Sag Calculator
Calculate the sagitta (SAG) of an arc using radius of curvature and chord diameter for suspension design, arches, and construction.
What is Sagitta (SAG)?
Sagitta, commonly abbreviated as SAG, is the distance from the midpoint of an arc to the midpoint of its chord. In other words, it measures how much an arc curves away from the straight line connecting its endpoints. This measurement is essential in many fields including suspension system design, architectural arch construction, and optical lens manufacturing.
The SAG Formula
The sagitta is calculated using the radius of curvature $R$ and the chord diameter $d$ with the following formula:
$$\text{SAG} = R - \sqrt{R^2 - \left(\frac{d}{2}\right)^2}$$
Where $R$ is the radius of curvature and $d$ is the chord diameter. The formula derives from the Pythagorean theorem applied to the right triangle formed by the radius, half the chord, and the sagitta.
Practical Applications
SAG calculations are critical in vehicle suspension tuning, where proper sag adjustment ensures optimal wheel contact, ride comfort, and handling. In construction, sagitta helps design arches and curved structures with precise curvature. The concept also appears in optics for determining lens curvature and in telecommunications for calculating cable sag between poles.
Frequently Asked Questions
How do I calculate SAG using the formula?
To calculate SAG, first determine the radius of curvature R and the chord diameter d. Then apply the formula: SAG = R - sqrt(R² - (d/2)²). For example, with R = 10 m and d = 13 m, the SAG is 10 - sqrt(100 - 42.25) = 10 - 7.5993 = 2.4007 m.
What is the SAG for a 5 m radius and 10 m diameter?
The SAG will be exactly 5 m. Substituting R = 5 and d = 10 into the formula: SAG = 5 - sqrt(25 - 25) = 5 - 0 = 5 m. This represents a semicircle where the sagitta equals the radius.
Why is proper SAG adjustment important in suspension?
Proper SAG adjustment ensures the suspension operates within its optimal range, maintaining consistent wheel contact with the road. This improves traction, ride comfort, and handling while preventing issues like bottoming out or excessive rebound. Incorrect SAG can lead to poor vehicle dynamics and reduced safety.
What factors affect the SAG of a suspension system?
Several factors influence suspension SAG including spring rate, preload settings, rider weight, additional loads, and the overall design of the suspension. Environmental conditions and component wear over time can also affect SAG performance. Regular adjustment is recommended when changing riding conditions or loads.
What is the difference between SAG and deflection?
SAG refers specifically to the depth of an arc measured from its chord, while deflection more broadly refers to the displacement of a structural element under load. In suspension systems, SAG is the static sag (rider sag) measured under the weight of the vehicle and rider, while deflection can refer to dynamic movement during operation.
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