Will it take off?

[dtximages]

Ok last thought:

If the plane were on skies. Yes it would take off because the runway speed is irrelevent (barring friction of course). but a wheel does not "slide" down the runway, it rolls. Therefore, for each inch the plane moves forward, there is exactly one inch of rubber meeting concrete. If this is ever disrupted, the wheel would have to be sliding. Since we always assume the wheel has traction with the runway, I have to be correct.

You cannot compare skis or a treadmill to this scenerio. Youre comparing two opposing forces to infinity.

Can God make a rock so heavy that even He cannot lift?

[DizRotus]

An experiment of a model is insufficient as the treadmill has limited top speed, the model aircraft would quickly overcome the limits of the treadmill and take off. This is not applicable to the story because the runway perfectly keeps up with the plane speed.<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" />

Im beginning to suspect that youre not serious. The model plane experiment in the video is completely applicable. In the final test the treadmill is doing more than matching the wheel speed of the plane; its exceeding it. Nevertheless, when the minimal thrust provided by the battery powered electric motor is applied, the plane moves forward in the same manner it did when the treadmill was not moving. The speed of the treadmill and planes wheels are irrelevant. THE PLANE WOULD TAKE OFF.

[sputnik]

----------snip----------

think about it.. how did the plane get from point A to point B. Wheel speed relative to the runway had to be greater than the runway speed in the opposing direction to get forward movement from the plane (i.e. if runway speed was negative (100mph) then wheel speed had to have at least been 101mph). argument over right there, the runway simply cant keep up with the plane. what if it could though? the plane would never move but the wheels would spin too fast immediately and the plane is now on its belly.

someone call mythbusters! haha

The treadmill cannot exert a horizontal force on the plane to oppose thrust force. The treadmill just spins the tires of the landing gear. Think of the ground as a fixed reference with a conveyor moving over it. Once thrust is applied, the plane will move forward on the conveyor at the same speed relative to the ground no matter how fast the conveyor spins the tires.

[maxg]

"PLANE SPEED = WHEEL SPEED WHEEL SPEED = (RUNWAY SPEED) therefore PLANE SPEED = (RUNWAY SPEED)"

Wrong before you start.

Plane starts moving (thrust)- the runway moves in the opposite direction and at the same speed. The wheels are turning at the sum of the plane's speed and the runway speed. The moving platform actually cannot match the speed of the wheels unless the plane is stationary - it is impossible as the wheels are the sum above.

[Travis In Austin]

the one thing that still bugs me and I have mentioned it before is thrust per pound......

Rockets and missiles develop lift without any wings or so due to having a better thrust per weight ratio..... your firecracker weighs less the the thrust of the engine creates hence it accelerates.

Airplanes mostly do not have a better thrust to weight ratio..... There are only two planes off the top of my head that actually do have more thrust then weight ratio. That is the F-15, and the Mig 29. Technically they could launch upwards but it is doubtful since their thrust to weight is not as great as needed to accelerate. Though they can climb at a true 90 degree angle (great for dog fighting) without the plane stalling..... Every play microsoft flight simulator? when you go straight up most of the time your engines will stall and you will crash.

Since most aircrafts cannot lift themselves up without the use of the wings I still wonder.

Jay,

Just about everything you have said above is a wrong assumption. The thrust to weight ratio does not matter becasue the plane is able to roll foward, relative to the ground, get air moving over it's wings, develope lift, and fly. It could be a Piper Cub, or a 747. The only difference is that the Cub is going to take off at a ground speed of about 50 to 60 mph. The fact is that if the plane can fly off of a regular runway, it is going to be able to take off of the conveyer runway in the same manner. Not only that, it will take off in the same distance as on a regular runway assuming the wind is the same, 0, or 5 mph headwind, etc.

Going straight up does not cause the engine to stall. The wings stall, meaning they are reach the point where they no longer develop lift. You do not crash because the wings stall, nor do you crash even if the engine quits.

Travis

[Coytee]

Ok, now seriously folks... for a change of pace, isn't this a LOT more interesting than SET -vs- PP battles?

(ducks quickly as the rotten tomatoes start to fly)

[A]

[DrWho]

Ok, now seriously folks... for a change of pace, isn't this a LOT more interesting than SET -vs- PP battles?

I didn't know they were even close enough to be considered battles?!? []

*follows coytee to his hiding spot* [A]

[Ray Garrison]

Oh. My. God.

