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  #101  
Old 05-02-2010, 07:33 PM
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Originally Posted by Fraser View Post
Not right. When an object is in free fall through the atmosphere there are two forces at work. One is the gravitational pull between the earth and the object (trying to speed things up) and the other is the aerodynamic drag of the object through the atmosphere (trying to slow things down). The object reaches its steady-state velocity when these two forces are balanced.

The gravitation pull between the object and earth is not however constant but is dependent on the mass of the object (as it is also dependent on the mass of the earth).
Dude, you are funny. First you tell me it's "Not right". Then you repeat the exact same thing I said, using slightly different words. Did you miss the part of my post where I very clearly mentioned cross-sectional area and COEFFICIENT of DRAG as the opposing vectors? Hello? As JCL so aptly pointed out, when comparing the 2 vehicles in play, the Cd difference is negligible, meaning both vehicles' acceleration would be slowed at the same rate. What you are referring to as steady-state velocity, also known as terminal velocity, does not negate the fact that the 4.6is and the X5M would still hit at the same time regardless of the mass difference. Since the Cd difference is negligible, they would attain this terminal velocity within maybe a millisecond of each other. Because the acceleration of gravity is a constant for all objects. And the Cd that acts against it is equivalent for the 2 vehicles in question.

Nothing in my original post is false. Perhaps you need to re-read it.
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  #102  
Old 05-02-2010, 07:42 PM
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StanF18: Provided the cliff is high enough for the two objects in question to reach their respective terminal velocities, the heavier object would reach the ground first provided the aero factors were the same. You original post says that weight/mass is not a factor, it is.
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  #103  
Old 05-02-2010, 08:06 PM
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Originally Posted by Fraser View Post
Think about this. Two objects. One is a large and very fine bird feather. The other is a moulding of that same feather made from lead. Same shape, same cross-sectional area, same cd. When you drop them together from a good height which will hit the ground first?

Hopefully the link below works. If gives a formula for terminal velocity. Shows how mass and therefore gravitational pull is a factor.

Terminal velocity - Wikipedia, the free encyclopedia
INCORRECT. Nice try, but here is why it fails. The cross-sectional area of these 2 "feathers" is actually not the same. The REAL bird feather's cross-sectional area and Cd are BOTH much greater due to the fact that the air encountering that bird feather is in contact with a multitude of miniature surfaces in between the "strands" of the actual feather. The bird feather and the lead feather, while at first APPEARING to have the same shape and cross-sectional area are altogether different objects due to multiple miniature exposed strands on the bird feather made of an entirely different, porous material. The reason for their differing fall rates is NOT their mass difference!!! The reason is the difference in cross-sectional area due to the bird feather's POROSITY. The air ENTERS the various pores and surfaces and thisd leads to substantially more drag than the lead feather.

The best way to illustrate the failure and misleading nature of your example is as follows. Take a solid iron cannonball (Cannonball A). Weigh it. Let's say it weighs 1000 pounds. Now: Take anther solid iron cannonball (Cannonball B) of the same shape and weight. if there was a way to then open up Cannonball B into 2 halves (like an orange), and take out let's say a good 500 pound chunk of iron from its center...then close it up and re-weld it to its original shape....You now have iron cannonball A weighing 1000 pounds. Yes? And you have iron cannonball B of the same size and material, but you have cored out its center and it NOW weighs only 500 pounds. How much $$$ do you want to bet that if you drop these 2 off a cliff at the same time, they would hit the bottom at the same time? That's because the drag acting on both is the same, due to the EXTERIOR PORTION of the cannonballs being the same size and material. The porosity and cross-sectional area is equivalent. At this point mass does NOT enter the equation.

Similarly, your example is misleading when applied to the 2 free-falling vehicles. Unlike the multiple exposed surfaces of the bird feather vs. the lead feather, The 3 fat guys inside the 4.6is have ZERO effect on the drag vector. So while their vehicle is consequently heavier, it would still accelerate at the same rate as the lighter X5M. And EVEN if the cliff is ultra high, and both vehicles eventually stop accelerating and start falling at a steady speed...i.e. TERMINAL VELOCITY....they would STILL hit bottom at the same time. Because the acceleration of gravity is a constant for ALL objects. And the drag that counteracts this "g" vector is equivalent for the 2 vehicles, regardless of the extra mass inside the 4.6is.

