# Phunny Physics

#### Steve Shannon

##### Well-Known Member
TRF Supporter
Steve,

Thank you for the correct and concise summary!!! albeit many repays back...

Thank you for the interesting riddle.

#### Incongruent

##### Well-Known Member
The formula is y=2s(x), with y defined as the speed of the conveyer belt, s defined as the speed of the plane and x representing time. The speed of the plane is graphed with y=s.

So using this model for the 1m/s example, the speed of the conveyer belt reaches twice the length of the runway. Mach 20.

The takeoff speed of the Boeing 747 is ~ 72 m/s. Assuming a linear acceleration, that can be modeled as s = (72/3500)x
This gives the conveyer belt a maximum speed of 504000, though, which seems kind of steep.

This might not be the right formula.

##### Roger Smith
For the plane to be moving forward its wheel speed needs to be greater than the belt's speed. If they are exactly equal the plane isn't moving, assuming the treadmill itself is stationary.

Turning things around ... if the conveyor belt is moving at 100 mph and the wheels of the plane aren't turning, wouldn't the airplane have to also be moving at 100 mph? If 100 mph is fast enough for the plane to take off, won't it take off?

Now, stop the conveyor belt. The wheels start spinning. But, the airplane is still going 100 mph. It can still take off.

Now, instantly start the conveyor belt moving in the other direction at 100 mph. Now the wheels are spinning really fast, but the airplane is still going 100 mph. It can still take off.

(Hint, the speed of the wheels and the speed of the conveyor belt are irrelevant. It's only plane's speed relative to the air that matters.)

--Roger

Last edited:

#### EXPjawa

##### Well-Known Member
I don't get why people are so hung up on the belt and wheel speeds, since neither are tied to what actually moves the plane. If you substituted wheels with floats (over looking the non-rotating aspect) and the belt for a river with a current, the airplane can still takeoff upstream. There maybe some extra drag initially, but once the floats are on plane it shouldn't matter. Same with wheels on a belt; they're a separate motion system that has no bearing on the airplane's forward thrust...

#### Nytrunner

##### Pop lugs, not drugs
This might not be the right formula.

Now we have an accurate assumption!

A better relation would be y(t)=-s(t) from the original problem state where the magic conveyor matches the speed of the wheels In the opposite direction.

Takeoff velocity is 72 m/s? Sure why not. Then the magic conveyor will be going -72 m/s....None of this Mach 10 or speed of light blather.

The wheels will always be spinning at the same speed as the conveyor belt.

If the conveyor belt is moving at 100 mph and the wheels of the plane aren't turning, wouldn't the airplane have to also be moving at 100 mph? If 100 mph is fast enough for the plane to take off, won't it take off?

(Hint, the speed of the wheels and the speed of the conveyor belt are irrelevant. It's only plane's speed relative to the air that matters.)

--Roger

Yes! I think a major confusion for people is that a wheel turns at revolutions/time and things move at distance/time.
By wheel "speed", you have to take the speed of the hub because that's the only point that moves forward on a fixed horizontal vector. ALL other points on the wheel are spinning and have different velocities based on their angular position and velocity. Get that in your head and just divide the difference in velocity between ground and hub by the radius and you have the angular velocity

I'll post my free-body diagram again just because it reminds me of simpler times.

The increased wheel rotation will make the plane work harder, but I can't imagine it imparting enough rolling resistance to override the engines.

#### dr wogz

##### Fly caster
Does a plane's wheel turn before it lands?

it's deployed its landing gear for final approach. the plane flares and touches down. When do the wheels start turning? when do they stop? does that have anything to do with the plane landing & reducing lift?

#### Incongruent

##### Well-Known Member
The turbulence created by the conveyer belt would prevent successful takeoff.

#### Lowpuller

##### Well-Known Member
EXP

If the river is flowing faster than the planes forward speed it won't take off.

#### Incongruent

##### Well-Known Member
Turning things around ... if the conveyor belt is moving at 100 mph and the wheels of the plane aren't turning, wouldn't the airplane have to also be moving at 100 mph? If 100 mph is fast enough for the plane to take off, won't it take off?

Now, stop the conveyor belt. The wheels start spinning. But, the airplane is still going 100 mph. It can still take off.

Now, instantly start the conveyor belt moving in the other direction at 100 mph. Now the wheels are spinning really fast, but the airplane is still going 100 mph. It can still take off.

