Trying to understand a few things. First is a Radian.
In reading the Wikipedia page on it...
The radius of a circle, in engine terms would be half the stroke, as the connecting rod journal axis creates a revolution, it makes a circle. A 4" stroke will create a 4" circle and the radius of that circle is 2". A Radian is a portion of the circles circumference equal to the radius. So, if the rod journal were at top dead center and you rotated the crank one Radian, the center axis of the journal would move along circular curve of the circumference 2". In a sense, creating a triangle 2" from the center of the crank to the rod journal at TDC, 2" along the circumference (of the circle the rod journal travels), and 2" from that point back to the center of the crankshaft.
I'm trying to figure out how many Radian the connecting rod journals axis travels in one stroke, from TDC to BDC. The best I make of it, and it's becoming more clear as I write this, is there are 3.14 (Pi) Radian in a semi-circle and 6.28 (two Pi) Radian in a circle. I should be able to check this against the equation for finding the circumference of a circle.
The circumference of a circle = Pi x Diameter = 3.14 x 4 = 12.56" circumference. Half of that circle (180°) = 6.28".
One Radian of a 4" circle = 2"... 3.14 Radians x 2" = 6.28". AWESOME, that checks out for a half circle, or one stroke from TDC to BDC.
I think I just wrapped my mind around that part.
What I'm ultimately trying to understand is the equation for finding peak piston velocity, which calls for replacing a constant known angle in a triangle into a known angular velocity, or a moving angle. Angular velocity - Wikipedia, the free encyclopedia The three points of this triangle being the wrist pin axis, rotating axis of the crankshaft, and the axis of the connecting rod journal. The known sides of that triangle are from the crank axis to the rod journal axis (half of stroke) and the connecting rod length. The known angle is degrees ATDC.
My best understanding at this point, is a known constant angle in the "Law of Cosines" formula (used to find unknown angles/legnths with known angles/legnths) the equation is replaced with a known angular velocity to find the unknown angular velocity. So if we know that the rod journal sweeps from 0° to 180° in a certain time, or a certain number of repetitions in a given time (RPM), we can calculate the speed of the wrist pin axis. That's what I understand on a theory basis, but haven't 100% wrapped my mind around it to the point of full understanding.
Any input you have to help me further understand would be deeply appreciated.