CELE Surveying (Geomatics) — Horizontal Curves (Simple, Compound, Reverse)Cheat Sheet
Horizontal Curves (Simple, Compound, Reverse) cheat sheet for CELE aspirants. If you could only take one sheet of paper into your review session, this is what it would look like. Professional Regulation Commission (PRC) — Board of Civil Engineering's most-tested concepts, all in one place.
Exam context
On the CELE 2026, the Surveying (Geomatics) subtest carries a "Core" weight in Professional Regulation Commission (PRC) — Board of Civil Engineering's pattern. Horizontal Curves (Simple, Compound, Reverse) lands at position 5th out of 9 in the standard review order. Target score is 70% weighted average, no sub-test below 50%, and roughly a meaningful share of items come from Surveying (Geomatics) on a typical CELE paper.
Horizontal Curves (Simple, Compound, Reverse) - Cheat Sheet
Your last-minute revision companion for horizontal curve geometry, stationing, and compound/reverse curve analysis. Focus on formula application, PC/PT calculation, and degree-of-curve conversions.
Sections
Formulas
Formula
T = R tan(I/2)
Meaning
T = tangent distance (m); R = radius of curve (m); I = intersection/deflection angle (degrees)
Watch Out
I MUST be in degrees here. Convert radians to degrees first (×180/π). Use tan(I/2), not tan(I).
When To Use
Finding distance from PI back to PC or forward to PT; always your first calculation.
Formula
L_c = (π R I) / 180
Meaning
L_c = arc length of curve (m); π = 3.14159...; I = deflection angle (degrees)
Watch Out
I MUST be in degrees. If I is in radians, use L_c = R × I (radians). Never use L_c = 2T in stationing.
When To Use
Finding total length of the circular arc from PC to PT. Always used to find Sta PT.
Formula
LC = 2R sin(I/2)
Meaning
LC = long chord (straight-line distance from PC to PT); I = deflection angle (degrees)
Watch Out
This is chord, not arc. LC < L_c always. Do not confuse with tangent distance T.
When To Use
When chord distance (not arc) from start to end of curve is needed; also field layout.
Formula
E = R(sec(I/2) − 1)
Meaning
E = external distance (perpendicular offset from PI to the curve); I = deflection angle (degrees)
Watch Out
sec(I/2) = 1/cos(I/2). Subtract 1 AFTER computing sec. E is always positive.
When To Use
Finding distance from PI perpendicular to the curve; used in design/clearance checks.
Formula
M = R(1 − cos(I/2))
Meaning
M = middle ordinate (perpendicular distance from midpoint of chord to curve); I = deflection angle (degrees)
Watch Out
M ≤ E always. Do not confuse with E (external). Use 1 − cos, not cos − 1.
When To Use
Finding sagitta or mid-chord offset; used in curve verification and layout.
Formula
Sta PC = Sta PI − T
Meaning
Station of point of curvature = station of intersection minus tangent distance
Watch Out
Subtract (not add) T from PI. PC is BEFORE the PI along the first tangent.
When To Use
Always the first stationing step; PC is where curve begins.
Formula
Sta PT = Sta PC + L_c
Meaning
Station of point of tangency = station of PC plus arc length of curve
Watch Out
Add L_c (arc), NOT 2T or T again. Sta PT = Sta PI + (T − L_c)? NO. Use Sta PT = Sta PC + L_c.
When To Use
Second stationing step; PT is where curve ends and second tangent begins.
Formula
R = 1145.916 / D
Meaning
R = radius (m); D = degree of curve (degrees per 20 m arc); 1145.916 ≈ 180 × 20 / π
Watch Out
This is ARC definition. If using chord definition, use sin(D/2) = 10/R instead. D and R are inversely proportional.
When To Use
Converting degree of curve to radius, or vice versa (arc definition, 20 m standard).
Formula
D = 1145.916 / R
Meaning
D = degree of curve (degrees per 20 m arc); R = radius (m)
Watch Out
Always state whether arc or chord definition. In Philippines, arc definition (20 m) is standard unless stated.
When To Use
Converting radius to degree of curve; shaper curves have higher D.
Common Values
Value
tan(I/2) varies; I = 30° → tan(15°) ≈ 0.268; I = 60° → tan(30°) ≈ 0.577
Symbol
I (degrees)
Quantity
Tangent distance factor
Value
1145.916 (for 20 m arc definition in SI units)
Symbol
k
Quantity
Arc conversion constant
Value
I = 20°, 30°, 40°, 45°, 60° (often multiples of 5° or 10°)
Symbol
I (degrees)
Quantity
Common deflection angles in design
Section Title
Simple Curve — Core Elements
Important Facts
- The tangent distance T is measured along the tangent line, not perpendicular to PI.
