Convert degrees to inches as arc length or chord on a circle of known radius, or as wheel alignment toe across a tire, and convert inches back to degrees.
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| Angle → Control Surface Width | Control Surface Width → Angle |
|---|---|
| 5° = 137.68 in width | 14 in width = 59.00° |
| 7.5° = 91.94 in width | 16 in width = 48.59° |
| 10° = 69.11 in width | 18 in width = 41.81° |
| 12° = 57.72 in width | 20 in width = 36.87° |
| 15° = 46.36 in width | 22 in width = 33.06° |
| 20° = 35.09 in width | 24 in width = 30.00° |
| 25° = 28.39 in width | 30 in width = 23.58° |
| 30° = 24.00 in width | 36 in width = 19.47° |
| 35° = 20.92 in width | 48 in width = 14.48° |
| 45° = 16.97 in width | 60 in width = 11.54° |
| Reference formulas (inches + degrees): width = 12 ÷ sin(angle), angle = asin(12 ÷ width), with a fixed perpendicular offset of 12 inches. Width must be at least 12 inches and this inverse uses the principal angle; width calculations in this table are reference examples. | |
| Width = 12 in | Width = 24 in |
|---|---|
| 1° → 0.2094 in (5.32 mm) | 1° → 0.4189 in (10.64 mm) |
| 2° → 0.4188 in (10.64 mm) | 2° → 0.8376 in (21.27 mm) |
| 3° → 0.6280 in (15.95 mm) | 3° → 1.2561 in (31.90 mm) |
| 5° → 1.0459 in (26.57 mm) | 5° → 2.0917 in (53.13 mm) |
| 7.5° → 1.5663 in (39.78 mm) | 7.5° → 3.1326 in (79.57 mm) |
| 10° → 2.0838 in (52.93 mm) | 10° → 4.1676 in (105.86 mm) |
| 12° → 2.4949 in (63.37 mm) | 12° → 4.9899 in (126.74 mm) |
| 15° → 3.1058 in (78.89 mm) | 15° → 6.2117 in (157.78 mm) |
| 20° → 4.1042 in (104.25 mm) | 20° → 8.2085 in (208.50 mm) |
| 30° → 6.0000 in (152.40 mm) | 30° → 12.0000 in (304.80 mm) |
| Formula: deflection = width × sin(angle). Inches shown with mm in parentheses (1 in = 25.4 mm). | |
Degrees to Inches Formula
The following formula calculates the perpendicular offset of a control surface’s tip from its original direction. Arc length and chord length use different formulas.
- Where LD is the linear deflection (inches)
- WCS is the width of the control surface (inches)
- a is the angle
Degrees to Inches Definition
For a pivot-to-tip width WCS and angle a, the exact perpendicular offset is LD = WCS × sin(a). Use degree mode for angles in degrees. This is a projection of the arm, not the distance traveled along its arc.
Degrees to Inches Example
How to convert degrees to inches?
- First, determine the control surface width.
Measure the control surface width in inches.
- Next, determine the angle.
Measure the angle in degrees.
- Finally, calculate the deflection.
Calculate the linear deflection in inches using the formula above.
FAQ
What is the significance of converting degrees to inches in practical applications?An angular measurement can determine a linear distance only when a circle radius or pivot-to-tip arm length and the intended geometry are known. Arc length follows the curve, a chord joins its endpoints, and perpendicular offset measures one coordinate of the tip’s motion.
How does the sine function facilitate the conversion from degrees to inches?For a pivot-to-tip arm of width WCS rotated through angle a, the tip’s perpendicular coordinate is WCS × sin(a). This projection is exact for the geometric model. Arc distance instead uses radius × angle in radians, while endpoint chord distance uses 2 × radius × |sin(angle/2)|.
Can this formula be used for large angles or should it be limited to small angles?The perpendicular-offset formula is exact at large as well as small angles for the stated pivot geometry. Only the approximation sin(a) ≈ a, with a in radians, requires small angles. Offset and arc distance differ: at 90°, offset equals the arm length while arc distance is π/2 times that length. The inverse sine returns a principal angle from −90° to 90°; other rotations, such as 30° and 150°, can produce the same offset.
