Aces High Bulletin Board
General Forums => Aircraft and Vehicles => Topic started by: F4UDOA on July 18, 2002, 05:20:00 PM
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Someone care to explain this chart?
How is it possible that the Tempest which climbs like a rocket only accelerates like a ThunderBolt??
Whats up with this??
(http://mywebpages.comcast.net/markw4/bdown3.jpg)
Ain't I a pest;)
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Rate of Climb = 60 x V x Angle of Climb
Angle of Climb = [550 X Prop Eff x sq rt of (Airdensity / 2)]
all divided by {Gross WT/ Power} x sq rt of {GWT/ Wing Area}
inhale
then subract total aircraft drag coeff - 1 / { pi x AR }
AR = wing aspect ratio....
so by equating climb to hp, you only neglect aspect ratio, prop effeciency, air density, gross weight, wing area, and overall drag.
otherwise, it is a perfect ratio.
Accelleration related only to the balance / imbalance of thrust vs drag.
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Prop optimization.
You can build a prop to climb, or to go fast. If you build it to climb you get good low speed effeciency and initial acceleration. If you build it to go fast you get shoddy low speed effeciency but better thrust at high speeds and more efficiency at higher alts.
Add more HP, and as HT said before, the issue only gets much worse.
Personally I am wondering what tests the used for "initial acceleration". The Moostang should not be that far above the Tempest V in any test I can think of.
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DOA, do u have a better quality scan? It's pretty hard to read aircraft designations, especially in turning circle diagram.
Edit: btw were is that page exactly from, and were can i get it?
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DOA Re Read the climb section, the tempest was the worst except for the Thunder bolt, appears acceleration is the same order.
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Naudet,
It was sent to me from a gent in the UK who also sent me the F4U-1 and F6F-3 trials at Boscombe downs:D. I will post the whole thing so you can have the entire report.
Hitech,
The climb was definitly not in that order. I didn't post that chart yet.
Here are the other pages.
(http://mywebpages.comcast.net/markw4/bdown1.jpg)
(http://mywebpages.comcast.net/markw4/bdown2.jpg)
(http://mywebpages.comcast.net/markw4/bdown4.jpg)
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Here's how the whole climb/accel thing works.
* = multiplicaton
d[]/dt = differentiation operator, e.g. df/dt = first derivative of f with respect to time.
t = time
E(t) = energy as a function of time.
P(t) = excess power as a function of time.
v(t) = TAS as a function of time.
h(t) = height as a function of time.
m = mass
g = gravitational constant
Total energy of the airplane, assuming the mass of the aircraft is not changing.
E(t) = 0.5 * m * v(t) * v(t) + m * g * h(t)
P(t) is defined as dE(t)/dt. The definition of power is the rate of change of energy with respect to time.
Therefore:
P(t) = d( 0.5 * m * v(t) * v(t) + m * g * h(t) )/dt
P(t) = m * v(t) * dv(t)/dt + m * g * dh(t)/dt
dv(t)/dt is defined as acceleration.
dh(t)/dt is defined as rate of climb.
Assuming level flight, dh(t)/dt = 0
P(t) = m * v(t) * dv(t)/dt + m * g * 0
P(t) = m * v(t) * dv(t)/dt
dv(t)/dt = P(t) / (v(t) * m)
That is, at any instant in time, acceleration in level flight is equal to excess power divided by the product of mass and TAS.
Assuming constant speed flight, dv(t)/dt = 0
P(t) = m * v(t) * 0 + m * g * dh(t)/dt
dh(t)/dt = P(t)/(m*g)
That is, at any instant in time, the sustained rate of climb is equal to excess power divided by the product of mass and the gravitational constant.
The only things I used to get this are the definition of energy, the rules of calculus, and the assumption that g and m are constant. Even if you assume g and m are not constant and crunch the numbers, the contribution of those variations is vanishingly small for the type of aircraft we are talking about.
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Gents,
First.
I get the point that physics says it so.
However if you look at the climb charts I've posted compared to the accleration charts they don't match. Point being that I believe there are some variables that the current physics model does not take into account.
Case and point is the Tempest in the AFDU. It climbs almost 5K per minute but does not acclerate well compared to the others in this chart.
Why? I dont think the match is wrong. But somethings wrong.
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Originally posted by F4UDOA
However if you look at the climb charts I've posted compared to the accleration charts they don't match. Point being that I believe there are some variables that the current physics model does not take into account.
