# How much fuel did this Boeing 787-9 have on board for this flying display?

Once I saw how an Airbus A350 did a validation flight prior to an airshow and flew back to Toulouse from London Farnborough without landing/refuelling (distance: 550.57 mi (886.06 km)). I thought that these aircraft must be very light to perform such maneuvers?

• Even with full fuel, if they don't have passengers/baggage/extra crew on board they are still very light. – Ron Beyer Jan 14 '18 at 23:19

Looks like he is zooming after taking off: gain as much horizontal speed as he can, then pull up very steeply to convert some of the kinetic energy into potential energy. He only spends about 4-5 seconds at the crazy steep angle.

For zooming at these speeds, the mass is not very relevant: it appears in both kinetic and potential energy terms and cancels out.

$$\frac{1}{2}\cdot m \cdot \Delta V^2 = m \cdot g \cdot \Delta h \Rightarrow \Delta h = \frac{\Delta V^2}{2 \cdot g}$$

He just needs to take a longer take-off run at higher take-off weight to reach the same speed.

• agree with 1/2mV2 =mAxdistance! It is now in my toolbox as V2 = Ax2d, a useful conversion of kinetic and potential energy. m does cancel out. Thanks! – Robert DiGiovanni Dec 19 '18 at 12:24

The Airbus A350 and Boeing 787 are ultra-long haul aircraft with ranges in the order of $$11\,000$$ to $$15\,000 \, \mathrm{km}$$ (depending on variant). The flight from Farnborough to Toulouse is much, much shorter than that. Hence, the fuel on board was not even close to maximum.

Without any passengers and cargo, this would make the plane very light compared to MTOW (Maximum TakeOff Weight).

For two aircraft identical except for take off weight rotating at the same speed, the heavier one cannot maintain the same climb angle as the lighter one for a given amount of thrust. There for, it is safer to perform a high angle takeoff with as low a weight as possible.

This concept is explained by comparing gravitational force mass x gravity in pounds to thrust force, also in pounds. At any angle the lighter aircraft has the advantage. Simplest case is straight up where net acceleration = ma - mg. At lower angles where the vertical lift component of the wing is involved, total net lift requirement is still greater for the heavier plane. Even if the heavier plane rotates at a higher speed, it's rate of speed loss will be greater once it starts to climb.