Lecture Notes: Horsepower and Torque

Key Concepts

• Horsepower:
  • A unit of measurement for power.
  • Defined as the rate at which energy is transferred from one object to another.
  • 1 horsepower = 746 Watts.
  • Also 1 horsepower = 550 foot-pounds per second = 33,000 foot-pounds per minute.
• Torque:
  • A measure of rotational force.
  • Causes objects to spin or rotate.
  • Torque = Force × Lever Arm (or radius).
  • Units of torque:
    • Newton meters (N·m) or
    • Foot-pounds (lb·ft).

Power and Work

• Power:
  • Work divided by time.
  • Power = Work / Time.
  • Work = Force × Displacement.
  • 1 Watt = 1 Joule/second.

Units of Measurement

• Torque Units:

  • Force (N or lb)
  • Distance (m or ft)
  • Work (N·m or lb·ft)

• Conversions:

  • 1 lb = 4.45 N
  • 1 m = 3.2808 ft
  • 1 Joule = 0.7373 foot-pounds

Horsepower Derivation

• Historical Origin:

  • Coined by James Watt based on horse’s average pulling power (330 lb over 100 ft in 1 minute = 33,000 ft·lb/min = 1 hp).

• Conversions:

  • From Watts to Horsepower:
    • Power (in Watts) / 746 = Horsepower
  • From Horsepower to Watts:
    • Horsepower × 746 = Power (in Watts)

• Angular Velocity and Torque Relation:

  • Power = Torque × Angular Velocity
  • Angular speed conversions:
    • RPM to radians/sec:
      • Omega = (2π × RPM) / 60

Key Equations

1. Power (in Watts) = Torque (in N·m) × Angular Velocity (in rad/s)
2. Horsepower = (Torque (in lb·ft) × RPM) / 5252

Practice Problems

Problem 1: Horsepower from Torque and RPM

• Given: Torque = 500 lb·ft, RPM = 2500
• Use: Horsepower = (Torque × RPM) / 5252
• Result: 238 HP = 177,555 Watts = 177.56 kW

Problem 2: RPM from Horsepower and Torque

• Given: Horsepower = 133.3 HP, Torque = 200 lb·ft
• Result: RPM = (Horsepower × 5252) / Torque = 3500 RPM

Problem 3: Torque from Horsepower and RPM

• Given: Horsepower = 500 HP, RPM = 3000
• Result: Torque = (Horsepower × 5252) / RPM = 875.3 lb·ft

Problem 4: Horsepower from Inches·Ounces

• Given: Torque = 75,000 in·oz, RPM = 4000
• Convert torque to lb·ft, then calculate horsepower using the formula.
• Result: 297.5 HP = 221,935 Watts = 221.9 kW

Summary

• Horsepower is a unit of power, while Torque refers to rotational force.
• Understanding the relationship between these concepts is essential for applications in physics and engineering, particularly in the context of engines and machinery.