Last edited by StanF18; 05-02-2010 at 08:11 PM.
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  #104  
Old 05-02-2010, 08:11 PM
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Now guys don't get me wrong, I absolutely love my XM. But my 2009 750Li I traded in on it was rated at 400hp and everyone that I know especially my wife which has had the most pilot time of both vehicles say my 750 was faster! No facts to back this theory up but in my opinion it should not even be a question. Mine is awesome but in no way feels like 550hp. Maybe my expectations were a little high for 100k and 550hp?
Sounds like you need a nice ECU tune for that beast, to put the smile back on your face.
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  #105  
Old 05-02-2010, 08:32 PM
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Originally Posted by StanF18 View Post
INCORRECT. The 3 fat guys inside the 4.6is have ZERO effect on the drag vector. So while their vehicle is consequently heavier, it would still accelerate at the same rate as the lighter X5M. And EVEN if the cliff is ultra high, and both vehicles eventually stop accelerating and start falling at a steady speed...i.e. TERMINAL VELOCITY....they would STILL hit bottom at the same time.
Assuming that the two X5s in question have the same aerodynamic drag but one is heavier because of all the extra people inside, the heavier one will have a higher terminal velocity. Therefore if the cliff is ultra high, as you say, and both are able to achieve their terminal velocity, the heavier one with the high velocity will hit the ground first.
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  #106  
Old 05-02-2010, 09:03 PM
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Originally Posted by Fraser View Post
Assuming that the two X5s in question have the same aerodynamic drag but one is heavier because of all the extra people inside, the heavier one will have a higher terminal velocity. Therefore if the cliff is ultra high, as you say, and both are able to achieve their terminal velocity, the heavier one with the high velocity will hit the ground first.
OK, I took a look at that article on Wikipedia. Assuming that their terminal velocity formula is correct (Wikipedia has been wrong in the past), mass is indeed a factor. I guess I am having trouble figuring this one out, in light of the physics experiment we did in college: Which showed mass was a non-issue for equivalently shaped free-falling bodies made of the same material. That experiment had an automated repeating pencil "woodpecker"-type device (with a pencil attached) that made a mark every 0.1 seconds on a piece of white tape trailing a falling steel sphere. The 2 steel spheres had rather different masses. But analyzing the pencil marks on the trail of tape: all the marks had exactly the same lengthening pattern for each of the spheres. In other words the increase in distance from one mark to the next, and then to the 3rd mark, and the 4th mark, and so forth....(which represents the ongoing acceleration of the object) was absolutely identical.

The feather is still a bad example...while the masses of the 2 feathers are different, the differences in Cd and A (cross-sectional area) are the main "culprits" in the much lower terminal velocity of the bird feather vs. the lead feather.
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  #107  
Old 05-02-2010, 09:07 PM
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time to call in Mythbusters methinks .
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  #108  
Old 05-02-2010, 09:24 PM
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I'm sure that Wikipedia is right on this occasion. Easier to post that link that upload page images of the physics book that I still have from old university days which has the same basic explanation of terminal velocity of a free-falling object. It gives the variables as mass, aero drag (Cd x cross-section area) and the density of the medium through which the object is falling. It also notes that while acceleration due to gravity is always the same in a perfect vacuum there is some variation in acceleration in a medium like air that is dependent on the density of the object vs the density of the medium, with denser objects accelerating faster than less dense objects in the same medium. In this case our X5 stuffed with bodies will be denser than an empty X5 so not only will the heavier X5 (+ bodies) achieve a higher terminal velocity, it will also accelerate slightly faster in getting to its terminal velocity.

Agreed that the feather example is not good as it would be impossible to replicate the feather's Cd in a lead casting.
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  #109  
Old 05-02-2010, 09:49 PM
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paging NASA , maybe an astrophysics dude could answer .
maybe electro magnetic forces and the composition of materials used in the experiments affect the results of said experiments .

anyhoo , I was given a figure to determine my terminal velocity in stable freefall and everyone has a predetermined figure .
when doing relative freefall ( formation ) some dudes required to wear oversleeves to create drag and some dudes required to wear weights to balance their body . everyone had to adjust body position to faal at the same speed , weight and drag being a factor to terminal velocity .

thrillseekers would pay for a tandem jump whereby they would be attached to a skydiver to experience high altitude freefall .
the tandem skydivers would fall faster than a single skydiver due to the weight factor with little additional drag so a small drogue parachute was deployed after exiting the aircraft to attain 120mph , it also improved stability .

A solo parachute was around 200 sq/ft
A tandem parachute was around 400sq/ft
so why do you think a tandem required double the canopy area .

climbing to 12000 ft in a cessna 206 took a boringly long time and sometimes the weather or windspeed changed , so we were told to return to the drop zone, the pilot would point straight at the ground and very soon reached a speed where we would become weightless .
need I say more .

edit : re the cessna , we were effectively weightless as soon as it began to descend . as it got faster we would begin to float around to a point where we had to hold on to the aircraft and when we held on I`m sure we were creating some sort if drag on the aircraft . whether this has anything to do with the fact we consist of mainly water I don`t know .

Last edited by amacman; 05-03-2010 at 10:33 AM.
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  #110  
Old 05-03-2010, 01:53 AM
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Quote:
Originally Posted by Fraser View Post
Assuming that the two X5s in question have the same aerodynamic drag but one is heavier because of all the extra people inside, the heavier one will have a higher terminal velocity. Therefore if the cliff is ultra high, as you say, and both are able to achieve their terminal velocity, the heavier one with the high velocity will hit the ground first.
I'm waiting to see the calculation of how high that cliff has to be for the terminal velocity to be a factor. I did the terminal velocity calculation, above, so I'll let someone else crunch the height calculation. I'm guessing it is up there with the highest cliff on earth, let alone the highest one that has a road to it.
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