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Length of Path of Approach Formula

GoMaximum Length of Path of Approach Formula

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Path of Approach is the portion of the path of contact from the beginning of contact to the pitch point. Check FAQs

P 1 = \sqrt{{R a}^{2} - {R w}^{2} \cdot {(\cos (Φ g))}^{2}} - R w \cdot \sin (Φ g)

P₁ - Path of Approach?R_a - Radius of Addendum Circle of Wheel?R_w - Radius of Pitch Circle of Wheel?Φ_g - Pressure Angle of Gear?

Length of Path of Approach Example

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Here is how the Length of Path of Approach equation looks like with Values.

Here is how the Length of Path of Approach equation looks like with Units.

Here is how the Length of Path of Approach equation looks like.

8.8074 = \sqrt{{18.63}^{2} - {12.4}^{2} \cdot {(\cos (32))}^{2}} - 12.4 \cdot \sin (32)

8.8074mm = \sqrt{{18.63mm}^{2} - {12.4mm}^{2} \cdot {(\cos (32°))}^{2}} - 12.4mm \cdot \sin (32°)

8.8074 = \sqrt{{18.63}^{2} - {12.4}^{2} \cdot {(\cos (32))}^{2}} - 12.4 \cdot \sin (32)

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Length of Path of Approach Solution

Follow our step by step solution on how to calculate Length of Path of Approach?

FIRST Step Consider the formula

P 1 = \sqrt{{R a}^{2} - {R w}^{2} \cdot {(\cos (Φ g))}^{2}} - R w \cdot \sin (Φ g)

Next Step Substitute values of Variables

∴

P 1 = \sqrt{{18.63mm}^{2} - {12.4mm}^{2} \cdot {(\cos (32°))}^{2}} - 12.4mm \cdot \sin (32°)

Next Step Convert Units

∴

P 1 = \sqrt{{0.0186m}^{2} - {0.0124m}^{2} \cdot {(\cos (0.5585rad))}^{2}} - 0.0124m \cdot \sin (0.5585rad)

Next Step Prepare to Evaluate

∴

P 1 = \sqrt{{0.0186}^{2} - {0.0124}^{2} \cdot {(\cos (0.5585))}^{2}} - 0.0124 \cdot \sin (0.5585)

Next Step Evaluate

∴

P 1 = 0.00880739265951993m

Next Step Convert to Output's Unit

∴

P 1 = 8.80739265951993mm

LAST Step Rounding Answer

∴

P 1 = 8.8074mm

Length of Path of Approach Formula Elements

Variables

Functions

Path of Approach

Path of Approach is the portion of the path of contact from the beginning of contact to the pitch point.

Symbol: P₁

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Path of Approach

Radius of Addendum Circle of Wheel

Radius of Addendum Circle of Wheel is radial distance between the pitch circle and the root circle.

Symbol: R_a

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Radius of Addendum Circle of Wheel

Radius of Pitch Circle of Wheel

Radius of Pitch Circle of Wheel is radial distance of the tooth measuring from the pitch circle to the bottom of the tooth space.

Symbol: R_w

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radius of Pitch Circle of Wheel

Pressure Angle of Gear

Pressure Angle of Gear also known as the angle of obliquity is the angle between the tooth face and the gear wheel tangent.

Symbol: Φ_g

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Pressure Angle of Gear

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)

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other Formulas to find Path of Approach

Go Maximum Length of Path of Approach

P 1 = r \cdot \sin (Φ g)

Other formulas in Length category

Go Length of Arc of Contact

L = \frac{P}{\cos (Φ g)}

Go Length of Path of Contact

P = \sqrt{{R a}^{2} - {R w}^{2} \cdot {(\cos (Φ g))}^{2}} + \sqrt{{r a}^{2} - r^{2} \cdot {(\cos (Φ g))}^{2}} - (R w + r) \cdot \sin (Φ g)

Go Length of Path of Recess

P 2 = \sqrt{{r a}^{2} - r^{2} \cdot {(\cos (Φ g))}^{2}} - r \cdot \sin (Φ g)

Go Maximum Length of Path of Contact

P = (R w + r) \cdot \sin (Φ g)

How to Evaluate Length of Path of Approach?

Length of Path of Approach evaluator uses Path of Approach = sqrt(Radius of Addendum Circle of Wheel^2-Radius of Pitch Circle of Wheel^2*(cos(Pressure Angle of Gear))^2)-Radius of Pitch Circle of Wheel*sin(Pressure Angle of Gear) to evaluate the Path of Approach, Length of Path of Approach formula is defined as the distance a wheel travels while making contact with the road surface, taking into account the radius of the wheel and the angle of the gear, providing a crucial parameter in vehicle dynamics and suspension system design. Path of Approach is denoted by P₁ symbol.

How to evaluate Length of Path of Approach using this online evaluator? To use this online evaluator for Length of Path of Approach, enter Radius of Addendum Circle of Wheel (R_a), Radius of Pitch Circle of Wheel (R_w) & Pressure Angle of Gear (Φ_g) and hit the calculate button.

FAQs on Length of Path of Approach

What is the formula to find Length of Path of Approach?

The formula of Length of Path of Approach is expressed as Path of Approach = sqrt(Radius of Addendum Circle of Wheel^2-Radius of Pitch Circle of Wheel^2*(cos(Pressure Angle of Gear))^2)-Radius of Pitch Circle of Wheel*sin(Pressure Angle of Gear). Here is an example- 12753.03 = sqrt(0.01863^2-0.0124^2*(cos(0.55850536063808))^2)-0.0124*sin(0.55850536063808).

How to calculate Length of Path of Approach?

With Radius of Addendum Circle of Wheel (R_a), Radius of Pitch Circle of Wheel (R_w) & Pressure Angle of Gear (Φ_g) we can find Length of Path of Approach using the formula - Path of Approach = sqrt(Radius of Addendum Circle of Wheel^2-Radius of Pitch Circle of Wheel^2*(cos(Pressure Angle of Gear))^2)-Radius of Pitch Circle of Wheel*sin(Pressure Angle of Gear). This formula also uses Sine (sin)Cosine (cos), Square Root (sqrt) function(s).

What are the other ways to Calculate Path of Approach?

Here are the different ways to Calculate Path of Approach-

Path of Approach=Radius of Pitch Circle of Pinion*sin(Pressure Angle of Gear)

Can the Length of Path of Approach be negative?

Yes, the Length of Path of Approach, measured in Length can be negative.

Which unit is used to measure Length of Path of Approach?

Length of Path of Approach is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Length of Path of Approach can be measured.

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Length of Path of Approach Formula

​GoMaximum Length of Path of Approach Formula

Length of Path of Approach Example

Length of Path of Approach Solution

Length of Path of Approach Formula Elements

Other Formulas to find Path of Approach

Other formulas in Length category

How to Evaluate Length of Path of Approach?

FAQs on Length of Path of Approach

Variable Name

GoMaximum Length of Path of Approach Formula