01
Fluid Dynamics & Reynolds Number
Plotting Moody friction factor charts against Reynolds numbers across laminar and turbulent regimes.
Kertas Teknikal & Kejuruteraan
paper.log-log
paper.log-log.desc
A4 Portrait · 210 × 297 mm
100%
Skala fizikal 1:1 sebenar. Ukur kotak penentukuran 50 mm pada cetakan.
CSS: 96 DPIBahagian 02 — Prinsip Matematik
Asas Geometri dan Formula Koordinat
Power Law Linearization
Log-log paper features logarithmic scaling along both axes. Power-law equations y = a · x^b transform into straight lines where the slope represents the exponent b and the y-intercept at x = 1 represents log10(a).
Formula:
y = a · x^b ⟹ log10(y) = log10(a) + b · log10(x)Asal-usul Sejarah & Evolusi Saintifik
Log-log plotting became a cornerstone of fluid dynamics, aerodynamics, and structural mechanics in the early 20th century, enabling engineers to empirically determine Reynolds numbers and friction factors.
Di GraphPages.com, semua operasi vektor diproses terus dalam pelayar anda tanpa mampatan pelayan, menjamin ketepatan ukuran fizikal dan margin sehingga 0.05 mm.
Bahagian 03 — Kegunaan Praktikal
Aplikasi Sebenar Merentasi Industri
02
Acoustics & Sound Pressure Levels
Analyzing decibel sound pressure vs. distance to verify the inverse square attenuation law.
03
Astrophysics & Kepler's Third Law
Verifying orbital period T² ∝ a³ where log(T) vs log(a) yields a line with exact slope 1.5.
04
Materials Science & Fatigue (S-N Curves)
Plotting cyclic stress amplitude against fatigue cycles to failure (Wöhler curves).
Bahagian 04 — Tutorial Melakar
Panduan Langkah demi Langkah Melakar pada paper.log-log
LANGKAH 01
Label Both X and Y Decades
Assign power-of-ten multipliers to each decade boundary on both axes (e.g. X: 10⁰ to 10², Y: 10⁻¹ to 10³).
LANGKAH 02
Locate Data Points Across Cycles
Find the appropriate decade for each variable, then use the internal subdivision ticks (2 through 9) to pinpoint values.
LANGKAH 03
Fit a Straight Line to Power-Law Data
Draw the best-fit line across the points. Power-law relationships will form a straight line.
LANGKAH 04
Calculate the Exponent
Measure the physical rise over run (ΔY / ΔX) using a millimeter ruler to determine the power exponent b.
Bahagian 05 — Penentukuran Pencetak
Panduan Persediaan Pencetak & Pengesahan Skala
Menjamin Ketepatan Skala Fizikal 1:1 Sebenar
Ensure decade widths along X and Y match your intended aspect ratio without skewing power-law slope measurements.
- Dalam dialog cetakan, pilih Skala: 100% atau Saiz Sebenar.
- Nyahaktifkan 'Fit to Printable Area' bagi mengelakkan herotan cetakan.
- Ukur palang penentukuran 50 mm pada margin bawah dengan pembaris fizikal.
Bahagian 06 — Soalan Lazim
Soalan Lazim (FAQ)
How do I calculate slope on log-log paper?
Measure the physical length of the rise (in mm) and divide by the physical length of the run (in mm) over one decade. The resulting dimensionless ratio is the power exponent b.
Can log-log paper display zero?
No. Logarithmic scales cannot include zero because log(0) is undefined. Values must be strictly greater than zero.
What decade grid configuration does this sheet use?
Our standard template provides 3 horizontal decades by 4 vertical decades, accommodating data ranges spanning 3 to 4 orders of magnitude.
Can I export this log-log grid as high-res PNG?
Yes. You can export directly as a 300 DPI PNG image or vector PDF using the controls above.
Buka dalam Studio Maya — paper.log-log
Lakarkan rajah, tandakan koordinat atau lukis bentuk geometri di atas grid ini secara terus dalam pelayar anda.