(Hint, the speed of the wheels and the speed of the conveyor belt are irrelevant. It's only plane's speed relative to the air that matters.)

--Roger

You're missing the point on how the conveyer belt matches the speed of the wheels in the opposite direction. That's one of the criteria for the scenario. If the wheels aren't spinning, as in the first part of the situation you describe, the conveyer belt won't turn. The conveyer belt is controlled by the speed of the wheels, not the plane.

So so you said the belt would be moving back at 100mph. But that (since the plane is moving forward at 100mph) would make it accelerate to 200 mph, driving the wheels to 300mph, and so on so forth. Eventually, the belt is going so fast that it impairs the plane's ability to take off, whether from the shock waves or turbulence or melting the wheels off.

##### Roger Smith
So so you said the belt would be moving back at 100mph. But that (since the plane is moving forward at 100mph) would make it accelerate to 200 mph, driving the wheels to 300mph, and so on so forth. Eventually, the belt is going so fast that it impairs the plane's ability to take off, whether from the shock waves or turbulence or melting the wheels off.

Oh, yeah, I never thought to consider all of that.

-- Roger

#### Nytrunner

##### Pop lugs, not drugs
So so you said the belt would be moving back at 100mph. But that (since the plane is moving forward at 100mph) would make it accelerate to 200 mph, driving the wheels to 300mph, and so on so forth. Eventually, the belt is going so fast that it impairs the plane's ability to take off, whether from the shock waves or turbulence or melting the wheels off.

This smells wrong.
Forward motion of the planes and wheel-hubs is equal. If the plane is going 100, so are the wheels. If the plane is going 200, so are the wheels.

#### Mushtang

TRF Supporter
A somewhat similar argument took place once about an ultra-light plane that can cruise at very low speeds, approx 35 mph, and whether or not it's able to fly in formation with a hot air balloon.

It can't.

#### Incongruent

##### Well-Known Member
This smells wrong.
Forward motion of the planes and wheel-hubs is equal. If the plane is going 100, so are the wheels. If the plane is going 200, so are the wheels.

The conveyer belt matches the speed of the wheel, so it also imparts spin. Since the conveyer also matches the speed of the wheels (in the opposite direction), the speed of the wheels is equal to the speed of the conveyer plus the speed of the plane, (not just that of the plane) and if the plane is moving at all, the result is a positive feedback loop.

#### Steve Shannon

##### Well-Known Member
TRF Supporter
The hubs always have the same velocity as the plane. Unless the wheels fall off.
If the plane's brakes are on and the wheels are locked up, the hubs are also traveling at the same velocity as the surface of the conveyor belt (unless the tires slip on the conveyor belt).

#### Nytrunner

##### Pop lugs, not drugs
I'm getting the impression Incon's either still confusing rotation with translation, or is just arguing for argument's sake.

That wheel's going to be ROTATING twice as fast as it would on ground. But that will not have any effect on the plane's forward motion behind making the engines work a little harder.

#### Incongruent

##### Well-Known Member
I'm getting the impression Incon's either still confusing rotation with translation, or is just arguing for argument's sake.

That wheel's going to be ROTATING twice as fast as it would on ground. But that will not have any effect on the plane's forward motion behind making the engines work a little harder.

I have a feeling if the original question wanted translation, it would have said entire plane rather than wheel. Since it said wheel, it's referring to how fast the wheels are rotating, which is dependent on the speed of the ground (conveyer belt) and the speed of the plane. If it were rotating twice as fast, the conveyer belt also doubles in speed, making the wheel spin faster still and so on so forth.

#### OverTheTop

##### Well-Known Member
TRF Supporter
Does a plane's wheel turn before it lands?

No. They spin up when they make the screeching noise at touchdown. Pondering why they don't spin them up is probably due to the differences between landing air speed and ground speed. Most of the tyres are designed to be minimum weight to conserve fuel and still be able to do their job. Centripetal force tries to tear the tyre apart as it spins, and there is not much safety margin due to keeping the mass down. I could envision that the variability in the rotational rate (if they used something like vanes to spin them up) could take them up into the danger zone for shredding the tread. If they were to drive them with motors it would be even more additional mass to carry, and also a problem if it seized up.

So, looks like the KISS principle prevails...

