A semi-trailing-arm suspension locates each wheel hub with a roughly triangular arm pivoted to the body at two inboard points. Because the pivot axis is oblique in plan view, wheel orientation and position change together as the rigid arm rotates.
Semi-trailing Arm Suspension Interactive Calculator
Relate target wheel rate to ideal spring rate using a clearly defined local displacement ratio.
Equation Used
- Motion ratio is a positive constant over the small selected motion.
- Spring behavior is linear and acts along its displacement coordinate.
- The reported wheel rate includes only the modeled spring contribution.
- Tire, bushing, damper, bump-stop and structural effects are excluded.
Motion ratio is defined here as spring displacement divided by wheel displacement.
Rigid arm and selected spring ratio
The wheel hub and spring attachment move with the arm about the line through its two inboard pivots. Actual camber, toe and wheel-path curves depend on the complete three-dimensional hardpoint geometry and on compliance.
The animation preserves a rigid triangular arm rotating about a fixed angled axis. It is an educational topology, not a vehicle-specific alignment prediction.
What the calculator determines
For a selected local motion ratio MR = spring displacement / wheel displacement and target wheel rate kw, the calculator reports the corresponding ideal spring rate, rate multiplier, spring motion per inch of wheel motion and spring force at one inch of wheel displacement.
Ideal linearized rate relation
Virtual work gives wheel force Fw = FsMR. With Fs = ksxs and xs = MR xw, kw = ksMR². Therefore ks = kw/MR². At one inch of wheel travel, spring travel is MR inches and spring force is ksMR.
Selected-input arithmetic
At 200 lb/in target wheel rate and MR = 0.85, ideal spring rate is about 276.8 lb/in. One inch of wheel motion gives 0.85 in spring motion and about 235.3 lbf spring force; projected back through the same ratio, wheel force is 200 lbf.
Model boundary
This is a local linear rate calculation with one constant displacement ratio. Real motion ratio can vary through travel and with spring inclination. Tire, bushing and damper stiffness, preload, bump stops, anti-squat, roll-center migration, loads, fatigue, alignment and compliance are excluded.
Camber and toe curves cannot be inferred from the two calculator inputs; they require measured or designed three-dimensional hardpoints and should be validated through kinematic/compliance analysis.
Questions
Why is the motion ratio squared?
The ratio affects both spring displacement and the force projected back to the wheel.
Does the calculator predict camber or toe?
No.
Is motion ratio always constant?
No. The selected value is a local linearization.
References & Further Reading
- Wikipedia contributors. Semi-trailing arm suspension. Wikipedia
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