Aces High Bulletin Board
General Forums => Aces High General Discussion => Topic started by: fscott on January 30, 2001, 11:38:00 AM
-
K, here's a real world question. Suppose you take the propellors off all the planes in AH. Hold them by their tails pointed straight down. Let's start them off with a good average stall speed of say 100 mph. Now, you dropped them. Tell me which aircraft will accelerate the best?
I assume this is a mere test of drag/weight ratio. So I am interested in which plane drops like a rock the best. This is a real-world question that deals with B&Z, since it is a technique of flying I'm really starting to like - with the propellor on of course.
fscott
-
"I assume this is a mere test of drag/weight ratio"
Yes it is.
It's probably the P-47D.
However some number crunching is required to be certain, and I don't have enough data to do it.
Wells? (http://bbs.hitechcreations.com/smf/Smileys/default/smile.gif)
-
my money is on pony
weight 70% of jug but has alot lower fpa than 70% of jug
-
I say the Pony as well.
-
Originally posted by fscott:
K, here's a real world question. Suppose you take the propellors off all the planes in AH. Hold them by their tails pointed straight down. Let's start them off with a good average stall speed of say 100 mph. Now, you dropped them. Tell me which aircraft will accelerate the best?
I assume this is a mere test of drag/weight ratio. So I am interested in which plane drops like a rock the best. This is a real-world question that deals with B&Z, since it is a technique of flying I'm really starting to like - with the propellor on of course.
fscott
Sparing you the physics behind all this, its not a weight issue but a drag issue pure and simple.
-Ding
-
In general the heavy planes but the difference at the starting 100mph will be very small the difference in acceleration will increase as the planes start moving faster. My guess is one of the buff's followed by the 47. Easy way to test is just do a 0 g push over on the planes at a low throttle but not cut throttle setting for 10 secs and see who ends up the fastest.
HiTech
-
Dingy you are incorect it's not just a drag issue, is a combination of drag and weight.
HiTech
-
Originally posted by hitech:
Dingy you are incorect it's not just a drag issue, is a combination of drag and weight.
HiTech
How so? You arguing with Galileo who proved that all objects fall (this is what the planes would be doing in an engine-off situation) at the same speed regardless of their weight? Now when you get those items in a drag inducing environment, you can see why a feather and a bowling ball fall at different rates.
Unless Im mistaken, the only force causing the plane to speed up in a free fall is gravity (calculated by F(grav) = Gm(1)m(2)/r^2). The force of gravity will favor the slightly more massive plane albeit NEGLIGIBLY due to the HUGE mass of the Earth (6*10^24 kg). Feel free to plug the numbers into that proven formula above and you'll see what I mean:
G = 6.67 * 10^-11
m(1) = mass of any plane ya choose....P51 is 5266 kg when loaded, B17 is 27,240 kg when loaded)
m(2) = mass of Earth, approx 6*10^24 kg
r = distance between the two masses in meters....doesnt matter whch value you choose.
When you talk about free fall in an atmosphere, the only force slowing the plane and working in opposition to gravity is drag . Drag DOES NOT have a mass component to it and if it does, please show me what it is I am missing?
-Ding
[This message has been edited by Dingy (edited 01-30-2001).]
-
Dingy- I believe you practicaly answered your own question. We're not talking about a vacuum here, therefore I would think the weight would have some influence. I would tend to think that the heavier of 2 objects having the same drag coe would fall faster.
But then again I may be crazy.
-
Originally posted by AcId:
Dingy- I believe you practicaly answered your own question. We're not talking about a vacuum here, therefore I would think the weight would have some influence. I would tend to think that the heavier of 2 objects having the same drag coe would fall faster.
Dunno maybe its me thats crazy but I've never seen weight figured in any airflow/drag calculations.
-Ding
-
Dingi attach your bolling ball to the feather, Obviously total drag of the new combined object has gone up from both the feather or the bolling ball, yet together they fall faster than just the feather. I.E. is a ratio of Drag and wieght.
HiTech
-
Originally posted by hitech:
Dingi attach your bolling ball to the feather, Obviously total drag of the new combined object has gone up from both the feather or the bolling ball, yet together they fall faster than just the feather. I.E. is a ratio of Drag and wieght.
