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Posted by M Fanoni [66.194.72.243] on Thursday, November 12, 2009 at 20:52:43 :
In Reply to: Re: rpm,= what speed posted by bill in Pa. [75.222.8.126] on Thursday, November 12, 2009 at 20:06:41 :
I guess what I was getting at is that knowing how to find the answer is much more important than finding the answer. You won't always have the program/website/cheat sheet.
If you think about it logically, the process is very simple and takes only a minute to compute.
If your crankshaft is spinning at 2000 RPMs, then that means the input shaft on your transmission is also spinning 2000 RPMs. Say you have a 3:1 reduction in second gear. Now the output shaft is spinning at 2000/3 = 667 RPMs. Next the shaft heads to the transfer case. Here you have (lets just assume) a 2:1 reduction because you are in low range. Now the drive line on the back side is turning 333 RPMs when it enters the differential. After running through the differential at 5.83 reduction, the axle shaft is spinning at 57 RPMs. As you know, the wheel is directly bolted to the axle shaft so that means the tire itself is also spinning at 57RPMs.
Things only get slightly tricky here. You need to know the distance from center of the axle shaft to the asphalt. This is known as the 'static loaded radius'. (Ideally, you want to know the kinetic loaded radius, but that's entirely too complicated). Finding this radius will allow us to get the effective diameter of the tire. Lets assume the static loaded radius is 16", which is to be expected for a 34" tire. Our effective diameter is twice the SLR, or 32". One last bit of information about the tire is its effective circumference. This is simply the constant "pi" multiplied by the effective diameter. Here it is 100.5".
Now, back to the axle shaft. We decided it is spinning at 57 RPMs and every revolution gets us ahead 100.5". Multiplying these two values together gets us 5740 inches per minute. That's our speed, but it's in pretty lame units. We can convert the inches to miles and the minutes to hours. We get 5740in/min * (1 ft/ 12 in) * (1 mile / 5280 ft) * (60 min / 1 hour) = 5.43 miles per hour.
That's with 34" tires, 3rd gear (3:1?), low range, 5.89 gears, at 2000 RPMs.