Nope, the theory is good, but those charts are only intended to compare the different aircraft with respect to one single performance attribute at a time! The climb and acceleration data cannot be cross referenced, they were never intended to be used that way. The climb data for the tempest was for a speed in excess of 180mph while the acceleration data is “initial acceleration” which may mean that the acceleration was averaged over a time interval as the aircraft accelerated from rest.
Hitech has already explained this to you in his very first response to your previous thread…Here it is, just in case you missed it:
Originally posted by hitech
F4UDOA, Your taking the word instantious wrong, meens at a single speed for acceleration. I.E. The acceleration from 169 to 170 is different than acceleration from 200 - 201.
Accelerations would be in a unit like Mph change in 1 sec.
Also climb rate at 200 is different than climb rate at 169.
The chart your looking at gives a climb rate at 1 speed, and an average acceleration over different speeds.
When we say Climb rate is always perportional to acceleration we meen that if you have an accelerations of 10 mph per sec and a climb rate of 5000 fps, at 160 mph.
Then if acceleration at 200 mph = 5 mph per sec the climb rate at 200 mph must be 2500.
Note you must hold a constant 200 during climb by either raising or lowering the nose.
And they will always be directly perportional.
HiTech
That’s exactly what’s happening in your second example, it isn’t because anything is wrong with the charts or the physics, you are simply trying to use the charts in a way they can’t be used!
Originally posted by F4UDOA
Case and point is the Tempest in the AFDU. It climbs almost 5K per minute but does not acclerate well compared to the others in this chart. Why? I dont think the match is wrong. But somethings wrong
That’s because the climb rate for the Tempest in those charts is at the highest speed of any of the other prop fighters, if you were to compare acceleration starting from that speed, it would have exactly the same ranking as it does for climb. The aircraft that accelerate much better at the lower speeds would compare less favorably to the tempest at the higher speeds. If the charts were meant to be cross-referenced they would reflect that, but they weren’t. So, it comes back to the same thing, the charts you have posted simply can’t be used the way you are trying to use them, that's the only reason they don't correlate the way you expect them to... Trust me, nothing is wrong!
Badboy
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funkedup, your definition of P(t) already includes the drag hidden in it. using this definition doesn't show you the dependancy on speed and the aerodynamics, which are the true interesting parts.
the "excess power" as you described it depends on drag just as much as on engine output and prop efficiency. just looking on engine power to weight ratio won't tell you much.
Bozon
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I've seen these charts before and IIRC these were published in the Flight or Aeroplane magazine.I don't know if the charts are very accurate. I have test data on Mustang which claims that it reached it's best climb speed around 195mph IAS at WEP.
gripen
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Originally posted by bozon
funkedup, your definition of P(t) already includes the drag hidden in it. using this definition doesn't show you the dependancy on speed and the aerodynamics, which are the true interesting parts.
the "excess power" as you described it depends on drag just as much as on engine output and prop efficiency. just looking on engine power to weight ratio won't tell you much.
Bozon
No toejam Sherlock. :)
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No toejam Sherlock.
it's elementry my dear Watson. :)
Bozon
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I think you need first the definition of inital acceleration.
Is the the acceleration when beginning a dive, pushing forward the stick? Or level flight, starting from cruising speed? or 0.7 v_max??
Very interesting to see that the climbrate of the AH TempestV matches the +12lb Temepst II with Centaurus engine (2600-3000PS??) btw...
niklas
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Initial accelleration is the accelleration that happens initially.
If we are talking level acceleration, and that is the only acceleartion that horsepower has anything to do with, then just after you max out the throttle, initially, that is initial acceleration. :) Otherwise, a rock initially accelerates at 32.2 ft/sec sq
The thing that makes the difference is aerodynamics. Drag at whatever the climb speed is varies greatly among all these designs. The aerodynamic qualities of the wing, prop, and fuselage make a great deal of difference. Excess horsepower is not the only climb factor; weight and aerodynamics balance the equation.
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And at which airspeed do you start the inital acceleration?
Imagine a fighter that has a stall speed of 50mph, the other at 100mph. Now how do you want to compare initial acceleration at 75mph when the 2nd aircraft can´t even fly at this speed????
Imagine a aircraft with a topspeed of 300mph, the other of 400mph (Similar shape, just different engine). Of course the 2nd aircraft will accelerate faster at 295mph where the other one is very very close to its own topspeed.
