When I’m riding, especially in a straight line at a constant speed, my mind takes wings. All sorts of analytical subjects appear in my head. For instance:
> How many painted stripes there are between my current position and that mountain over there? My mind will estimate the length of and spacing between the stripes, the estimated distance to the mountain, and go to work on the calculation.
> If I get 40 mpg at 90 mph, and 60 mpg at 60 mpg, what kind of gas mileage am I probably getting now at 70 mph?
> If my engine is screaming at 12,000 rpms, how fast are the pistons actually moving?
That last question stuck with me and I investigated. I used a 2004 Yamaha R1 as my subject. The engine has a stroke of 53.5 mm and a readline of 13,750 rpms.
In case you don’t want to read the details, here are the RESULTS:
**** MAXIMUM PISTON VELOCITY AT REDLINE IS ~86 MPH. ****
To me, that doesn’t seem all that fast. I’d expected top velocity to be in the hundred’s of miles per hour.
But, considering that the viscosity of motor oil is such that it will not flow more quickly than its properties will allow, an article I read in Sport Rider magazine stated that this piston velocity is approaching the upper limit that a modern engine can achieve. It will take better and different oils, and possibly some improvements in metallurgy to achieve higher rpms for a given engine stroke.
Considering Formula 1 engines, which top out in the 20,000 rpm range, there is probably something more that can be done in motorcycle engines with current technologies.
The new 2006 Yamaha R6 has a redline of 17,500 rpms and that is impressive. However, I’ll bet, if anyone wants to perform the calculations using the new R6 as the subject, that the maximum piston velocity is pretty close to that of the R1.
Lee
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DETAILS
This is a method to calculate maximum piston velocities. All that must be known is the stroke of the piston and the engine's redline to calculate the maximum velocity.
Knowns:
1. The total stroke of the engine is calculated from the top-dead-center to the bottom-dead-center of the reciprocation cycle.
2. The total stroke of the engine is equal to the distance from the crankshaft pin to the center of the crankshaft, times 2.
Analysis:
The engine's stroke tells you the diameter of the circle the engine's crankshaft pin traverses. The piston can only go up and down as far as the crankshaft pin it is attached to allows it to travel. Thus, half of the engine's stroke is the radius (R) of the circle the crankshaft pin makes as it rotates.
It can be proved that the maximum linear velocity of the piston occurs at the points of zero acceleration on the up and down strokes of the piston. These 2 points are at 0 and 180 degrees as shown on a normal 360 circle drawing which are halfway up in an upstroke and halfway down in a downstroke. The maximum linear velocity of the piston is a function of the sine of the angle between a vertical line drawn between the top-dead-center and the bottom-dead-center of the reciprocation cycle, and a line drawn from the center of the crankshaft pin to the center of the crankshaft when the pin is at 0 or 180 degrees in its rotational cycle. When the crankshaft pin is at 0 or 180 degrees, the angle between the 2 lines is 90 degrees. The sine of 90 degrees is one. Therefore, the maximum linear velocity of the piston is a function of the engine's rotational speed times the sine of 90 degrees (1) times the circumference of the circle the crank pin traverses.
If a piston's stroke is of length S, then "1/2 x S" equals the radius of the circle the engine's crankshaft traverses ( R ).
Circumference of a circle: C = 2 x pi x R
PMLV (Piston's Maximum Linear Velocity) = C (Circumference) x RS (Rotational Speed) x sine 90 degrees
- or -
PMLV = C x RS x sine 90 degrees
Therefore: PMLV = 2 x pi x R x RS x sin 90 degrees
Calculations:
pi ~ 3.1416
R = 53.5mm / 2 = 26.75 mm
RS = 13750 revolutions / minute
sine 90 degrees = 1
PMLV = 2 x 3.1416 x 26.75 x 13750 x 1 = 2,311,039.5 mm / minute
To convert this number to some more meaningful numbers, we transmogrify the result, above, using this formula to convert mm per minute to miles per hour:
PMLV (to convert from mm/min to mph) =
1 meter x 39.37 in x 1 ft x 1 mile x 60 min
-------------------------------------------------------- =
1000 mm x 1 meter x 12 in x 5280 ft x 1 hour
39.37 x 60
-------------------- =
1000 x 12 x 5280
2,362.2
------------- = .000037282 miles / hour
63,360,000
Finally, to convert our calculated PMLV from mm/minute to mph, we multiply:
PMLV = 2,311,039.5 x .000037282 = 86.16 miles per hour
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Originally Posted by Suki
