On a normal runway tyres have twice as much KE as you would expect because they are rolling. But in the 747 they are about 1,000 kg vs the aircraft’s 200,000kg or more, so I make it about 0.5%, absorbed evenly through the take-off run.
On landing, I suppose the aircraft’s translational KE will drop by the same 0.5% over a much shorter period when the wheels touch, but because KE is speed squared, that’s only 0.25% off the airspeed.
Note: I don’t land 747s, so I am happy to be corrected :-)
Thaty’s a great analysis David 
You have worked on the principle that the engine thrust will go wholly into the wheels’ moment of inertia.
Actually I wonder how much effect the moment of inertia has on the takeoff run, in real life… It may be significant – a few %? I don’t know how to calculate it.
For fun, I looked at how the belt could stop the aircraft from moving, i.e. maintain zero ground speed.
A 747 seems to weigh at least twice its maximum take off thrust of 1MN, so friction at the bottom of the wheels could certainly do that (with coefficient of friction >0.5).
But this implies that over the 0.6m radius between the the bottom of each wheel and its axle, you would have a torque of about 1MN x 0.6m, so the wheels will spin up very fast, and must continue their angular acceleration to maintain the frictional force.
From some data at Lufthansa I think the 16-wheel landing gear has a moment of inertia of 464 kg.m.m or similar.
A quick and rough calculation shows that within half a second, the wheels are spinning at 100 revs per second, and the belt has just gone supersonic :-)
Now, real conveyor belts can not do that, and real wheels can not survive that, but even in an unreal world:
The air just above this Mach 1+ runway-sized belt will be moving at a good fraction of the belt speed.
So within a second or so, the stationary aircraft would have sufficient airspeed to reduce its effective weight enough, to reduce the maximum available wheel friction enough, to allow the aircraft to accelerate forward. (Though the local wind shear might be “interesting”)
Eppur si muove!
But relevance is relative. In regard to the friction in the wheels: I don’t expect the conveyer belt to be required to be much longer either. The only difference is the tyre rotating at a higher speed, and whilst that adds a little rolling resistance and bearing drag, the surface type and hardness will make a much greater impact. I.e. soft field versus paved runway.
So, pretty much TODR as normal per POH. As the question says, as wide and long as a runway.
AnthonyQ wrote:
“Speed of the wheels” ie how fast they spin is irrelevant to the aircraft accelerating and moving forward in the airmass and taking off…it’s that simple.
The “problem” with this thought experiment is that it assumes that some things will be “real” and some things “perfect” and that furthermore it is not clear what is what.
As long as there is friction in the wheels, they are not irrelevant. What effect they actually have depends on how you interpret the question.
Wow you guys!….I think Peter is the only one who gets the silly thought experiment for what it was trying to show!
“Speed of the wheels” ie how fast they spin is irrelevant to the aircraft accelerating and moving forward in the airmass and taking off…it’s that simple.
I can’t imagine how you all would have treated Einstein and his beam of light or Schrödinger and his cat had you been presented with them at the time….after you ripped them to shreds they’d probably have given up and gone home!
As you were…
I can only speak for the roller benches I know and the issue there is energy absorption. If you want to test a vehicle to top speed (hence max power), you need to make sure that the roller bench distributes the power to somewhere, e.g. by powering a generator. And this also gives the limit, as the electric machines have a design limit for rpm and power.
The reason why you have the straps in place is normally a second safety barrier. You technically don’t need them if everything works well, but if it does, this is your safety net.
For an aircraft of course, you need the straps to keep it in place, but as your primary safety measure as it will abruptly roll out of the bench, if power is set.
With an aircraft or car?
What do you think the consequences would be? I’m having trouble picturing the setup.
I had forgotten that if you ask the “right” question it is guaranteed to result in pages of replies. 
If I were a cynic I might wonder if Peter has a stock of old faithfulls to breathe some life into times when there are fewer contributions! Not that is a criticism, because they are always good fun.
What about if you just attach the three wheels to a set of three rollers like they use for cars. When my garage was mapping my car we had over 140 mph and I did wonder the consequences if the straps gave way. They said there was no car they couldnt test and no top speed outside limits. Is that really so?
