Find arc length, straight chord or perpendicular arm offset from an angle and size, or solve for the corresponding angle. Degrees and inches are linked by the selected geometry, not by a universal conversion factor.
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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.