So where did they start the acceleration process? You have to know it, else it´s useless.
The AFDU made some dive acceleration comparisons, maybe this accelerations refer to dive acceleration.
niklas
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perhaps initial accelleration is the wrong term...
dv/dt is a better definition, at whatever V your interested in...
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Right, but dv/dt is a curve, with endless many data points. This chart shows only ONE single point out of it, the reference for ONE conditition. So if you want to interpret this table, you have to know WHAT single point they took out of a large group of possibillities.
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Niklas,
Don't you think it's curious that the Acceleration of the Tempest is not as good as the P-51 and only marginally better than the P-47??
I would think the Luftwaffles would be all over this??
BTW, this is the second set of test data I have provided with A/C climbing and accelerating in a different order. I guess actual test results don't account for much?
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F4UDOA: You are turning into a true posting duffas.
When mutliple people all with degrees in math,physics,eng excetera, are all telling you the exact same thing. I would tend do belive them first, then try figure out why the document is confusing you, not try show how all these people are wrong.
Read, belive, try to understand, what we are trying to tell you. Wrather than grasping at straws trying to prove somthing that is incorect.
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Originally posted by hitech
F4UDOA: You are turning into a true posting duffas.
All right..there is my laugh today...back to work
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I've actually found this thread very interesting and have been following it. In my opinion, Hitech's post was a bit nasty and really uncalled for...I think he must be taking something personally (which maybe I'm missing.) Anyway, some people like to understand facts instead of just accepting them on face value. Kudos to all those who are taking the time to help those of us who are without the knowledge try to understand how it works.
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Stupid freakin' BBS kept timing out on me trying to post this...now there are two. Let's see if 3 show up now.
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Hitech,
I think Pyro should censor your post and ban you from the boards for name calling:o
Seriously I've been called allot worse than dufus even just today.
However if I am a dufus I guess the pilots that flew the AFDU were also. As well as the pilots that from SETP that flew the A/C in 1989.
What I see on these boards is a number of people with a greater understanding of the math behind flight than I do. What I do not see is any explanation of the data I have presented. I'm not trying not to see it. In fact I'm trying very hard to see it.
Please humor one more time.
Maybe I have chosen a bad example. Take a look at the FW190A. It is at both ends of the spectrum and at all altitudes near the worst in climb and top speed, but near the best in acceleration.
If someone with better math skills than I using the data I have provided explain why the FW190A is at different ends of the spectrum in climb and acceleration as shown clearly in this test.
Please do not show me a generic equation. I have Aeronautics books too. But I do not have the backround to put together these equations.So please stop being so condesending and do the math.
I'm a big boy so you can call me names. But if it were not for people like me asking why people like you would still think the earth was flat;)
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DOA,
Compare the 190 vs Meteor. The 190 will outclimb the Meteor at whatever speed and height the 'initial acceleration' test was done at. Likewise, when flown at the Meteor's best climb speed of 220 mph, the Meteor will accelerate better. The speeds have to be the same if you're going to compare climb and acceleration directly.
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F4UDOA,
this acceleration/climbrate problem has enough variables in it to allow just a bout any possible result.
If you wanted to show that the p-47 was a better plane than the spit, you could do the tests at 400mph. the p-47 in some speeds and altitudes will outclimb and out accelerate the spit.
on other conditions it won't.
actually on most of the possible spectrum of condition it won't so we say the spit is a better climber than the p-47, and so on.
If the guys that made the report really wanted to get a certain conclusion, they will get it, more or less. you can see this happening in reports in science and medicine as well.
I can't for some reason view the first pic you attached now (I could on the univercity computer), so I can't see what what conditions the experiment was done. anyway, the data will only tell a part of the story.
Bozon
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Originally posted by Holden McGroin
Initial accelleration is the accelleration that happens initially.
If we are talking level acceleration, and that is the only acceleartion that horsepower has anything to do with, then just after you max out the throttle, initially, that is initial acceleration. :) Otherwise, a rock initially accelerates at 32.2 ft/sec sq
The thing that makes the difference is aerodynamics. Drag at whatever the climb speed is varies greatly among all these designs. The aerodynamic qualities of the wing, prop, and fuselage make a great deal of difference. Excess horsepower is not the only climb factor; weight and aerodynamics balance the equation.
A rock? No way, I am sure we are not talking rocks here. Apples maybe? Holden are you really I. Newton incognito?
