Shuttle Loom Velocity Calculation

This solution calculates the mean velocity of a shuttle within the shed of a loom.

Loom Parameters

• Reed Width (W): 1.75 m
• Shuttle Speed: 180 rpm
• Shuttle Entry Angle: 120°
• Shuttle Exit Angle: 240°
• Shuttle Length (L): 0.25 m

Calculating Time Interval

First, determine the time it takes for the crankshaft to complete one revolution and then calculate the specific time the shuttle is active within the shed.

• Crankshaft speed = 180 revolutions per minute (rpm).
• Convert speed to revolutions per second (rps):

  $ \text{Speed} = \frac{180 \text{ rev}}{60 \text{ s}} = 3 \text{ rps} $

• Calculate the time period (T) for one revolution:

  $ T = \frac{1}{\text{Speed}} = \frac{1}{3} \text{ s} $

• Determine the angle traversed by the crankshaft while the shuttle is active:

  $ \text{Angle traversed} = \text{Exit Angle} - \text{Entry Angle} = 240^\circ - 120^\circ = 120^\circ $

• Calculate the time interval ($\Delta t$) the shuttle is active within the shed. This corresponds to the time taken for the crankshaft to rotate through the calculated angle:

  $ \Delta t = \frac{\text{Angle traversed}}{360^\circ} \times T = \frac{120^\circ}{360^\circ} \times \frac{1}{3} \text{ s} = \frac{1}{3} \times \frac{1}{3} \text{ s} = \frac{1}{9} \text{ s} $

Calculating Shuttle Distance

The total distance the shuttle effectively travels during this active period is the sum of the reed width and the shuttle's own length.

• Effective distance (D) = Reed Width + Shuttle Length

  $ D = W + L = 1.75 \text{ m} + 0.25 \text{ m} = 2.0 \text{ m} $

Calculating Mean Velocity

Finally, calculate the mean velocity using the effective distance and the time interval.

• Mean Velocity = Distance / Time

  $ V_{\text{mean}} = \frac{D}{\Delta t} = \frac{2.0 \text{ m}}{1/9 \text{ s}} = 2.0 \times 9 \text{ m/s} = 18.0 \text{ m/s} $

The calculated mean velocity is 18.0 m/s, which falls within the expected range.