- PC and PT are EQUIDISTANT from PI; Sta PT ≠ Sta PI + T (common mistake).
- Sta PT = Sta PC + L_c, NOT Sta PC + 2T.
- The arc length L_c is always GREATER than the chord LC (except when I = 0).
- External distance E ≤ T always; they are NOT the same.
- Middle ordinate M < E always.
- Deflection angle I and central angle are identical for a simple circular curve.
- The formula R = 1145.916/D uses the arc definition (20 m standard); chord definition yields a different constant.
- In the Philippines (NSCP references), the 20 m arc definition is standard unless explicitly stated as chord definition.
- For compound curves, the curves turn the SAME way; for reverse curves, they turn OPPOSITE ways.
Key Definitions
Term
PC (Point of Curvature)
Example
If PI is at 10+120 and T = 80 m, PC is at 10+040.
Definition
Start point of the circular curve; located T units back from PI along the first tangent.
Term
PT (Point of Tangency)
Example
If PC is at 10+040 and L_c = 160 m, PT is at 10+200.
Definition
End point of the circular curve; located L_c units ahead of PC along the arc.
Term
PI (Point of Intersection)
Example
If Sta PC = 10+040 and T = 80, then Sta PI = 10+120.
Definition
Intersection of the two tangent lines (before/after the curve); does NOT lie on the curve.
Term
Deflection Angle (I)
Example
If two roads meet at 40°, the deflection angle I = 40°.
Definition
Interior angle between two tangent lines at PI; same as the central angle subtended by the arc.
Term
Degree of Curve (D)
Example
D = 4° means a 20 m arc subtends 4° at the center; R = 1145.916/4 = 286.48 m.
Definition
Central angle (in degrees) subtended by a standard 20 m arc of the curve.
Term
Radius of Curve (R)
Example
R = 300 m is a gentle curve; R = 80 m is sharp (e.g., parking lot exit).
Definition
Radius of the circular arc; larger R means gentler curve, smaller R means sharper curve.
Term
Tangent Distance (T)
Example
If R = 300 m and I = 40°, T = 300 tan(20°) ≈ 109.19 m.
Definition
Distance along the tangent from PI to either PC or PT; symmetric.
Term
Compound Curve
Example
A 400 m radius followed by a 250 m radius, both curving left.
Definition
Two circular curves of different radii in sequence, turning the SAME direction; share a common tangent point.
Term
Reverse Curve
Example
A left-turn curve followed by a right-turn curve; used on winding mountain roads.
Definition
Two circular curves turning OPPOSITE directions (S-shape); typically separated by a short tangent for superelevation.
Diagrams To Know
- Simple curve plan view showing PC, PI, PT, tangent lines, radius, and chord.
- Deflection angle I at PI with both tangent lines extended.
- External distance E perpendicular from PI to curve.
- Middle ordinate M from midpoint of chord to curve.
- Station markers at PC, PI, and PT with distances labeled.
- Degree of curve D showing 20 m arc and central angle.
Formulas
Formula
R = 1145.916 / D (arc definition, 20 m)
Meaning
R = radius (m); D = degree of curve per 20 m arc (degrees); constant = 180 × 20 / π
Watch Out
Always specify arc or chord definition. This formula is for ARC definition only. Chord definition uses sin(D/2) = 10/R.
When To Use
Converting D to R when degree of curve is given; standard in Philippines.
Formula
D = 1145.916 / R (arc definition, 20 m)
Meaning
D = degree of curve per 20 m arc (degrees); R = radius (m)
Watch Out
Same caution: ARC definition only. Higher R → lower D (sharper curves have higher D).
When To Use
Finding D when R is given.
Formula
sin(D/2) = 10 / R (chord definition, 20 m chord)
Meaning
D = degree of curve (central angle for 20 m chord); R = radius (m)
Watch Out
Different from arc definition. Chord D slightly larger than arc D for same R. Verify which definition applies.
When To Use
Chord definition conversion (less common in PH but may appear on exams).
Common Values
Value
R = 1145.92 m
Symbol
D = 1°
Quantity
1° curve (arc def.)