BTW to all you pin head aeronautical ninjaqueers, I'm with F4UDOA all the way on this one. At least I can understand what HE is complaining about, for the rest I have no clue. :)
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Originally posted by Holden McGroin
Initial accelleration is the accelleration that happens initially.
Otherwise, a rock initially accelerates at 32.2 ft/sec sq
There you go again messing everything up by throwing rocks into the fray.
OK, what kind of rock; granite, quartz, or pumie.
I just got interested in the alphabet that was preceeded by the letter "d" (i.e. dv/dt). What does "d" mean?
Can it accelerate also?;)
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For a current perspective, http://www.dfrc.nasa.gov/trc/ftintro/accel/nasaccel.html discusses the NASA Dryden Flight Research Center's procedures for level acceleration tests.
Note the document states that level acceleration results are directly used to compute maximum rates of climb.
One point about the Fw 190A--it's stated in a US test report that the 190A had an advantage in acceleration tests because it had simpler engine controls than US fighters, and full power could be applied more quickly. Depending on the test procedure, this might have been enough to bump it up the acceleration rankings a bit.
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F4UDOA,
this acceleration/climbrate problem has enough variables in it to allow just a bout any possible result.
Thank you Bozon. You just made my point for me.
DOA,
Compare the 190 vs Meteor. The 190 will outclimb the Meteor at whatever speed and height the 'initial acceleration' test was done at. Likewise, when flown at the Meteor's best climb speed of 220 mph, the Meteor will accelerate better. The speeds have to be the same if you're going to compare climb and acceleration directly.
Wells, like you said the speed has to be the same. And thats not all. How about AoA. That has to be the same as well or you can't compare Cdi either. My point is that there are many variables in to determine best climb because speed and AoA vary when measuring climb but have nothing to do with level acceleration.
So if my last staement is true then you can say that climb and accleration are not directly linked because climb uses more variables
For instance. How can you say that an A/C has high induced drag if you don't know what the Cl is at the AoA used in it's climb?? And none of that matters in acceleration. Is this not a true staement??
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Originally posted by bozon
F4UDOA,
this acceleration/climbrate problem has enough variables in it to allow just a bout any possible result.
Not true Bozon, the data is simply being misunderstood.
Badboy
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Originally posted by F4UDOA
Wells, like you said the speed has to be the same.
Isn’t that exactly what people have been telling you all along?
And thats not all. How about AoA. That has to be the same as well or you can't compare Cdi either. My point is that there are many variables in to determine best climb because speed and AoA vary when measuring climb but have nothing to do with level acceleration.
Not true, the speed and AoA have just as much to do with acceleration as they with climb, because they both influence the excess power.
So if my last staement is true then you can say that climb and accleration are not directly linked because climb uses more variables
Your last statement was not true, neither is this one.
For instance. How can you say that an A/C has high induced drag if you don't know what the Cl is at the AoA used in it's climb?? And none of that matters in acceleration. Is this not a true staement??
Nope, and I hate to be blunt, because you are obviously struggling to comprehend data you don’t understand, but unfortunately your statements in this post are almost completely incorrect.
Badboy
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Originally posted by F4UDOA
Please do not show me a generic equation. I have Aeronautics books too. But I do not have the backround to put together these equations.So please stop being so condesending and do the math.
Ok, let me try to illustrate what everyone has been trying to explain to you with an example. You, or anyone else, can use the Ps equation to verify the figures. For the sake of the example, let’s compare six different aircraft in two groups. The first three all have different maximum climb rates but their best climb rates all occur at approximately the same speed, those are the first three aircraft in the diagram below. They are ranked in order of their climb rate, and because their climb rates all occur close to the same speed, their level acceleration can be compared also, notice that when you rank them in order of their acceleration, the order is the same.
Now, look at the second group of aircraft. Aircraft 4 has the best climb rate but it appears to have the worst acceleration. The ranking for acceleration now appears to have no correlation with the climb rates at all. This is what you have noticed, and you have incorrectly assumed that something is wrong.
The second group of aircraft don’t have the same ranking because of the variation in airspeeds in the climb. Aircraft 5 appears to have the best acceleration, but if Aircraft 4 had the same climb rate at Aircraft 5’s airspeed it would not have been ranked 3rd it would have had the best acceleration of both groups, as shown at the bottom.
The best climb rates for real aircraft occur at different speeds, acceleration tests for a group of aircraft would normally be conducted at the same speed, that’s why you think there is something wrong. Nothing’s wrong, you are seeing a situation similar to the second group or aircraft below.
