- #1
Please identify this physics symbol
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Discussion Overview
The discussion revolves around identifying the symbol "w" in a formula related to calculating the inertia of a piston assembly in a two-stroke engine. Participants explore the meaning of angular speed and the angle used in the calculations, as well as the formulation of the inertia equation itself.
Discussion Character
- Technical explanation
- Mathematical reasoning
- Debate/contested
Main Points Raised
- One participant inquires about the meaning of "w" in the context of piston inertia calculations.
- Another participant suggests that "ω" represents angular speed of the crankshaft and "θ" refers to its angle, requesting more context for clarity.
- A participant seeks clarification on whether angular speed refers to the rotational speed of the crank and if the angle is measured from the vertical axis.
- One participant proposes that the angle of the crank is from the horizontal axis based on the behavior of the piston speed at specific angles.
- A participant shares a formula for calculating piston inertia but initially encounters issues, later correcting it by adding parentheses and confirming it works with conventional angle definitions.
- The corrected formula yields specific inertia values at top dead center (TDC) and bottom dead center (BDC), but these values do not align with those from an external calculator, raising questions about the accuracy of the results.
Areas of Agreement / Disagreement
Participants express uncertainty regarding the angle measurement and the interpretation of the formula. There is no consensus on the correct values for piston inertia, as the results differ from an external source.
Contextual Notes
Participants discuss the need for consistent units (metric) and the implications of angle definitions on the calculations. Some assumptions about the angle's reference point and the formula's structure remain unresolved.
- #2
BvU
Science Advisor
Homework Helper
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Hello jag, 
I'm pretty sure the ##\omega## is the angular speed of the crankshaft and ##\theta## is its angle. If you could provide some more context, maybe we can settle this with more certainty.
I'm pretty sure the ##\omega## is the angular speed of the crankshaft and ##\theta## is its angle. If you could provide some more context, maybe we can settle this with more certainty.
- #3
jaguar57
- 8
- 0
I'm making a spreadsheet and part of it needs to know the piston inertia every 15 degrees.
By "angular speed" do you mean the rotational speed of the crank where the connecting rod connects to it?
And the angle is from the vertical axis?
By "angular speed" do you mean the rotational speed of the crank where the connecting rod connects to it?
And the angle is from the vertical axis?
- #4
Dale
Mentor
- 36,705
- 15,620
The w is the lower case Greek omega: ##\omega##. It is usually used for angular frequency which in SI units is measured in radians/secondjaguar57 said:
- #5
jaguar57
- 8
- 0
Since cos(0)=1 and cos(90)=0 then I guess I can assume that the angle of the crank is from the horizontal axis since near 90 and 270 degrees (assuming o degrees is with the piston at the top of its movement) the piston has the highest speed?
Do I need to have all weights in kg and all lengths in meters? (I prefer the metric system)
Do I need to have all weights in kg and all lengths in meters? (I prefer the metric system)
- #6
jaguar57
- 8
- 0
this is how I made the formula but it's not working for me:
PISTON INERTIA = (piston assembly kg + .66 x con rod kg) x (piston stroke meters/2) x (radians(crankshaft angle change)/second)^2 x COS(crank angle) + ((piston stroke meters/2)/(connecting rod meters)) x COS(2 x crank angle) - ((.5 x piston stroke meters)^3 / (4 x (connecting rod meters)^3) x COS(4 x crank angle))
PISTON INERTIA = (piston assembly kg + .66 x con rod kg) x (piston stroke meters/2) x (radians(crankshaft angle change)/second)^2 x COS(crank angle) + ((piston stroke meters/2)/(connecting rod meters)) x COS(2 x crank angle) - ((.5 x piston stroke meters)^3 / (4 x (connecting rod meters)^3) x COS(4 x crank angle))
- #7
jaguar57
- 8
- 0
I got it to work after seeing I forgot to put a pair of parentheses. Here it is corrected:
PISTON INERTIA = (piston assembly kg + .66 x con rod kg) x (piston stroke meters/2) x ((radians(crankshaft angle change per second)^2 x COS(crank angle) + ((piston stroke meters/2)/(connecting rod meters)) x COS(2 x crank angle) - ((.5 x piston stroke meters)^3 / (4 x (connecting rod meters)^3) x COS(4 x crank angle)))
And it did work using the conventional angling of the crank with 0 degrees being with the piston at the top of its stroke.
TDC inertia for my engine is 287 (after converting N/m2 to lbf) and -186 at BDC. But that doesn't agree with the Wallace Racing piston inertia calculator at http://www.wallaceracing.com/Calculate-Inertia-Force-of-Piston.php
PISTON INERTIA = (piston assembly kg + .66 x con rod kg) x (piston stroke meters/2) x ((radians(crankshaft angle change per second)^2 x COS(crank angle) + ((piston stroke meters/2)/(connecting rod meters)) x COS(2 x crank angle) - ((.5 x piston stroke meters)^3 / (4 x (connecting rod meters)^3) x COS(4 x crank angle)))
And it did work using the conventional angling of the crank with 0 degrees being with the piston at the top of its stroke.
TDC inertia for my engine is 287 (after converting N/m2 to lbf) and -186 at BDC. But that doesn't agree with the Wallace Racing piston inertia calculator at http://www.wallaceracing.com/Calculate-Inertia-Force-of-Piston.php
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