Value
R = 572.96 m
Symbol
D = 2°
Quantity
2° curve
Value
R = 286.48 m
Symbol
D = 4°
Quantity
4° curve
Value
R = 143.24 m
Symbol
D = 8°
Quantity
8° curve
Section Title
Degree of Curve & Radius Conversion
Important Facts
- Degree of curve and radius are inversely proportional: D ∝ 1/R.
- Higher D = sharper curve; lower D = gentler curve.
- The arc and chord definitions yield slightly different D for the same R; arc D < chord D.
- In the Philippines, unless specified, assume ARC definition (20 m standard).
- A 1° curve is very gentle (R ≈ 1146 m); an 8° curve is quite sharp (R ≈ 143 m).
- D is always expressed as a positive number; no negative degrees.
- For horizontal highway design, typical D ranges from 0.5° to 12° (gentle to sharp).
Key Definitions
Term
Degree of Curve (Arc Definition)
Example
D = 3° → R = 1145.916/3 = 381.97 m.
Definition
Central angle (degrees) subtended by a 20 m arc; most common in Philippines.
Term
Degree of Curve (Chord Definition)
Example
D = 3° (chord) → sin(1.5°) = 10/R → R ≈ 381.66 m (slightly different).
Definition
Central angle (degrees) subtended by a 20 m chord; used in some US/older specs.
Term
Sharp Curve
Example
D = 8° → R = 1145.916/8 ≈ 143.24 m (sharp).
Definition
Curve with small radius (high D); sharper = smaller R and larger D.
Term
Gentle Curve
Example
D = 1° → R = 1145.916/1 ≈ 1145.92 m (very gentle, near straight).
Definition
Curve with large radius (low D); gentler = larger R and smaller D.
Diagrams To Know
- 20 m arc subtending central angle D at radius R.
- Relationship curve: D vs R (hyperbola; inverse proportionality).
- Comparison: arc definition vs chord definition for same D.
Formulas
Formula
Sta PC = Sta PI − T
Meaning
PC station = PI station minus tangent distance; PC is where curve begins.
Watch Out
SUBTRACT T (not add). PC is BEFORE PI on the tangent line.
When To Use
First step in all curve stationing; always use this.
Formula
Sta PT = Sta PC + L_c
Meaning
PT station = PC station plus arc length; PT is where curve ends.
Watch Out
Add L_c (arc), NOT 2T or T. Do NOT use Sta PI + (T − L_c)—this is wrong.
When To Use
Second step in stationing; PT marks end of circular curve.
Formula
Sta PT = Sta PI + T − L_c (alternative, less preferred)
Meaning
Alternative form: Sta PT can be computed from PI directly.
Watch Out
This works mathematically but is error-prone; always use Sta PC + L_c instead.
When To Use
If you forget the PC → PT formula; verify T > L_c is false for typical curves (T < L_c).
Formula
Station increment along arc = (L_c / 20) × D
Meaning
Each 20 m arc subtends D degrees; useful for setting out intermediate points.
Watch Out
This is for equal-arc divisions. Equal-chord divisions use a slightly different approach.
When To Use
Dividing the curve into equal-arc stations for field layout.
Section Title
Stationing & Curve Layout
Important Facts
- Stations are CUMULATIVE; they always increase along the route.
- PC marks the START of the curve; PT marks the END.
- From PI, PC is backward (subtract T); PT is forward (add L_c from PC).
- T is measured along the tangent, not perpendicular; T is usually > M and > E.
- For a typical 40° curve with R = 300 m: T ≈ 109 m, L_c ≈ 209 m; so PT is about 100 m PAST PI in terms of arc distance.
- Never skip the PC → PT calculation; always add L_c to Sta PC.
- When setting out a curve in the field, intermediate stations are spaced 20 m apart (or per project spec).
Key Definitions
Term
Stationing
Example
Sta 5+000 = 5000 m from origin; Sta 10+120 = 10,120 m.
Definition
Cumulative distance along a route from a reference point (origin); written as 10+240 means 10,240 m.
Term
Station Format
Example
5+500 = 5.5 km; 12+085 = 12.085 km or 12,085 m.
Definition
Represented as 'km + m'; e.g., 10+240 means 10 km + 240 m = 10,240 m total.
Term
Continuous Stationing
Example
If Sta PT = 10+220, the next tangent continues from 10+220 (not reset).
Definition
Stations increase monotonically along the route; they do not reset at curves.
Diagrams To Know
- Linear stationing diagram with PI, PC, PT labeled and distances T, L_c marked.
- Station progression table: Sta PI → Sta PC → Sta PT with T and L_c shown.
