved track; springs and equalizing members provide the vertical load path. The calculator below isolates one exact plan-view geometry question—required truck swivel for a circular curve—and one ideal static load-sharing calculation. It is not a derailment, flange-climb, ride-dynamics or route-approval model.
Street-car Truck Interactive Calculator
Enter the distance between the two truck pivot centers and a circular track centerline radius. The plan view shows the exact chord–tangent swivel angle at each pivot; the load result simply divides total car weight equally among eight wheels.
Equation Used
- D is the straight-line distance between the two vertical truck pivot centers, not overall body length and not the wheelbase within one truck.
- Both truck centers lie on one circular track centerline of radius R, and the body centerline is the chord joining them.
- The load result assumes two four-wheel trucks and equal static vertical load on all eight wheels.
- The drawing is schematic. Truck wheelbase, gauge, suspension travel, center-plate details and body overhang are not dimensioned.
- Wheel/rail profile, gauge widening, flange clearance, cant, speed, suspension forces, friction, hunting, flange climb, structural strength and route clearance are omitted.
Truck-center spacing is the distance between the two body pivots. The angle calculation uses that spacing and curve radius; the wheel-load result assumes equal static sharing among eight wheels.
How a Pivoted Streetcar Truck Supports the Body
John A. Brill's 1902 car-truck patent describes a pivotal equalizing truck with side frames, spring links, equalizers and a truck bolster. Wheelsets support the side frames, resilient and equalizing members transmit vertical load, and the bolster supports the body while allowing relative rotation in plan view.
The interactive view has two parts. The top view shows how two pivot centers on a circular track are joined by the car-body chord while each truck aligns with its local tangent. The lower schematic shows equal static load sharing across eight wheels. Neither view predicts dynamic wheel forces or safe operation.
Terms used in this model
- Truck pivot center: the plan-view rotation center between a truck and the car body.
- Truck-center spacing D: the straight chord distance between the two pivot centers.
- Track centerline radius R: the radius of the ideal circular path through the pivot centers.
- Required swivel theta: the angle between the body chord and the tangent direction at either pivot.
- Comparison limit: a user-entered value for arithmetic comparison only; it is not supplied or approved by this page.
What the Geometry Is Useful For
The chord–tangent calculation is useful during early layout work because it exposes how required truck rotation changes with truck-center spacing and curve radius. Increasing D increases the angle; increasing R reduces it.
That result is only one packaging input. A real streetcar or light-rail vehicle also requires manufacturer drawings and an approved swept-envelope, wheel/rail, suspension, clearance and dynamic assessment. The calculator cannot decide whether a vehicle may safely traverse a route.
Truck Swivel on a Circular Centerline
The two truck pivot centers form a chord of length D in a circle of radius R. If 2alpha is the central angle subtended by that chord, D = 2R sin(alpha). The angle between the chord and the tangent at either endpoint is the same alpha, so the required swivel magnitude is:
The second exact calculation is an ideal static average for a two-truck, eight-wheel car:
The displayed utilization and margin are simple comparisons against the user-entered limit: utilization = 100theta/thetalim and margin = thetalim - theta. They do not establish an allowable limit.
Worked Example: Ideal Circular Geometry
For a hypothetical car with 18 ft between truck pivot centers on a 35 ft centerline-radius curve, D/(2R) = 18/70 = 0.2571. Therefore theta = asin(0.2571) = 14.9 degrees.
If the user enters 18 degrees as a comparison limit, the arithmetic utilization is 14.9/18 × 100 = 82.8%, leaving 3.1 degrees of comparison margin. For an entered total weight of 30,000 lb, the ideal equal static average is 30,000/8 = 3,750 lb per wheel.
These results do not include body overhang, truck wheelbase, gauge, flange contact, superelevation, speed, weight transfer or suspension behavior. They are geometry and static averages, not route acceptance criteria.
What the results mean
- Use this page for: transparent sensitivity of ideal swivel angle to D and R, plus an equal static wheel-load average.
- Use vehicle drawings for: actual pivot spacing, mechanical rotation stops, body/truck clearances and suspension geometry.
- Use a swept-envelope study for: body-end throw, center throw, platform and wayside clearances on the real alignment.
- Use qualified rail engineering analysis for: wheel/rail contact, flange climb, hunting, curving forces, speed, cant and route approval.
A positive comparison margin here does not imply that any omitted check passes; a negative margin only says the ideal geometric angle exceeds the value entered by the user.
Frequently Asked Questions
Is truck-center spacing the same as overall car length?
No. It is the straight-line distance between the two truck pivot centers. Overall car length also includes body overhang beyond those pivots.
Is truck-center spacing the same as truck wheelbase?
No. Truck wheelbase is the axle-center spacing within one truck. This calculator uses the distance between the two truck pivots under a two-truck car.
Does the swivel result prove that a car can take the curve?
No. It answers only the ideal plan-view chord–tangent geometry. Mechanical stops, swept clearance, wheel/rail contact, gauge, suspension, speed and dynamic forces require separate verified inputs and analysis.
Why is the wheel load W/8?
The page assumes two trucks, four wheels per truck and equal static load sharing. Actual wheel loads vary with mass distribution, suspension setup, track geometry and dynamic weight transfer.
What does a negative comparison margin mean?
It means the calculated ideal swivel angle is larger than the user-entered comparison value. The entered value is not an approved vehicle limit unless it came from the applicable manufacturer or engineering documentation.
References
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