HiTech
HT, Im sorry but Im not sure what kind of point you are trying to make here. We still have normal physics to deal with.
IN A VACUUM, all objects fall at the same speed.
IN A DRAG INDUCING ATMOSPHERE, when an object is in free fall, the only forces acting on an object are a) gravity in a downward direction and b) drag in an upwards direction. We've already shown (and I think you agree) that the mass of an object has negligible effect on the downward force of gravity but no one has been able to show that mass has an effect on either parasitic or induced drag. You've been working on this longer than I have, show me how parasitic and induced drag is calculated.
-Ding
[This message has been edited by Dingy (edited 01-30-2001).]
-
The weight is only a factor in wing loading. The drag is the biggest factor in the situation describe. In a vacuum a bowling ball and a feather fall at the same speed. It is wind drag that is that major player here. The terminal velocity is in direct proportion to the drag/frontal area of the aircraft. NO IF AND OR BUT'S! I say the P-51. The major reason the water cooled inline V engined plane were in vogue in WWII was FRONTAL AREA! Look at the level fight low alt speed of most of the WWII aircraft. Generally the inline V engined planes are the fastest at sea level.
-
Heres a counterexample to yours HT, take a 16 lbs bowling ball and a 50 lbs parachute and attach them together. When the parachute opens, the objects fall SLOWER than the bowling ball alone yet it weighs more than the bowling ball by itself. LOL!
(http://bbs.hitechcreations.com/smf/Smileys/default/biggrin.gif)
-Ding
-
just a thought what are the terminal velocitys of the different aircraft in a unpowered state . seems to me that if one had a significantly higher terminal velocity and they were droped from a high altitude it would pretty much be the fastest in this situation. depending on how much the velocitys vairied from plane to plane . and would the terminal velocity decrease as the craft encountered the thicker atmosphere nearer to sea level ? but my money is on the p47 twice the weight and not twice or anywhere near that amount drag ( unless im missin a geometric progression somwhere in drag/pressure ) and the terminal velocitys would be in the mach 2 plus ranges anyway right so all that would hit the ground would be the engine and alot of little pieces anyway. ( pw r2800 planes will be all about equal then ) (http://bbs.hitechcreations.com/smf/Smileys/default/smile.gif)
-
You are correct jimdandy but just as top speed of a plane is when drag = thrust, in fscott's question of a plane no propler being droped you come up with the fowlling
F = M * A
Force = Weight - Drag
Mass = Weight / 32.2
Hence Accel. =
(Weight - Drag) / Mass or solving
Weight/Mass - Drag/Mass or in other terms
Accel = 32.2 - Drag/Mass
HiTech
-
Originally posted by Jimdandy:
The weight is only a factor in wing loading. The drag is the biggest factor in the situation describe. In a vacuum a bowling ball and a feather fall at the same speed. It is wind drag that is that major player here. The terminal velocity is in direct proportion to the drag/frontal area of the aircraft. NO IF AND OR BUT'S! I say the P-51. The major reason the water cooled inline V engined plane were in vogue in WWII was FRONTAL AREA! Look at the level fight low alt speed of most of the WWII aircraft. Generally the inline V engined planes are the fastest at sea level.
I'm throwing down the gauntlet on the one HT! If I'm wrong I'll pay double my fee next month. If I'm right next month is free.
Signed,
Scott D. Barnes
-
hitech that does not make sense
a buff would win?no
in the initial dive will be the most pronoinced difference, since initially it is govered most greatly by weight( e at 100 mph little paracitic drag on any plane in ah)
at the end is is governed by drag to weight, terminal velocity reached when they are equal. since the p51 has the lowest FPA in the game and a moderate weight im sure it will win
compression effects neglected
-
Dingy, although you have gotten completely off my orginal question, you fail to see that the open parachute creates HUGE drag compared to it's weight, whereas the bowling balls have much less drag. That's why it's a drag/weight ratio.
My original question still no answer, only guesses. Assume no one really knows?
