The 747 on the conveyor belt dilemma solved with Simcenter Amesim

With 70% of BSIM’s team being engineers, our coffee-break convo is very much on the geeky-techy side.

There’s always an engineering myth to debunk, a physical phenomenon to disagree upon. And it usually ends with one of our engineers downing his coffee and setting out on a simulation mission to prove whatever theory he had, and how the rest of us were wrong.

We’ve discussed the aerodynamics of a flying cow, argued about how to cook the perfect Thanksgiving turkey with CFD-3D simulations, how to simulate the best tennis serve – I could go on.

Our latest fixation? It’s an oldy but a goody: the 747 on the conveyor belt. 

Imagine a 747 on a conveyor belt, as wide and long as a runway. The conveyor belt is designed to move at the same speed as the airplane’s wheels, but in the opposite direction. The dilemma: will the plane take off?

Ring a bell? If you’re part of the engineering community, you’ve definitely heard of this one before. It’s intriguing because the problem involves absolute and relative reference systems, physics laws, and moving parts.

Even the MythBusters on Discovery channel spent some time on this one: check it out – once you’ve finished reading our article!

Also, there’s something about how the question is set up – it plays with your mind, am I right?! Such cunning absence of detail. It’s almost like they’re purposefully making it vague.

Anyway, what we noticed was that every engineer will go about solving it differently, depending on their background. 

Our mechatronic engineer said: “So there’s an active control system closing the feedback to regulate the conveyor speed.” Our mechanical engineers were kind of annoyed: “How big can this conveyor belt even be anyway!?”  Someone in the back went: “In what direction is this conveyor belt running”? “Hey, what about the wheels? Can the aircraft break?”

None of us felt we could solve this: we just didn’t have enough information. But after a while, two separate parties had formed.

Group 1 thought the airplane couldn’t take off: they believed the conveyor belt couldn’t annul the relative aircraft-air speed. There wouldn’t be any lift generation below the wings, meaning no take off.

Group 2 thought the aircraft would take off, because the engine’s thrust was mainly dependant on the interaction between the aircraft and the surrounding air, and what happened between the wheels and the conveyor was a secondary phenomenon.

But no one group was able to convince the other.

So that is when Giancarlo, one of our mechanical engineers, took it upon himself to settle the case. Off he went to set up his system simulation model, with Simcenter Amesim.

“Starting from some basic assumptions, this is how I reproduced the problem within the software:

• One 2D body representing the aircraft together with the landing gear arm
• Two 2D bodies representing the wheels of the front and the rear landing gears
• A 2D movement source representing the sliding belt surface
• A force source acting on the main aircraft body
• A contact simulating the interaction between the wheel and the conveyor belt

This is what my Simcenter Amesim sketch looked like:

At this early modelling stage, I wasn’t considering any aerodynamic forces, as I assumed the most important question we had to answer was: 

“Will the plane be moving in relation to an absolute reference system?” 

Let’s not forget that if speed exists in an absolute system, where we assume the speed of the air is close to zero, then we’ll necessarily have a non-null speed of the aircraft relative to the air. This means we’ll have lift and take off. 

Model parametrization was based on the data from a small ultralight aircraft that was available to us. But we could have chosen any aircraft data. The contact between the wheels and the belt was modelled with Amesim’s contact profile tool, which is available in the 2D library:

Clearly, we set the wheel stiffness at a significantly lower value than the ground stiffness, to ensure increased deformability under the effect of the aircraft weight.

The simulation was also meant to prove Group 2’s theory : 

“The aircraft will take off, no matter the speed and the movement direction of the conveyor belt.”

That “no matter” part of the sentence meant I had to simulate 2 different scenarios:

• the conveyor belt traveling at the same speed and in the same direction of the landing gear wheels
• the conveyor belt traveling at the same speed, but in a different direction to the landing gear wheels

But Group 2 got a bit picky, and wanted me to add in three extra simulation scenarios:

• the conveyor belt is actually off
• the conveyor belt speed is equal to wheel-edge tangent speed. According to the rolling mechanical principle, if there is no slipping at the contact point, then the maximum tangential speed will be twice the dragging speed.

I used a closed-loop control signal to represent the conveyor belt speed, based on the landing gear’s instantaneous speed, that could be employed as it is, or used to obtain the wheel’s tangential speed. 

I set the expression of f(x) to reproduce various configurations inside Simcenter Amesim’s study manager: ‘x’ is a scalar speed.

I launched our 5 simulation cases and looked at the results. When I plotted the speed of the aircraft in the direction of movement, this is what I observed:   

The airplane was subjected to thrust only in the 4-7 sec time range. 

The aircraft is definitely moving – so we can definitely declare the null aircraft speed theory wrong. I also noticed the simulation results were different in each of the 5 cases. This proves Group 2’s theory: the aircraft will take off no matter how the conveyor belt behaves.

So, what is actually changing in our 5 simulation scenarios? To find out, we must look at the wheels’ rotation speed, the front ones. 

Let’s analyse what happens in each scenario, knowing the airplane will take off:

• In the first scenario, in red, we can see the rotation speed is null, because in this case, the conveyor belt follows the dragging speed of the wheels both in terms of modulus and direction; so it’s effectively like the conveyor belt were chasing the aircraft, leaving the wheels still, when compared to the aircraft relative reference system;
• In the second scenario, in blue, we can see the relative speed is going in a negative direction. It then climbs back up to zero after 7s, because of the friction created by the wheel-conveyor belt contact.
• In the third scenario, the yellow one, the wheels have the same rotation speed we’d have on a typical runway, as this scenario presents a conveyor belt speed of zero.
• In the fourth scenario, in green, I set the conveyor belt speed at twice the drag speed and in the same direction. We are therefore looking at a self-regenerating phenomenon, by which when the aircraft exhausts its thrust and continues to accelerate indefinitely, it’s dragged along by the conveyor belt. 
• In our last scenario, the pink one, I set the conveyor speed at double the landing gear wheels drag, but in the opposite direction. The plane is still moving, but it has more of a braking effect. In fact, this is the scenario where we have the smallest absolute speed values and the fastest deceleration, once the thrust is exhausted.”

So that settles it!  

Group 2 won – not sure which side our colleague and article author Giancarlo was on, or if he’d admit it if he was in Group 1.   

We proved Group 2’s theory with one of the simulation tools BSIM resells, Simcenter Amesim from Siemens Digital Industry Software. 

Simcenter Amesim allowed Giancarlo to quickly set up a predictive model and run multiple simulation scenarios, with a few basic, simple assumptions. 

While simulation tools often require a vast amount of data, Simcenter Amesim’s model-based, scalable approach allows engineers to employ simulation for new engineering products. And perform what-if analyses to assess the viability of their engineering choices long before 3D CAD model and detailed data availability.  

Further developments 

We could replace the 2D bodies with components from Simcenter Amesim’s aerospace library, which includes aerodynamic effects and specific models for the wheel-landing gear-ground contact. 

By doing so, we’d actually be able to observe the aircraft taking off and avoid any future “court appeals” from Group 1! 

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