Whoops

#### Zeus-cat

##### Well-Known Member
Think of it another way, the plane's engines (or are they motors???) are creating thrust. ANYWAY, they produce a lot of thrust. That thrust has to do something, and that thrust is pushing the plane forward. If the wheels are rotating at the same speed as the belt rotates then the plane will simply drag the wheels along as it accelerates.

#### Incongruent

##### Well-Known Member
The belt is dependent on the speed of the wheel. Because the wheel is on the conveyer, the wheel is, in turn, rotated by the belt.

If the plane brakes, it will stop. The brakes are required to be able to hold the aircraft idle while the engines are throttled all the way up. (Reference)

#### Steve Shannon

##### Well-Known Member
TRF Supporter
The belt is dependent on the speed of the wheel. Because the wheel is on the conveyer, the wheel is, in turn, rotated by the belt.

If the plane brakes, it will stop. The brakes are required to be able to hold the aircraft idle while the engines are throttled all the way up. (Reference)

That's true, it will be stopped relative to the surface of the conveyor belt. But if the conveyor is driven by some other force or even allowed to move, the plane would still be moving relative to the ground.

Steve Shannon

#### Incongruent

##### Well-Known Member
That's true, it will be stopped relative to the surface of the conveyor belt. But if the conveyor is driven by some other force or even allowed to move, the plane would still be moving relative to the ground.

Steve Shannon

Accoording to the question, the conveyer matches the speed of the wheel. No other force is allowed in the scenario, because otherwise, the conveyer would not match the speed of the wheel anymore.

#### SwingWing

##### Well-Known Member
can we tackle the downwind turn next!?!

Last edited:

#### Steve Shannon

##### Well-Known Member
TRF Supporter
Accoording to the question, the conveyer matches the speed of the wheel. No other force is allowed in the scenario, because otherwise, the conveyer would not match the speed of the wheel anymore.

So that means the conveyor bearings are allowed to freewheel, right? If the non-turning tire is moved forward by the thrust of the engine(s) the surface of the conveyor will move to keep up.

Steve Shannon

#### dave carver

##### ....what hump?
No. They spin up when they make the screeching noise at touchdown. Pondering why they don't spin them up is probably due to the differences between landing air speed and ground speed. Most of the tyres are designed to be minimum weight to conserve fuel and still be able to do their job. Centripetal force tries to tear the tyre apart as it spins, and there is not much safety margin due to keeping the mass down. I could envision that the variability in the rotational rate (if they used something like vanes to spin them up) could take them up into the danger zone for shredding the tread. If they were to drive them with motors it would be even more additional mass to carry, and also a problem if it seized up.

So, looks like the KISS principle prevails...

There are some wheel that are at speed when the plane lands. Big tires can just shred if they go from 0 to 150 or whatever speed they are flying at. I think they are called pre-rotators or something like thay.

#### OverTheTop

##### Well-Known Member
TRF Supporter
There are some wheel that are at speed when the plane lands.
Interesting. Do you know which ones?

#### Incongruent

##### Well-Known Member
So that means the conveyor bearings are allowed to freewheel, right? If the non-turning tire is moved forward by the thrust of the engine(s) the surface of the conveyor will move to keep up.

Steve Shannon

Let's simplify things a bit.

We we have a stock Boeing 747, no modifications.
It is on a magical runway sized conveyer belt that matches exactly the speed of the wheels on said 747 in the opposite direction. Magic. No exceptions or anything like that.
Can the Boeing 747 take off from the magical conveyer belt?

#### hornet driver

##### Well-Known Member
Let's simplify things a bit.

We we have a stock Boeing 747, no modifications.
It is on a magical runway sized conveyer belt that matches exactly the speed of the wheels on said 747 in the opposite direction. Magic. No exceptions or anything like that.
Can the Boeing 747 take off from the magical conveyer belt?
No , the 747 is stationary. What color was the belt?

#### Incongruent

##### Well-Known Member
No , the 747 is stationary. What color was the belt?

The belt is a black color, made of 100% responsibly sourced poached alligator skin leather reinforced with Kevlar and covered in asphalt slats, then barfed and deficated on by magic rainbow unicorns and well trampled by an army of infuriated garden gnomes, why do you ask?

Replies
42
Views
2K
Replies
3
Views
917
Replies
39
Views
1K
Replies
1
Views
248
Replies
0
Views
123