"America's 100,000 quotes the P51D with lke .0176 drag factor. I know it has the lowest drag, but does it's weight of 7100 lbs allow it fall faster than a P47D of 10,000 lbs and drag of .0213? Also, I heard someone say the Fw190a5 gad a drag coefficient of .0230, and I know it's a really fasdt diver too, although that's with the propellor. I am only interested in raw drag/weight without added thrust.
I thought HT would know this.
fscott
-
Originally posted by Dingy:
Sparing you the physics behind all this, its not a weight issue but a drag issue pure and simple.
-Ding
IMO, weight is also an issue. The drag forms a force "barrier" that fights against the force your plane has at a determinate point. This force increases with speed, and, at some point, the force is so big that you stop gaining speed. In this case, your mass and acceleration are constants, so, at any point, the heavier aircraft has most force than the lighter one. For same drag coeficient, the drag force should be greater to decelerate the heavier than the lighter, so, the heavier aircraft can gain speed for a longer time. Anyway, you usally will disintegrate your aircraft prior to getting to the point where drag force can compensate your 9.8 * M force to make your speed constant.
-
figure it out yourself i dont wanna do math
m*g=CD*.5*rho*u^2*a
m=mass (kg)
g=9.8 m/s^2
CD=drag coefficient
rho=density at terminal altitude(kg/m^3)
u=velocity(m/s)
a=planform area of wing
solve for u, convert to mph
-
Originally posted by Jimdandy:
I'm throwing down the gauntlet on the one HT! If I'm wrong I'll pay double my fee next month. If I'm right next month is free.
Signed,
Scott D. Barnes
He's right folks. The man wins the $30 question. LOL!
HT I forgot buoyancy. Damn I it will be an expensive month next month. <S> (http://bbs.hitechcreations.com/smf/Smileys/default/biggrin.gif) Your right.
Terminal velocity (vt) equals
vt=(mg/k)^1/2 where k= a proportionality constant that depends on the frontal area and the property of the fluid.
Damn damn damn I hate it when I flap my gums with out thinking first. (http://bbs.hitechcreations.com/smf/Smileys/default/biggrin.gif) I'm going to go sulk now. (http://bbs.hitechcreations.com/smf/Smileys/default/biggrin.gif)
[This message has been edited by Jimdandy (edited 01-30-2001).]
[This message has been edited by Jimdandy (edited 01-30-2001).]
-
I would have to agree with Galileo on this one. If you remove the factor of thrust (propeller) than you are left with two falling objects. They will fall at the same rate regardless of mass. The only variable is drag. And I believe the Pony has the least amount of drag. When you add trust, the plane with the best thrust to drag ratio would have the highest top speed in a dive. And the plane with the best thrust to wieght ratio would have the best acceleration in a dive.
-
Ok now Im really confused since all this goes against how I understood Galileos experiments. When he drop objects of different weight off the Tower of Piza, he showed that objects of different weight fall at the same speed, right? Or is what he showed incorrect. I think thats where Im getting hung up.
-Ding
[This message has been edited by Dingy (edited 01-30-2001).]
-
Originally posted by Zigrat:
figure it out yourself i dont wanna do math
m*g=CD*.5*rho*u^2*a
m=mass (kg)
g=9.8 m/s^2
CD=drag coefficient
rho=density at terminal altitude(kg/m^3)
u=velocity(m/s)
a=planform area of wing
solve for u, convert to mph
I'm not sure if you are saying HT is wrong or if he's right. If you are saying he's wrong, mass is weight so the gravitational pull of the earth on the object towards the ground would increase it's speed quicker (in an atmosphere). Wouldn't it?
Hmm I forgot my physics class and what the teacher told me for my response to Dingy.. oh well maybe some day it will resurface. ;-)
-SW
[This message has been edited by AKSeaWulfe (edited 01-30-2001).]
-
Originally posted by Dingy:
Ok now Im really confused since all this goes against how I understood Galileos experiments. When he drop objects of different weight off the Tower of Piza, he showed that objects of different weight fall at the same speed, right? Or is what he showed incorrect. I think thats where Im getting hung up.
-Ding
[This message has been edited by Dingy (edited 01-30-2001).]
