Formula solvers — Y

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y-Component from Magnitude and Angle

v_y = |\vec{v}| \sin\theta

Vectors & MatricesTrigonometryPhysicsResolves a vector into its vertical part from the vector's length and the angle it makes with the positive x-axis.

Yarn Count Conversion — Direct and Indirect Systems

\rho_L = \frac{K}{N}

Textiles & FabricThe one relation that crosses between the two ways of numbering a yarn. Direct systems — tex, decitex, denier — state mass per unit length and get bigger as the yarn gets coarser. Indirect systems — English cotton count Ne, metric count Nm, worsted Nw, linen lea — state length per unit mass and get bigger as the yarn gets finer. Their product is a constant fixed by whatever hank length and unit of mass the system was built on.

Yarn Diameter from Linear Density

d = \sqrt{\frac{4 \, \rho_L}{\pi \, \rho}}

Textiles & FabricA yarn treated as a solid cylinder of uniform bulk density: linear density divided by bulk density is the cross-sectional area, and the diameter follows. This is the relation hiding inside the old rule d = 1/(28√Ne) inches, and writing it in full shows what that 28 was quietly assuming about how tightly the fibres are packed.

Yield per Watt

Y = \frac{m}{P}

Indoor & GreenhouseDry yield divided by the lighting power that produced it, in grams per watt — the efficiency figure indoor growers compare rooms and fixtures by.

Youden's J Index

J = \mathrm{Se} + \mathrm{Sp} - 1

Epidemiology & Diagnostic AccuracyYouden's 1950 single-number summary of a test: sensitivity plus specificity minus one. It runs from 0 for a test no better than a coin to 1 for a perfect one, and its maximum is a common rule for picking a cut-off.

Young's Modulus (E = σ/ε)

E = \frac{\sigma}{\varepsilon}

Strength of MaterialsMechanicsPhysicsYoung's modulus as the ratio of normal stress to normal strain, the stiffness constant of a material in its elastic range.