Calculator Inputs
Enter the roadway, vehicle, and lighting values below. Large screens show three columns, smaller screens show two, and phones show one.
Example Data Table
These example cases show how the calculator interprets different sag-curve conditions using the default headlight beam assumptions.
| Case | Speed (mph) | G1 (%) | G2 (%) | L (ft) | SSD (ft) | Required L (ft) | Available HSD (ft) | Status |
|---|---|---|---|---|---|---|---|---|
| Moderate curve, comfortable margin | 45 | -1.5 | 2.5 | 500 | 368.22 | 315.08 | 532.27 | Pass |
| High-speed curve, insufficient length | 60 | -2.0 | 4.0 | 700 | 586.79 | 843.75 | 500.52 | Fail |
| Very small grade break, beam not governing | 55 | 0.5 | 1.5 | 300 | 492.16 | Not governing | Not governing | Pass |
Formula Used
The calculator combines a stopping-distance check with standard sag-curve headlight equations for available and required nighttime visibility.
1) Required stopping sight distance
SSD = v × t + v² / (2 × a_eff)
Where v is speed in distance per second, t is reaction time, and a_eff is braking deceleration adjusted by the controlling grade.
2) Minimum sag-curve length for headlight sight distance
When S < L: L = (A × S²) / [200 × (h + S × tan β)]When S ≥ L: L = 2S − [200 × (h + S × tan β)] / A
Here A is the algebraic grade difference in percent, h is headlight height, β is beam angle, S is required sight distance, and L is curve length.
3) Available headlight sight distance on the entered curve
For S < L, solve: A × S² − (200L tan β)S − 200Lh = 0Positive root: S = [(200L tan β) + √((200L tan β)² + 800ALh)] / (2A)For S ≥ L: S = (LA + 200h) / (2A − 200 tan β)
The calculator applies the equation that matches the actual relationship between sight distance and curve length.
How to Use This Calculator
- Select the preferred unit system for the project.
- Enter design speed, reaction time, and braking deceleration.
- Enter the entering and exiting grades for the sag vertical curve.
- Provide the actual curve length, headlight height, and beam angle.
- Leave the SSD grade override blank to let the calculator choose the controlling downgrade automatically.
- Click the calculate button to view results above the form.
- Review adequacy, margin, required curve length, and K values.
- Use the CSV or PDF buttons to save the result summary.
FAQs
1) What does headlight sight distance mean on a sag curve?
It is the distance a driver can see at night when the headlight beam strikes the roadway on a sag vertical curve. Designers compare that visible distance against the stopping sight distance requirement.
2) Why are G1 and G2 both required?
The difference between the two tangent grades creates the sag curve severity. The calculator uses the algebraic difference, A = |G2 − G1|, to determine whether the curve can provide adequate nighttime visibility.
3) Why can the result say “Not governing”?
Very small algebraic grade differences can stay within the standard beam divergence assumption. In that situation, headlight control is not the limiting design case, so the calculator reports a non-governing condition.
4) What is the controlling SSD grade?
It is the grade used to estimate stopping distance. By default, the calculator chooses the worst downgrade or level grade because downgrades increase the distance needed to stop.
5) Can I use custom headlight height and beam angle?
Yes. The calculator allows custom values, which is helpful for sensitivity studies, special design checks, or comparing agency defaults against alternate assumptions used in a project review.
6) What does the K value show?
K is the horizontal distance needed for a one-percent grade change. A higher K value means a flatter vertical curve, which usually improves comfort and available headlight sight distance.
7) Why can a curve fail even when the actual length looks large?
High speed, steep grade changes, and longer stopping distances can demand much more visibility than the curve provides. The result depends on the required sight distance, not only the absolute curve length.
8) What should I adjust after a failing result?
Common fixes include lengthening the sag curve, reducing the design speed assumption, flattening the grade break, or reevaluating conservative stopping-distance inputs when agency guidance permits.