That's true if you jump to a vacuum. Think of it this way. Put the plane in oil. It will have buoyancy no mater where it is pointing straight down or not. The area displaces a small amount of air like a boat on the water. So even though the wing is thin and the nose of the plane is small it will try to support a small amount of weight do to the buoyancy of the fluid. Thus a heaver plain with a small frontal area will dive faster. The small area would be like putting a D9 Cat on a toy boat and expecting it to float. It wouldn't but the toy boat would non the less still be providing a small amount of buoyancy. In a vacuum there is nothing thus no buoyancy to contend with. Galileo holds true in a vacuum or for objects of similar drag at low speeds in air. A feather it truly the perfect example of this.
Now stop rubbing it in! (http://bbs.hitechcreations.com/smf/Smileys/default/biggrin.gif) LOL
-
Okay I think this is what my physics teacher told me in H.S.> How fast an object falls in relation to another depends on the ratio of it's drag vs it's weight and the other objects ratio of drag vs weight.
Sound right?
-SW
-
I'll say it again folks he is right. I just burnt some cash on my wrong answer so I wouldn't be agreeing if he weren't. He is right. You have to think of the falling plane as a really crappy boat in water. It is WAY to small to support the plane and keep it from falling (sinking) but it does still provide some flotation. Buoyancy is a function of mass and area. Thus the heavy plane with a smaller retaliative frontal area will fall a little faster. Just like a boat with to much weight.
-
Im wrong...after blowing an entire afternoon researching this, I found this website:
Elephant and Feather (http://www.glenbrook.k12.il.us/gbssci/phys/mmedia/newtlaws/efar.html)
Basically I understand it such:
The downward force due to gravity is opposed by the upwards force of air resistance. Two objects of different weights have different downward forces due to gravity. An object dropped from a height will accellerate downwards until the upwards force of air resistance equals the downwards force of gravity. At this point the object has reached terminal velocity.
There are two factors that affect the upwards force of air resistance....the speed an object is travelling and its frontal area. Its this frontal area (among other things) which we think of drag in an airplane.
Still dont quite follow what Galileo proved given this but the sources backing up HT are out there.
Now as far as what plane acclerates fastest, I would have to say, whatever is on my 6.
-Ding
-
OK, say Norm from Cheers and Carla from Cheers go skydiving. Norm weighs more than Carla, and he's a lot "bigger" than Carla.
Norm wears a parachute, and Carla doesn't. Will they both hit the ground at the same time? I think not.
(http://bbs.hitechcreations.com/smf/Smileys/default/wink.gif)
-
Just as a little side bar to this conversion.
The P-38L when tested had the best initial dive acceleration. Followed by the F4U and P-51D tied and then the P-47D.
Of course this was with power on but none the less my money is on the P-38. It had the wing loading of a cement truck.
-
Originally posted by Dingy:
Still dont quite follow what Galileo proved given this but the sources backing up HT are out there.
Now as far as what plane acclerates fastest, I would have to say, whatever is on my 6.
-Ding
Galileo proved the above AND that in the absence of drag things will fall at the same rate no matter the weight.
-
You all are doing this the wrong way, take out the Ol' ping pong balls. One empty and the other filled with sand. They have always done the trick of turning any aerodynamics thread into a long brain damaging experiment in torture if you try to read one.
// fats
-
Originally posted by fats:
You all are doing this the wrong way, take out the Ol' ping pong balls. One empty and the other filled with sand. They have always done the trick of turning any aerodynamics thread into a long brain damaging experiment in torture if you try to read one.
// fats
That is a great example fats. Thx.
-
Gallileo used objects of different weight but of the same aerodynamic properties to demonstrate that weight(mass) does not have anything to do with acceleration. If I remember correctly (we were both pretty drunk at a time), he dropped a cannon ball and a musket bullet - both round objects.
Even then the objects would evantually fall at different speed due to difference in density (lead is more dense then iron) and weight to crossection ratio (crossection is proportional to square of size while weight is proportional to cube).
Since the height of the tower was much lower then what would be necessary for such objects to reach terminal velocity (where resistance of air equals the force of gravity), there was no noticeable difference. Since the common wisdom of the times was that an object ten times as heavy would fall ten times as fast, he made his point very convincingly.
