Top E Planes

[Brooke]

Heh!  While I was typing some math, Badboy posted an actual experiment.   

[FLOOB]

No, that's not the way it works and I'm going to try to explain it differently for you, and confirm it with an experiment of my own.  

Ok, that part is correct and to confirm that we can use Newton's second law like this:

Newton's second law is f = ma

On the moon the only force is gravity and the force due to gravity is given by mg so the equation becomes:

  mg = ma

Now you see that the mass cancels out on both sides leaving g = a

which means that the acceleration equals gravity and the mass makes no difference. That is what you are saying, and I agree that on the moon or in a vacuum that is true. However, you then extend that to motion in the atmosphere and you simply can't do that. When you take into account the additional forces, the acceleration then depends on mass as well.

Yes, that's exactly what happens on the moon, no atmosphere, no resistance, no difference in speed and we just used Newton's second law to confirm that.

No, you can't extend your argument about what happens on the moon to what happens in atmospheric flight, that's a non sequitur. I will shortly prove that mathematically and confirm it experimentally.

Again, this is incorrect, both the drag and the mass affect the acceleration. In order to prove that first we can use Newton's second law to demonstrate the truth of it mathematically and then carry out an experiment to confirm it. The experiment was fun, I took some time between teaching today and a couple of my students volunteered to do the experiment so I could show it to you. It isn't as dramatic as dropping cannon balls from a tower, but the results are just as impressive.

Ok, firstly the math and again we will begin with Newton's second law, f=ma. However now the force is not just the force of gravity, there is also the air resistance which is represented with the letter d, so the force is now the gravity acting downwards and the resistance acting upwards so we have f = mg-d and Newtons law can now be written as:

   ma = mg - d

now if we divide both sides by m we get:

     a = g - d/m

You can read this as the acceleration equals gravity minus the drag divided by the mass. This makes it clear that the acceleration has an upper limit of g, and how much acceleration depends on the value of three things, g, d and m. You can also see that if you apply this equation to two objects that are identical in every way accept their mass, the heavier one will fall faster because d/m will be smaller, and it will reach a higher terminal velocity.

Now for the experiment.

After I read your message I devised an experiment to confirm the theory that was quick and easy to carry out.

Firstly I took two identical table tennis balls, and used a syringe to fill one with water.  

(Image removed from quote.)

These two balls then had identical drag, the only difference being that one had greater mass.

According to you, they should both accelerate at the same rate and hit the ground together. According to Newton's second law the heavier one should accelerate faster and hit the ground first.

This is what happened when one of my students dropped the two table tennis balls at the same time, the ball filled with air is in his left hand and the one filled with water is in his right hand.

www.leonbadboysmith.com/video/Experiment.MOV

If you use the pause button to watch what happens you will see that the lighter ball in the left hand appears to be released a fraction of a second before the other and when it passes the dropper's chin it is slightly in the lead, but the heavier ball quickly overtakes the lighter ball and hits the ground with a lead of about four ball diameters. This experiment confirms the theory. In an atmosphere, mass does affect how fast things fall.

Fortunately, it actually works in accordance with Newton's laws, if not those Apollo astronauts would never have made it to the moon in the first place.

Hope this helps...

Badboy
 

That's because the heavier ball has more inertia. Inertia is proportional to mass, gravity isn't. Scroll up and see what I wrote about parachutes.

[FLOOB]

Drop these two on the moon (where rho is almost zero), and they will drop the same.  Drop them in our sea level atmosphere, and you will get very different behavior.

But not because gravity acts on things differently on earth than it does on the moon or a vacuum.

[Brooke]

But not because gravity acts on things differently on earth than it does on the moon or a vacuum.

Of course not.  I don't think that I implied that.  (However, if you want to get picky in terms on non-Newtonian physics, there is some uncertainty about 90% or more of the mass-energy in the universe, the possibility that the cosmological constant is more than just a fudge factor, and so forth, and how some fundamental things, which we previously thought were constants, might vary in space or time or both.  But that, too, was not part of or implied in my discussion.  )

[GScholz]

Power/weight ratio, power/drag ratio and weight/drag ratio. Those are the only things that matter in a zoom climb after the rotation into a climb has been made. Wing loading plays a part in how much drag is generated during the rotation into climb. Gravity affects all objects equally (no matter on Earth or the Moon) and is irrelevant.

High power to weight.
High power to drag.
High weight to drag (or more intuitively low drag to weight).

The aircraft with the best overall of those stats will zoom climb the best.


The reason a one pound steel ball falls faster than a ten pound cotton ball is because it has a higher weight to drag ratio, noting more. Eliminate aerodynamic drag (as if on the Moon) and they both accelerate and fall equally fast regardless of weight/mass. Typically the bigger the plane the better weight to drag ratio it has. That's why bigger ships and aircraft are usually more efficient and economical than smaller ones.

[FLOOB]

So do we all agree that gravity is not proportional to mass?

[GScholz]

What do you mean by "proportional" ?

Gravity on Earth is a constant 1G acceleration towards the ground, regardless of size or mass.

[FLOOB]

Scroll back to see how this thread jumped the tracks.

Is there a formula that can express how fast I don't care? That's my new catch-phrase, "watch how fast I don't care". Feel free to use it.

[GScholz]

[(speed*care)^-2]

[Badboy]

That's because the heavier ball has more inertia. Inertia is proportional to mass, gravity isn't. Scroll up and see what I wrote about parachutes.

No, it really is just because the ball filled with water had greater mass. Also, what you said about parachutes in your earlier example simply confirms that.

The speed that a parachute falls at is given by the equation SQRT(2.m.g/Rho.Cd.A) and you can clearly see that greater mass will cause it to fall faster.

Notice that in that equation if you hold gravity and drag constant, the only thing that will change the speed is the mass.

Regards

Badboy

[Randy1]

Yet the Brewster seems to defy all of that.  Not sure why we developed the P51.   

[FLS]

So do we all agree that gravity is not proportional to mass?

You don't know what proportional means? It's basic multiplication. It's why the Sun has more gravitational force than the Moon.

[FLS]

Yet the Brewster seems to defy all of that.  Not sure why we developed the P51.   

Post your data. Show us what is wrong with the Brewster.

[Karnak]

Yet the Brewster seems to defy all of that.  Not sure why we developed the P51.   

Have you tested it?  You post with the confidence that ought to be backed by data, yet is uninformed.

How do I know?  Because I have tested it.  The Brewster does nothing unexpected.  In power on and power off tests it decelerates much, much faster than the Fw190D-9 regardless of the initial speed of the test.

[BnZs]

Have you tested it?  You post with the confidence that ought to be backed by data, yet is uninformed.

How do I know?  Because I have tested it.  The Brewster does nothing unexpected.  In power on and power off tests it decelerates much, much faster than the Fw190D-9 regardless of the initial speed of the test.

Correct. What it does do well is hold itself stable against its own torque as the speed falls off in a straight zoom. This is an important part of getting the most out of a zoom, that is why the P38 is probably the best zoomer, even though it doesnt have the best thrust/weight or the lowest drag airframe.