The formula to calculate the Efficiency of Inclined Plane when Effort Applied to Move Body Downward is:
\[ \eta = \frac{\cot(\alpha_i) - \cot(\theta_e)}{\cot(\alpha_i - \Phi) - \cot(\theta_e)} \]
The Efficiency of an Inclined Plane tells us what fraction of the input energy (kinetic energy) does useful work (lifting). The Angle of Inclination of a Plane to Horizontal is formed by the inclination of one plane to another measured in degrees or radians. The Angle of Effort is the angle which the line of action of effort makes with the weight of the body W. The Limiting Angle of Friction is defined as the angle which the resultant reaction (R) makes with the normal reaction (RN).
Let's assume the following values:
Using the formula:
\[ \eta = \frac{\cot(0.40142572795862) - \cot(1.4835298641949)}{\cot(0.40142572795862 - 0.03490658503988) - \cot(1.4835298641949)} = 0.901002280284652 \]
The Efficiency of the Inclined Plane is 0.901002280284652.
| Angle of Inclination (radians) | Angle of Effort (radians) | Limiting Angle of Friction (radians) | Efficiency |
|---|---|---|---|
| 0.35 | 1.4835298641949 | 0.03490658503988 | 0.889809277549508 |
| 0.36 | 1.4835298641949 | 0.03490658503988 | 0.892278388468858 |
| 0.37 | 1.4835298641949 | 0.03490658503988 | 0.894594690633127 |
| 0.38 | 1.4835298641949 | 0.03490658503988 | 0.896769847916867 |
| 0.39 | 1.4835298641949 | 0.03490658503988 | 0.898814310964909 |
| 0.4 | 1.4835298641949 | 0.03490658503988 | 0.900737468167793 |
| 0.41 | 1.4835298641949 | 0.03490658503988 | 0.902547774505130 |
| 0.42 | 1.4835298641949 | 0.03490658503988 | 0.904252861943283 |
| 0.43 | 1.4835298641949 | 0.03490658503988 | 0.905859634387738 |
| 0.44 | 1.4835298641949 | 0.03490658503988 | 0.907374349644816 |