- Curve layout showing intermediate stations at 20 m arc intervals.
Formulas
Formula
No single formula; analyze as two simple curves in sequence
Meaning
Compound curve = Curve 1 (R₁, I₁) + Curve 2 (R₂, I₂), same direction, different radii.
Watch Out
Do NOT use the single-curve formulas directly. Treat as two separate curves; compute PC₁, PT₁ = PCC, PT₂ separately.
When To Use
When you encounter two curves turning the same way with different radii.
Formula
T_total = T₁ + T₂
Meaning
Total tangent distance ≈ sum of individual tangents (not exact, but approximation).
Watch Out
This is approximate; exact calculation requires detailed geometry of the two curves and their common tangent point (PCC).
When To Use
Rough estimate of total tangent offset for two-curve compound.
Section Title
Compound Curves
Important Facts
- Compound curves turn the SAME direction (both left or both right).
- Radius changes at the PCC; deflection angles I₁ and I₂ are separate.
- Total deflection = I₁ + I₂.
- Use R₁ and I₁ to calculate Curve 1; use R₂ and I₂ for Curve 2.
- PCC = PT of Curve 1 = PC of Curve 2 (same station).
- Design practice: Compound curves used to transition from sharp to gentle curve (e.g., entering a highway).
- NSCP or road design standards specify minimum curve radii; compound curves help meet standards while fitting terrain.
Key Definitions
Term
Compound Curve
Example
A 400 m radius curve followed by a 250 m radius curve, both curving left; PCC is the transition point.
Definition
Two circular curves of different radii (R₁ ≠ R₂) in sequence, curving the SAME direction; share a common tangent point (PCC).
Term
PCC (Point of Compound Curvature)
Example
If Curve 1 ends at Sta 8+500, then PCC = Sta 8+500 (also PT of Curve 1, also PC of Curve 2).
Definition
Common tangent point where the two curves meet; end of first curve and start of second.
Term
First Tangent to Compound
Example
Road in a straight line until Sta PC₁.
Definition
Initial straight section before the first curve.
Term
Final Tangent to Compound
Example
Road straightens out after Sta PT₂.
Definition
Final straight section after the second curve.
Diagrams To Know
- Plan view of compound curve showing two arcs, both curving the same direction, with PCC marked.
- Curve 1 and Curve 2 with centers at different distances, sharing a tangent line at PCC.
- Station progression: PC₁ → PCC → PT₂ (where PCC = PT₁).
- Deflection angles I₁ and I₂ at respective intersections, summing to total deflection.
Formulas
Formula
No single formula; analyze as two curves in opposite directions
Meaning
Reverse curve = Curve 1 (R₁, I₁, left) + Curve 2 (R₂, I₂, right), or vice versa.
Watch Out
Deflection angles are measured at separate PIs; the curves do NOT share the same PI.
When To Use
When two curves turn opposite ways (S-shape); often with a tangent section between.
Formula
Offset between parallel tangents = E₁ + E₂ (if radii equal)
Meaning
If R₁ = R₂ and I₁ = I₂, the offset of the final tangent from the initial is 2E.
Watch Out
This assumes equal radii and angles; if different, recalculate using geometry of each curve separately.
When To Use
Estimating lateral shift when reverse curves are symmetric.
Formula
Tangent between reverse curves (if required) has length = T_between
Meaning
Length of straight section connecting PT₁ and PC₂; depends on design standards.
Watch Out
Length T_between is NOT computed by formula; it is a design specification (depends on speed, superelevation rate).
When To Use
High-speed roads require tangent between reverse curves for superelevation runoff.
Section Title
Reverse Curves
Important Facts
- Reverse curves turn OPPOSITE directions; do NOT confuse with compound curves (which turn the SAME way).
- If no tangent is between them, PT₁ = PC₂; the curves are back-to-back.
- On high-speed roads, a tangent section is inserted between reverse curves for superelevation runoff (NSCP or AASHTO standards).
- Total deflection = I₁ + I₂, but the curves turn opposite ways.
- Offset between initial and final tangents (lateral shift) = E₁ + E₂ if radii and angles are equal.
- Common on mountain passes and winding roads (e.g., Phil. highways in Cordillera region).
- Design check: Ensure minimum tangent length between reverse curves per road class (NSCP 2015, Table 200 series).
- Field layout: Set out Curve 1 (left), then tangent or immediately Curve 2 (right).
Key Definitions
Term
Reverse Curve
Example
Left-turn curve followed by a right-turn curve; looks like the letter 'S' in plan view.
