Excel Worksheet problems -- Piston and connecting rod connected to a crankshaft

[Franklie001]

Homework Statement

Excel worksheet / sine waves

Relevant Equations

Hi everyone i am trying to solve this coursework for university but i am stuck at the last part of the question. Anyone able to help me find the solution for the last part please?

 

[berkeman]

Can you post the whole question (including whatever was above the text that you posted)? And can you describe your work so far please?

 

[Franklie001]

Oh sorry. Here you are
So basically i had to find in the first question the distance y of the piston from the centre of rotation of the crankshaft. I've done that.
I am stuck at the last part of the question which ask to find the minimum value of L to the nearest 0.5m over the period of 1 second but i have no idea how to find that.

 

[haruspex]

which ask to find the minimum value of L to the nearest 0.5m over the period of 1 second

No, it asks for the minimum L such that the optimum injection period is at least 1s long.
In part ii you found that period for two cases. Just try different values of L, keeping r+L fixed, to find one where the injection period is at least 1s. Then fine tune that to get the minimum L.

 

[Franklie001]

Do i need to use an equation to find the minimum L?

Something like r+L=1s ??

 

[haruspex]

Do i need to use an equation to find the minimum L?

Something like r+L=1s ??

L and r are lengths. They cannot add up to a time!
You are given example values of L and r, and told that r+L must stay fixed. Use that to write the equation for the general case.

 

[Franklie001]

Is that referring at the initial part of the wave when t1=0s and t2=1?

 

[haruspex]

Is that referring at the initial part of the wave when t1=0s and t2=1?

L and r are constants in a given design. They do not change with time.

 

[Franklie001]

Sorry it's still not clear to me how should i solve that question.

How do i put in relation r+L and the period ?

 

[haruspex]

Sorry it's still not clear to me how should i solve that question.

How do i put in relation r+L and the period ?

You are told that in one particular set up r=0.1m and L=0.3m. You are also told that r+L is the same in all set ups. So what is the general equation relating r and L?

 

[Lnewqban]

Sorry it's still not clear to me how should i solve that question.

How do i put in relation r+L and the period ?

A very small value of r makes the amplitude of the stroke of the piston very small, and its linear velocity very low, for one full rotation of the crankshaft (which takes 4 seconds).

A very big value of r has the geometrical limitation of the piston hitting the crankshaft when in the lowest position.
It also makes the amplitude of the stroke of the piston very big, and its linear velocity very high, for one full rotation of the crankshaft.

For any combination of r and L, the crankshaft still takes 4 seconds to complete one full turn; therefore, the injection of 1 second must match 1/4 of a turn.
That means the ideal injection should happens within 1/8 of turn before and 1/8 turn after r and L get aligned and the piston is at its highest position.

That condition is satisfied only for one linear speed of the piston.