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Anasazi
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Title:
The title should actually read Finding the acceleration of a piston with respect to a cranks angle
I have found a formula for calculating the acceleration of a piston, with respect to a cranks angle, however I've also found a couple of online calculators that give this result - my problem is that the results are completely different, and I'm not sure which is correct - if either.
I am using the formula found on this page:
http://www.codecogs.com/reference/physics/kinematics/velocity_and_acceleration_of_a_piston.php
On the right hand side I have the formula for acceleration:
[itex]a = -rw^2(cos\theta+(cos2\theta/n)[/itex]
where:
[itex]r[/itex] = crank radius
[itex]l[/itex] = rod length
[itex]\theta[/itex] = crank angle
[itex]w[/itex] = crank angular velocity
[itex]n[/itex] = [itex]l/r[/itex]
The values I have got are as follows:
[itex]r[/itex] = 4 (cm)
[itex]l[/itex] = 15 (cm)
[itex]\theta[/itex] = 1 (rad)
[itex]w[/itex] = 50 (rad/s)
[itex]n[/itex] = 3.75
Putting all of this into the formula I should get:
[itex]A = cos\theta = 0.5403[/itex]
[itex]B = cos2\theta = -0.4161[/itex]
[itex]C = -rw^2 = - 4 x (50^2) = -10000 [/itex]
[itex]C x ( A + ( B / 3.75 ) ) = -4293.4[/itex]
So, the acceleration of the piston at an angle of 50 rads is -4293.4 cm/s, which equates to -4.293 m/s, which I'm guessing means it is going backwards?
There are a couple of problems here. It seems after playing with the values within a spreadsheet, the minimum acceleration is approx -12.6666, yet the maximum acceleration is 7.3541, why such a difference, surely the maximum acceleration to be equal in both directions?
In comparison, an online calculator I found here (http://www.bigboyzcycles.com/PistonSpeed.htm, when given the following data:
Stroke (inches): [itex] ( r x 2 ) / 2.54 = 3.1496 [/itex]
Crankshaft Speed (RPMs): [itex] w / 0.104719755 = 477.465 [/itex]
Connecting rod length (inches): [itex] l / 2.54 = 5.905511 [/itex]
Gives 416 ft/s, which equates to 126m/s...
So, for reasons unknown to me I'm getting a huge difference between these calculations. Neither one is giving me much confidence.
Thank you.
The title should actually read Finding the acceleration of a piston with respect to a cranks angle
Homework Statement
I have found a formula for calculating the acceleration of a piston, with respect to a cranks angle, however I've also found a couple of online calculators that give this result - my problem is that the results are completely different, and I'm not sure which is correct - if either.
Homework Equations
I am using the formula found on this page:
http://www.codecogs.com/reference/physics/kinematics/velocity_and_acceleration_of_a_piston.php
On the right hand side I have the formula for acceleration:
[itex]a = -rw^2(cos\theta+(cos2\theta/n)[/itex]
where:
[itex]r[/itex] = crank radius
[itex]l[/itex] = rod length
[itex]\theta[/itex] = crank angle
[itex]w[/itex] = crank angular velocity
[itex]n[/itex] = [itex]l/r[/itex]
The values I have got are as follows:
[itex]r[/itex] = 4 (cm)
[itex]l[/itex] = 15 (cm)
[itex]\theta[/itex] = 1 (rad)
[itex]w[/itex] = 50 (rad/s)
[itex]n[/itex] = 3.75
Putting all of this into the formula I should get:
[itex]A = cos\theta = 0.5403[/itex]
[itex]B = cos2\theta = -0.4161[/itex]
[itex]C = -rw^2 = - 4 x (50^2) = -10000 [/itex]
[itex]C x ( A + ( B / 3.75 ) ) = -4293.4[/itex]
So, the acceleration of the piston at an angle of 50 rads is -4293.4 cm/s, which equates to -4.293 m/s, which I'm guessing means it is going backwards?
There are a couple of problems here. It seems after playing with the values within a spreadsheet, the minimum acceleration is approx -12.6666, yet the maximum acceleration is 7.3541, why such a difference, surely the maximum acceleration to be equal in both directions?
In comparison, an online calculator I found here (http://www.bigboyzcycles.com/PistonSpeed.htm, when given the following data:
Stroke (inches): [itex] ( r x 2 ) / 2.54 = 3.1496 [/itex]
Crankshaft Speed (RPMs): [itex] w / 0.104719755 = 477.465 [/itex]
Connecting rod length (inches): [itex] l / 2.54 = 5.905511 [/itex]
Gives 416 ft/s, which equates to 126m/s...
So, for reasons unknown to me I'm getting a huge difference between these calculations. Neither one is giving me much confidence.
Thank you.
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