When an object is falling at it's terminal velocity, the force of gravity which is proportional to it's mass is equal to the force of drag which is proportional to crossection area, aerodynamic coefficient and approximately a square of speed.
So of two objects (planes) with the same crossection area and aerodynamic properties, the heavier one will reach higher speed before the drag equalizes the force of gravity (weight) and it stops accelerating.
miko
-
Miko2d hit it on the head.
-
Originally posted by hitech:
Dingy you are incorect it's not just a drag issue, is a combination of drag and weight.
This is very simple. Weight is involved because we are talking about forces - mass * acceleration for the airplane and the retarding force of drag.
The drag force will depend on speed, profile, surface roughness, etc. and the force pulling the airplane down is the product of the aircraft mass times the acceleration due to gravity.
A very light airplane of the same dimensions as a very heavy one will fall slower. It is the same as the bowling ball / feather thing. In air they fall at different rates. In a vacuum they will fall at the same rate as the retarding force is 0.
------------------
Rape, pillage, then burn...
-
Originally posted by Jimdandy:
HT I forgot buoyancy. Damn I it will be an expensive month next month. <S> (http://bbs.hitechcreations.com/smf/Smileys/default/biggrin.gif) Your right.
Bouyancy has nothing to do with it. In the very extreme it might have an exceptionally minor effect but with the density of almost every single airplane part being so much greater than air, bringing bouyancy into this is ludicrous.
Did that many here sleep through their science and physics classes?
------------------
Rape, pillage, then burn...
-
This is getting silly. Galileo did not do his experiments in a vacuum. Weight does NOT effect a falling objects ACCELERATION. Weight and drag determine an objects terminal velocity or top speed while falling and NOT its acceleration. A feather reaches terminal velocity almost immediately, while a bowling ball takes much longer. The P47 was known as the best diving airplane not because of its acceleration in a dive but because of the tremendous speeds it could reach. This is because of its high terminal velocity (due to weight) and relatively low drag and high thrust. You take a p47 with a full tank of gas and a p47 with 1/4 tank of gas and race them in a dive.....the 1/4 tank will initially pass the full tank because of its superior thrust to weight ratio .... however it will reach terminal velocity(TV) sooner than the full tank because of its lighter and therefore less drag is required to equal its lighter weight. When the 1/4 tank reaches TV the full tank will catch up and pass the 1/4 tank, because it still has gravity working for it, until it also reaches TV. The full tank will also increase its lead because it will reach its excess thrust limit at a higher velocity than the 1/4 tank.
-
ljkdern, the last thing I wanted to do was argue on this, all I wanna know is which dern plane has the best drag/weight ratio!
You need to look at it this way. Take a sopa bubble the size of a bowling ball, and take a bowling ball. The drop them both on a zero windless day. The bowling ball will accelerate significantly quicker because it has more weight. The greater weight allows it to push through the air quicker. Whereas the bubble will reach terminal velocity almost immediately. No need to argue weight is a factor.
fscott
-
Wow.
-
Wow is right...sigh... the soap bubble and the bowling ball accelerate at the same rate- the soap bubble reaches terminal velocity almost immediately while the bowling ball continues to accelerate until it reaches terminal velocity. Until one or the other reaches terminal velocity they are accelerating at the same rate. The bowling ball doesnt accelerate faster...it accelerates longer. The bowling ball will hit the ground first because it has a much higher terminal velocity.
PS I would also like to know which aircraft has the best drag to weight ratio.
-
FScott,
If your looking for the affects of drag vrs weight then maybe dive isn't the question you should be asking. If you want the best idea of drag(parasite drag at high speed) then you should look at sea level HP+ weight + drag = Vmax. This should give you the best idea of the profile drag for each A/C based on how much HP is available versus top speed. Drag then becomes the limiting factor.
I may be way off in what your looking for but it's just an idea.
-
ljkdern I say this with all due respect - you are dead wrong.
-
We all know a human being broke the sound barrier without a aerodynamic body (as in some form of shell to reduce drag of some form -- including wings, or otherwise) surrounding him? Enclosed in nothing more then a pressure suit.
