Sure, but in both examples the planes are moving forward. On a treadmill the plane wouldn't be moving through wind, it'd essentially be staying in the same location, right? Where would the wind/lift come from?
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Is this a European or African 747?
Why would there be no "wind" with the introduction of the treadmill? The plane is moving forward as a result of the thrust from the prop/ engine - not from the wheels/ treadmill.
The wheels are not "propelling" the treadmill. Wheels on a plane are not geared and "free wheeling". Thus the plane will be pulled forward regardless of the wheels' movement. The treadmill has nearly as much bearing on this question as it would "could a helicopter take off on a treadmill".
You are right about the wheels not being powered or moving the plane. But I don't think that is relevant.
The plane has to move forwards wrt the air in order for the wings to generate lift. If the treadmill rolls the plane backwards at the same speed as the wheels turning, then no matter how much thrust the engines produce, the plane does not move forwards wrt the air. Therefore no lift and no takeoff. At least that is my interpretation of the word problem.
PJ Hermann says "consult the Bible --- Lan & Roskam!"
But it's not moving forward. The treadmill is slinging it backwards at the same speed it is trying to move forwards. It's really a question of Newtonian frame of reference.
When you run on a treadmill, if you move forwards at the same speed as the treadmill is moving you backwards - do you move forwards? No. Whether you are propelled forwards by your feet, or a jet engine, doesn't matter.
No it won't lift off. Moving forward is what causes lift. This is really just a lesson in general relativity.
It does matter though. If you are running or in a car, it is the force generated by your feet or tires against the ground that propels you forward. That forward force can be balanced by a treadmill by using the surface to creating an equivalent force in the opposite direction instead. This creates that stationary appearance.
In the plane, there is no forward force exerted by the plane on the surface, and more importantly, no backward force exerted by the surface on the body of the plane. The wheels of the plane will rotate to match whatever speed the treadmill is set to. What propels the body of the plane forward is the force generated by the propellers/jets, which cannot be negated by the treadmill, no matter how fast it goes because the treadmill cannot exert backward force on the body of the plane. No matter the speed of the treadmill, the plane will be able to propel itself forward and once it has enough speed to generate lift, it will take off.
In order to prevent lift-off, you would need to put the plane in a wind tunnel facing backwards with enough tailwind to prevent the wings from generating enough verticle force for take-off
A plane’s propulsion forward doesn’t depend on any interaction with the runway, it doesn’t send torque through the wheels and depend on mechanical grip. A plane could move forward, and therefore takeoff, even if it were on ice. The treadmill is a red herring.
The issue here is that there isn't any mechanism to transfer the energy from the treadmill into the body of the plane. The wheels spin freely on the plane, sort of like the front wheel of a bike. The moving treadmill surface and the friction with the tires will spin the wheels of the plane, but there is no mechanism to then transfer that into the body of the plane to cancel out the thrust of the jets. Therefore, the plane will still accelerate, it will move forward and increase velocity relative to the air thus creating lift and eventually taking off. The only difference being that the wheels will be spinning faster than they would be if you were on a regular runway and not a giant treadmill.
Going back to the bike example. Put the front wheel on the treadmill, and the back wheel on solid ground. Start peddling and that back wheel pushes the bike, just like the jet pushes the plane. The free spinning front tire will start turning faster to compensate as the treadmill speeds up, but it won't push the bike back because it is just spinning freely. That drive wheel in the rear will still propel the bike forward.
If the plane propels itself forward so much that it leaves the treadmill, then the original question is moot.
BM, aero... I must admit this isn't as simple as I had thought.
What you are saying the forward translation of the plane is not tied to the speed/rotation of the wheels. Essentially, the wheels spin frictionlessly on the axle (assuming the axle is fixed to the aircraft). So, if the engines were off, and someone turned the treadmill on, the plane would just sit there because the wheels would counterspin to the treadmill. Do I understand you right?
Then if you turned the engines on, it would push the axle forwards, increasing the rpm of the wheels more, which would increase the speed of the treadmill. That makes sense.
Here's the BUT I can't square away in my head. Say the wheel has circumference of 2m and is spinning at 50 rpm. That's 100m/min. The treadmill is moving backwards at 100m/min. How has the wheel moved moved forwards wrt the treadmill? Because even if it is spinning frictionlessly on the axle, it is still on the axle. And if the wheel hasn't translated forward relative to the treadmill, then the axle can't have either.
What you are saying the forward translation of the plane is not tied to the speed/rotation of the wheels. Essentially, the wheels spin frictionlessly on the axle (assuming the axle is fixed to the aircraft). So, if the engines were off, and someone turned the treadmill on, the plane would just sit there because the wheels would counterspin to the treadmill. Do I understand you right?
Then if you turned the engines on, it would push the axle forwards, increasing the rpm of the wheels more, which would increase the speed of the treadmill. That makes sense.
Here's the BUT I can't square away in my head. Say the wheel has circumference of 2m and is spinning at 50 rpm. That's 100m/min. The treadmill is moving backwards at 100m/min. How has the wheel moved moved forwards wrt the treadmill? Because even if it is spinning frictionlessly on the axle, it is still on the axle. And if the wheel hasn't translated forward relative to the treadmill, then the axle can't have either.
For the people who think the plane won't take off, try this one. Put wheels on the side of rocket sitting on a launch pad. Now put a vertical treadmill beside it. Can you use the treadmill to prevent the rocket from taking off? Before you go down a gravity hole, I'll let you put wheels on 2 sides and use 2 treadmills pushing against the rocket with a force equal to gravity.
Now put the rocket on its' side on top of a treadmill. Can the treadmill running keep the rocket from moving forward?
In both cases the rocket is going to do rocket things and no magic treadmill is going to stop it.
Now put the rocket on its' side on top of a treadmill. Can the treadmill running keep the rocket from moving forward?
In both cases the rocket is going to do rocket things and no magic treadmill is going to stop it.
You can never actually match the treadmill speed to the wheel speed. As soon as the plane moves forward at all the treadmill starts to speed up but the wheel will go faster (treadmill speed plus plane speed). The treadmill speeds up more to match, but again the wheel is going at treadmill + plane speed. Eventually the treadmill runs at "infinite speed" but the wheel will be going at "infinite speed + plane speed". I'll let somebody else argue whether something can actually be more than infinite
The only way the initial premise makes any sense is if the treadmill runs at a speed equal to the planes forward speed. If a plane takes off at 100mph it will reach that speed, and at that point the treadmill will be running 100mph in the opposite direction, and the wheels will be spinning at 200mph.
That is kind of the hitch in the way the original question is framed, the speed of the wheels has no impact on the ability for the plane to take off.
Another way to look at this is to frame the question this way: If you take a plane and set it on flat, solid ground and pointed the plane into a head-wind, is it possible for the wind to be fast enough to allow the plane to lift off?
For a large airliners the takeoff speed is usually between 150-180 mph, so theoretically possible but those are hurricane force winds. But there are small aircraft can reach take off at 60mph, meaning they could go airborne with zero vertical momentum by pointing into a 60+mph headwind.