Definition
Two circular curves turning OPPOSITE directions (S-shape or back-to-back curves); typically used on mountain or winding roads.
Term
First Curve (Reverse)
Example
Sta PC₁ = 5+000, Sta PT₁ = 5+250.
Definition
Initial curve, e.g., turning left; ends at PT₁.
Term
Second Curve (Reverse)
Example
Sta PC₂ = 5+250 (or later if tangent inserted), Sta PT₂ = 5+500.
Definition
Subsequent curve, turning opposite direction (e.g., right); starts at PC₂ = PT₁ (if no tangent) or after tangent.
Term
Superelevation Runoff
Example
A 50 m tangent between reverse curves allows the banking to transition from left-tilted to right-tilted.
Definition
Transition length where the road is tilted from banking one direction to the opposite; needed between reverse curves at high speed.
Diagrams To Know
- Plan view of reverse curve showing S-shape with two curves turning opposite directions.
- Curve 1 (left turn), tangent section (or zero tangent), Curve 2 (right turn).
- Centers of Curve 1 and Curve 2 on opposite sides of the combined path.
- Station progression: PC₁ → PT₁ → [tangent if present] → PC₂ → PT₂.
- Initial tangent, final tangent, and lateral offset illustrated.
Formulas
Formula
Check: LC² = (2R sin(I/2))² = 4R² sin²(I/2)
Meaning
Verify chord length using sine formula.
Watch Out
Squaring LC should equal 4R²sin²(I/2); use for verification only.
When To Use
Double-check LC calculation in the field or on exam.
Formula
Relationship: L_c > LC (always, for I > 0)
Meaning
Arc length is always greater than chord length.
Watch Out
If L_c ≈ LC, the angle I is very small (near-straight); if L_c >> LC, angle I is large (sharp curve).
When To Use
Quick sanity check: if L_c ≤ LC, you have an error.
Formula
Relationship: E ≈ T for small angles; E < T for larger angles
Meaning
External distance and tangent distance are not equal; E decreases relative to T as I increases.
Watch Out
For I > 40°, the ratio E/T becomes noticeably different; verify your calculation.
When To Use
Sanity check; neither should be zero or vastly different for normal curves.
Formula
Station check: Sta PT − Sta PC = L_c (always)
Meaning
Arc length equals the difference in stations between PT and PC.
Watch Out
If Sta PT − Sta PC ≠ L_c, you made an error in stationing (often in PI or T calculation).
When To Use
Verify stationing is correct.
Section Title
Curve Verification & Field Checks
Important Facts
- GOLDEN RULE: Sta PT = Sta PC + L_c. If this is NOT satisfied, recalculate.
- Tangent distance T increases with both R and I; larger curve or bigger angle → longer tangent.
- External distance E is much smaller than T for typical curves.
- Middle ordinate M is the smallest of all elements (M < E < T).
- For I = 0°, all elements → 0; for I → 180°, curve becomes a semicircle.
- In the field, verify at least one element (e.g., measure LC and compare with computed value) to confirm curve layout.
- Degree of curve D increases with sharpness; sharper curves are more sensitive to layout errors.
- Always convert angles to degrees (or radians consistently) before applying formulas.
Diagrams To Know
- Side view showing T, E, and M relationships.
- Cross-check table: inputs (R, I) → all outputs (T, L_c, LC, E, M) with verification.
Must Remember
- Sta PT = Sta PC + L_c, NOT Sta PC + 2T or Sta PI + T. This is the #1 stationing error.
- Tangent distance T = R tan(I/2); deflection angle I MUST be in degrees (not radians).
- Degree of curve: R = 1145.916/D uses arc definition (20 m standard in Philippines). Chord definition is different.
- Compound curves turn the SAME direction; reverse curves turn OPPOSITE directions (S-shape).
- External distance E = R(sec(I/2) − 1) and middle ordinate M = R(1 − cos(I/2)); they are NOT the same, and E > M always.
- Long chord LC = 2R sin(I/2); arc length L_c = πRI/180. LC < L_c always (except when I = 0).
- PC is located T units BEFORE PI (subtract T); PT is located L_c units after PC (add L_c).
- At a reverse curve, if no tangent is inserted, PT₁ = PC₂ (curves are back-to-back). High-speed roads require a tangent for superelevation.
- Formula verification check: Sta PT − Sta PC = L_c (always true if calculations are correct).
