Scale Things

Overview

Engineering reference data for Scale Things in miscellaneous.

Key Formulas

Unit Conversion

$y = x \cdot k$

Multiply by conversion factor.

Linear Interpolation

$y = y_1 + \frac{(x - x_1)(y_2 - y_1)}{x_2 - x_1}$

Estimate between two known points.

Percentage

$p = \frac{\text{part}}{\text{whole}} \times 100\%$

Part as fraction of whole.

Variables

Symbol	Description	Unit
$x$	Input value	—
$y$	Output value	—
$k$	Conversion factor	—

Scale Factor Properties

When scaling objects, the relationships between linear dimensions, area, and volume follow predictable mathematical patterns:

Scale Factor (k): The ratio of the new size to the original size.

$k = \frac{\text{scaled dimension}}{\text{original dimension}}$

Area Scaling: $A_{\text{scaled}} = k^2 \cdot A_{\text{original}}$

Volume Scaling: $V_{\text{scaled}} = k^3 \cdot V_{\text{original}}$

Common Engineering Scales

Context	Typical Scales
Architectural drawings	1:50, 1:100, 1:200
Engineering drawings	1:1, 1:2, 1:5, 1:10
Maps (topographic)	1:25,000; 1:50,000; 1:100,000
Model building	1:87 (HO), 1:160 (N)
Micro/nano scale	1:10⁶, 1:10⁹

Scale Conversion

To convert between scale representations:

$\text{Actual dimension} = \text{Drawing dimension} \times \text{Scale factor}$

$\text{Drawing dimension} = \frac{\text{Actual dimension}}{\text{Scale factor}}$

Tip: When scaling models for testing, ensure all critical dimensionless numbers (Reynolds number, Froude number, etc.) remain consistent to maintain dynamic similarity.

References

• Original Source