I took a brief (well, 9 month) hiatus (got a Sony a100 DSLR, have been hanging out at dpreview.com), come back here, and find:

1. This thread is still alive?

2. There are still some people who don't get this?

3. Oldtimer is channeling Julian Hirsch?

It *DOES NOT MATTER WHAT THE SURFACE UNDER THE WHEELS IS DOING*. Whether the conveyor belt is moving forward, stationary, or backward, at whatever velocity, has no bearing (yuk yuk) on what the plane does. Suppose the plane was magnetically levitated above the belt, not touching it. Obviously, if the belt begins moving backwards while the plane taxies forward, the plane doesn't care. It'll move forward, gain airspeed, and take off. now, let it sit on its wheels. the only difference is the wheels rotate, which has nothing whatsoever to do with the plane's forward motion. Whether the belt is moving beneath the plane at a slow speed, the same speed but opposite in direction to the plane, or traveling backwards at Warp 9 the plane still moves forwards and takes off when the airspeed is sufficient. (Assuming the wheel bearings have negligable friction.)

Geez. I gonna go take some pictures of my speakers.

[pauln]

The

wheels still seem to be causing some confusion. That's because the role of the

whole thing about the wheels is to provide confusion to make analyzing the

problem challenging and fun, so let's clarify about the wheels and their

speeds...

What the hell, let's analyze all the speeds:

The

fundamental reference is the ground. The speed of the ground under the conveyor

is zero. This is not required for the plane to take off; it could do so during

an Earthquake comprising a single back-wards (or forwards) longitudinal lurch

aligned to the plane's direction of motion that matched the plane's speed (or

didn't match, doesn't matter).

The

speed of the still air (wind speed) is zero with reference to the ground. This

is not required for the plane to take off but it makes all the other speeds less

complicated to understand. The still air speed is equivalent to the still

ground speed.

The

speed of the plane relative to the still air - let's have the plane point West.

The

speed of the conveyor relative to the still air - let's have the top of the

conveyor go East ( the bottom part goes West at the same speed)

Note:

The plane's wheels parts have a variety of speeds depending on the part of the

wheel one is thinking about (because the angular speed of the wheel varies with

radii with reference to it's hub).

The

middle part of the wheels (the hub) has the same speed as the plane with

reference to the still air (with reference to the plane itself the hubs have

zero speed).

The

top part of the wheel is moving West in the direction of the plane's motion

faster than the speed of the plane with reference to the still air. How much

faster varies with how big the radius makes the wheel's circumference, the

bigger the faster, but in all cases where the wheel is of non zero radius the

top is going faster than the plane.

Likewise,

the bottom part of the wheel where it contacts the conveyor is going East with

reference to the plane at slower speed than which the plane is going West with

reference to the still air. The speeds of the top and bottom of the wheel are

equal and opposite in direction with reference to the plane.

Also,

the bottom part of the wheel is dead still with reference to the conveyor -

even though the wheel is turning and rolling on the conveyor. If you will

examine a rolling wheel you can convince yourself that this is true for all

non-skidding rolling wheels (of course all rolling wheels have to skid a tiny

bit - that is how the ground imparts

force to make them turn beyond the angular momentum the wheel already has and

the losses to friction (rolling friction)).

Notice

something interesting and very important here... the contact patch (bottom of

the wheel) is going East with reference to the plane, West with reference to

the still air, and is not moving with reference to the conveyor.

Before

figuring out more about all these speeds, lets summarize and give them formal

names. The subscripts will help keep track - they are just like the ones for

speaker perameters:

Vg Ground speed

Vw Wind speed relative to the ground

Vpg Plane speed relative to ground

Vpc

Plane speed relative to the conveyor

Vcg Conveyor speed relative to the ground

Vwtp

Speed of wheel top relative to the plane

Vwtc

Speed of wheel top relative to the conveyor

Vwhp

Speed of wheel hub relative to the plane

Vwhc

Speed of wheel hub relative to the conveyor

Vwbp

Speed of wheel bottom relative to the plane

Vwbc

Speed of wheel bottom relative to the conveyor

So,

what can we know about all these speeds? Lets do the easy ones first

First,

lets assume the ground is not moving so

Vg=0

And

the wind is not blowing so

Vw=0

We

know that the wheel bottom is motionless with reference to the conveyor so

Vwbc=0

(see the calculations below for proof if you don't believe this after just

thinking about it)

And

we know that the speeds of the top and bottom of the wheel are opposite and

equal with reference to the plane so

Vwtp

= (-Vwbp)

And

we know that the wheel hub and plane have the same speed in reference to

anything

Vpg

= Vwhg ...equal with reference to the ground

And

Vpc

= Vwhc ...equal with reference to the conveyor

For

Vwtp and Vwbp, (wheel top and bottom with reference to the plane) we may find their

speeds by dividing the distance traveled around the wheel in one revolution

divided by the time it takes to make one revolution.

