Quite right - I'll get my coat.You can't because this isn't your thread
we have a mystery object on the belt being winched along
physics puzzle no.2
- Thread starter noseall
- Start date
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As I pointed out in an different post, if the conveyor's speed is to EXACTLY match the wheels' (circumferential) speed ALL THE TIME, both the conveyor and the wheels must be massless. Remember those old problems you got for your physics homework? "A rope passes over a light pulley ---".
In this situation, as soon as the winch moves the object - which it will - the conveyor and the wheels will both be travelling at the same speed; light speed. This remains true whether the object moves or not. Problem solved.
Now let's come back to the world of real conveyors and wheels. The control system will have a lag in it and so the winch will start to move the object. The winch will keep moving the object and the control system will go mad trying to achieve its objective but we'll assume it has as much power as it needs to do this.
The only important forces now are those on the wheels. The winch is pulling the axles forwards and the conveyor is pulling the tyres backwards. Result, the angular momentum in the wheels increases. At first the increase will be, to all intents and purposes, linear but, if the conveyor has enough power, this momentum will begin to rise faster than Newtonian mechanics predicts. At some point it will approach an asymptote where it's angular velocity can rise no further. The pull of the winch will now be used only to increase the angular momentum of the wheels. The object can move no further.
In this situation, as soon as the winch moves the object - which it will - the conveyor and the wheels will both be travelling at the same speed; light speed. This remains true whether the object moves or not. Problem solved.
Now let's come back to the world of real conveyors and wheels. The control system will have a lag in it and so the winch will start to move the object. The winch will keep moving the object and the control system will go mad trying to achieve its objective but we'll assume it has as much power as it needs to do this.
The only important forces now are those on the wheels. The winch is pulling the axles forwards and the conveyor is pulling the tyres backwards. Result, the angular momentum in the wheels increases. At first the increase will be, to all intents and purposes, linear but, if the conveyor has enough power, this momentum will begin to rise faster than Newtonian mechanics predicts. At some point it will approach an asymptote where it's angular velocity can rise no further. The pull of the winch will now be used only to increase the angular momentum of the wheels. The object can move no further.
You are both quite wrongly assuming a directly proportional relationship between the linear velocity of the aircraft and the rotational velocity of the circumference of the wheel itself ... There isn't one chaps because there are things between them called wheel bearings.
Consider a car (just to confuse you further) going round a corner ... The badge on the front of the car travels linearly x, the inner axle could move linearly 0 with no rotational velocity at all and the outer wheel could move x times 2 with a much faster rotational velocity.
There are plenty of sites google'able which explain the laws of flight and provide formulae which express it but, to summarise ...
For an aircraft to move forward the thrust being applied to the airframe must exceed the weight of the aircraft and the aerodynamic drag being applied to it ... Note, nothing here about rotational speed of its wheels.
All that will happen as the aircraft starts to move forwards is that its wheels will rotate much faster than normal but this cannot possibly affect the linear travel of the airframe because there is no direct relationship between them.
For the wheel speed to play any significant part in the take off of the aircraft it would need to produce drag significant enough to negate the thrust being applied i.e. by applying the brakes ... Wheel bearings are designed to be insignificant in drag terms
This is the dummy trap which this question poses and you can't see past.
MW
Consider a car (just to confuse you further) going round a corner ... The badge on the front of the car travels linearly x, the inner axle could move linearly 0 with no rotational velocity at all and the outer wheel could move x times 2 with a much faster rotational velocity.
There are plenty of sites google'able which explain the laws of flight and provide formulae which express it but, to summarise ...
For an aircraft to move forward the thrust being applied to the airframe must exceed the weight of the aircraft and the aerodynamic drag being applied to it ... Note, nothing here about rotational speed of its wheels.
All that will happen as the aircraft starts to move forwards is that its wheels will rotate much faster than normal but this cannot possibly affect the linear travel of the airframe because there is no direct relationship between them.
For the wheel speed to play any significant part in the take off of the aircraft it would need to produce drag significant enough to negate the thrust being applied i.e. by applying the brakes ... Wheel bearings are designed to be insignificant in drag terms
This is the dummy trap which this question poses and you can't see past.
MW
This is all very educational megawatt, but completely irrelevant to the question
I taxi to the holding area, do a few pre-flight checks, and get clearance from ATT to take off, so far so good you will agree.
I go to the end of the runway, because its only a short runway with no headwind I have an early stage of flap to increase the lifting ability of the wings, ok loads of throttle 2400rpm should do it, and we're rolling, then the problem started.
I notice the wheels were going faster than the ground, so I abort the flight and have another look at Softus's post, and too my horror it clearly says that can't happen
I taxi to the holding area, do a few pre-flight checks, and get clearance from ATT to take off, so far so good you will agree.
I go to the end of the runway, because its only a short runway with no headwind I have an early stage of flap to increase the lifting ability of the wings, ok loads of throttle 2400rpm should do it, and we're rolling, then the problem started.
I notice the wheels were going faster than the ground, so I abort the flight and have another look at Softus's post, and too my horror it clearly says that can't happen
Those people who believe the plane can not take off, tell us that the plane can be doing 100mph, whilst the conveyor below travels in the opposite direction at 100 mph, so the plane is not moving.