- For compound curves, treat as two independent simple curves; no single combined formula (analyze Curve 1 and Curve 2 separately).
Last Minute Tips
- ANGLE UNITS: Always ensure I (deflection angle) is in DEGREES when using T = R tan(I/2) and L_c = πRI/180. If given in radians, convert (multiply by 180/π).
- STATIONING TRAP: The most common error is computing Sta PT incorrectly. Write the formula Sta PT = Sta PC + L_c on your answer sheet FIRST to avoid the mistake of adding 2T or using T − L_c.
- ARC vs CHORD: When given a degree of curve D, confirm the definition (arc or chord). In the Philippines, assume ARC definition (20 m standard): R = 1145.916/D. If exam specifies chord, use sin(D/2) = 10/R.
- COMPOUND vs REVERSE: Compound = same direction, PCC is the common point. Reverse = opposite directions (S-shape), often with a tangent between. If problem says 'two curves turning left, then right,' it's a REVERSE curve.
- QUICK SANITY CHECKS: (1) L_c > LC always. (2) E < T always. (3) M < E always. (4) T > 0, E > 0, M > 0 for any I > 0. (5) All should decrease as I → 0. If any fail, recalculate.
Comparison Tables
Rows
Values
- Single arc (one direction)
- Both curves turn SAME direction
- Curves turn OPPOSITE directions
Property
Direction of turn
Values
- One radius (R)
- Two radii (R₁, R₂)
- Two radii (R₁, R₂)
Property
Number of radii
Values
- One PI
- Two PIs (at separate locations)
- Two PIs (at separate locations)
Property
Number of PIs
Values
- N/A
- PCC (point of compound curvature); PCC = PT₁ = PC₂
- PT₁ and PC₂ may be separate (tangent between) or back-to-back
Property
Common point
Values
- Not applicable
- Usually no tangent; curves are continuous
- May have tangent section (required at high speed per NSCP)
Property
Tangent between curves
Values
- Single angle I
- I_total = I₁ + I₂
- I_total = I₁ + I₂ (but opposite senses)
Property
Total deflection
Values
- Single arc
- Two arcs, same curvature sense
- S-shape or back-to-back arcs
Property
Plan view shape
Values
- Most common; highway/rail curves
- Transition from sharp to gentle curve; entrance ramps
- Mountain roads, winding passes; superelevation transition needed
Property
Typical use
Columns
- Feature
- Simple Curve
- Compound Curve
- Reverse Curve
Table Title
Simple vs Compound vs Reverse Curves
Rows
Values
- T, L_c, LC, E, M
- T = R tan(I/2); L_c = πRI/180; LC = 2R sin(I/2); E = R(sec(I/2)−1); M = R(1−cos(I/2))
- I in degrees. All five formulas are independent and give all major elements.
Property
R and I
Values
- R, then all elements
- R = 1145.916/D; then apply above formulas
- D in degrees (arc definition). Convert D to R first.
Property
D and I
Values
- Sta PC and Sta PT
- Compute T and L_c; Sta PC = Sta PI − T; Sta PT = Sta PC + L_c
- Always compute T first, then Sta PC, then L_c, then Sta PT. Never Sta PT = Sta PI + (T − L_c).
Property
Sta PI, R, I
Values
- Sta PT
- Sta PT = Sta PC + L_c
- Simplest check: Sta PT − Sta PC should equal L_c exactly.
Property
Sta PC and L_c
Values
- D
- D = 1145.916/R
- Arc definition (20 m standard in PH). Gives D in degrees.
Property
R, and need D
Values
- Check LC or E or M by measurement
- Measure one element; compute from R and I; compare
- Best to measure LC (long chord) in field; compare with 2R sin(I/2).
Property
Need to verify a curve in field
Columns
- Given Information
- Find
- Formula(s)
- Watch Out
Table Title
Formula Selector: Which Formula When?
Rows
Values
- 0.2588
- 0.9659
- 0.2679
- 0.2679
Property
15°
Values
- 0.3420
- 0.9397
- 0.3640
- 0.3640
Property
20°
Values
- 0.4226
- 0.9063
- 0.4663
- 0.4663
Property
25°
Values
- 0.5000
- 0.8660
- 0.5774
- 0.2679
Property
30°
Values
- 0.5736
- 0.8192
- 0.7002
- 0.3640
Property
35°
Columns
- Angle (degrees)
- sin(θ)
- cos(θ)
- tan(θ)
- tan(θ/2)
Table Title
Common Angle Values & Trig Functions (Quick Ref)
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