We dont know the radii of the wheels, but we

do know that the circumference of the wheel is 2 pi times the radius; (2pir).

So this is the arc length of one rotation of the wheel.

With

Vwhc (the speed of the wheel hub with reference to the conveyor in feet per

second) we know that the number or revolutions of the wheel will be

Vwhc/2pir

The time for each revolution during that

second at Vwhc therefore is also Vwhc/2pir

Note,

we will use the plane's speed with reference to the conveyor to calculate the

wheel's top and bottom speed with reference to the plane, ground, and the

conveyor.

For

Vwtp (the top of the wheel speed with reference to the plane) we take the

distance traveled around the wheel with one revolution (2pir) and divide it by

the time it takes to do so (1/(Vwhc/2pir))

Therefore

the angular speed of the edge of the wheel with respect to the plane is

(2pir)/(1/(Vwhc/2pir)) which simplifies to just Vwhc, so

Vwtp

= Vwhc

For

Vwbp (the bottom of the wheel) we get the same magnitude of opposite sign

(opposite direction).

Vwbp

= -(Vwhc)

Both

of these speeds are added to the speed of the conveyor to get the wheels top and bottom speeds

with reference to the conveyor, Vwtc and Vwbc.

Vwtc

= Vwhc + Vcg

Vwbc

= Vwhc - Vcg ... = 0 I'll show below in an example calculation

Lets

put in some numbers to see how this works. Let the planes speed (same as the

hubs speed) in relation to the conveyor be 30 feet per second.

Note:

this would be the case when the speed of the plane with reference to the ground

is 15 feet per second and the conveyor is going in reverse at 15 feet per

second.

And

let the wheels be 18 inches in diameter (radii of 9 inches or ¾ foot).

Wheel

circumference is 2pir which is 2*3.14*.75 feet=4.71 feet

The

plane/hub speed is 30feet/second compared to the conveyor.

The

number of revolutions in 30 feet of travel is 30/4.71=6.37 and since the 30

feet of travel took 1 second

The

revolutions per second is 6.37

The

time period for one revolution is 1/6.37 (one second divided by the number of

revolutions during that second) =0.157 seconds

For

Vwtp (the top of the wheel speed with reference to the plane) we take the

distance traveled around the wheel with one revolution (4.71 feet) and divide

it by the time it takes to do so (0.157 seconds) and get 30 feet per second.

Notice that this is with reference to the plane. Since the plan is going 15

feet per second with reference to the ground, the top of the wheel is going 45

feet per second with respect to the ground because you add the speeds.

Likewise,

the same calculation for the bottom of the wheel with respect to the plane will

be 30 feet per second, but since the plane is going 15 feet per second with

respect to the ground you add them and get the bottom of the wheel going 15

feet per second with reference to the ground. Both the bottom of the wheel and

the conveyor are both going 15 feet per second so the bottom of the wheel

really is stationary with reference to the conveyor.

So

we have verified that

Vwbc=0

the contact point at the bottom of the wheel in reference to the conveyor is stationary.

[customsteve01]

I can't believe this thread still pops up from time to time, thanks to WHO???

Its just so simple its stupid.

The answer is YES, and if you don't understand it by now your not going to ever understand it.

Steve

[maxg]

Oh. My. God.

I took a brief (well, 9 month) hiatus (got a Sony a100 DSLR, have been hanging out at dpreview.com), come back here, and find:

1. This thread is still alive?

2. There are still some people who don't get this?

3. Oldtimer is channeling Julian Hirsch?

It *DOES NOT MATTER WHAT THE SURFACE UNDER THE WHEELS IS DOING*. Whether the conveyor belt is moving forward, stationary, or backward, at whatever velocity, has no bearing (yuk yuk) on what the plane does. Suppose the plane was magnetically levitated above the belt, not touching it. Obviously, if the belt begins moving backwards while the plane taxies forward, the plane doesn't care. It'll move forward, gain airspeed, and take off. now, let it sit on its wheels. the only difference is the wheels rotate, which has nothing whatsoever to do with the plane's forward motion. Whether the belt is moving beneath the plane at a slow speed, the same speed but opposite in direction to the plane, or traveling backwards at Warp 9 the plane still moves forwards and takes off when the airspeed is sufficient. (Assuming the wheel bearings have negligable friction.)

Geez. I gonna go take some pictures of my speakers.

