</font><font color="blue" class="small">( Does ground speed and pto speed remain linear across the full range of engine rpm's? )</font>
I would say that in most cases they would be close through SOME of the engine RPM range, particularly around the engine's rpm that the PTO speed is rated at, but not through the ENTIRE RPM range.
I will try to re-word the question in order to eliminate the word "linear" so that everyone can throw in their 2 cents worth (I'm trying to make use of my Mechanical Engineering degree that I haven't used in a while...).
Another way to word the question would be:
When the engine's RPM is doubled (or tripled), is the tractor's ground speed and PTO speed also doubled (or tripled)?
A similar question that most tractorbynet readers could relate to deals with automotive applications: Take a pickup truck with manual transmission in 2nd gear (or any other gear); if the engine RPM is doubled (from 1000 rpm to 2000 rpm), does the ground speed double? If the engine RPM is increased by a factor of "4" (from 1000 rpm to 4000 rpm), does the ground speed increase by a factor of "4"?
A Related Story? Many years ago I purchased a push lawn mower with a Hi-Low engine speed adjustment. I always mowed the lawn using the lower engine speed in an attempt to "save wear and tear on the engine". Later I noticed that newer designs of the same type lawn mower did not have the lower speed option and thus only had "Full Speed". When I enquired as to the purpose of the design change, the answer I got was that the air cooled engines depended upon the higher engine speed to create proper air flow across the engine, and that customers that were using the low speeds were having more problems with their engines overheating. While I never had any problems with my engine, I took that as a lesson learned and now I operate equipment using design parameters.
As stated in another post, I agree that by trying to "save wear and tear on your tractor" and operating at lower engine speeds you may actually be creating additional wear and tear.
Kelvin