Horsepower (metric) (PS) to Foot-pounds per second (ft-lb/s) conversion

What is Horsepower (metric)?

This section will provide a comprehensive overview of metric horsepower, including its definition, origins, calculation, and real-world applications.

Definition and Origin

Metric horsepower (PS, PferdeStärke in German, or cheval-vapeur in French) is a unit of power defined as the power required to raise a mass of 75 kilograms against Earth's gravitational force over a distance of one meter in one second. It is slightly less than the imperial horsepower.

Calculation

The value of one metric horsepower is:

$$1 \text{ PS} = \frac{75 \text{ kg} \cdot 9.80665 \text{ m/s}^2 \cdot 1 \text{ m}}{1 \text{ s}} \approx 735.499 \text{ watts}$$

Therefore, approximately:

$1 \text{ PS} \approx 0.98632 \text{ hp}$ (Imperial Horsepower)

$1 \text{ hp} \approx 1.01387 \text{ PS}$

Historical Context

The term "horsepower" was originally coined by James Watt to compare the output of steam engines to the power of draft horses. While Watt's original definition is related to the imperial horsepower, the metric horsepower evolved separately on the European continent, primarily for similar comparisons involving machinery and animal power.

Real-World Examples

• Automobiles: Engine power is commonly specified in metric horsepower in many parts of the world. For example, a typical family car might have an engine rated at 150 PS.
• Motorcycles: Motorcycle engine power is also frequently stated in metric horsepower.
• Agricultural Machinery: Tractors and other farming equipment often have their power output measured in PS.
• Industrial Pumps and Motors: The power of pumps, fans, and electric motors used in industrial applications can be rated in metric horsepower. For example a pump may be rated at 5 PS.

Fun fact

While not commonly named after any specific person or law, it's interesting to know how metric horsepower is used across Europe. It gives the user a good understanding of the "power" of a machine.

What is foot-pounds per second?

Foot-pounds per second is a unit of power, commonly used in mechanical engineering and physics, especially in the United States. It represents the amount of work done (in foot-pounds) per unit of time (in seconds). Let's break it down.

Definition of Foot-Pounds per Second

Foot-pounds per second (ft⋅lb/s) is a unit of power that expresses the rate at which work is performed. One foot-pound is the amount of energy required to raise a one-pound object a distance of one foot against gravity. Therefore, foot-pounds per second tell you how quickly that work is being done.

Understanding the Components

• Foot-pound (ft⋅lb): This is a unit of energy or work. It's calculated as the force in pounds multiplied by the distance in feet.

  $$\text{Work (ft⋅lb)} = \text{Force (lb)} \times \text{Distance (ft)}$$

• Second (s): This is the unit of time.

Combining these gives you:

$$\text{Power (ft⋅lb/s)} = \frac{\text{Work (ft⋅lb)}}{\text{Time (s)}}$$

Conversion to Other Units

Foot-pounds per second can be converted to other common units of power:

• Watts (W): The standard SI unit of power.

  $$1 \text{ ft⋅lb/s} \approx 1.35582 \text{ W}$$

• Horsepower (hp): A common unit of power, especially for engines.

  $$1 \text{ hp} = 550 \text{ ft⋅lb/s}$$

  Therefore:

  $$1 \text{ ft⋅lb/s} \approx 0.001818 \text{ hp}$$

Historical Context

While there isn't a specific "law" tied directly to foot-pounds per second, the concept of power and its measurement is closely related to the work of James Watt. He improved the steam engine, and horsepower was originally defined to compare the power of steam engines to that of horses. While horsepower is more commonly associated with Watt, foot-pounds per second provides a more granular and fundamental way to express power.

Real-World Examples

• Lifting Objects: A motor lifting a 100-pound object 5 feet in 2 seconds is doing work at a rate of:

  $$\text{Power} = \frac{100 \text{ lb} \times 5 \text{ ft}}{2 \text{ s}} = 250 \text{ ft⋅lb/s}$$

• Pumping Water: A pump lifting water 20 feet at a rate of 10 pounds per second is performing work at a rate of:

  $$\text{Power} = 10 \text{ lb/s} \times 20 \text{ ft} = 200 \text{ ft⋅lb/s}$$

• Small Electric Motors: Many small electric motors are rated in terms of horsepower or watts, but you can convert those ratings to foot-pounds per second to understand the rate at which they can perform work. For example, a motor rated at 1/4 horsepower is approximately 137.5 ft⋅lb/s.

Importance

Foot-pounds per second are valuable for calculating the rate at which machines perform work, enabling engineers to design and analyze mechanical systems. Understanding this unit provides a fundamental grasp of power and its relationship to work and time.