If the plane is not moving, the wheels will not turn, therefore the conveyor can not move.
Remember the conveyor REACTS to wheel MOVEMENT not vice verca.
For the conveyor to react to wheel movement, the plane must be moving FORWARDS.
The conveyor just speeds up to match the wheel speed as the plane speeds up, and then takes off.
To put it simply, the plane must be moving FORWARD to generate wheel spin for the conveyor to react to.
doitall.... comments please.
If the plane is not moving, the wheels will not turn, therefore the conveyor can not move.
Remember the conveyor REACTS to wheel MOVEMENT not vice verca.
For the conveyor to react to wheel movement, the plane must be moving FORWARDS.
The conveyor just speeds up to match the wheel speed as the plane speeds up, and then takes off.
To put it simply, the plane must be moving FORWARD to generate wheel spin for the conveyor to react to.
doitall.... comments please.
Very observant trazor
For the plane to take off following the rules of the original post the wheels must turn faster than whatever it is stood on.
Forget how the damn thing works or whether it is scientifically possible,
The wheels have to turn faster.
For the plane to take off following the rules of the original post the wheels must turn faster than whatever it is stood on.
Forget how the damn thing works or whether it is scientifically possible,
The wheels have to turn faster.
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Situation one.
Matching wheelspeed at any instant in time.
( Aircaft induced wheel speed ) plus ( conveyor induced wheelspeed ) = ( total wheelspeed )
Conveyor constantly accelerates to match a rotational velocity which is, itself, being increased by conveyor velocity increase.
therefore
( conveyor induced wheelspeed ) = ( total wheelspeed ) minus ( Aircaft induced wheel speed )
There is no point with aircraft and conveyor, in motion, that ( conveyor induced wheelspeed ) equals ( total wheelspeed ).
Whereas in situation two.
Conveyor speed to match aircraft ground speed
i) ( conveyor speed ) = ( Aircaft ground speed )
And
ii) ( total wheelspeed ) = ( conveyor speed ) plus ( Aircaft ground speed )
Then
iii) ( total wheelspeed ) = 2x( conveyor speed )
---- OR ----
( total wheelspeed ) = 2x( Aircaft ground speed )
Wheels spin at twice 'Aircaft ground speed' at any instant throughout exercise... until aircraft thrusting forward through the air - Bish -bash-bosh.....lifts off.
Matching wheelspeed at any instant in time.
( Aircaft induced wheel speed ) plus ( conveyor induced wheelspeed ) = ( total wheelspeed )
Conveyor constantly accelerates to match a rotational velocity which is, itself, being increased by conveyor velocity increase.
therefore
( conveyor induced wheelspeed ) = ( total wheelspeed ) minus ( Aircaft induced wheel speed )
There is no point with aircraft and conveyor, in motion, that ( conveyor induced wheelspeed ) equals ( total wheelspeed ).
Whereas in situation two.
Conveyor speed to match aircraft ground speed
i) ( conveyor speed ) = ( Aircaft ground speed )
And
ii) ( total wheelspeed ) = ( conveyor speed ) plus ( Aircaft ground speed )
Then
iii) ( total wheelspeed ) = 2x( conveyor speed )
---- OR ----
( total wheelspeed ) = 2x( Aircaft ground speed )
Wheels spin at twice 'Aircaft ground speed' at any instant throughout exercise... until aircraft thrusting forward through the air - Bish -bash-bosh.....lifts off.
We are getting their with you.Now think about this.
If the plane can never move forward, then the wheels will never turn, then the conveyor will never move.
The plane MUST move forward for the conveyor to ever react.
There is a thread just like this on another forum, 618 pages long! This one has a way to go to catch up
The plane does take off...I saw it myself.
The plane pushes with it's engines against the air, since the conveyor is not moving this air backwards the plane will move forward as normal.
The conveyor, matching the planes speed moves in the opposite direction but the conveyor has little influence on the body of the plane since it must act through a low friction bearing.
It would be different if the wheels had the brakes on, the force of the conveyor would be directly transmitted to the aircraft.
Because the wheels rotate, any force that the conveyor generates is just expended in rotating the wheels faster and heating up the bearings more.
The plane may feel slightly more drag through it's wheels because of the friction in the wheel bearings but this friction is minimal and easily overcome.
The result of the conveyor spinning backwards is to double the speed of the wheels rotation.
So, the plane is moving left at 220mph, the conveyor is moving right at 220mph, the wheels are spinning at 440mph..the plane takes off.
The plane does take off...I saw it myself.
The plane pushes with it's engines against the air, since the conveyor is not moving this air backwards the plane will move forward as normal.
The conveyor, matching the planes speed moves in the opposite direction but the conveyor has little influence on the body of the plane since it must act through a low friction bearing.
It would be different if the wheels had the brakes on, the force of the conveyor would be directly transmitted to the aircraft.
Because the wheels rotate, any force that the conveyor generates is just expended in rotating the wheels faster and heating up the bearings more.
The plane may feel slightly more drag through it's wheels because of the friction in the wheel bearings but this friction is minimal and easily overcome.
The result of the conveyor spinning backwards is to double the speed of the wheels rotation.
So, the plane is moving left at 220mph, the conveyor is moving right at 220mph, the wheels are spinning at 440mph..the plane takes off.
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