"I thought, hey this is pretty weird, I've got shockwave forming off my arms and legs!"
(http://bbs.hitechcreations.com/smf/Smileys/default/smile.gif)
Just an example of the effects of drag, weight, and acceleration, and atmospheric pressure.
Btw Ding I think I found the equation for why Wolvie is so damn short. There's only 1 extranous root...
------------------
(http://bigdweeb.homestead.com/files/sig.jpg)
There is no escaping Murphy's Law!
(http://bigdweeb.homestead.com/files/tiger.gif)
33rd FW www.33rd.org (http://www.33rd.org)
-
Oh btw, given the reason there is no gravitational reaction between, (say a human jumping) because of the Earth's liquid center, and mass.
As the tides rise, the molten core of the earth reacts the same, albeit not as visable because of core pressure. Using the above example, a tiny fraction of the earth actually does move with every object that pulls away from the earth. A very tiny fraction.
This was the reasoning behind the infamous "Chinese Jump Theory", practically a doomsday weapon if Japan ever PO's China.
- Da Bess
-
Jig it was Joe Kittinger. Giant F___ing Cojones. http://www.wpafb.af.mil/museum/afp/afp200.htm (http://www.wpafb.af.mil/museum/afp/afp200.htm)
(http://www.wpafb.af.mil/museum/eagles/kitt-3.jpg)
[This message has been edited by funked (edited 01-31-2001).]
-
Too al participants, I'm deeply sorry for starting this thread, and the other one too. Our time could be spent much better by blown out of the sky by fscott.
So... My next question: When I rip your wings off with my .50's, what is my awesomeness to weight ratio? I weigh about 190 lbs.
fscott
-
Considering Kittinger's right glove de-pressurized while ascending to 100,000ft, and countinuing instead of aborting, I'd say so. Like Yeager breaking those ribs while watching the nudie rodeo a Pancho's Barnes place before taking the X-1 through the transition (http://bbs.hitechcreations.com/smf/Smileys/default/biggrin.gif)
I have the full AvHi write up on Kittinger from F-51 training through the flying circus he's in now. MH and Exc were some cool projects.
- Da Bess
-
Whereas fscott is apologizing for starting this thread, I salute everyone who participated in here and submitted info. Its great to know I can still learn things in a game I love so much! <S> All!
-Ding
-
Originally posted by ljkdern:
Wow is right...sigh... the soap bubble and the bowling ball accelerate at the same rate.... Until one or the other reaches terminal velocity they are accelerating at the same rate. The bowling ball doesnt accelerate faster...it accelerates longer.
Bzzzt - wrong again. All forces are present from the very beginning. They will not accelerate at the same rate because the force speeding up the heavier object will be greater and in the case of the bowling ball / feather argument, the drag force will be much smaller in proportion to the drag force on the feather. The drag on items like the feather will have a greater balancing effect. BUT THESE FORCES ARE PRESENT FROM THE BEGINNING AND THE DRAG WILL GROW AS THE SPEED OF THE OBJECT INCREASES.
What you state would cause a discontinuity in the speed/acceleration of the items. They will not "shift gears" at some point. The speed curves will be smooth - there will be no corner as you imply.
------------------
Rape, pillage, then burn...
-
If the object is to determine which AIRPLANE will dive the best, you probably need to talk about the forces on the AIRPLANE, not soap bubbles (http://bbs.hitechcreations.com/smf/Smileys/default/wink.gif)
A diving aircraft has, obviously, gravity working to accelerate it. But it also has THRUST from its engine, dependent on the engine/prop combo's capability to accelerate it, and drag, dependent on the shape and size of the airframe, working on it. So you have:
Mass x gravity (different for each plane)
Thrust (different for each plane)
Drag (different for each plane)
Of COURSE they're going to fall at different rates. The reason is that the sum of the forces on the two planes is NOT equal, otherwise they wouldn't accelerate at ALL.
Sum the forces on each plane. Divide the resultant force by the plane's mass. That gives you the resultant acceleration of the plane, which will only be constant until the forces change, which will occur when the drag and thrust change due to atmospheric conditions and airspeed as the altitude decreases.
