01
Antenna Radiation Patterns
Plotting RF antenna gain, side lobes, and half-power beamwidths (HPBW) in telecommunications engineering.
工学・技術用方眼紙
極座標紙
同心円と放射角度線
A4 Portrait · 210 × 297 mm
100%
正確な1:1物理スケール。印刷後50mm校正枠をご確認ください。
CSS: 96 DPIセクション 02 — 数学的原理と幾何標準
幾何学的基礎と座標計算式
Polar Coordinate Transformation Formula
Polar graph paper plots points based on a distance r from a central pole origin and an angle θ from a positive horizontal polar axis. Concentric circles represent radial increments, while radial lines represent angular increments (typically 15° or π/12 radians).
計算式:
x = r · cos(θ), y = r · sin(θ); r ∈ [0, R_max], θ ∈ [0, 2π)歴史的起源と科学の進展
Polar coordinates originated with Sir Isaac Newton and Jacques Bernoulli in the late 17th century to describe orbital mechanics and spirals that are mathematically unwieldy in standard Cartesian coordinates.
GraphPages.com では、すべてのベクター描画処理がブラウザ内で直接実行されるため、用紙余白や目盛りの寸法精度が 0.05 mm 以内に保たれます。
セクション 03 — 分野別活用シーン
産業・学術分野における実務応用
02
Microphone Polar Directionality
Documenting cardioid, omnidirectional, and figure-8 acoustic pickup patterns in audio engineering.
03
Complex Trigonometric Functions
Visualizing rose curves (r = a · cos(kθ)), Archimedean spirals (r = a + bθ), and cardioids.
04
Navigation & Radar Radar Displays
Drafting nautical navigation bearings, sonar sweeps, and celestial azimuth-elevation observations.
セクション 04 — 作図・プロットガイド
極座標紙 でのステップ別作図手順
ステップ 01
Locate the Polar Pole & Zero Axis
The center point represents r = 0. The positive horizontal ray pointing right corresponds to θ = 0° (0 radians).
ステップ 02
Scale Concentric Radial Rings
Assign a uniform physical value per concentric ring (e.g. 1 ring = 10 dB, 1 meter, or 0.5 units).
ステップ 03
Locate Points (r, θ)
Rotate counterclockwise to angle θ, then count outward along the radial spoke to distance r.
ステップ 04
Connect Angular Observations
Trace curves through plotted points smoothly, keeping radial distances calibrated to the concentric rings.
セクション 05 — プリンター校正ガイド
プリンター設定と実寸検証ガイド
100% 実寸印刷の正確性を保証するために
Concentric rings are mathematically exact circles. Ensure printer driver scaling is set to 100% to prevent circles from distorting into ovals.
- 印刷ダイアログで「倍率：100%」または「実際のサイズ」を選択してください。
- 「用紙に合わせる」などの自動縮小設定を必ずオフにしてください。
- 余白に印刷された 50 mm 校正バーを定規で測り、正確性を確認してください。
セクション 06 — よくあるご質問
よくあるご質問 (FAQ)
How many angular divisions are on this polar graph paper?
The grid includes 24 primary radial spokes spaced at 15° intervals (π/12 radians), with heavier major axes at 90° intervals (0°, 90°, 180°, 270°).
Can I use polar graph paper for antenna gain plots?
Yes. Engineers frequently use polar paper to plot antenna directivity and acoustic microphone response in decibels (dB).
What is the relationship between polar and Cartesian coordinates?
Conversion between systems uses x = r · cos(θ) and y = r · sin(θ), with r = √(x² + y²) and θ = atan2(y, x).
Is this vector PDF suitable for large poster prints?
Yes. All circles and spokes are native vector lines that scale cleanly from A4 and Letter up to A2 and Tabloid.
仮想スタジオで開く — 極座標紙
ブラウザ上でこの方眼紙に直接ダイアグラムを描いたり、座標をマークしたり、図形を描画できます。