Sorry, I know this topic has most likly come up before, and one would think it would be put to rest by now, but just the other day online the topic of diving away from your enemy as a tactic came up, and as usual (almost expected) someone mentioned the P-47 ability pull away from (read better acceleration) the enemy plane in a dive due to the P-47 being heavier.
I had just landed, and resting and I figured I would point out that the P-47 being heavier (read more mass) has nothing to do with the P-47s ability to pull away from the enemy plane, due to the fact that gravity is (for all intents and purposes) constant. I went on to point out the values that are affected by more mass is the momentum and kinetic energy of the P-47 relative to lighter fighters.
I than attempted to explain the P-47 dive acceleration myth by pointing out the P-47 was a very structurally sturdy aircraft, which allowed the pilots to push the P-47 to the edge of its envelope in speed in a dive without worry. Where as other planes would have started to shake prior to this point enough that the pilot would have stopped chasing, or at least pulled back on the throttle in fear of his plane breaking up. Which I will come back to later (see below)
By this time in the chat, several people (most notably Panthera) disagreed with me and stated a heavier (read more mass) plane will accelerate faster than a lighter plane. Panthera gave an example of how a bowling ball will drop faster than a balloon of the same size. I was quick to point out that a bowling ball and a balloon both hit the ground at the same time in a vacuum, which is a classic test used to show heaver objects hit the ground at the same time as lighter objects. Which means they both fell at the same rate (read speed) and therefore both had equal accelerations, which is to be expected due to gravity being a constant and acting equally on all objects.
Which is the whole purpose of the bowling ball vs balloon in a vacuum test. I went on to explain what does affect the acceleration of an object in the atmosphere is it's surface area which causes drag, and in an airplanes case, it's thrust. To which Panthera responded with:
All objects, regardless of surface area, will drop at the same rate in a vacuum.
Note he said 'surface area' which shows he is confused about the purpose of the vacuum drop test. The purpose of the vacuum drop test is to show
All objects, regardless of mass, will drop at the same rate
But don't take my word for it!
Light and heavy objects fall at the same rate
And keep in mind here that Galileo does not qualify it by saying in a vacuum. Galileo conclusion came from rolling balls of different size (read mass) down a angled slide and made note of the fact that they all reached the bottom at the same time.
Granted, there are other factors in play in Galileo's test, and he was comparing like objects (balls) but his conclusion was correct. On that note, the modern vacuum test is a extension of Galileo's test to show that once you remove the forces of drag due to an atmosphere all objects fall at the same rate. And the only way two objects can fall a the same rate is if they both have the same acceleration, in our case, Earth's gravity.
Now back to the P-47, in my example above, where I pointed out the P-47 was a very sturdy aircraft, which allowed a pilot to push it to the edge of it's speed envelope in a dive. I believe this is where the P-47 gets its reputation from, with regards to diving away from an enemy plane. As shown above, we know the P-47's dive acceleration is NOT due to it being a heavier object, therefore if two planes, say a P-47 and Fw190 were to start a dive from the same initial velocity and dive angle, the plane with more thrust and less drag would be the one that accelerates (read dives) better.. It is not until you get near the planes max speed that this 'could' change, where a sturdy aircraft like the P-47 could continue on and a less sturdy aircraft may not be able to continue on in fear of breaking up. As a mater of fact, that is exactly what was found in a test performed in WWII where they compared a P-47 to a captured Fw190 in a dive.. Initially the Fw190 pulled away (read better acceleration) from the P-47, but eventually the P-47 caught up and passed it.
So, in summary, take two identical WWII planes, fill one up with 100% fuel, and the other with 25% fuel, dive them side by side at the same angle, same throttle settings (read thrust) and they will both accelerate equally which in turn means they will both dive at the same rate (read speed). The only time the extra mass will assist is once the planes reach their terminal velocity.. Assuming they do not fall apart, the plane with more mass (more fuel) will be able to go faster due to a bigger force (F=ma) countering the drag.. But chances are it will be so small, relative to the thrust (read force) it may go un-noticed, that and the chances are high that poorly constructed planes would break upon reaching terminal velocity, which is why this case is seldom considered, except for free falling objects with no thrust. The P-47 was an exception to the rule, it was a very sturdy aircraft, which is probably why it was used after WWII for high speed dive testing new propeller types.
Hope this helps!
For those who are not convinced, feel free to Google it NASA has some nice high school examples on the subject, but here is one I think is helpful
http://www.physicscl...1DKin/U1L5e.cfm" onclick="window.open(this.href);return false;">http://www.physicscl...1DKin/U1L5e.cfm