Badboy
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Standbye.
I'm digesting your information......
Thanks
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The fun is that the author wrote down a nice contradiction:
"For instance, the Tempest V which is faster than the Spitfire XIV, takes less time to reach ANY given speed, but the Spit has the best acceleration"
Looks like the author doesn´t have any imagination about physics. When the Spit accelerates faster it will DEFINITLY reach starting speed +10mph earlier. Things may change at +100mph or so, but at the beginning the Tempest will NOT reach ANY speeds faster.
It´s remarkable that small compact aircraft seem to have better intial acceleration. This can have imo also other reasons:
Large aircraft have large engines with large propeller. Initial acceleration is measured in a reasonable short time period. That means there are other factors that come into the game:
How fast can the engine run up to full RPM?
How fast can the prop pitch mechanism adjust itself (large props high inertia slow adjustment )
How does the torque change effects movements of the aircraft around the axis(drag) which have to be compensated by large ruder inputs (drag)
And: At what altitude was the acceleration test done btw? At 10000, 15000ft things look different
niklas
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Nice post Badboy.
F4UDOA- several of us have been trying to explain it over and over to you and I think we're getting exasperated just as you're getting exasperated with not understanding. I hope Badboy's chart helps. He's right on regarding your interpretation of the data which is leading you to believe that there is a lack of correlation between climb and acceleration which is simply not true.
I'm afraid you're next question is going to be "why?" which leads to all the ugly math that seems to have gotten us nowhere in helping with the explanation ;). From niklas' responses I think he has gotten it so it wasn't all for not ;).
To be honest I'm disappointed in my own lack of being able to explain and help you understand the physics behind it all. As Badboy says there is absolutely nothing amiss. If needed I can "have another go" at explaining the "why" behind it all again :).
Tango, XO
412th FS Braunco Mustangs
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So, let's look if i got everthing right. And i am the prototype of the aerodynamics amateur, no books and no advanced math or physics.
Climb and accel are directly linked to each other cause they both are "results" of available excess power.
The problem now is that this is right only for the same points of both curves.
If i can say Plane A climbs better than all other planes at speed X i can also say that at speed X it will accelerate the best.
But i CANNOT automaticly say that plane A will also accelerate best at any speed different from speed X.
So if i want to proof that Plane A is overall the best climber (and than also the best accelerator) i would have to compare Plane A with all other planes over the whole speedrange (to simplify i asume all planes have the same minimum and maximum flying speeds) at any speed between min and max flying speed.
If i now compare real planes i face the trouble that they all have differnet power curves and propeller designs. Due to this their excess power curves will vary greatly, but always the plane with more excess power available at one point than the other planes at that point will outclimb and outaccel the others than at this point.
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Naudet:
Bingo! You've got it! :)
Some points of clarification:
So if i want to proof that Plane A is overall the best climber (and than also the best accelerator) i would have to compare Plane A with all other planes over the whole speedrange...
Key word here being "OVERALL". I think you've got it down but just want to clarify for others that the plane that's the "overall best climber" does not mean it's also the plane with the "best rate of climb". "Best Rate of Climb" comparison usually refers to plane to plane comparisons of the best rates of climb of aircraft which occurs at a SINGLE SPECIFIC velocity which is DIFFERENT from aircraft to aircraft. Another way to look at it is that "best rate of climb" = where the "maximum rate of climb" occurs for an aircraft.
If i now compare real planes i face the trouble that they all have differnet power curves and propeller designs. Due to this their excess power curves will vary greatly...
Again I think you understand the concept but just want to clarify for others that when we speak of power curves it relates to a heck of a lot more than engine brake horsepower, but is a complex relationship of variables including thrust, drag, velocity etc. etc.
Tango, XO
412th FS Braunco Mustangs
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Originally posted by Cogen
There you go again messing everything up by throwing rocks into the fray.
OK, what kind of rock; granite, quartz, or pumie.
I just got interested in the alphabet that was preceeded by the letter "d" (i.e. dv/dt). What does "d" mean?
Can it accelerate also?;)
D stands for Dumbs**t, and the international standard for igneous rock is covalent basalt. for sedimentary; nile sandstone.
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Originally posted by Mino
A rock? No way, I am sure we are not talking rocks here. Apples maybe? Holden are you really I. Newton incognito?
A rock is right between seria and A ran, and who in the hell is this guy incognito?