Welcome back Ray,

We were starting to wonder where you were and thought the best way to get you back was to dis-inter your favorite thread.

Worked too.....

[maxg]

Paul,

You have way too much time on your hands....

Nice answer - bit detailed - but you didn't cover the impact of the food being served on the plane - nor the length of the pilot's nose.

[Coytee]

I can't believe this thread still pops up from time to time, thanks to WHO???

Glad you brought that up....I think Doc Who should be stoned....

[*-)]

[DizRotus]

I think Doc Who should be stoned<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" />

There are those who think that he often is . . .

[sputnik]

Now, go easy on the lad. Although he is being an irritating troublemaker lately, he was the first person to post the correct answer clear back on page one (even though he had to gripe about the wording.)

I think the question is worded very poorly because it imples that the plane is motionless from the perspective an observor not on the plane nor moving runway (basically the perspective of the iar). The plane is going to move forward just like normal....the only thing that will be different is that the wheels of the plane are going to sping twice as fast while the wheels are still touching the runway.

-----snip-----

[DrWho]

I can't believe this thread still pops up from time to time, thanks to WHO???

Glad you brought that up....I think Doc Who should be stoned....

[*-)]

lol, YOU were the one that brought it up again! []

As far as being stoned....I've always felt drugs are a key ingredient to rock and roll. But if you can act stoned outta your mind without being stoned, then you've got GREAT rock and roll....

[pauln]

Paul,

You have way too much time on your hands....

I know. I'm always scouting for a chance to bend my mind to a problem needing a solution. I left the working world the end of last year and although one might think it would be great to have all one's time free I'm restless for challenge. I've reread all my difficult books, worn down my bicycle, walked the dog about 300 miles, listened to a lot of music, and played the blues in local clubs regularly. After 20 years of professional work, business travel, and countless long hours here and overseas I thought I would enjoy being free, but I am rediscovering what I think I have always known - I need interesting difficult intellectual challenges to keep me really happy.

When I spent my working days and nights reading, writing, and presenting formal analyses and solutions to complex problems I had no idea the importance those activities served to keeping me intellectually and creatively satisfied. Lately, I have been thinking of returning to the working world to put my mind at ease where is seems to be happiest - addressing the hardest problems I can find in a critical environment. You'll know when that happens - my posts will become short again...[]

[dkp]

Paul,

You have way too much time on your hands....

I know. I'm always scouting for a chance to bend my mind to a problem needing a solution. I left the working world the end of last year and although one might think it would be great to have all one's time free I'm restless for challenge. I've reread all my difficult books, worn down my bicycle, walked the dog about 300 miles, listened to a lot of music, and played the blues in local clubs regularly. After 20 years of professional work, business travel, and countless long hours here and overseas I thought I would enjoy being free, but I am rediscovering what I think I have always known - I need interesting difficult intellectual challenges to keep me really happy.

When I spent my working days and nights reading, writing, and presenting formal analyses and solutions to complex problems I had no idea the importance those activities served to keeping me intellectually and creatively satisfied. Lately, I have been thinking of returning to the working world to put my mind at ease where is seems to be happiest - addressing the hardest problems I can find in a critical environment. You'll know when that happens - my posts will become short again...[]

Paul,

Not to hijack this wonderful thread (I actually love this sort of thing), have you considered substitute teaching at a local high school? You seem to have intellect to spare and I'm wondering if that wouldn't be just the stimulation the doctor ordered? My neighbor is a retired electrical engineer who started teaching upon retirement and just loves it. Food for thought, as they say.

-David

[Coytee]

Not to hijack this wonderful thread (I actually love this sort of thing), have you considered substitute teaching at a local high school? You seem to have intellect to spare and I'm wondering if that wouldn't be just the stimulation the doctor ordered? My neighbor is a retired electrical engineer who started teaching upon retirement and just loves it. Food for thought, as they say.

Along with that, plan a nice relaxing trip to the mountains in East Tennessee.... while in this neighborhood, I'll give ya the keys to the Jubes.

[Y]

edit: And while here, we can go to the store to see if there are any cans of corn on sale... []

[Islander]

I can't believe this thread still pops up from time to time, thanks to WHO???

Glad you brought that up....I think Doc Who should be stoned....

[*-)]

lol, YOU were the one that brought it up again! []

As far as being stoned....I've always felt drugs are a key ingredient to rock and roll. But if you can act stoned outta your mind without being stoned, then you've got GREAT rock and roll....

Like Frank Zappa, who was against drugs and said he'd never used them. He made great rock and roll, plus great jazz/rock fusion.