The following gives the correct distances of the piston from tdc for a given crank angle .

crank angle from tdc distance of piston from tdc 0 0,0

30 8.3

60 29.8

90 54.4

120 79.8

150 94.9

180 100

plot a graph of crank angle against piston distance from tdc and find the piston distance from tdc when the crank angle is 75,160,210 and 250

To analyze the relationship between the crank angle and the distance of the piston from the top dead center (TDC), we can start by plotting the given data points on a graph. This will help us visualize how the piston moves as the crank angle changes. After plotting the graph, we can use interpolation to estimate the piston distances at the specified crank angles of 75, 160, 210, and 250 degrees.

Data Points Overview

Here are the distances of the piston from TDC at various crank angles:

• 0 degrees: 0.0 mm
• 30 degrees: 8.3 mm
• 60 degrees: 29.8 mm
• 90 degrees: 54.4 mm
• 120 degrees: 79.8 mm
• 150 degrees: 94.9 mm
• 180 degrees: 100.0 mm

Graphing the Data

To create the graph, you would typically plot the crank angle on the x-axis and the distance from TDC on the y-axis. Each of the data points can be marked on the graph, and then you can connect them to visualize the trend. The graph will likely show a curve that rises steeply at first and then levels off as the crank angle approaches 180 degrees.

Estimating Piston Distances

Now, let's find the piston distances for the specified crank angles using interpolation. Since 75 degrees falls between 60 and 90 degrees, we can use linear interpolation to estimate the value:

Calculating for 75 Degrees

Using the formula for linear interpolation:

y = y1 + (x - x1) * (y2 - y1) / (x2 - x1)

Where:

• x = 75
• x1 = 60, y1 = 29.8
• x2 = 90, y2 = 54.4

Plugging in the values:

y = 29.8 + (75 - 60) * (54.4 - 29.8) / (90 - 60)

y = 29.8 + 15 * 24.6 / 30

y = 29.8 + 12.3 = 42.1 mm

Calculating for 160 Degrees

Next, for 160 degrees, we interpolate between 150 and 180 degrees:

• x1 = 150, y1 = 94.9
• x2 = 180, y2 = 100.0

y = 94.9 + (160 - 150) * (100.0 - 94.9) / (180 - 150)

y = 94.9 + 10 * 5.1 / 30

y = 94.9 + 1.7 = 96.6 mm

Calculating for 210 Degrees

For 210 degrees, we can use the values at 180 and 150 degrees:

• x1 = 180, y1 = 100.0
• x2 = 150, y2 = 94.9

Since 210 degrees is beyond the given data, we can assume the piston distance remains constant at 100 mm:

y = 100.0 mm

Calculating for 250 Degrees

Similarly, for 250 degrees, we can assume the piston distance remains at 100 mm, as it is beyond the maximum angle provided:

y = 100.0 mm

Summary of Results

Here are the estimated distances of the piston from TDC for the specified crank angles:

• At 75 degrees: 42.1 mm
• At 160 degrees: 96.6 mm
• At 210 degrees: 100.0 mm
• At 250 degrees: 100.0 mm

This analysis illustrates how the piston behaves as the crank angle changes, providing insights into the mechanics of the engine's operation. If you have any further questions or need clarification on any of these steps, feel free to ask!