It's a differential equation, not an example of what Galileo "tested." It's not a vacuum, it takes place over thousands of feet of constantly changing atmosphere, not 200 feet of "dense" air at the surface, and it's not a "constant acceleration" problem either, so the fact that acceleration due to gravity is independent of mass, while interesting, isn't very relevant (http://bbs.hitechcreations.com/smf/Smileys/default/wink.gif)
--jedi
-
P.S. as soon as you attach a powered propeller to your falling body, about 99% of the guys in the sim (including me) are essentially disqualified from having even the slightest clue about what's going on there (http://bbs.hitechcreations.com/smf/Smileys/default/wink.gif)
Oh yeah. Don't forget the lift on the wings in the dive. It's generating induced drag dependent on the amount of lift. It varies with speed and density (and thus altitude, which is...er...constantly changing in the dive), unless you're at zero angle of attack, which means it varies with the G-loading.
So add that into the differential equation somewhere (http://bbs.hitechcreations.com/smf/Smileys/default/smile.gif)
-
I think I know why the idea that all objects fall at the same rate in a vacuum causes such confusion. It's because it has always been taught as a fundamental Law and not an effect. Most people tend to think of it as an absolute but really it's just and effect of a few simple principles.
If you begin with just the very simple simple laws.
1.
Force = Mass * Acceleration
2.
Force of gravity at a fixed distance, call this force GF always is a Constant value (Call this GC) times the Mass of the object so we end up with the 2nd equation. (Side Note the GF is what we call Weight)
GF = GC * Mass.
Please keep in mind gravity is just a force, nothing more nothing less.
So very simply combining the 2 equations you get.
GC * Mass = Mass * Acceleration
Now just canceling out the 2 Masses you get
GC = Acceleration
I.E. All objects accelerate/fall at the same rate when no other forces such as drag are at work.
This is really nothing earth shattering, but is really what makes all objects fall at the same rate, and just a different way of understanding why.
HiTech
-
This type of question often leads to a good deal of confused thinking. Here is an explanation I use with my own students (http://bbs.hitechcreations.com/smf/Smileys/default/smile.gif)
What actually happens is by no means obvious, so I'm going to resort to a little math, just to maintain clarity and credibility (http://bbs.hitechcreations.com/smf/Smileys/default/smile.gif)
Let's consider two aircraft that are externally identical in every way. However, one aircraft is much heavier than the other. They both have exactly the same thrust and drag. Now we will assume that they both dive from some initial speed and we want to know what happens next. But firstly, let's pause to consider the average layman has to say about it
"I thought Galileo proved that all objects fall with the same acceleration?"
Ok what happened is this... He noticed that he could drop metal balls of different weights, from a building and they would hit the ground at the same time, at least he couldn't measure the difference. This is how the math clocks out. Using Newton's law f = ma where f is the force acting on a ball, m is its mass and a is its acceleration towards the ground. We are interested in how the objects accelerates so we write it like this:
a = f/m (1)
That simply says that the acceleration is the force pulling the balls down to the ground divided by their mass. Now if you consider the drag acting on the balls to be negligible, the only force left to consider is the force due to gravity, so we get:
f = mg (2)
Now if you substitute that value for f back into our first expression (1) we get:
a = mg/m
The mass m cancels out leaving:
a = g and g is about 9.8 m/s^2 or 32.2 ft/s^2
This means that if we can ignore drag (which is approximately true for balls that are heavy and smooth) the balls will accelerate at the same rate, regardless of their mass!! Certainly for casual observations that appears to be true.
However, the situation is very different if we consider an aircraft where the drag and thrust can't be ignored, because they are no longer negligible.
So let's consider our aircraft, but firstly let's just consider the drag, and we can call it d for short. Now we can still write Newton's law just as we did in expression (1) but now when we write down the force acting on the aircraft we need to include the drag too, so we get:
f = mg - d (3)
We write a negative sign because drag always opposes the motion. Now look what happens if we substitute the value for the force in expression (3) back into expression (1), we get:
a = mg/m - d/m
a = g - d/m (4)
Now here is the crunch! The mass doesn't cancel out of the drag term, so the mass will now have an influence on the acceleration. But what influence?
