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Crank Angle Formula

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Crank Angle refers to the position of an engine's crankshaft in relation to the piston as it travels inside of the cylinder wall. Check FAQs

θ = a \sin (- \frac{e}{r}) - α

θ - Crank Angle?e - Exhaust Lap?r - Eccentricity or Throw of Eccentric?α - Angle of Advance of the Eccentric?

Crank Angle Example

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Here is how the Crank Angle equation looks like with Values.

Here is how the Crank Angle equation looks like with Units.

Here is how the Crank Angle equation looks like.

15.4946 = a \sin (- \frac{-2}{2.7}) - 32.3

15.4946° = a \sin (- \frac{-2mm}{2.7mm}) - 32.3°

15.4946 = a \sin (- \frac{-2}{2.7}) - 32.3

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Crank Angle Solution

Follow our step by step solution on how to calculate Crank Angle?

FIRST Step Consider the formula

θ = a \sin (- \frac{e}{r}) - α

Next Step Substitute values of Variables

∴

θ = a \sin (- \frac{-2mm}{2.7mm}) - 32.3°

Next Step Convert Units

∴

θ = a \sin (- \frac{-0.002m}{0.0027m}) - 0.5637rad

Next Step Prepare to Evaluate

∴

θ = a \sin (- \frac{-0.002}{0.0027}) - 0.5637

Next Step Evaluate

∴

θ = 0.270430976381706rad

Next Step Convert to Output's Unit

∴

θ = 15.4945535962767°

LAST Step Rounding Answer

∴

θ = 15.4946°

Crank Angle Formula Elements

Variables

Functions

Crank Angle

Crank Angle refers to the position of an engine's crankshaft in relation to the piston as it travels inside of the cylinder wall.

Symbol: θ

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Crank Angle

Exhaust Lap

Exhaust Lap is the displacement of the valve from its mid-position at release and compression.

Symbol: e

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Exhaust Lap

Eccentricity or Throw of Eccentric

Eccentricity or Throw of Eccentric is the extent to which the mantle veers from its axis, so it defines the rate at which the material falls through the chamber.

Symbol: r

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Eccentricity or Throw of Eccentric

Angle of Advance of the Eccentric

Angle of advance of the eccentric the angle in excess of 90° that a steam-engine valve gear is in advance of the crank.

Symbol: α

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Angle of Advance of the Eccentric

sin

Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

Syntax: sin(Angle)

asin

The inverse sine function, is a trigonometric function that takes a ratio of two sides of a right triangle and outputs the angle opposite the side with the given ratio.

Syntax: asin(Number)

Other formulas in Steam Engine Valves and Reversing Gears category

Go Angle of Advance of Eccentric

α = a \sin (\frac{s + l}{OE})

Go Eccentricity or Throw of Eccentric

r = \frac{t}{2}

Go Steam Lap at Admission and Cutoff

s = r \cdot (\sin (θ + α))

Go Displacement of Valve from its Mid-Position

x = r \cdot \sin (θ + α)

How to Evaluate Crank Angle?

Crank Angle evaluator uses Crank Angle = asin(-Exhaust Lap/Eccentricity or Throw of Eccentric)-Angle of Advance of the Eccentric to evaluate the Crank Angle, Crank Angle formula is defined as the angular displacement of a crank from the inner dead center position, which is a critical parameter in the design and operation of steam engine valves and reversing gears, as it affects the engine's performance and efficiency. Crank Angle is denoted by θ symbol.

How to evaluate Crank Angle using this online evaluator? To use this online evaluator for Crank Angle, enter Exhaust Lap (e), Eccentricity or Throw of Eccentric (r) & Angle of Advance of the Eccentric (α) and hit the calculate button.

FAQs on Crank Angle

What is the formula to find Crank Angle?

The formula of Crank Angle is expressed as Crank Angle = asin(-Exhaust Lap/Eccentricity or Throw of Eccentric)-Angle of Advance of the Eccentric. Here is an example- 887.7725 = asin(-(-0.002)/0.0027)-0.563741348394062.

How to calculate Crank Angle?

With Exhaust Lap (e), Eccentricity or Throw of Eccentric (r) & Angle of Advance of the Eccentric (α) we can find Crank Angle using the formula - Crank Angle = asin(-Exhaust Lap/Eccentricity or Throw of Eccentric)-Angle of Advance of the Eccentric. This formula also uses Sine (sin), Inverse Sine (asin) function(s).

Can the Crank Angle be negative?

Yes, the Crank Angle, measured in Angle can be negative.

Which unit is used to measure Crank Angle?

Crank Angle is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Crank Angle can be measured.

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Crank Angle Formula

Crank Angle Example

Crank Angle Solution

Crank Angle Formula Elements

Other formulas in Steam Engine Valves and Reversing Gears category

How to Evaluate Crank Angle?

FAQs on Crank Angle

Variable Name