Ok, look at expression (4) again, it is saying that the acceleration is going to be reduced by the drag (yep that makes sense) but as the mass gets larger, the actual value of d/m will get smaller, meaning that for the same amount of drag, heavier objects will accelerate more quickly!!
However, it causes no end of problems because our everyday experience tells us that heavy objects are more difficult to accelerate than lighter ones.
Now take another look at expression (4)... The acceleration is maximum when the d/m term is as small as possible, which means that for the best acceleration in a dive you want a combination of low drag and high weight, which means that the smallest drag/weight ratio possible will give you the best acceleration.
That's the answer to your question... But the situation is not as simple as that, we are still ignoring the thrust involved, and for aircraft that can produce large amounts of thrust, we can consider what will happen if we call the thrust t and include it. Our expression for the force now becomes:
f = mg + t - d
If we now substitute that into expression (1) we get:
a = g + t/m - d/m
What happens now depends on how big the thrust and drag are. For example, consider an aircraft that begins to dive from a low speed, at maximum thrust. Now because the speed is low, the drag will be relatively low, so just to clarify this point, lets ignore the drag term just as we previously ignored the thrust. Now we are left with:
a = g + t/m
That tells us that the thrust will increase the acceleration (once again, that makes sense) but that the larger mass makes that increase smaller.
So, if our two aircraft have a high thrust to weight ratio and start to dive from low speed, the lighter one will actually accelerate more quickly!! That is contrary to the previous situation. However, because the thrust will get smaller (for a prop aircraft) as the aircraft gets faster, and the drag will increase as the velocity squared, the drag will very quickly become the dominant factor, and so the heavier aircraft will generally very quickly, if not always, exceed the acceleration of the lighter one. Indeed, you often see pilots referring to the better dive acceleration of heavier aircraft, which supports the theory (http://bbs.hitechcreations.com/smf/Smileys/default/smile.gif)
But it does open the possibility for exceptions to the rule, a draggy aircraft with low thrust will accelerate poorly no matter how heavy it is (http://bbs.hitechcreations.com/smf/Smileys/default/smile.gif)
Now, the argument doesn't stop there, because even though one might suspect that acceleration is the most important factor in combat, the actual top speed, or terminal velocity that you can reach in a dive, might also be important?
So, if we extend the argument to include terminal velocity, it turns out that if you
are happy to ignore thrust, you can compare the ratio of the terminal velocities of two aircraft as the square root of the ratio of their weights.
So if one of the two aircraft in my previous example was four times heavier than the other, its terminal velocity would be twice as fast.
So, not only does the heavier aircraft accelerate better, it reaches a higher terminal velocity!!
That's more important than you might at first think, because when most folk consider terminal velocity, they imagine a vertical dive... I suspect that few pilots that enter a vertical power dive ever get anywhere close to their terminal velocity, at least not many that live to talk about it (http://bbs.hitechcreations.com/smf/Smileys/default/smile.gif)
The point is that there is a terminal velocity for every dive angle, dive at 30 degrees in a heavier aircraft and you will still accelerate better, and reach a higher terminal velocity for that angle of dive.
That is why the heavy US aircraft were always able to extend away from the lighter Japanese aircraft. Even if two aircraft can match speed in level flight, the heavier one could still extend away with better acceleration and higher terminal velocity, for as long as the dive could be maintained.
Hope that helps.
Leon "Badboy" Smith
-
OK....I would like to apologize. It turns I was wrong. Most of the last few messeges are beyond my comprehension but I was able to figure out why a heavier object will accelerate faster than a lighter one in my own simple mind. If only for my own benefit I will explain how I came to this conclusion: (ignoring thrust) Both objects begin at the same acceleration and gradually decrease their acceleration until reaching terminal velocity. Since the heavier object has a higher terminal velocity that can mean only one thing...its decrease in acceleration as it falls happens at a slower rate than the decrease in acceleration of the lighter object. I think it happens this way because of inertia. A given amount of drag force will have more effect on a lighter object than it will on the heavier object...thus it will cause the lighter object to slow more quickly. I may be wrong again but I think im getting closer (http://bbs.hitechcreations.com/smf/Smileys/default/smile.gif)